Design, Fabrication and Metrology of Precision Molded Freeform
Plastic Optics
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University
By
Likai Li
Graduate Program in Industrial and Systems Engineering
The Ohio State University
2014
Dissertation Committee:
Dr. Allen Y. Yi, Advisor
Dr. Jose M. Castro
Dr. Thomas W. Raasch
Copyright by
Likai Li
2014
Abstract
The main focus of this dissertation is to seek scientific knowledge and fundamental
understanding of molding process for freeform optical lens fabrication by integrating
freeform optical design, precision freeform molding making, numerical modeling of
polymer lens forming process, and evaluation of the molded freeform optics. Compared
with conventional optics, freeform optics provides more flexibilities and better
performance.
However, due to the complex nature of freeform optics manufacturing processes, the
productivity and quality is difficult to improve, which subsequently results in higher
manufacturing cost. Therefore, in order to create affordable freeform lenses with high
quality, the method combining ultraprecision diamond machining and optical molding is
proposed. Ultraprecision diamond machining is a process that allows us to generate
precision freeform optical features on mold surfaces without post polishing, while
microinjection/compression molding is proven high volume manufacturing process used
to reduce production cost. The diamond machining for both regular metal materials and
brittle materials are discussed to obtain high quality molds with optical finish. In
addition, two novel process designs are presented to fabricate hybrid glass-polymer
achromatic lenses using compression molding and injection molding, respectively.
Once the low cost molded freeform optical components are achieved, their optical
performance needs to be characterized to ensure quality in mass production. The
ii
refractive index variation and geometric deformation are two important factors that
influence the final optical performance considerably. So, finite element method is utilized
to simulate the manufacturing processes to obtain inhomogeneous refractive index
distribution and thickness variation. The obtained FEM information is used to derive and
predict the optical performance based on wavefront optics theory. In order to verify the
simulated results, conventional measurement setups are modified based on characteristics
of specific freeform optics to evaluate its optical properties. The numerical simulation
and experimental results are in good agreement with each other.
Therefore in order to solve the major challenges in manufacturing affordable high quality
freeform optics, this dissertation will include several key steps: 1) Establish point-topoint mapping freeform optics design strategy using freeform microlens array for
uniform beam shaping as an example; 2) Evaluate ultraprecision mold machining on both
regular metal materials and brittle materials to achieve high quality molds with optical
finish; 3) Develop novel manufacturing process designs to fabricate compression molded
hybrid achromatic glass-polymer microlens array and injection molded hybrid glasspolymer achromatic lens; 4) Establish a methodology combining finite element method
and wavefront optics theory to model the optical performances of molded freeform
lenses; 5) Design proper measurement systems including Shack-Hartmann sensor and wet
cell based optical interferometer to evaluate the molded freeform lenses and verify the
previously modeled results.
Overall, this dissertation describes a comprehensive understanding of affordable freeform
optics manufacturing.
iii
Dedication
This dissertation is dedicated to my parents, Mr. Zhengping Li and Mrs. Xihong Han.
iv
Acknowledgments
I owe my gratitude to all those people who have made this dissertation possible and
because of whom my PhD experience has been one that I will cherish forever.
I would like to express my most sincere gratitude to my advisor, Prof. Allen Yi. I thank
him for guiding me into the world of precision optics. It is my great pleasure to work with
him, a patient and understanding advisor. Prof. Yi offers me enough free space to expand
my knowledge independently. We share the wonders and frustrations of the engineering
research during my entire PhD life. He is always ready to provide me guidance,
encouragement and support. As an old Chinese saying goes, he is a good mentor but also
a nice friend.
I enjoyed working with Prof. Thomas Raasch for building up the Shack-Hartmann sensor
and conducting the wavefront optics metrology. I like to thank assistance and comments
from other faculty members at Ohio State who I have worked with: Prof. Jose Castro and
Prof. James Lee. My thanks also go to my colleagues in Germany for providing me
support on fabrication of molded glass and plastic optics: Fritz Klocke, Fei Wang,
Kyriakos Georgiadis and Olaf Dambon at Fraunhofer Institute for Production Technology
(IPT) in Aachen; Ingo Sieber and Ulrich Gengenbach at Karlsruhe Institute of
Technology (KIT) in Eggenstein-Leopoldshafen; Erik Beckert, Ralf Steinkopf at
Fraunhofer Institute for Angewandte Optik und Feinmechanik (IOF) in Jena. In addition,
v
I thank the continuous professional technical support from the engineers of Moldex3D
North America in Michigan.
Sincere thanks are extended to all my colleagues and fellow students, for our
inspiring discussion and incredible cooperative work: Dr. Lei Li, Dr. Yang Chen, Dr.
Lijuan Su, Dr. Can Yang, Dr. Hao Zhang, Dr. Bo Tao, Dr. Jingbo Zhou, Peng He, Hui Li,
David McCray, Neil Naples, Joshua Hassenzahl and Amin Moghaddas. Perhaps my
lunch conference with nine-year classmates Peng and Hui would be the most
unforgettable meeting during my life.
I would like to appreciate the Graduate Research Fellowship from NSF Center for
Affordable Nanoengineering of Polymeric Biomedical Devices (CANPBD) and the
Presidential Fellowship from the Graduate School of The Ohio State University.
I am indebted to my parents, Mr. Zhengping Li and Mrs. Xihong Han. They plant the
tree. It has always been watered and growing.
Last but not least, my special thanks are due to my wife Ziwei Zhao. During my PhD life,
she is the only person who always accompanies me and knows my happiness and pains.
Without her, this dissertation could have been finished one year earlier though.
vi
Vita
September 1987 ..............................Born, Jintan, Jiangsu, China
July 2009 .........................................B.S. Precision Engineering
University of Science and Technology of China
Hefei, Anhui, China
December 2011 ...............................M.S. Industrial and Systems Engineering
The Ohio State University, Columbus, OH
September 2009 ~ April 2014 .........Graduate Research Fellow
Department of Integrated Systems Engineering
The Ohio State University, Columbus, OH
May 2014 ~ present ........................Presidential Graduate Fellow
Graduate School
The Ohio State University, Columbus, OH
Publications
1. Li, L., Raasch, T. W., Sieber, I., Beckert, E., Steinkopf, R., Gengenbach, U., &Yi,
A.Y. (2014). Fabrication of microinjection-molded miniature freeform alvarez
lenses. Applied Optics, 53 (19), 4248-4255.
vii
2. He, P., Li, L., Li, H., Yu, J., Lee, L. J., & Yi, A. Y. (2014). Compression molding
of glass freeform optics using diamond machined silicon mold. Manufacturing
Letters, 2 (2), 17-20.
3. Li, L., Raasch, T. W., & Yi, A. Y. (2013). Simulation and measurement of optical
aberrations of injection molded progressive addition lenses. Applied Optics, 52
(24), 6022-6029.
4. Li, L., & Yi, A. Y. (2013). An affordable injection-molded precision hybrid
glass–polymer achromatic lens. The International Journal of Advanced
Manufacturing Technology, 69 (7), 1461-1467.
5. He, P., Wang, F., Li, L., Georgiadis, K., Dambon, O., Klocke, F., & Yi, A. Y.
(2011). Development of a low cost high precision fabrication process for glass
hybrid aspherical diffractive lenses. Journal of Optics, 13 (8), 085703.
6. Li, L., & Yi, A. Y. (2011). Design and fabrication of a freeform microlens array
for uniform beam shaping. Microsystem Technologies, 17 (12), 1713-1720.
7. Li, L., He, P., Wang, F., Georgiadis, K., Dambon, O., Klocke, F., & Yi, A. Y.
(2011). A hybrid polymer–glass achromatic microlens array fabricated by
compression molding. Journal of Optics, 13 (5), 055407.
8. Sieber, I., Martin, T., Yi, A., Li, L., & Ruebenach, O. (2014). Optical design and
tolerancing of an ophthalmological system. In SPIE Optical Engineering+
Applications (Vol. 9195, pp. 919504).
9. Li, L., Raasch, T. W., Yi, A.Y., Sieber, I., Gengenbach, U., Beckert, E., &
Steinkopf, R. (2014). Fabrication of microinjection-molded miniature freeform
viii
alvarez lenses. In ASPE/ASPEN Summer Topical Meeting, Kohala Coast,
Hawaii, USA.
10. Sieber, I., Yi, A., Li, L., Beckert, E., Steinkopf, R., & Gengenbach, U. (2014).
Design of freeform optics for an ophthalmological application. In Proc. of SPIE
(Vol. 9131, pp. 913108-1).
11. Li, L., Yi, A. (2013). Design and manufacturing of an affordable injection molded
precision hybrid glass-polymer achromatic lens. In Proc. of ANTEC Annual
Conference, Cincinnati, OH, USA.
12. He, P., Wang, F., Li, L., Georgiadis, K., Klocke, F., & Yi, A. Y. (2010).
Compression molding of refractive and diffractive hybrid glass lenses. In ASPE
Annual Conference, Atlanta, GA, USA.
Fields of Study
Major Field: Industrial and Systems Engineering
ix
Table of Contents
Abstract ............................................................................................................................... ii
Dedication .......................................................................................................................... iv
Acknowledgments............................................................................................................... v
Vita.................................................................................................................................... vii
Table of Contents ................................................................................................................ x
List of Tables ................................................................................................................... xiv
List of Figures ................................................................................................................... xv
Chapter 1.
Introduction ................................................................................................... 1
1.1
Optical design ....................................................................................................... 1
1.2
Ultraprecision machining ..................................................................................... 3
1.3
Molding processes ................................................................................................ 5
1.4
Molded freeform optics modeling and metrology................................................ 7
Chapter 2.
Research Objectives .................................................................................... 10
Chapter 3.
Freeform Optics Design .............................................................................. 11
3.1
Design of the freeform microlens array ............................................................. 11
3.2
Manufacturing process for the freeform microlens array................................... 16
x
3.2.1
Geometric design of tool path ..................................................................... 16
3.2.2
Fabrication of freeform microlenses ........................................................... 17
3.3
Geometric and optical evaluations ..................................................................... 19
3.3.1
Surface geometry measurement .................................................................. 19
3.3.2
Ray tracing simulations............................................................................... 21
3.3.3
Optical performance measurement ............................................................. 22
Chapter 4.
4.1
Precision Machining for Optical Molding .................................................. 26
Diamond machining on regular metals .............................................................. 26
4.1.1
Slow tool servo machining.......................................................................... 26
4.1.2
Diamond turning ......................................................................................... 29
4.1.3
Surface coating for nickel glass mold ......................................................... 30
4.2
Diamond machining on silicon wafer ................................................................ 32
4.2.1
Modeling of 3D damage distribution .......................................................... 34
4.2.2
Machining experiments ............................................................................... 37
4.2.3
Glass molding experiments ......................................................................... 39
4.2.4
Results and discussions ............................................................................... 41
4.3
Tool path optimization ....................................................................................... 48
Chapter 5.
5.1
Molding Processes for Achromatic Lenses................................................. 51
Achromatic lens design ...................................................................................... 52
xi
5.2
Compression molded hybrid achromatic microlens array.................................. 53
5.2.1
Optical design of hybrid microlens array.................................................... 54
5.2.2
Compression molding processes ................................................................. 55
5.2.3
Simulation of compression molding ........................................................... 62
5.2.4
Geometry and optical evaluation ................................................................ 68
5.3
Injection molded hybrid glass-plastic achromatic lens ...................................... 72
5.3.1
Design of fabrication processes .................................................................. 72
5.3.2
Microinjection molding simulations ........................................................... 76
5.3.3
Lens fabrications ......................................................................................... 80
5.3.4
Optical measurements ................................................................................. 82
Chapter 6.
Modeling of Optical Performance of Molded Freeform Optics ................. 84
6.1
FEM modeling for precision molding ................................................................ 85
6.2
Prediction of optical performance influenced by molding process .................... 88
Chapter 7.
7.1
Optical Metrology of Molded Freeform Optics .......................................... 91
Shack-Hartmann wavefront sensing measurement ............................................ 92
7.1.1
PAL design.................................................................................................. 93
7.1.2
PALs fabrication ......................................................................................... 94
7.1.3
Simulated wavefront pattern of PALs......................................................... 96
7.1.4
Wavefront measurement of PALs ............................................................... 97
xii
7.1.5
7.2
Results and discussions ............................................................................... 99
Interferometer measurements ........................................................................... 105
7.2.1
Optical design ........................................................................................... 106
7.2.2
Manufacturing of Alvarez lenses .............................................................. 107
7.2.3
Wavefront prediction and simulation........................................................ 109
7.2.4
Results and discussions ............................................................................. 113
Chapter 8.
Conclusions ............................................................................................... 121
References ....................................................................................................................... 123
Appendix A: Replicated Microoptical Arrays for Multiple 3D Optical Trapping ......... 137
A.1 Introduction .......................................................................................................... 137
A.2 Competitive analysis ............................................................................................ 137
A.3 Experiment setup and results ................................................................................ 138
A.4 Summary and future work .................................................................................... 141
xiii
List of Tables
Table 4.1. Rough and fine machining parameters ............................................................ 38
Table 5.1. Mechanical and thermal properties of P-SK57 glass. ..................................... 62
Table 5.2. Structural relaxation rarameters of P-SK57 used in numerical simulation. .... 63
Table 5.3. Boundary Conditions for Glass and Polymer Molding. .................................. 63
Table 5.4. Mechanical and thermal properties of polycarbonate. .................................... 66
Table 5.5. Viscoelastic parameters of polycarbonate used in numerical simulation. ...... 67
Table 5.6. Design parameters for the aspherical surface.................................................. 76
Table 5.7. Simulation process conditions used for two different thicknesses.................. 78
Table 6.1. Material parameters of PMMA. ...................................................................... 86
Table 6.2. Injectin molding condition. ............................................................................. 87
Table 7.1. Injection molding conditions for design of experiment ................................ 104
Table 7.2. Microinjection molding conditions ............................................................... 109
xiv
List of Figures
Figure 3.1. Geometry of ray tracking using Snell's law. .................................................. 13
Figure 3.2. (a) Geometrical layout of light redistribution from the microcell region L to
the target region M. In the example illustrated in this figure, P = 4 and Q = 3; (b) shaded
model of the light redistribution by the freeform microlens. ............................................ 14
Figure 3.3. (a) A single freeform microlens surface. (b) Layout of ray tracing of a single
freeform microlenslet projecting onto the target surface. (c) Close-up view of ray tracing
of a single freeform microlenslet. ..................................................................................... 16
Figure 3.4. Schematic of tool compensation. ................................................................... 17
Figure 3.5. (a) Pictures of the finished mold insert and the injection molded freeform
microlens arrays. (b) Two buffer areas indicated in the pictures are designed to protect
the tool cutting edge from making oversize cut into the work piece. ............................... 19
Figure 3.6. The solid lines are measured 2D surface profiles along the line y=0 mm from
the center to the edge (corresponding to Figure 3.3(a)) of the mold insert and the molded
lens. The dashed lines are geometry errors of surface profiles along the line y=0 mm of
molding insert and molded piece. ..................................................................................... 20
Figure 3.7. (a) Surface roughness measurement of the mold insert. (b) Surface roughness
measurement of the molded microlens. ............................................................................ 21
Figure 3.8. Simulated light distribution on the target surface. ......................................... 22
Figure 3.9. Measured light distribution on the target surface. ......................................... 23
xv
Figure 3.10. (a) Comparison of the simulated and experimental corresponding line
distributions along the x axis across the center of the illumination. (b) Comparison of the
simulated and experimental line distribution along the y axis across the center of the
illumination. ...................................................................................................................... 24
Figure 3.11. Schematic of overcut due to the radius of the diamond tool. ...................... 25
Figure 4.1. Broaching tool path for: (a) glass microlens array, (b) polycarbonate
microlens array. The spacing between neighboring steps is reduced and the return tool
paths are removed for clarity. ........................................................................................... 27
Figure 4.2. Pictures of the finished (a) copper nickel mold for glass and (b) aluminum
mold for polymer. ............................................................................................................. 28
Figure 4.3. Picture of the finished ultraprecision diamond turned mold inserts for the
hybrid lens microinjection molding. ................................................................................. 29
Figure 4.4. SEM (scanning electron microscope) photo of the Pt-Ir coating with nickel
adhesion layer. .................................................................................................................. 31
Figure 4.5. Brittle to ductile transition based on STS machining process configuration. 35
Figure 4.6. Flowchart of the 3D damage distribution calculation program ..................... 36
Figure 4.7. Design of a square microlens array. Unit is m. ........................................... 37
Figure 4.8. Microscopic pictures of the microlens arrays machined under conditions of
(a) condition 1 and (b) condition 2 in Table 4.1............................................................... 39
Figure 4.9. Silicon mold and molded glass microlens array. ........................................... 40
Figure 4.10. (a) Measured profiles of the silicon mold and (b) the molded glass microlens
array. (c) Geometry deviation between the mold and molded glass optics. Unit is mm. . 41
xvi
Figure 4.11. Calculated 3D damage distributions of a microlens machined under (a)
condition 1 and (b) condition 2. (c) and (d) are the top views of (a) and (b) respectively.
Microscopic pictures of a microlens machined under (e) condition 1 and (f) condition 2.
Unit is mm......................................................................................................................... 43
Figure 4.12. Calculated subsurface damage distributions of a microlens if the constant
damage depth model is used. Unit is mm. ........................................................................ 44
Figure 4.13. 3D damage distribution simulations of the microlens on silicon at the
middles of the (a) 5th, (b) 8th, (c) 11th and (d) 18th machining pass of the machining
experiments conducted under condition 2. Unit is mm. ................................................... 46
Figure 4.14. Cutting path planning strategies: (a) constant cutting depth; (b) constant
cutting ratio. Unit is mm. .................................................................................................. 47
Figure 4.15. Cross sections of concave, spherical lenslets on convex, spherical substrates.
(a) Traditional, unblended, discontinuous lenslet. The thick blue line is machined,
discontinuity and all. (b) Traditional lenslet blended with a torus. The thick blue line is
machined, blend and all. (c) Lenslet with blending in the air. Only the thick blue line is
machined, which is exactly the whole, original lenslet. Original lenslet aperture is marked
by 2 magenta asterisks. ..................................................................................................... 49
Figure 4.16. Lenslet close-ups. (a) Traditional STS method with unblended lenslets.
Sliced apertures are clearly visible, rendering the component useless. (b) Close up of
unblended lenslet. (c) Blended lenslets machined with the original blend torus method.
The tool path and physical array are both clearly continuous. (d) Close of up blended
lenslet. A reduction in aperture radius can be seen as compared to a discontinuous lenslet
of the same size. (e) Totally discontinuous lenslets machined with the BTA method. The
xvii
tool path in this case was totally continuous. (f) Close up of lenslet machined with BTA
method. The aperture is discontinuous and visibly seems to be of superb quality. This
method does not compromise an optical design in any way. ............................................ 50
Figure 5.1. Geometric layout of the achromat doublet design. ........................................ 54
Figure 5.2. Chromatic focal shift of one hybrid polymer-glass microlens doublets. ....... 55
Figure 5.3. Molding processes for the hybrid polymer-glass microlens array: (a)~(c)
glass molding process, (d)~(f) polymer molding process. ................................................ 57
Figure 5.4. (a) Molding force and lower mold position as function of time. (b) Molding
force and temperature control as function of time. ........................................................... 58
Figure 5.5. (a) Molded glass microlens array. (b) The finished hybrid polymer-glass
microlens array.................................................................................................................. 61
Figure 5.6. Material properties of the P-SK57 glass used in the simulation. (a) Thermal
conductivity [W/m°C] as a function of temperature [°C]. (b) Specific heat [J/kg °C]
variation as a function of temperature [°C]. (c) Coefficient of thermal expansion [/°C] as
a function of temperature [°C]. (d) Stress relaxation properties curve: shear constant [Pa]
versus time [s] (in logarithm scale). .................................................................................. 64
Figure 5.7. (a) Meshed FEM model of glass molding for microlens. (b) Final shape of the
glass microlens after cooling. ........................................................................................... 65
Figure 5.8. Comparison of simulated and experiment surface profiles of one microlens
for (a) P-SK57 glass and (b) polycarbonate. ..................................................................... 68
Figure 5.9. 2D surface profiles and geometry errors along the diameter of the mold and
the molded sample of one single microlens. (a) Surface profiles of the mold and molded
glass lens. (b) Surface profiles of the mold and molded polymer lens. ............................ 69
xviii
Figure 5.10. Schematic of the setup for measuring the chromatic focal shift: (1) laser
source, (2) linear polarizers, (3) pinhole, (4) field lens, (5) hybrid lens mounted on a
precision translation stage and (6) CCD camera............................................................... 70
Figure 5.11. Comparison of calculated and experiment results of chromatic focal shift of
the hybrid polymer-glass doublet...................................................................................... 71
Figure 5.12. Manufacturing processes of the hybrid glass-polymer lens by microinjection
molding. The right mold insert is used to house the glass lens while the left side has the
aspherical surface for the polymer lens. The blue area is the glass lens and the red is the
injection molded polycarbonate polymer.......................................................................... 73
Figure 5.13. Achromatic doublet design (unit: mm). ....................................................... 74
Figure 5.14. (a) Meshed Model I for the injection molded part and the part insert and (b)
meshed microinjection molding system model including the cooling channels and mold
base. .................................................................................................................................. 77
Figure 5.15. Comparison of simulation (a and c) and experimental results (b and d) of the
melt front flow pattern for Model I during filling............................................................. 78
Figure 5.16. Melt front (shown in time) of the injection molded polymer part of Model II
during filling. .................................................................................................................... 79
Figure 5.17. Simulated part deformation under different packing pressure. ................... 80
Figure 5.18. Picture of a complete hybrid glass-polymer lens manufactured by
microinjection molding (shown with gate, runner and spruce). ....................................... 81
Figure 5.19. Comparison of the calculated and measured results of the chromatic focal
shift of the hybrid lens. ..................................................................................................... 82
xix
Figure 6.1. Meshed FEM model of a Progressive Addition Lens (PAL). Node(i,1) is
numbered along number i line at the bottom surface of PAL, and Node(i,N) is the node
along number i line at its top surface. ............................................................................... 85
Figure 7.1. Freeform surface of the backside of the PAL. The first polynomial term was
removed to show the freeform geometry. ......................................................................... 94
Figure 7.2. Finished ultraprecision diamond turned mold inserts for PAL injection
molding. ............................................................................................................................ 95
Figure 7.3. PALs manufactured by microinjection molding. .......................................... 95
Figure 7.4. Schematic of the wavefront measuring system. 1: Distant source; 2: PAL
under test; 3 and 4: 150 mm fl lenses; 5: Shack-Hartmann sensor. .................................. 98
Figure 7.5. Simulated refractive index variation of an injection molded PAL. ............... 99
Figure 7.6. Simulated thickness change in xy plane of the molded PAL. ...................... 101
Figure 7.7. Spherical power M of the molded PAL (a) design (b) simulation (c)
measurement ................................................................................................................... 102
Figure 7.8. Cylindrical component J0 of the injection molded PAL (a) design (b)
simulation (c) measurement ............................................................................................ 103
Figure 7.9. Comparison of (a) design, (b) simulated and (c) measured cylindrical
component J45 of the injection molded PAL................................................................... 103
Figure 7.10. Top freeform surface of Alvarez lens. ....................................................... 107
Figure 7.11. (a) Finished ultraprecision diamond machined mold for injection molding.
(b) 3D model of the molded Alvarez lens with small straight pins and flats designed for
assembly. ......................................................................................................................... 108
Figure 7.12. An injection molded Alvarez lens. ............................................................ 109
xx
Figure 7.13. FEM mesh model of the Alvarez lens. Node (i, 1) is numbered along the
vertical line at coordinates (xi, yi) at the bottom surface, and Node (i, N) is the node along
the vertical line at coordinates (xi, yi) at its top surface. ................................................. 110
Figure 7.14. Interferometry setup for measuring wavefront pattern of microinjection
molded Alvarez lens immersed in a wet cell. 1: He-Ne laser light source; 2: optical pin
hole; 3: collimation lens; 4: beam splitter A; 5: flat mirror A; 6: flat mirror B; 7: Alvarez
lens immersed in a wet cell; 8: beam splitter B; 9: CCD camera; 10: PZT stage. .......... 112
Figure 7.15. (a) Simulated and (b) measured bottom surface deformations of the
microinjection molded Alvarez lens. .............................................................................. 114
Figure 7.16. Simulation plot of the deformed microinjection molded Alvarez lens with a
magnification scale of 50X. ............................................................................................ 115
Figure 7.17. (a) Simulated and (b) measured wavefront pattern describing refractive
index distribution of the microinjection molded Alvarez lenses. ................................... 116
Figure 7.18. (a) Nominal and (b) measured wavefront pattern describing surface power
distribution of the microinjection molded Alvarez lenses. (c) Difference between the
simulated and the measured results................................................................................. 117
Figure 7.19. Optical path change on the freeform surface. ............................................ 119
Figure A.1. Optical setup of the integrated multiple trapping system. .......................... 139
Figure A.2. Compression molded glass microlens array used in hybrid glass-polymer
microlens assmely. .......................................................................................................... 140
Figure A.3. (a) Multiple laser focal spots generated by the optical setup discussed before
(b) trapped polystyrene beads ......................................................................................... 141
xxi
Chapter 1. Introduction
A freeform optical component in this research is loosely defined as an optical element
that is not symmetric around its optical axis. It provides some attractive features to
optical designers to create innovative products: a) more design flexibilities of surface
geometry; b) ability to correct multiple aberrations with fewer or one optical surfaces; c)
reduced number of optical elements, package size and weight; d) easy system integration
(Fang, et al., 2013). Because of the benefits brought by freeform optics, manufacturing of
freeform optics is a promising technology today in various fields, such as biomedical
engineering, mobile electronic device, energy, automobile, aerospace and so on.
The entire freeform optics manufacturing consists of design, machining, forming,
metrology and characterization. All these fields and their standardization are still
developing. This dissertation focuses on the fabrication processes of affordable freeform
plastic optics and its related optical design and metrology.
1.1
Optical design
Usually the freeform optics design can be realized by multi parameter optimization and
direct mapping. In the approach of multi-parameter optimization, the freeform surface
can be described a certain polynomial equation with multiple parameterized coefficients.
According to design requirements, a merit function is defined that how far the current
design is away from the target, while the coefficients defining the freeform surface are
1
varied to find local or global minimum of the merit function. However, due to intrinsic
complicated nature of freeform optics, the results usually are not satisfied.
Therefore, some advanced direct mapping methods are proposed to solve the challenges
in the freeform optics design. Partial differential equation (PDE) is used to establish the
relationship between the target surface, freeform optical surface and space vector of
incident light (Ries & Rabl, 1994). This method is based on the energy conservation and
tailoring theory which redistribute the radiation of light source onto a given desired
distribution (Winston, et al., 2005; Ries & Muschaweck, 2002). Ries & Muschaweck
obtained the tailored freeform surface for an arbitry irradiance distribution by solving a
set of partial deiffential equation with the curvature and slope. However, when the target
patten becomes more complicated, the solutions of partial differential equation method
are more challenging. Oliker presented an alternate freeform reflector design with riorous
mathematical theory but for a generic application (Oliker, 2005; Oliker, 2006). He
established an iteration process of combining a series of elliptical reflector into one
freeform surface to redistribute the irradiance of a point light source to an arbitrary
pattern. Similar to Oliker’s idea, Michaelis et al. developed a method that assembles sets
of Cartesian ovals into a freeform refraction surface in order to redistribute light into
arbitrary pattern (Michaelis, et al., 2011). These two approaches avoids the complicated
process of solving partial differential equation set.
Another method for constructing the equation between the source surface and target
surface is called point-to-point mapping (Fang, et al., 2013). In order to achieve certain
irradiance distribution, Parkyn & Pelka proposed to divide the source and the target
surface into grids using the same topology (Parkyn & Pelka, 2006). The edge relations of
2
corresponding pairs of source grid and target grid are utilized to derive the normal vectors
of the lens to generate smooth surface. The topology of target grid is based on the
intensity distribution of the source grid. This point-to-point mapping method has
frequently been applied to LED package illumination (Wang, et al., 2010; Belousov, et
al., 2008; Luo, et al., 2010).
The freeform microlens array discussed in this dissertation was designed by the point-topoint mapping method (Li & Yi, 2011). It is capable of redistributing a collimated light
into a pre-determined, in this case, a uniform pattern. This freeform microlens array
design requires fewer optical elements compared with classic uniform illumination
system, and also reduces alignment difficulty. The fabricated optical element in this
research could achieve light re-distribution at the target with approximately 80%
uniformity.
1.2
Ultraprecision machining
In recent years, different methods have been investigated for fabrication of optical
freeform surfaces in order to obtain high quality components. These techniques include
diamond micromilling (Brinksmeier & Autschbach, 2004; Stoebenau & Sinzinger, 2009),
ultraprecision diamond turning (Yi & Li, 2005; Yi, et al., 2006), diamond flycutting
(Stoebenau & Sinzinger, 2009) and ultraprecision grinding (Van Ligten & Venkatesh,
1985). Diamond micromilling is an alternative to machining aspheric or complex lenses
with small positive and negative curvatures. Diamond flycutting can be employed to
generate optical elements with small radius of curvature and high aspect ratio.
Ultraprecision grinding is capable of providing very fine surfaces but it is difficult to set
3
up and has relatively long machining cycles. On the other hand, diamond turning process
is one of the widely used machining processes in optical industry, for example, well
established fast tool servo (FTS) is applied in the area of contact lens and freeform lens
manufacturing (Michaelis, et al., 2008). In a fast tool servo process, the diamond tool is
mounted on a piezoelectric actuator which is capable of oscillating at extremely high
frequency, and the oscillation position is determined according to both the radial and the
angular position of the workpiece. However fast tool servo method also has limitations,
such as the typical travel range is less than 1 mm (Tohme & Lowe, 2003). The approach
used in this dissertation is slow tool servo (STS) diamond machining which is a similar
but uniquely different process to fast tool servo. In slow tool servo machining, z axis slide
provides the control in the direction of cutting depth. This arrangement allows large
deviation on machined surfaces but has limits on the dynamic movement of the cutting
tool due to inertia of the heavy mechanical slide used.
The slow tool servo diamond machining can be easily applied to fabricate regular metal
mold materials with optical quality, such as aluminum and copper nickel alloy. However,
the machining on brittle materials, for example crystalline silicon, leads to micro
fractures during material removal. Hence, ultraprecision machining of (crystalline)
silicon has been studied frequently in the last two decades. The focus of the
investigations has been largely on the basic understanding of the brittle to ductile
transition (Blake & Scattergood, 1990). One of the key findings of these studies shows
that a large negative rake angle is a critical process condition in reducing fractures and
enhancing tool life (Blackley & Scattergood, 1991). In practice, diamond tool tip is
simply titled against the silicon substrate, therefore the clearance angle is usually much
4
larger than the nominal value. Fang et al. introduced a concept of extrusion as opposed to
shearing to explain the nanometer scale diamond turning mechanism (Fang, et al., 2005).
A large negative rake angle increases the pressure on the substrate and resulting in threedimensional volumetric deformation (Patten & Gao, 2001). In a more classic view using
shearing (plane) concept, energy is more concentrated on the shearing plane, generally a
2D scenario (Yan, et al., 2009).
Therefore it is of great interest to understand and predict the damage distribution threedimensionally and further optimize the machining process when freeform optics is in
consideration. In this dissertation, the subsurface damage model was modified to study
3D damage distribution in slow tool servo diamond machined silicon. The prediction of
the 3D damage distributions on freeform surfaces were compared with experimental
results and their close match demonstrated the feasibility of using this modeling
technique to effectively assist freeform diamond machining on silicon or other similar
brittle materials. In addition, the development of the damage distribution and two
different machining strategies were analyzed in order to understand brittle material
machining process and improve surface quality.
1.3
Molding processes
The third step, replication process, has to be a low cost manufacturing process. For
optical manufacturing, microinjection molding (Lee, et al., 2004) and hot compression
molding (Yi & Jain, 2005) are two most common techniques that can be utilized. In
injection molding, material is heated up above its transition temperature, then mixed, and
finally forced into a mold cavity where it cools and hardens to the configuration of the
5
mold cavity. As a subset of injection molding, microinjection molding process is
considered as one of the significant technologies of manufacturing high precision micro
features with mass-production capability. Microinjection molding offers molded parts
more accuracy and less variability by means of its special design features, i.e., a)
plasticizing screw and injection plunger are separated, and both are manufactured with
high precision to provide stable and uniform polymer melt, b) direct clamping pressure
by central ram construction provides even distribution of clamping pressure on the platen.
For hot compression molding process, the general setup is a piece of glass or polymer
sandwiched between two mold halves. The blank is heated up in the vacuum furnace
above its transition temperature and then squeezed between the two mold halves.
Afterwards the positions of the mold halves are held for a certain period of time, and
annealing is started when compression is completed.
The good availability of these two replication processes ensures that the study of these
two methods can be done easily both in industry and education research institute.
Moreover, a wide range of transparent materials including polymer and glass both, such
as polymethylmethacrylate (PMMA), polycarbonate (PC), P-SK57 glass, and BK7 glass,
can be selected to work with these two methods.
This dissertation presents an innovative compression process for hybrid polymer-glass
microlens array (Li, et al., 2011). Both of the glass and polymer optical elements were
fabricated by thermal compression molding. First a P-SK57 glass blank was pressed in a
compression molding operation into the shape of a finished microlens array together with
the fiducial features for subsequent alignment in thermal forming of polymer lenses.
Annealing was performed after the compression molding process to minimize thermal
6
shrinkage. Compression molding is inherently designed for freeform (including
microlenses) optical element fabrication (Yi, et al., 2006). One of the major advantages
of a hybrid polymer-glass microlens lies in its improved performance from the thermal
stability of glass and the benefit of lower manufacturing cost using commercial grade
optical polymers.
Besides compression molding, microinjection molding was utilized to apply the aspheric
polycarbonate layer directly onto the N-BK7 glass lens surface in this unique study for its
capabilities of precision micro feature replication and mass production (Li & Yi, 2013).
So the combination of polycarbonate (flint glass) and N-BK7 (crown glass) can also be
used to correct chromatic aberration. To ensure high precision in the fabricated hybrid
lens, mechanical alignment features were created on the mold inserts to position the
finished polymer lens along with the insert that housed the glass lens. It was
demonstrated in this study that with properly designed manufacturing processes, an
integrated hybrid glass-polymer lens could be fabricated without further mechanical
alignment.
1.4
Molded freeform optics modeling and metrology
The high quality requirement for freeform optical devices often leads to high
manufacturing cost. Microinjection molding encounters several quality issues for optical
applications. These include thermally induced shrinkage, non-uniform refractive index
and birefringence. To ameliorate these quality related issues, a finite element method
(FEM) has been used to model the process (Kim & Turng, 2006) and analyze its
influences on optical performance of injection molded freeform optics. For example, Park
7
and Joo simulated the ray tracing inside an injection molded lens according to the FEM
results (Park & Joo, 2008). Suhara constructed the refractive index distribution of an
injection molded lens by using computed tomography technique (Suhara, 2002). Yang et
al. studied the impact of packing pressure on refractive index variation of an injection
molded flat lens and compared the simulated results with experiments (Yang, et al.,
2011). Li et al. previously analyzed the optical aberrations of injection molded
progressive addition lenses (Li, et al., 2013), and investigated how to apply injection
molding to hybrid glass-polymer lens fabrication (Li & Yi, 2013). This study focuses on
how injection molding process influences freeform optics in terms of the part’s surface
deformation and refractive index variation.
In this dissertation, an innovative metrology setup was proposed to evaluate the optical
wavefront patterns in the molded lenses by using a Shack-Hartmann sensor or an
interferometer based wavefront measurement system (Li, et al., 2013; Li, et al., 2014).
The measurement system based on a Shack-Hartmann wavefront sensor was used to
measure the wavefront of the lens which is pivoted around horizontal and vertical axes.
The intersection of the two axes mimics the center of rotation of an eye behind the lens.
For the other setup, the interferometer based measurement system utilized an optical
matching liquid to reduce or eliminate the lenses’ surface power such that the wavefront
pattern with large deviation from the freeform lenses can be measured by a regular
wavefront setup.The previously obtained FEM simulation results were used to explain the
differences between the nominal and experimentally measured wavefront patterns of the
microinjection molded lenses. In summary, the proposed method combining simulation
8
and wavefront measurements is shown to be an effective approach for studying injection
molding of freeform optics.
9
Chapter 2. Research Objectives
The main focus of this dissertation is to seek scientific knowledge and fundamental
understanding of molding process for freeform optical lens fabrication by integrating
freeform optical design, precision freeform molding making, numerical modeling of
polymer lens forming process, and evaluation of the molded freeform optics.
Overall, this dissertation describes a comprehensive understanding of affordable freeform
optics manufacturing. In order to solve the major challenges in manufacturing affordable
high quality freeform optics, this dissertation will include several key steps:
1) Establish point-to-point mapping freeform optics design strategy using freeform
microlens array for uniform beam shaping as an example;
2) Evaluate ultraprecision mold machining onto both regular metal materials and brittle
materials to achieve high quality molds with optical finish;
3) Develop novel manufacturing process designs to fabricate compression molded hybrid
achromatic glass-polymer microlens array and injection molded hybrid glass-polymer
achromatic lens;
4) Combine finite element method and wavefront optics theory to model the optical
performances of molded freeform plastic lenses;
5) Design proper measurement systems including Shack-Hartmann sensor and wet cell
based optical interferometer to evaluate the molded freeform lenses and verify the
previously modeled optical performances.
10
Chapter 3. Freeform Optics Design
Optical systems using freeform lenses are becoming a viable solution to both imaging
and non-imaging optics for its ability of reducing the number of elements in an optical
system and accurately controlling light irradiation. A freeform lens in this research is
loosely defined as an optical element that is not symmetric around its optical axis. The
first reported freeform lens applied to large scale commercial use was a folding single
lens reflex (SLR) pack film camera developed by Polaroid SX-70 in 1972 (Plummer,
1982). The freeform lenses in that design were injection molded. Ultraprecision grinding
and polishing were adopted to fabricate the molds, which was laborious and difficult to
control. However, there are many applications that can benefit from freeform optics, such
as LED illumination (Ding, et al., 2008; Wang, et al., 2010), projection displays (Yi, et
al., 2006), phase aberration correction (Yi & Raasch, 2005), computational imaging
(Kubala, et al., 2003), and compact prism display system (Cheng, et al., 2009), to name a
few.
3.1
Design of the freeform microlens array
Michaelis et al. generalized a method to design a freeform element in given optical
system (Michaelis, et al., 2011), while the basic concept of the simple optical design here
is to use a panel with freeform microlens array to redistribute the incoming light into a
pre determined pattern on the target (Sun, et al., 2009). The aim of this research design is
11
focused on the development of the fabrication process. The proposed method is
demonstrated in a generic freeform microlens array design therefore permits its
immediate implementation in optical industry. For the optical design, first of all, it is
assumed that the incoming light is collimated. Second, once the light energy area is
meshed into tiny cells, each cell can be statistically treated as having uniform radiation
even if the entire radiation of incoming light is not uniform. Third, the relative location of
the neighboring microlens cells is ignored, since the microlens cell size is considered to
be much smaller than the distance between the freeform microlens panel and the target
plane. As a result, the uniform redistributed patterns on the target plane produced by
these microlens cells overlap at the same location on the target plane. Therefore the shape
of only one microlens cell needs to be calculated for redistributing the light on to the
target plane. Based on the hypothesis discussed above, the desired redistributed radiation
pattern can be determined.
In a classic uniform illumination system called fly’s-eye condenser, one or two pieces of
microlens array are typically used along with a condenser lens to achieve uniform
irradiance at the target plane. Schreiber et al. manufactured a double sided array and
analyzed the aberration and diffraction caused by the microlens array in their fly’s-eye
condenser system (Schreiber, et al., 2005). Buttner et al. investigated influence of
microlens diameter, on-axis microlens aberration and array illumination to the fly’s-eye
system consisting of either one or two microlens arrays (Buttner & Zeitner, 2002).
However, compared to the design in this research, this conventional uniform illumination
system requires more optical elements which involves in more alignment. Both of the
conventional and freeform microlens arrays have great usage potentials in optical
12
industry, particularly in LED illumination. However, the intrinsic light divergence from
the emitting surface of the LED sources will lead to decreased homogenization effect. A
discussion bridging microlens array and LED uniform illumination can be found in
(Buttner & Zeitner, 2002).
To build the ray tracing model, vector form of the Snell's law’s is used. The incident ray
is travelling in a direction defined by vector r, and the reflected and refracted ray
direction can be defined as vector rL and rR respectively, which are shown is Figure 3.1.
N is the normal vector at incident point O on the incident surface (the front surface of the
microlenses). After the ray passes through the incident surface, the refracted ray reaches
point E on the target surface. The refractive indices of the surrounding medium of the
incident and refractive light space are n1 and n2, respectively. Since | r | = n1 and | rR | =
n2, the normal vector of N can be obtained using Equation (1) from reference (Chaves,
2008):
N
r  rR
r  rR
Figure 3.1. Geometry of ray tracking using Snell's law.
13
(1)
According to the “edge-ray principle”, if the light coming from the edge of the light
source is refracted by the freeform microlens onto the edge of the target region, the light
within the source region will be redistributed within the target region (Chaves, 2008).
Figure 3.2. (a) Geometrical layout of light redistribution from the microcell region L to
the target region M. In the example illustrated in this figure, P = 4 and Q = 3; (b) shaded
model of the light redistribution by the freeform microlens.
As mentioned above, only one microlens cell needs to be calculated. Thus, if both the
microlens cell and the redistributed region are meshed into P × Q grids (the grid sizes are
the same) and each grid node of the microcell region is mapped to the corresponding grid
node of the redistributed region on the target, the directions of the refracted ray can be
determined, as shown in Figure 3.2. In addition, the direction of the incident rays is
assumed to be perpendicular to the target surface from the assumption. Since r and rR are
already obtained, the normal vectors at the grid nodes of the microcell region can be
easily calculated using:
14
Ni, j 
1
j
1
i
1
 ( A(
 )  i , B(
 )  j ,(C  nm  )  k )
Q 1 2
P 1 2
j
1 2
i
1 2
2
2
(2)
A(
 ) B (
 )  (C  nm  )
Q 1 2
P 1 2
2
i  0,1, 2,..., P  1
j  0,1, 2,..., Q  1
 A  A1  A2
B  B  B
1
2



  A2 ( j  1 )2  B 2 ( i  1 ) 2  C 2
Q 1 2
P 1 2

where A1 and B1 are the length and width of the rectangular target respectively, A2 and B2
are the length and width of the source rectangle respectively, C is the distance between
the target and the source, and nm is the refractive index of the material of the freeform
microlens.
If the microcell mesh is dense enough, an accurate freeform microlens can be generated
and represented by B-spline function (Piegl & Tiller, 1997). The proposed design was
aimed to redistribute the collimated light from a 1 mm×2 mm size rectangle into a 20
mm×40 mm size rectangle. The illumination distance was set as 200 mm. Each microlens
was divided into 99×199 meshes. Polymethylmethacrylate (PMMA) was chosen as the
microlens material whose refractive index was 1.492 at the wavelength of 632.8 nm. The
generated freeform microlens is shown in Figure 3.3. The maximum profile deviation of
the design value of the freeform lens with respect to a spherical lens is 3.4 µm.
15
Figure 3.3. (a) A single freeform microlens surface. (b) Layout of ray tracing of a single
freeform microlenslet projecting onto the target surface. (c) Close-up view of ray tracing
of a single freeform microlenslet.
3.2
3.2.1
Manufacturing process for the freeform microlens array
Geometric design of tool path
Since the grid points of the lens surface and their normal vectors were known, the tool
path could be generated. The model of the tool path generation with tool geometry is
schematically shown in Figure 3.4 with a fixed tool nose radius. Suppose the radius of
the tool nose is R. OT is the center of the tool nose, PO is the cutting point, and N is the
freeform surface normal vector at PO. nT is the normal vector of the cutting plane, so it
16
can be assumed as (0, 1, 0). Vector nC is the projection of the freeform surface normal
vector N in the cutting plane. nC0 is the unit vector of nC. The position of the tool center
OT can be obtained by Equation (4):
 nC  N  ( N  nT )  nT

 n  nC
 C0 n
C

(3)
OT  PO  R  nC 0
(4)
Figure 3.4. Schematic of tool compensation.
3.2.2
Fabrication of freeform microlenses
In this research, ultraprecision machining was performed on the Freeform Generator 350
(Moore Nanotechnology, Inc., Keene, New Hampshire). A diamond tool with radius
0.378 mm was utilized in the current study. Since the radius of the tool and the normal
vectors of the mesh nodes were known, the tool radius compensation was included in the
tool trajectory generation. The material of the mold insert was 6061 aluminum alloy.
17
Prior to machining the freeform surface, the top surface of the mold insert was diamond
turned flat. The rotational speed of the C axis was set at 2,000 rpm. The cutting depth and
the feedrate of the finishing cutting were 2 m and 5 mm/min, respectively. In most
cases, two types of tool path generation methods are available for slow tool servo
process, i.e., spiral path and linear broaching path. The broaching path generation was
selected to fabricate the freeform microlens array because of the rectangular shape of the
microlens (Li, et al., 2006). In this process, the workpiece was moving along the y axis,
while the positions of x axis and z axis were determined by the cutting path with proper
tool radius compensation. Once an individual pass was finished, the tool was retracted
and moved to the next starting point for next vertical pass. This process eliminated the
need for alignment for the symmetry axis of the tool with the C axis, compared with the
fast tool servo diamond turning.
The size of one freeform microlens in this study was 1 mm×2 mm, and the number of the
matrix of the microlens array was 8×4. The entire machining process was divided into 10
cycles while for each cycle the depth of cut was 10 m. For rough cutting, the diamond
tool cross-feed step size was 30 m, and the feedrate was 40 mm/min. For finish cutting,
the cross-feed step size was 10 m, and the feedrate was 20 mm/min.
Microinjection molding process was applied to replicate the low cost freeform microlens
array. The processing parameters used in this research are: the injection temperature was
250˚C, the injection speed was 200 mm/s, the injection pressure was 180 MPa, the
packing pressure was 80 MPa, and the packing time was 3 sec. The optical grade PMMA
18
(Plexiglas® V825, GE polymerland) was used to perform this experiment. The mold
insert and the molded samples are shown in Figure 3.5.
Figure 3.5. (a) Pictures of the finished mold insert and the injection molded freeform
microlens arrays. (b) Two buffer areas indicated in the pictures are designed to protect
the tool cutting edge from making oversize cut into the work piece.
3.3
3.3.1
Geometric and optical evaluations
Surface geometry measurement
The surface profile measurement was performed on a Wyko NT9100 noncontact optical
profilometer. The solid lines of Figure 3.6 show the designed and measured surface
profiles along the line y=0 mm of microinjection molding insert and molded part. As
shown by the dashed lines in Figure 3.6, both of the measured mold insert and the
molded microlens profiles match the designed freeform profile well. For the mold insert,
the maximum error between the achieved and the designed profile is 0.3 m. For the
19
microlens, the maximum error of the profile in height is around 0.5 m, and the
maximum peak-peak deviation of the geometry error is roughly 600 nm.
Figure 3.6. The solid lines are measured 2D surface profiles along the line y=0 mm from
the center to the edge (corresponding to Figure 3.3(a)) of the mold insert and the molded
lens. The dashed lines are geometry errors of surface profiles along the line y=0 mm of
molding insert and molded piece.
Figure 3.7 are the measurements for surface roughness of the mold insert and molded
microlens. The Ra values of the surfaces of the mold insert and the molded microlens are
29 nm and 25 nm, respectively. No post polishing was performed after the diamond
machining.
20
Figure 3.7. (a) Surface roughness measurement of the mold insert. (b) Surface roughness
measurement of the molded microlens.
3.3.2
Ray tracing simulations
The overall size of the freeform microlens array is 8 mm×8 mm, and the distance
between the microlens array panel and the target surface is 200 mm. To evaluate the
performance of the freeform microlens array, the optical setup was simulated in Zemax
(3001 112th Avenue NE, Suite 202, Bellevue, WA 98004-8017). Non-sequential ray
tracing mode was applied to trace the propagation of the rays after refracted by the
freeform microlens array. Rays were randomly generated by a rectangular light source,
and after refraction, the rays reached the rectangular detector. To build the model of the
freeform microlens array, polygen object was utilized in this simulation. Polygen object
is one of the user-defined objects in Zemax, which consists of a collection of
quadrangles. The neighboring fours vertexes of the entire series of quadrangles were
selected from the fitted freeform surface nodes.
21
Figure 3.8. Simulated light distribution on the target surface.
For a single freeform microlens, total 20,100 quadrangles were defined based on the
model of polygon object. Zemax used the built-in object type “Array” to arrange 32
microlenses in an 8×4 array. Light source and detector were placed on the designed
positions. The number of rays used in analysis was 1,000,000. The size of the rectangular
source was 8 mm×8 mm, and at the end of this optical setup the intensity was detected by
a 50 mm×40 mm size rectangular detector that had a resolution of 200 ×100 pixels. The
uniform distribution was the core in this study rather than the absolute intensity of the
light, thus the simulated results of the absolute luminance of light source was ignored.
Figure 3.8 is the detector image of the irradiation refracted by the microlens array.
3.3.3
Optical performance measurement
A He-Ne laser was used as the illumination source. A translucent plastic plate worked as
the target plane surface. Figure 3.9 shows the grey value of the red pixel of the
illumination picture taken behind the translucent plastic plate. The value of the red pixel
ranges from 0 to 255, which quantitatively represents the intensity of light.
22
Figure 3.9. Measured light distribution on the target surface.
In order to compare the simulated and the experimental results, the simulated and
measured intensity of the light was normalized. The uniformity is defined as Equation
(5):
u  1
I max  I min
I avg
(5)
Where Imax is the maximum intensity value, Imin is the minimum intensity value and Iavg is
the averaged intensity value of all the pixels. As a result, for simulated result, 82.1%
uniformity of designed area is achieved in the illuminated area; for experimental result,
82.0% uniformity of target area is obtained.
23
Figure 3.10. (a) Comparison of the simulated and experimental corresponding line
distributions along the x axis across the center of the illumination. (b) Comparison of the
simulated and experimental line distribution along the y axis across the center of the
illumination.
Figure 3.10 illustrates the comparison of the line distributions along x axis and y axis
across the center of the illuminated area of the experimental and simulated results.
Majority of the line distributions along x axis and y axis from simulated and experimental
results are consistent with each other, as shown in Figure 3.10. Thus, the uniformity of
the redistributed illumination was achieved.
However, there are factors that may lead to the uniformity error. For instance, the
illumination image was taken behind the translucent plastic plate, which might cause the
surrounding scattering shown in Figure 3.9. Also, in the optical measurement the light
source was laser while interference between the radiations refracted by the different cells
was not considered, so the optical design needs to be improved when coherent effects are
included. The usage of LED source can be employed to avoid the interference problem
24
caused by the laser, but the lights need to be corrected. Moreover, the exact value of the
refractive index of PMMA before and after molding was not known at certain wavelength
used in the experiment which also possibly leaded to more errors. In addition, the size
limitation of the diamond tool might cause the manufacturing quality as well. As
discussed above, tool compensation calculation was included in the tool path generation.
In the compensated tool path, the edge of the tool bit was considered as an arc with a
fixed radius and the position of the cutting point on the edge of the tool bit depended on
the normal vector of the surface that was being machined. Thus, it was almost impossible
to avoid the overcut by a fixed radius cutter toward a convex surface during the diamond
machining process, as illustrated in Figure 3.11. Smaller diamond tool will reduce the
overcut area, which can achieve higher uniformity of the beam shaping. However, studies
also indicated that a too small cutting tool could result in deterioration of the machined
surface quality (Li, et al., 2010). Figure 3.9 indicates that the uneven radiation
distributions on both the left and the right side were created by the overcut problem.
Figure 3.11. Schematic of overcut due to the radius of the diamond tool.
25
Chapter 4. Precision Machining for Optical Molding
Various micromachining techniques were developed in recent years, such as
photolithography, thermal reflow, laser micromachining, micro milling, micro electrical
discharge machining and ultraprecision diamond machining. One of the approaches used
in this thesis research is slow tool servo diamond machining, a noncleanroom method
requiring minimal setup with a considerable manufacturing flexibility. In slow tool servo
machining (Yi & Li, 2005), a mechanical slide (z axis in the setup in system used in this
study) provides the control in the direction of the depth of cutting. This arrangement
allows large deviations on optical surfaces to be machined but limits the dynamic
response of the cutting tool due to the inertia of the heavy mechanical slides. In this
section, both the glass and polymer molds were fabricated by the slow tool servo
machining technique. Ultraprecision machining was performed on the Freeform
Generator 350 (Moore Nanotechnology, Inc., Keene, New Hampshire). The basic
information of this machining process can be found in (Yi & Li, 2005). The diamond
machining for both regular metal materials and brittle materials are discussed.
4.1
4.1.1
Diamond machining on regular metals
Slow tool servo machining
A diamond tool with a radius of 0.378 mm was utilized in the current study. The tool
nose radius of the diamond cutter was compensated off line in the calculation for tool
26
path trajectory. Linear broaching method was adopted to generate the tool paths. In this
process, the workpiece was moving along the y axis, while the positions of x axis and z
axis were determined by the cutting path with tool radius compensation. Once an
individual pass was finished, the tool was retracted and moved to the starting point for the
next vertical pass. The number the microlens array is 4×4 and the spacing between
horizontal or vertical centers of a pair of the neighboring lenslets or pitch in both
direction is 2.2 mm (Li, et al., 2011). Figure 4.1 depicts the broaching CNC (Computer
Numerical Control) tool paths for both the glass and polymer microlens arrays.
(a)
(b)
Figure 4.1. Broaching tool path for: (a) glass microlens array, (b) polycarbonate
microlens array. The spacing between neighboring steps is reduced and the return tool
paths are removed for clarity.
The material used for glass mold was 715 copper nickel alloy (www.farmerscopper.com,
Galveston, TX). For polymer molding, 6061 aluminum alloy was employed. Prior to
machining the microlens array pattern, the top surface of the mold was diamond turned
flat. The rotational speed of the C axis (main spindle) was set to at 2,000 rpm. The cutting
27
depth and the feedrate of the finishing cutting were 1 m and 1 mm/min, respectively.
For the microlens array pattern, the entire machining process was divided into 18 cycles
(infeed) on the nickel mold, 9 cycles (infeed) on the aluminum mold. For each cycle the
depth of cutting was 10 µm. For rough cutting, the diamond tool cross-feed step was 30
µm, and the feedrate was 40 mm/min. For finish cutting, the cross-feed step was 10 µm,
and the feedrate was 20 mm/min. In addition, the rectangular pocket on the top surface of
the aluminum mold was micromilled by an ultraprecision high speed air bearing spindle
made by Professional Instrument (ISO 6000, maximum speed 60,000 rpm). The two
chisel shaped cavities used for positioning were machined by broaching simultaneously
with the microlenses to ensure high position tolerance. Figure 4.2 shows the finished
copper nickel mold for glass compression molding and aluminum alloy mold for polymer
compression molding.
(a)
(b)
Figure 4.2. Pictures of the finished (a) copper nickel mold for glass and (b) aluminum
mold for polymer.
28
4.1.2
Diamond turning
In the fabrication process of axisymmetric mold, the diamond turning of the mold inserts
used in this study was also performed on the Freeform Generator 350 (Moore
Nanotechnology, Inc., Keene, New Hampshire). This diamond machining technique
provides a lot of flexibility in generating complex freeform surface while still
maintaining high precision. The mold material was 6061 aluminum alloy. A diamond tool
with controlled radius 2.6055 mm was used in the study. The tool nose radius of the
diamond cutter was compensated off line for tool path trajectory. In the finishing
machining path for the aspherical optical surface, the cutting depth was 1.5 m and the
feedrate was 1 mm/min. Figure 4.3 shows the finished aluminum mold for the hybrid
lens injection molding. The surface roughness of the optical surface is approximately 8
nm as measured by Wyko NT9100 optical profilometer.
Figure 4.3. Picture of the finished ultraprecision diamond turned mold inserts for the
hybrid lens microinjection molding.
29
4.1.3
Surface coating for nickel glass mold
Molds for precision glass molding must withstand high mechanical stresses and oxidation
under high temperatures. In order to improve the lifetime of the molds under these
difficult conditions, protective coatings are applied on the optical surfaces of the molds
(Ma, et al., 2008). The goal of these thin film coatings is to reduce the interactions
between the glass and the mold, thus reducing the opportunity of glass adhering to the
mold surface during and after molding. Ceramic coatings (TiAlN, SiC, and CrBN), noble
metal coatings such as Pt-Ir and DLC coatings (Aoki, et al., 1987; Hagerty, et al., 1988;
Hirabayashi, et al., 1991) have all been used for this application. Comparisons of ceramic
and noble metal coatings indicated that noble metal coatings showed better characteristics
in contact with glass samples (Klocke, et al., 2010). Based on that experience, a Pt-It
coating was deposited on the nickel alloy mold.
Since the substrate was 715 copper nickel instead of the usually used tungsten carbide,
the deposition parameters had to be adjusted. Firstly, the temperature of the substrate
during coating was reduced from 450°C to 150°C in order to reduce the possibility of
structural changes or recrystallization in the substrate material. Secondly, the duration of
the physical etching of the substrate prior to coating was reduced from 20 min to 5 min,
since copper and nickel alloy is more easily sputtered than tungsten carbide. During
physical etching, a few nanometers of the substrate surface material were sputtered by
argon ion plasma before coating. This cleans and activates the surface thus improving the
adhesion of the subsequently deposited coating. However, if the cleaning and activation
process is used excessively, it can lead to increased surface roughness. Using the adjusted
etching parameters, no change in surface roughness was observed before and after
30
coating. Thirdly, a 50 nm nickel adhesion layer was deposited between the substrate and
the Pt-Ir coating. Since nickel was also present in the substrate, strong adhesion was
ensured. This prevents delamination of the coating during molding, especially around the
sharp edges where mechanical stresses are the highest. Finally, a 250 nm Pt-Ir coating
was deposited using unbalanced magnetron sputtering with a segmented target, the
composition of the coating consists of 40 % Pt and 60% Ir. Figure 4.4 shows the Pt-Ir
coating with nickel adhesion layer. The low coating thickness ensures that neither the
form accuracy nor the surface roughness of the mold is affected by the thin Pt-Ir coating
layer.
Figure 4.4. SEM (scanning electron microscope) photo of the Pt-Ir coating with nickel
adhesion layer.
31
4.2
Diamond machining on silicon wafer
Silicon is a versatile engineering material for a wide range of applications such as
electronics, biology (Silicon, 2013) and mold applications (He, et al., 2013; He, et al.,
2014) because its attractive material properties and precision manufacturing processes
that have been developed over the last few decades. Among the processes available,
photolithography is a conventional industrial processing technology for high volume
silicon production. However, this technology requires cleanroom environment and
complex processing procedures. More importantly, it cannot be used to create true
freeform features on silicon substrate. As such, ultraprecision diamond machining of
single crystalline silicon has been investigated as an alternative in non-axisymmetric or
freeform optics fabrication.
Compared with photolithography technique, diamond machining can be readily used to
create high precision freeform surfaces and structures, but the biggest challenge for this
process is the brittle nature of the silicon material. Because silicon is brittle, it is difficult
to avoid the micro fractures on and below the wafer surface caused by diamond
machining. Studies of silicon machining have been conducted to address this issue. For
example, Blake and Scattergood proposed the diamond machining theory for brittle
materials that in ductile-regime, the micro fracture damage could be eliminated if the
effective cutting depth was below the critical cutting depth (Blake & Scattergood, 1990).
Blackley and Scattergood further analyzed the influences to the fracture damage from
various machining parameters, such as rake angle, tool radius, and machining
environment (Blackley & Scattergood, 1991). Shibata et al. and Leung et al. extended the
investigations to diamond turning process (Shibata, et al., 1996; Leung, et al., 1998). Yan
32
et al. examined the thickness and structure of the subsurface damage of diamond
machined silicon (Yan, et al., 2009). Yu et al. determined the subsurface damage depth
using a novel method (Yu, Wong, & Hong, A novel method for determination of the
subsurface damage depth in diamond turning of brittle materials, 2011). To study
freeform optics, Yu et al. and Jasinevicius et al. investigated the application of diamond
machining on brittle materials to unconventional optical components (Yu, Wong, &
Hong, Ultraprecision machining of micro-structured functional surfaces on brittle
materials, 2011; Jasinevicius, et al., 2013).
However, the previous studies assumed that subsurface damage depth remained constant
during the entire machining process whereas our experimental studies showed that
different damages were created when different depth of cut was used. Moreover, in a few
studies designed for slow tool servo (STS) diamond machining, only 2D damage
prediction was reported (Yu, Wong, & Hong, Ultraprecision machining of microstructured functional surfaces on brittle materials, 2011). To accurately predict the
damages in machining, 3D damage distribution prediction is of great interest especially
when non-axisymmetric or freeform optics are employed. The 3D damage distribution
modeling in our study can accurately predict the pitting damages caused by diamond
machining and can be further utilized to optimize the machining process without
conducting the actual experiments. This modeling approach has great industrial potentials
in freeform optics field, such as, machining of infrared glass lens, and compression
molding of glass optics (He, et al., 2013).
The main objectives of this silicon machining research are organized as follows: firstly,
develop a novel subsurface damage model for the STS diamond machining of silicon and
33
apply this model to simulate the damage distribution three-dimensionally. Secondly,
verify the damage predictions by comparing them with the machining experiments.
Finally, fabricate a molded glass microlens array by using the machined silicon as mold.
In addition, the applications and optimization of the 3D simulation of damage distribution
will be discussed.
4.2.1
Modeling of 3D damage distribution
In the past, researchers proposed the hypothesis that brittle materials undergo brittle to
ductile transition at a critical cutting depth tc (Blake & Scattergood, 1990). When
effective cutting depth is below this threshold, machining is carried out in plastic
deformation mode, which is called ductile regime machining. Hence, the machining for
brittle materials should be maintained within ductile regime to achieve optical quality
surface finish. They also assumed that subsurface damage is generated at a constant depth
even when the cutting depth is beyond that threshold (Blake & Scattergood, 1990; Yu,
Wong, & Hong, A novel method for determination of the subsurface damage depth in
diamond turning of brittle materials, 2011). Nevertheless, unlike previous assumption,
our studies of STS machining discovered that more micro fracture damages can be
observed with the increase of cutting depth. Therefore, the subsurface damage model is
revised as shown in Figure 4.5.
34
Figure 4.5. Brittle to ductile transition based on STS machining process configuration.
In this subsurface damage model illustrated in Figure 4.5, similar with previous
researches, no micro fracture damage occurs if the cutting depth is less than tc, and it is
assumed that the micro fracture with a depth of yc is initialized beneath the cutting
surface when the local cutting depth is equal to the critical cutting depth tc. In addition,
our experiments show that when the cutting depth is more than a certain value (about 2
µm in our studies), the machining produces the fish-scale-shaped cracks which are much
more severe than the micro factures or pitting damages under brittle-ductile transition
mode. This cutting depth value for crack initialization is marked as tcr in Figure 4.5.
Therefore, with a cutting depth larger than tcr the surface damage is increased
tremendously; on the other hand, with a cutting depth between tc and tcr, it is assumed that
the micro fracture damage depth has an approximately linear relationship with the cutting
depth beyond the critical cutting depth. This linear relationship assumption is based our
experimental experience, and needs to be investigated further in the future. In this way,
the revised subsurface damage model can be used to simulate the 3D distribution of
35
subsurface micro fracture damages of the diamond machined silicon. The influence of
crystalline direction of silicon to the micro fracture generation during the STS machining
was not taken into account in this study.
Figure 4.6. Flowchart of the 3D damage distribution calculation program
Based on the subsurface damage model discussed above, a MATLAB computer code was
programmed to simulate how material is removed while calculating the consequent local
damage depth. Figure 4.6 shows the flowchart of this computer program. If the current
effective cutting depth at the cutting point is small than tc, no new damage is generated,
36
and the local damage depth is reduced by the effective cutting depth until it reaches zero.
On the contrary, if the current effective cutting depth at the cutting point is larger than tc,
the damage depth is updated as a linearly function of the effective cutting depth. Thus,
with the information of tool path and subsurface damage model, the damage distribution
of STS diamond machined silicon can be visualized three-dimensionally.
4.2.2
Machining experiments
The STS machining on silicon wafer was performed on the Freeform Generator 350 FG
(Moore Nanotechnology System, Inc., Keene, New Hampshire). The machining tool path
can be either spiral or broaching method. In this study, the broaching tool path was
adopted (Li, et al., 2011; Li & Yi, 2011). The diamond tool crossfeed rate was 20
mm/min. The tool nose radius of the diamond cutter was 3.05 mm, the rake angle was 24.95° rake angle and the clearance angle was 10°. The odorless mineral oil was used as
coolant during the entire machining process. The distance between each broaching path
before the compensation for tool radius was 5 µm.
Figure 4.7. Design of a square microlens array. Unit is m.
37
An array of square microlenses with 7.1119 mm radius and 0.36 x 0.36 mm apertures was
machined on a single crystalline silicon wafer. The sag of each microlens was 4.5 µm.
Figure 4.7 shows the layout of the square microlens array. The fabrication process
consisted of rough and fine machining. Two sets of rough and fine cutting combinations
were experimented in order to balance surface quality and cycle time because even
though more fine cutting passes could reduce micro factures it would considerably
increase machining time. The detailed parameters of rough and fine cutting are
summarized in Table 4.1.
Table 4.1. Rough and fine machining parameters
Condition
1
2
Depth of rough cut
(nm)
333
350
# of
passes
12
10
Depth of finish cut
(nm)
100
100
# of
passes
5
10
According to the machining results, the machining condition 2 was later adopted to
fabricate the silicon mold for glass molding experiments for its damage free surface
finish. Figure 4.8 shows the microscopic pictures of the microlens arrays machined under
the conditions listed in Table 4.1. It shows that the left edge of the microlenses machined
under condition 1 has micro fractures in contrast to the microlenses with optical quality
machined under condition 2. The damages on the edge of the microlenses in the left
column (produced by the overcut of the round diamond tool) are negligible because those
spots are not used as effective optical area. Furthermore, these damages can be eliminated
by increasing the number of the fine cutting while the machining cycle time needs to be
increased considerably.
38
(a)
(b)
Figure 4.8. Microscopic pictures of the microlens arrays machined under conditions of
(a) condition 1 and (b) condition 2 in Table 4.1.
4.2.3
Glass molding experiments
A coating process is necessary to protect silicon mold from damage due to adhesion
between silicon and glass at high temperature (Yi & Jain, 2005). It has been demonstrated
that a thin film coating of graphene-like structure on silicon mold can be an effective way
to prevent adhesion (He, et al., 2013). In the coating process, the silicon mold was placed
in a nitrogen gas purged furnace. Benzene in the form of bubbles was introduced into
furnace as carbon source with Ar gas at an elevated temperature. After coating, a thin
layer of graphene-like structures is deposited on the silicon wafer, which has silver like
metal appearance.
Precision glass molding is a hot forming process to replicate optical features from molds
to glass blanks. It has been used as a high volume, low cost process to fabricate various
optical components (He, et al., 2011; Li, et al., 2011; Yi & Jain, 2005). In a molding
process, glass preform is heated to an elevated temperature then compression molded
between two optical polished molds. Controlled cooling is applied after glass was pressed
39
to prevent thermal crack and reduce residual stresses in the molded glass optics (Tao, et
al., 2014).
The molding experiment was carried out on a DTI glass molding press. A 5 x 10 x 0.6
mm glass sheet was used to replicate the micro features from the silicon mold. The
molding temperature was 560 °C for the selected glass type P-SK57 (Schott Glass). The
heating ramp rate was limited at 2 °C/s and the soaking time was 10 min. Those heating
parameters were chosen to balance uniform temperature distribution and production
efficiency. A molding force of 200 N was applied to glass when the molding system
reached the desired temperature. After 1 min of holding time, the system was cooled with
an initial cooling rate of 0.6 °C/s from 560 °C to 480 °C then cooled with nitrogen forced
cooling. The molded glass was removed from the mold at about 200 °C.
Figure 4.9. Silicon mold and molded glass microlens array.
Figure 4.9 shows the silicon mold and the achieved molded glass microlens array. The
machined surface was measured by Wyko NT 9100 optical profiler. The surface
40
roughness Ra value of the damage free area is about 15 nm. Figure 4.10 shows the
measured profiles of the machined mold, molded glass optics and the geometry deviation
between the mold and the molded part. The optical profilometer collected multiple
measurement data and then stitched them into a single surface covering the entire
measured area. The stitched measurements indicate about 500 nm maximum geometry
deviation for the entire molded part. The peak-valley deviation within the aperture of
each microlens is mainly due to the local tilt. So if the local tilts are subtracted, the
geometry deviation turns to be less than 100 nm. The large local tilt possibly results from
the accuracy of the stitching algorithm and the x-y stage translation of the Wyko
profilometer.
Figure 4.10. (a) Measured profiles of the silicon mold and (b) the molded glass microlens
array. (c) Geometry deviation between the mold and molded glass optics. Unit is mm.
4.2.4
Results and discussions
In order to apply the subsurface damage model to the 3D machining simulation, similar
experiments such as the ones Yan et al. conducted were carried out to determine the value
of the critical cutting depth tc (Yan, et al., 2009). This value was determined to be 130 nm
41
in our experiments. The initial subsurface damage depth yc was set as 700 nm based on
previous studies (Blake & Scattergood, 1990; Blackley & Scattergood, 1991; Yu, Wong,
& Hong, A novel method for determination of the subsurface damage depth in diamond
turning of brittle materials, 2011). The empirical coefficient of the linear relation was set
as 2.5. Therefore, the 3D distribution prediction of the subsurface micro fracture damages
can be generated based on how the machining path is calculated, as illustrated in Figure
4.11 (a) and (b). Since the machining path of each microlens is the same, only the 3D
damage distribution of the microlens in the most left column are shown as an example for
the above two machining conditions. The round left edge of the microlens is due to the
overcut of the round tool nose and therefore only the microlenses in the most left and
right column have this pattern.
The experiments of the STS diamond machining on silicon wafers were performed under
the same machining conditions used in the calculation of subsurface damages. The
calculation shows that the surface micro fracture damages of these two experiment
conditions have different degrees of damages and distribution patterns, as shown in
Figure 4.11 (e) and (f).
Figure 4.11 demonstrate that the calculated and experimental results are in good
agreement with each other. The revised subsurface damage model discussed in Section
4.2.1 was applied to calculate the 3D damage distribution of the STS diamond machined
silicon, providing more details of the damaged surface.
42
(a)
(b)
(c)
(d)
(e)
(f)
Figure 4.11. Calculated 3D damage distributions of a microlens machined under (a)
condition 1 and (b) condition 2. (c) and (d) are the top views of (a) and (b) respectively.
Microscopic pictures of a microlens machined under (e) condition 1 and (f) condition 2.
Unit is mm.
43
For example, Figure 4.11(c) shows the damage pattern (red dots) along the right edge of
the lens. In addition, the density of the red dots representing the damaged area in Figure
4.11 (d) is less than Figure 4.11 (c). These details can be confirmed in the corresponding
experimental micro fracture damage distributions shown in Figure 4.11(e) and Figure
4.11(f). The minor differences between the calculated and experimental results may be
due to the fluctuation of the temperature control of the machine during the machining
process, the accuracy of the subsurface damage model, and the material uniformity.
Figure 4.12 shows the calculated damage distribution of a microlens when the constant
damage depth is applied. From Figure 4.12 it can be concluded that if the constant
damage depth model is used in the calculation for 3D damage distribution, neither the
detailed damage distribution of Figure 4.11(c) nor the variation of damage degree in
Figure 4.11(d) can be obtained. It should be noted that the tc was increased to 1,000 nm
for Figure 4.11(a) to compare these two subsurface damage depth models, because even
no damage was predicted with the same tc value 700 nm used in the other calculations.
(a)
(b)
Figure 4.12. Calculated subsurface damage distributions of a microlens if the constant
damage depth model is used. Unit is mm.
44
Additionally, the calculation of the 3D damage distribution can provide the micro
fracture layouts at any stage during the machining process without “interrupting” it,
which helps us understand the ductile mode machining for brittle materials. Figure 4.13
show the development of the damage distribution during the entire machining process
using machining condition 2 as an example. The damage is not initialized (Figure
4.13(a)) for the first couple of passes because of the small effective cutting depth, and
starts to grow when the geometric slope between the neighboring paths increases (Figure
4.13(b)). During this stage, it shows that large rough cutting depth does not necessarily
result in large effective cutting depth. The damaged area then continues increasing
(Figure 4.13(c)) until the condition 2 was switched to the finer cutting depth which is
even smaller than the critical cutting depth (Figure 4.13(d)), such that ductile regime
machining mode is maintained. This way, the damaged area is reduced significantly in
effective area that requires optical quality after the fine cutting passes (Figure 4.13(b)).
This study confirms the previous researches that the brittle-ductile regime machining
damage is associated with many factors, such as geometry, tool radius and cross feedrate.
This study is a visual approach to present the development of damage distribution in
brittle-ductile machining mode. Therefore, this technique will be very helpful for
monitoring the 3D damage distribution of diamond machined brittle materials especially
when complex freeform geometries or multiple machining passes are involved.
45
(a)
(b)
(c)
(d)
Figure 4.13. 3D damage distribution simulations of the microlens on silicon at the
middles of the (a) 5th, (b) 8th, (c) 11th and (d) 18th machining pass of the machining
experiments conducted under condition 2. Unit is mm.
46
(a) (b)
Figure 4.14. Cutting path planning strategies: (a) constant cutting depth; (b) constant
cutting ratio. Unit is mm.
Since single point diamond machining is conducted at nanometer scale, the micron scale
freeform optics features have to be divided into several steps to avoid fracture damages of
brittle materials. Hence, two different dividing strategies were compared to minimize
damages as shown in Figure 4.14. Figure 4.14(a) uses a constant cutting depth for each
pass, while Figure 4.14(b) employs a constant ratio of the final sag for the cutting depth
for each pass. In order to compare these two machining dividing methods, the machining
condition 2 listed in Table 4.1 was selected as an example for the constant cutting depth
method. For the constant cutting ratio method, the cutting depth of condition 2 in Table 1
was set as the maximum cutting depth for each pass. For example, the maximum cutting
depth is 350 nm and the final sag height is 4.5 µm, the ratio for this pass is
0.35/4.5=0.0778. According to the calculate damage distribution results, the constant
cutting depth method has 3.54% damaged area, whereas the constant cutting ratio method
47
results in 7.95% damaged area. The difference is due to the fact that the damages were
initialized at the very beginning of the machining under the latter condition. Therefore the
accumulated damages incurred during initial cutting could not be removed by the
following passes using the latter method. The calculated results suggest that even the
same maximum cutting depth can still lead to different degrees of damage when different
machining strategies are utilized.
With the increasing use of freeform optics in the past few years, diamond machining on
silicon or other brittle materials has been explored frequently. The STS diamond
machining is capable of providing true 3D feature generation on silicon, compared with
limited and complicated cleanroom technologies. However, the brittleness of silicon
impedes its diamond machinability. Thus, it is important to understand the damage
distribution of STS diamond machined silicon in 3D when freeform optics is involved. In
this research, we have demonstrated a unique process utilizing single point STS diamond
machining process to create microlens arrays on single crystalline silicon substrate with
zero or minimum damages.
4.3
Tool path optimization
In machining of the microlens array on either flat substrate or curved substrate, it was
found that the sharp discontinuities occur at peripheral regions of microlenses due to the
discontinuous surface normal vectors at the edge of the microlenses (Scheiding, et al.,
2011). Therefore, two alternative modifications have been proposed to improve the
surface quality and reduce cycle time as shown in Figure 4.15 (Naples, 2014).
48
Figure 4.15. Cross sections of concave, spherical lenslets on convex, spherical substrates.
(a) Traditional, unblended, discontinuous lenslet. The thick blue line is machined,
discontinuity and all. (b) Traditional lenslet blended with a torus. The thick blue line is
machined, blend and all. (c) Lenslet with blending in the air. Only the thick blue line is
machined, which is exactly the whole, original lenslet. Original lenslet aperture is marked
by 2 magenta asterisks.
Figure 4.15(a) shows the traditional, unblended, discontinuous lenslet. Figure 4.15(b)
illustrates the first alternative by removing the lenslet/substrate intersection discontinuity
with a “blend” torus that a tangent to the lenslet and substrate. In this way, relatively
small acceleration gradients can be achieved among all the mechanical slides, so one is
able to greatly reduce machining time and improve the overall quality of the array. There
is, however, a variation on the blend torus method that allows one to machine perfectly
49
discontinuous lens arrays on flat and non-flat substrates without physically machining a
blend torus on the part. In the further optimized strategy shown in Figure 4.15(c), the
physically machined part is the originally designed lenslet, while the machining path on
the Blend Torus is in the Air (BTA). Figure 4.16 shows close lenslet close-up pictures
for allthree methods (spherical lenslets machined on spherical substrates).
Figure 4.16. Lenslet close-ups. (a) Traditional STS method with unblended lenslets.
Sliced apertures are clearly visible, rendering the component useless. (b) Close up of
unblended lenslet. (c) Blended lenslets machined with the original blend torus method.
The tool path and physical array are both clearly continuous. (d) Close of up blended
lenslet. A reduction in aperture radius can be seen as compared to a discontinuous lenslet
of the same size. (e) Totally discontinuous lenslets machined with the BTA method. The
tool path in this case was totally continuous. (f) Close up of lenslet machined with BTA
method. The aperture is discontinuous and visibly seems to be of superb quality. This
method does not compromise an optical design in any way.
50
Chapter 5. Molding Processes for Achromatic Lenses
In recent years various techniques of creating achromatic lenses have been investigated
for polychromatic applications in order to correct chromatic aberration. These efforts
include, for example, chromatic aberration characterizing and measuring method
(Juskaitis & Wilson, 1999; Seong & Greivenkamp, 2008; Dorrer, 2004; Fernández, et al.,
2005), post-processing algorithm (Wach, et al., 1998; Kozubek & Matula, 2000; Wang, et
al., 2006), liquid achromatic lens (Sigler, 1990; Reichelt & Zappe, 2007), diffractive
achromatic lens (Stone & George, 1998; Dobson, et al., 1997), electron optical achromats
(Rempfer, et al., 1997) and superachromatic lenses (Herzberger & McClure, 1963). In
addition, other researches related to lowering chromatic aberration were conducted in the
field of telescopes, surface defect analysis (Tiziani, et al., 2000), focusing of ultrashort
light pulses (Kempe & Rudolph, 1993) and scaling laws for aberration in optics
(Lohmann, 1989). Achromatic lenses are usually designed in the form of achromatic
doublets, in which materials with different optical dispersion characteristics are
assembled together to form a hybrid lens or a diffractive optical achromat, where the
complementary dispersion characteristics of the diffractive structure and the optical
material are utilized.
The most common approach to creating hybrid lenses is to use two materials with
different dispersion properties in the form of achromatic doublets. One of the advantages
of using doublets is that it allows wide range selection of the glass materials compared
51
with standard micromachining techniques such as RIE etching where only limited
number of materials available. Historically, Abbe number is used to quantify material
dispersion in relation to refractive index. For flint glass, the Abbe number is less than 50
while for crown glass it is more than 50. Therefore, both selecting the proper materials
and the assembly of these two materials to the required tolerance are key process steps to
manufacturing hybrid lenses. Oliva et al. proposed the best normal flint glass suitable for
the design of lens systems working in the infrared up to 2.5 µm (Oliva & Gennari, 1998).
Zwiers et al. fabricated a hybrid polymer-glass aspherical lens using UV-polymerizable
coatings (Zwiers & Dortant, 1985). Lim et al. compensated the shrinkage error during the
UV imprinting process for fabricating hybrid lenses (Lim, et al., 2008). Verstegen et al.
analyzed the shape accuracy of optical components influenced by the reaction mechanism
(Verstegen, et al., 2003).
5.1
Achromatic lens design
The refractive index of an optical material varies as a function of wavelength. Therefore
the focal length of a glass lens varies as a function of light color. As aforementioned,
Abbe number is the measure of variation of refractive index with wavelength, and is
defined as (Laikin, 2010):
V
nD  1
nF  nc
(6)
where nD, nF and nC are the refractive indices of the material at the wavelengths of the
Fraunhofer D, F and C spectral lines (589.2 nm, 486.1 nm and 656.3 nm respectively).
The lower the Abbe number V an optical material has, the higher its dispersion is. On the
52
other hand, the power of the lens can be expressed in the form of the lens surface
curvatures and its refractive index if the lens is used in air:
  (n  1)(c1  c2 )
(7)
where n is the refractive index of the lens material, c1 and c2 are the curvatures of the two
surfaces of the lens.
The common technique for achromatic doublets to correct chromatic aberration is to
cement flint glass and crown glass together using UV (ultraviolet) curing adhesive. The
total optical power of such a cemented doublet is equal to the sum of the powers of two
single lenses. The requirements to correct chromatic aberration are described in Equation
(8) (Laikin, 2010):
  1  2

 1 2
V  V  0
 1
2
(8)
where  is the total power of the doublet, 1 and 2 are the power of flint glass lens and
crown glass lens, respectively, V1 and V2 are the Abbe numbers of two single lenses,
respectively. From here the power of two lenses can be obtained from Equation (9):
V1

1  V  V 

1
2

V
2
2  


V

V2

1
5.2
(9)
Compression molded hybrid achromatic microlens array
Microlens arrays play an important role in optical industry. For instance, components
used in telecommunication devices, digital projectors, machine vision systems and
53
compact imaging applications. The application of microlens array in low cost multiple
optical trapping can be found in Appendix A. Therefore, there is a growing demand to
develop large volume, high precision production techniques for manufacturing microlens
arrays.
5.2.1
Optical design of hybrid microlens array
In our study, Polycarbonate (PC) was used for being widely available in industry with an
Abbe number V1 of 29.91. P-SK57 glass was selected as crown glass with an Abbe
number V2 59.60 for its low glass transition temperature to alleviate the requirement for
high temperature molding conditions. The nominal refractive index of polycarbonate
used in this research is 1.5855, and the refractive index of P-SK57 is 1.5870. The
material parameters are obtained from the optical design software Zemax. The design
effective focal length is then 10 mm, and the diameter of each microlenslet is chosen as 2
mm.
Figure 5.1. Geometric layout of the achromat doublet design.
54
After obtaining the calculated lens parameters, these data were entered into Zemax for
further optimization. Figure 5.1 shows the geometric layout of the achromat doublet
design. The radius R1 of the convex surface of the crown glass microlens is 2.92167 mm,
and the radius R2 of the convex surface of the flint glass microlens is 5.88252 mm. The
edge thicknesses of the glass and polymer microlens in Figure 5.1 are 1.82354 mm and
1.63221 mm.
Figure 5.2. Chromatic focal shift of one hybrid polymer-glass microlens doublets.
Figure 5.2 illustrates the chromatic focal shift of this doublet for wavelength from 486.1
nm to 656.3 nm calculated using Zemax. The maximum focal shift range is 7.16 µm. The
capability of chromatic aberration correction by the hybrid polymer-glass doublet is
clearly demonstrated in Figure 5.2.
5.2.2
Compression molding processes
The fabrication process is schematically illustrated in Figure 5.3. Figure 5.3(a)~(c)
describe the compression molding process for the glass microlens array. The general
setup was that a piece of P-SK57 glass was sandwiched between two mold halves. The
55
glass piece was heated up in the vacuum furnace above its transition temperature and then
squeezed between the two mold halves. The positions of the mold halves were held for a
certain period of time, and cooling was started after compression was completed. Two
chisel shaped shaped cavities were designed on the glass mold and would be machined
simultaneously when the microlens array was created so the polymer lens layer could be
precisely aligned in a self-assembly fashion. The thickness of the glass piece was
controlled by the vertical gap between the two mold halves as in Figure 5.3(b). The
molded glass piece was then used as the top mold half for the subsequent polymer
compression molding procedure shown in Figure 5.3(d). The forming of the polymer
microlens array was shown in Figure 5.3(d)~(f).
Two chisel shaped shaped cavities with identical shapes on the nickel alloy mold, that
would be used as fiducial features, were also machined on the top surface (Figure 5.3(d))
of the aluminum mold using identical design parameters and the same relative position to
the microlens array pattern uninterruptedly. The horizontal relative position of the chisel
shaped shape cavities next to the microlens array pattern was the same as that in the glass
mold. The chisel shaped cavities were used to precisely align the glass and polymer parts
during forming of the polymer half. As to the polycarbonate compression molding, the
glass piece was first placed on the top surface of the polymer sheet. After the entire
system was heated to 10 ˚C above the transition temperature of the polymer, pressure was
applied to the bottom half of the mold to form the polymer microlens array. As with the
compression process for glass, cooling came after the molds have been held for a while.
In both the glass and polymer molding processes, internal stresses were introduced by the
pressing action. Furthermore, during and after annealing, stress relaxation as a function of
56
time occurred because of the viscoelastic nature of these two materials, and thus a
permanent lens-shaped curvature was developed (Firestone & Yi, et al., 2005).
Figure 5.3. Molding processes for the hybrid polymer-glass microlens array: (a)~(c)
glass molding process, (d)~(f) polymer molding process.
The glass molding experiments were conducted on a Toshiba GMP-211 V machine at
Fraunhofer Institute for Production Technology (IPT) in Germany, and the details of the
machine and glass molding process can be found in (Yi & Jain, 2005, Yi, et al., 2006,
Chen, et al., 2008). The molding conditions were selected based on the previous
experience. These conditions were found to be effective but not optimized as the focus of
this dissertation is the implementation of compression molding to the hybrid lens array.
The hybrid lenses were molded under the following steps: (Firestone, et al., 2005)
(1) Vacuum was applied to remove the oxygen before the nitrogen purge. Nitrogen
was used during the entire process as a protective atmosphere and the forced
nitrogen flow was applied during cooling for adjusting the cooling rate.
57
(2) The lower mold was pushed upward to the heating position, which left about 2
mm gap between glass blank and the upper mold to allow materials to expand
during heating. The molds and glass blank were heated up from the initial
temperature to the molding temperature of 570 °C at a rate of 2.4 °C/s.
(a)
(b)
Figure 5.4. (a) Molding force and lower mold position as function of time. (b) Molding
force and temperature control as function of time.
(3) After the molds reached the molding temperature, a soaking phase of about 4
minutes was carried out to ensure that the entire mold and lens system had a
homogenous temperature distribution. At the beginning of the molding phase,
vacuum was applied again to ensure no nitrogen bubbles existed between the
glass blank and the mold. The lower mold was moved upward again at a velocity
of 0.44 mm/s to initialize the compression. When the glass blank touched the
upper mold, the lower mold was continuously pressing the glass blank at a
constant load of 1.5 kN by a servo feedback system. During the entire process,
position of the lower mold and the molding force were precisely monitored and
58
recorded with a sampling frequency of 1 Hz. The monitoring file of lower mold
position control during molding process is shown in Figure 5.4(a). Cooling began
after the lower mold arrived at the desired position.
(4) With the start of cooling, the molding force was reduced to a constant holding
force of 186 N during the gradual cooling phase with a cooling rate of 0.84 °C/s
lasting for 87 seconds. The cooling rate was controlled by the forced nitrogen
flow. Once the system reached 500 °C, a faster cooling rate of 1 °C/s was
employed until the mold temperature reached 215 °C. The contact between
molded glass lenses and the upper mold was released to allow the lens to cool
freely. The displayed molding force of 255 N at the fast cooling stage is actually a
result of air pressure by the forced nitrogen flow. The temperature control for
molding and cooling is shown in Figure 5.4(b). At last, the lenses were removed
from the molding machine and cooled down to room temperature. Figure 5.5(a)
shows the sample of a molded glass microlens array.
The polycarbonate molding experiments were conducted on an experimental apparatus at
The Ohio State University designed for compression molding of both glass and polymer
optics. The details of the machine and its operation can be found in (Firestone, et al.,
2005). The polycarbonate microlens array and the final microlens array assembly were
completed as follows:
(1) The polycarbonate blanks were placed in a vacuum oven to remove moisture to
prevent bubbles from occurring inside the polycarbonate blank during molding.
The temperature of the vacuum oven was set at 70 ˚C, and the entire drying time
59
was 48 hours. The polycarbonate blanks used in this study are LEXAN® clear
polycarbonate sheet with 2.26 mm measured thickness.
(2) A vacuum environment is also critical to compression molding of polycarbonate
microlens array to avoid oxidation and remove air from the gap between the
polycarbonate blank and the mold. Heating began when the air pressure dropped
to 27 Pa. The temperature of the mold halves was increased to 205 ˚C from room
temperature in 20 minutes. To enhance the heat transfer and reduce heating time,
the lower mold was moved upward until the contact was made with the upper
mold. The load between the polycarbonate blank sandwiched by the mold halves
was held at 60±8 N and controlled by adjusting the lower mold position using an
encoder based feedback element. The heating was provided by four 700 W
watlow electrical heating elements. The details of the heating unit can be found
elsewhere (Fischbach, et al., 2010).
(3) It took 20 minutes for temperature of the molds to reach the steady state, and then
the molding process was initialized. The air pressure inside the heating chamber
was 4 Pa, and molding force was around 140 N. The molding speed was set as 8
m/s. The lower mold stopped moving upward when the upper glass mold
touched the top plate fixed in the heating chamber and the load increased to
around 380 N.
(4) Cooling was started before the vacuum was turned off, because the polycarbonate
blank was molded at just 10 ˚C above its transition temperature and required time
to allow the residual stresses to dissipate. The cooling started at a slow rate of
60
0.0139 ˚C/s for 1 hour. At about 110 ˚C, vacuum was turned off and it took
another 3 hours for the entire system to cool down to room temperature.
(a)
(b)
Figure 5.5. (a) Molded glass microlens array. (b) The finished hybrid polymer-glass
microlens array.
The polycarbonate blank was bonded to the glass top mold half, but did not stick to the
bottom aluminum alloy mold, therefore the hybrid polymer-glass mircrolens array could
be removed easily from the mold after molding. Finally, the hybrid polymer-glass
mircrolens array was obtained, as shown in Figure 5.5(b). To secure the plastic lens half
to the glass lens substrate, a drop of hot glue can be applied.
The annealing process is crucial to residual stresses that lead to birefringence. The
annealing in both the thermal compression moldings of P-SK57 and polymer was very
carefully controlled to reduce the residual internal stresses. The internal residual stresses
were measured using a polarimeter (PS-100-SF, Strainoptics, Inc., 108 W. Montgomery
61
Ave, North Wales, PA 19454 USA), and both the residual internal stresses of glass and
hybrid lenses were below 1 MPa that can be safely neglected in this experiment.
5.2.3
Simulation of compression molding
Table 5.1. Mechanical and thermal properties of P-SK57 glass.
Material Properties
Value
Elastic modulus, E [Mpa]
93,000
Poisson’s ratio, v
0.25
Density, ρ [kg/m3]
3,200
Friction coefficient, µ
0.5
Thermal conductivity, kc [W/m°C]
Figure 5.6(a)
Specific heat, Cp [J/kg °C]
Figure 5.6(b)
Transition temperature, Tg [°C]
493
Coefficient of thermal expansion, α [/°C] Figure 5.6(c)
Finite element method (FEM) has been extensively utilized to study the lens shape
change, internal stresses and refractive index change in optical elements in recent years
(Yi & Jain, et al., 2005; Chen, et al., 2008; Yi, et al., 2006; Su, et al., 2008). Thermal
forming processes affect the final optical performance of a microlens array. For glass
molding, the Narayanaswamy model can be used to describe the structural relaxation
characteristics during the forming of glass microlens arrays (Narayanaswamy, 1971). One
single microlens in axisymmetric form was created in MSC/MARC. Both the top and
bottom mold halves were simplified as rigid bodies because the Young's modulus of the
mold material is much higher than the glass when the temperature is above its transition
temperature. The entire simulation can be divided into two major steps: (1) the glass
blank was molded after the entire system was heated up above its transition temperature,
62
(2) uniform cooling was applied to all meshed glass blank during the cooling phase. The
mechanical and thermal properties of P-SK57 are listed in Table 5.1, its structural
relaxation parameters are listed in Table 5.2, and Table 5.3 describes the details of the
boundary conditions for all the two-step simulation.
Table 5.2. Structural relaxation rarameters of P-SK57 used in numerical simulation.
Material Properties
Value
493
Reference temperature, T [°C]
73,300
Activation energy/gas constant, ΔH/R [°C]
1
Fraction parameter, x
Figure 5.6(d)
Stress relaxation curve
Table 5.3. Boundary Conditions for Glass and Polymer Molding.
Mechanical boundary condition
Thermal boundary condition
63
Molding
Cooling
No slip
Isolated
Simple shear friction
Uniform cooling
(a)
(b)
(c)
(d)
Figure 5.6. Material properties of the P-SK57 glass used in the simulation. (a) Thermal
conductivity [W/m°C] as a function of temperature [°C]. (b) Specific heat [J/kg °C]
variation as a function of temperature [°C]. (c) Coefficient of thermal expansion [/°C] as
a function of temperature [°C]. (d) Stress relaxation properties curve: shear constant [Pa]
versus time [s] (in logarithm scale).
The molding temperature for the glass microlens array was 570 ˚C, and the mold traveled
805 m at a velocity of 5.5 µm/s to complete the molding process. The cooling rate
applied in this simulation from 0 to 87 s was about 0.84 ˚C/s and 1.01 ˚C/s from 88 to
366 s. The lenses were then cooled down to 25 ˚C in 1,000 s. The FEM simulation was
64
based on the transient mechanical-thermal coupled analysis. The glass blank was meshed
into 7,260 four-node isoparametric quadrilateral elements as shown in Figure 5.7(a), and
Figure 5.7(b) illustrates the molded deformable model after cooling.
(a)
(b)
Figure 5.7. (a) Meshed FEM model of glass molding for microlens. (b) Final shape of the
glass microlens after cooling.
The principles of compression molding process for P-SK57 and polycarbonate are
similar. The Williams-Landel-Ferry (WLF) equation was used to describe the
temperature dependence of rheological properties (Juang, et al., 2002). An axisymmetric
model of one single microlens was built for reducing the number of elements and
calculating time. The top glass mold half and bottom aluminum alloy mold half were
simplified as rigid bodies during relevant simulation. Two simulation steps, i.e.,
compression molding and uniform cooling, consist of the entire process. The mechanical
and thermal properties of polycarbonate are listed in Table 5.4 (Autodesk Moldflow
65
Insight, 2011; Mirkhalaf, et al., 2010), its viscoelastic parameters are listed in Table 5.5
(Juang, et al., 2002), and the boundary conditions for the polymer molding are the same
as for the glass molding shown in Table 5.3.
Table 5.4. Mechanical and thermal properties of polycarbonate.
Material Properties
Value
Elastic modulus, E [Mpa]
2,280
0.37
Poisson’s ratio, v
Density, ρ [kg/m3]
1,191.5
0.3
Friction coefficient, µ
Thermal conductivity, kc [W/m°C]
0.31
Specific heat, Cp [J/kg °C]
2,052
Transition temperature, Tg [°C]
150
Solid coefficient of thermal expansion, αg [/°C]
7×10-5
Liquid coefficient of thermal expansion, αl [/°C] 5.72×10-4
Molding temperature for the polymer microlens array was 160 ˚C, 10 ˚C above its
transition temperature [39, 40]. The top mold half moved downward at a speed of 7.28
m/s for 100 s to press the polymer blank. It took one hour for the polycarbonate sheet to
cool down to 110 ˚C, and another 3.16 hours to 25 ˚C. The FEM simulation was also
based on transient mechanical-thermal coupled analysis. The polycarbonate blank was
meshed into 3,738 four-node isoparametric quadrilateral elements (see Figure 5.7(a)),
and the FEM model of the molded polycarbonate microlens is shown in Figure 5.7(b)
after cooling.
66
Table 5.5. Viscoelastic parameters of polycarbonate used in numerical simulation.
Material Properties
Reference temperature, T [°C]
Empirical constant, C1
Empirical constant, C2
Value
160
7.68
24.35
Time [s] Shear modulus [Pa]
0.158
1.995×105
0.316
9.9×105
1
1×106
10
1.585×106
Shear modulus vs. time
(a)
(b)
Figure 5.7. (a) Meshed FEM model of the polymer microlens. (b) Final shape of the
polymer microlens after cooling.
In order to verify whether this FEM simulation could be used to accurately predict the
compression molding process and the final shape of the microlens, surface geometry
measurements for the microlens were performed on a Wyko NT9100 noncontact optical
profilometer (Bruker AXS Inc., 5465 East Cheryl Parkway Madison, WI). Figure 5.8
67
shows the surface profile comparisons of simulated and experimental results. Simulation
results were found to be in good agreement with experimental results. Therefore, future
work would include reducing the error of the lens curvature to obtain a complete
spherical surface by optimizing the process.
(a)
(b)
Figure 5.8. Comparison of simulated and experiment surface profiles of one microlens
for (a) P-SK57 glass and (b) polycarbonate.
5.2.4
Geometry and optical evaluation
The surface measurement was also performed on the Wyko NT9100 optical profilometer.
The solid lines shown in Figure 5.9 are the designed and the measured surface profiles
along the diameter of the mold and a single microlens in the molded microlens array.
Figure 5.9(a) shows the P-SK57 glass convex surface and Figure 5.9(b) shows the
polycarbonate convex surface. Shown as the dashed lines in Figure 5.9, both the
measured profiles of the mold and the molded microlens match the designed profile well.
For P-SK57 glass compression molding, the maximum error of the mold in height is
68
about 1.8 m and the maximum error of the molded microlens is around 2.7 m. For
polycarbonate compression molding, the maximum error of the mold in height is
approximate 1.0 m and the maximum error of the molded microlens is about 1.8 m.
The surface roughness of the mold and molded part was measured as well. For glass
microlens array, the surface roughness Ra value of the copper nickel mold and the molded
glass microlens are 28.05 nm and 48.59 nm, respectively. For polymer microlens array,
its Ra value for aluminum alloy mold and the molded microlens are 28.27 nm and 26.47
nm, respectively. As mentioned before, no post machining polishing was performed to
either the nickel or the aluminum mold. The surface roughness of the molded glass
microlens is higher than the mold surface, but the Ra value of the molded polycarbonate
microlens is only slightly better than the aluminum mold.
(a)
(b)
Figure 5.9. 2D surface profiles and geometry errors along the diameter of the mold and
the molded sample of one single microlens. (a) Surface profiles of the mold and molded
glass lens. (b) Surface profiles of the mold and molded polymer lens.
69
The schematic of the setup for measuring chromatic aberration and the focal length is
shown in Figure 5.10. Collimated lasers with three different wavelengths (λ = 405 nm,
532 nm and 632.8 nm) were used as the light source. To visualize the image of the focal
spot, a zoom lens imaging system (VZMTM 450i, Edmund Optics, Inc., 101 East
Gloucester Pike, Barrington, NJ 08007-1380) and a CCD camera (PL-B957F, pixeLINK,
1465 N. Fiesta Blvd., Gilbert, AZ 85233-1002) were used in the optical setup. The
criterion for locating the focal spot is finding the smallest spot by varying the position of
the hybrid lens, while the image of the focal spot is viewed through the zoom lens
system.
Figure 5.10. Schematic of the setup for measuring the chromatic focal shift: (1) laser
source, (2) linear polarizers, (3) pinhole, (4) field lens, (5) hybrid lens mounted on a
precision translation stage and (6) CCD camera.
To measure the chromatic focal shift of the microlens, λ = 405 nm laser was the first to be
used in this measurement. The precision stage on which the microlens was mounted was
adjusted until the focal spot could be observed from the CCD camera, and the position of
the stage d1 was recorded. Second, a laser with wavelength of λ = 532 nm was used and
the stage was adjusted to find the new focal position. The focal position at this
70
wavelength was recorded as d2. Third, λ = 632.8 nm laser was employed and the focal
position was recorded as d3. The chromatic focal shift from 405 nm to 532 nm is d1-d2
and the shift from 532 nm to 632.8 nm is d3-d2. For d1-d2, the measured average is 60.1
µm with a standard deviation less than 5.1 µm as comparing to the calculated value is
65.5 µm. For d3-d2, the measured average is 5.4 µm with a standard deviation less than
2.1 µm, while the calculated value is 4.06 µm. As shown in Figure 5.11, the chromatic
shift for 532 nm laser is assumed to be zero and the blue solid curve represents the
calculated results of chromatic focal shift with respect to wavelength in Zemax. The
measured chromatic shifts are plotted as red asterisks in this figure for comparison. The
theoretical values and experimental results are consistent to each other.
Figure 5.11. Comparison of calculated and experiment results of chromatic focal shift of
the hybrid polymer-glass doublet.
The focal lengths of the hybrid microlens array were also evaluated in this study. A HeNe laser of wavelength 632.8 nm was used in this measurement. First, a molded lenslet
was moved manually along the optical axis such that the flat surface of the microlens was
71
focused on the CCD camera. Then the microlens was moved away from the camera until
the sharp focus of the collimated beam was displayed in the monitor. The distance
between these two positions was the focal length. In order to evaluate the uniformity of
the microlens array, the focal length of each microlens was measured in the same fashion.
The measured focal length is 9.864 mm with a standard deviation less than 0.054 mm.
Therefore, a hybrid polymer-glass achromatic microlens array was fabricated by
compression molding. Polycarbonate and P-SK57 were selected for the doublets array
since they have opposite dispersion properties. The geometry error is about 2.7 m for
the molded glass microlens, and is approximately 1.8 m for the molded polymer
microlenses. As for the surface roughness, the Ra value of the glass microlens is 48.59
nm, and is 26.47 nm for the polymer microlens. The focal length measurement verifies
that this hybrid polymer-glass achromatic microlens is capable of correcting chromatic
aberration as designed. Future work would include designing new precision assembly
technique, optimizing the thermal compression molding process to compensate the
geometry, analyzing refractive index change caused by the molding process, and
improving ultraprecision machining method to increase the optical quality of the mold
surface. If the requirement for optical performance increases, the knowledge of the exact
values of the material properties becomes crucial since it significantly influences the
initial calculation of the optical design and the simulation of the compression molding.
5.3
5.3.1
Injection molded hybrid glass-plastic achromatic lens
Design of fabrication processes
72
Unlike conventional UV curing method for polymer coatings, in this research
microinjection molding was utilized to apply a layer of polymer to the glass lens surface.
The competitive advantages of injection molding over conventional UV curing method
come from the fact that injection molding is ideal for mass production thus can
significantly lower manufacturing cost. As a subset of injection molding, microinjection
is considered as one of the crucial technologies for its uniqueness of replicating high
precision micro scale features.
(a)
(b)
(c)
(d)
Figure 5.12. Manufacturing processes of the hybrid glass-polymer lens by microinjection
molding. The right mold insert is used to house the glass lens while the left side has the
aspherical surface for the polymer lens. The blue area is the glass lens and the red is the
injection molded polycarbonate polymer.
Figure 5.12 shows the manufacturing processes for the hybrid lens by microinjection
molding. Firstly, two mold inserts are diamond machined to the print. In the layout used
in this study, the left mold has the aspherical curvature, and the right mold is used to
73
house the glass lens. Once the glass lens with spherical surface is placed in the circular
pocket of the right insert, two mold halves are closed and the polymer melt is injected
into the cavity between the glass lens and the aspherical surface.
Figure 5.13. Achromatic doublet design (unit: mm).
The diameter of the polymer lens is slightly larger than the glass lens as shown in Figure
5.13. In this design the edge of the polymer lens will apply compression stress to the
glass lens after the melt polymer cools down. Therefore, the glass lens and the polymer
lens are integrated into one hybrid glass-polymer aspherical lens that can be removed
from the mold without further alignment in a single uninterrupted process. The fitting
tolerance for the glass lens outside diameter and the circular pocket inside diameter is of
slide fit so as to leave some room during polymer filling stage to avoid cracking while
still allows the glass lens to be positioned within the accuracy of a couple of microns.
Additionally, the axial alignment accuracy of these two mold inserts is secured by the
mold base assembly.
74
The manufacturing process design is then followed by the optical design. Polycarbonate
(PC) is chosen as the higher dispersion flint glass with Abbe number of 29.9 while NBK7 is chosen as the lower dispersion crown glass with Abbe number of 64.1. These two
materials are selected for their availability and low cost.
Figure 5.13 shows the geometric layout of the achromatic doublet design. The radius of
the spherical glass lens is 51.5 mm and its thickness from the top to the flat bottom is
3.59 mm. In this design, the thickness t of the center of the polymer layer is relatively
thin which can be difficult to manufacture. In addition the change of the polymer
thickness ranging from 0.1 mm to 2 mm does not significantly affect its optical
performances, such as RMS spot size or chromatic focal shift. The actual value will be
discussed according to the process simulation in the next section. The aspherical
curvature of the polycarbonate lens is described by the equation below:
z
cr 2
1  1  1  k  c r
2 2
 r2
(10)
where z is the sag of the aspherical surface which is a function of the radial coordinate, c
is the curvature or the reciprocal of the radius, r is the radial coordinate, k is the conic
constant and  is a constant coefficient. Table 5.6 shows the design values of these
parameters for the hybrid lens in this study. With the geometry design of the hybrid glasspolymer lens, the chromatic focal shift from wavelength 486.1 nm to 656.3 nm in
ZEMAX clearly demonstrates its capability for chromatic aberration correction. The
nominal focal length of the hybrid lens is 200 mm, and the maximum focal shift range
from wavelength 486.1 nm to 656.3 nm is 480.5 m.
75
Table 5.6. Design parameters for the aspherical surface.
c
k
α
5.3.2
-1/88.51123
-1.16867
2.3731×10-4
Microinjection molding simulations
Since considerable thermal and fluidic phenomena are involved in the microinjection
molding, the visualization of molding process can help understand and improve the
manufacturing process. For example, flow pattern (Kim & Turng, 2006), welding lines,
refractive index variation (Yang, et al., 2011), geometrical curve deviation and internal
stresses (Lu & Khim, 2001), can be predicted by finite element method (FEM)
simulation, and the predicted information accompanied by the experimental results will
feedback to the parameter control of the mold machining and microinjection molding to
optimize the fabrication of the hybrid lens in the further study.
A commercial FEM software package Moldex3D was used in this injection molding
research. In this simulation, the mold base and cooling pipes were also included in the
meshed model to improve accuracy. The glass lens was modeled as a part insert, and
Moldex3D assumed the part insert and the injected part were completely bonded together
after filling, sharing the same interface temperature and deformation. This way, the insert
injection molding modeling can evaluate the deformation of the polymer lens in the
integrated part. Moreover, for the challenges of injecting the polymer melt into the thin
cavity and controlling the shrinkage of the polymer lens, the simulation was focused on
melt front flow pattern during filling and warpage after cooling.
76
As mentioned in the before, the thin center of the polymer lens might lead to an unfilled
hole or weld line defects. Thus two different center thickness designs of the polymer part
were modeled in FEM simulation, one being 0.1257 mm for Model I and the other one
being 0.7257 mm for Model II. Figure 5.14(a) shows the meshed Model I for the injected
polycarbonate part and the glass lens part insert. The three dimensional mesh is based on
layer-by-layer strategy to increase the accuracy of the numerical analysis (Park & Joo,
2008). Figure 5.14(b) shows the entire meshed model for the injection molding
simulation including the cooling channels and mold base. After the meshed models were
imported into the Moldex3D software package, the molding process was simulated to
find a better thickness design. The Sabic Lexan OQ1020 was selected as the material for
simulation and its material database was provided by the software. Table 5.7 summarizes
the process conditions used for the two different thickness designs of the injection
molded hybrid glass-polymer lens.
(a)
(b)
Figure 5.14. (a) Meshed Model I for the injection molded part and the part insert and (b)
meshed microinjection molding system model including the cooling channels and mold
base.
77
Table 5.7. Simulation process conditions used for two different thicknesses.
Injection
temperature
330 °C
Injection
time
0.1 s
Packing
pressure
80 MPa
Packing
time
5s
Cooling
temperature
82 °C
(a)
(b)
(c)
(d)
Cooling
time
35 s
Figure 5.15. Comparison of simulation (a and c) and experimental results (b and d) of the
melt front flow pattern for Model I during filling.
The melt front patterns during the filling stage were obtained by the post processing
analysis in Moldex3D, as shown in the left column in Figure 5.15. There were two
highly possible issues in injection molding, one being an unfilled hole and the second one
being welding lines in the center. Both issues were later confirmed in the experiment as
shown in the right column in Figure 5.15. The minor difference between the simulation
78
and experiment may result from the material properties provided in the commercial
software, the interface assumption between the glass and the polymer melt in simulation,
and the actual operation status of the machine used in the experiment. However, the
simulation for Model II shows that the melt front passes the center and pushes the
potential welding line to the edge of the polymer lens as illustrated in Figure 5.16, thus
the larger thickness of 0.7257 mm was adopted in further study for the hybrid lens.
Figure 5.16. Melt front (shown in time) of the injection molded polymer part of Model II
during filling.
Besides the melt front flow patterns, the effect of the packing pressure to the deformation
of the polymer lens edge was also studied in simulation because too much shrinkage may
result in large deformations and high internal stresses. 40 MPa and 80 MPa were used as
the two levels of the packing pressure in the process simulation, while other process
parameters were kept the same as listed in Table 5.7. Figure 5.17 shows the results of
the deformations of the molded part under the two packing pressures. The results show
that the edge deformation on the condition with packing pressure 80 MPa is smaller than
79
with the packing pressure 40 MPa, thus a higher packing pressure is adopted in all later
experiments.
Figure 5.17. Simulated part deformation under different packing pressure.
5.3.3
Lens fabrications
The diamond turned mold inserts were installed in the microinjection molding machine
(LD30EH2, Sodick Plustech) for molding test. The microinjection molding machine
employed in this study can apply up to 30 ton maximum clamping force and 250 mm/s
maximum injection velocity. The uniqueness of this machine is that its injection system is
consisted of a screw plasticizing unit and a plunger injection unit for precisely managing
the micro feature replication by their independent controls. The diameter of the
plasticizing screw is 18 mm, and a 16 mm diameter injection plunger can produce an
injection stroke up to 70 mm. The optical grade polycarbonate (SABIC Lexan OQ1022
Resin) was used in this experiment.
80
Figure 5.18. Picture of a complete hybrid glass-polymer lens manufactured by
microinjection molding (shown with gate, runner and spruce).
In this experimental test, firstly, the polycarbonate pellets were placed in an electrical
dryer for 24 hours at 100 °C in a ventilation environment to remove the moisture.
Secondly, the processing parameters were entered the machine as follows: the injection
temperature was 330 °C, the injection speed was 200 mm/s, the maximum injection
pressure was 150 MPa, the packing pressure was 80 MPa with a 5 seconds packing time
and the temperature of the cycled cooling water was 82 °C with a 35 seconds cooling
time. Next, a glass lens was placed in the circular pocket of the right mold insert
illustrated in Figure 5.12(b). When the temperature of the glass lens reached a steady
state from room temperature to the temperature of the mold insert, the mold halves were
closed. Lastly, the polymer melt was injected into the cavity to form a polymer layer over
the glass lens surface. The cooling time was set to be relative long to reduce stresses
81
formed during the filling stage. A complete hybrid glass-polymer lens manufactured by
microinjection molding is shown in Figure 5.18. The surface roughness of the
polycarbonate lens is about 8 nm which is close to the measurement result of the mold
insert mentioned in the first paragraph of this section.
5.3.4
Optical measurements
The schematic of the setup for measuring the chromatic aberration is the same as shown
in Figure 5.10. Three different wavelengths ( = 405 nm, 532 nm and 632.8 nm) lasers
were employed as the light source. Similar procedures were repeated for the other three
wavelengths laser. Hence, the chromatic focal shift from 532 nm to 632.8 nm is d2-d1 and
the shift from 405 nm to 532 nm is d3-d2. For d2-d1, the measured average is 248 m with
a standard deviation 12.1 m as comparing to the calculated value of 157 µm. For d3-d2,
the measured average is 2,563 m with a standard deviation 50.4 m, while the
calculated value is 2,115 m.
Figure 5.19. Comparison of the calculated and measured results of the chromatic focal
shift of the hybrid lens.
82
Figure 5.19 shows the calculated focal shift of the hybrid lens with respect to wavelength
by ZEMAX. The focal shift from 486.1 nm to 656.3 nm is very small as discussed in the
optical design. The measured chromatic shifts are plotted as red asterisks in this figure for
comparison. The experimental results show a good agreement with the theoretical values.
Some factors, such as the optical alignment, the optical properties of the material, the
stability of the laser source and manufacturing quality control, may result in the
difference between the measured and theoretical data. In addition, the hybrid lens was
examined by the polarimeter (PS-100-SF, Strainoptics, Inc., North Wales, PA), and the
residual stresses in the center part of the polymer lens were below 10 MPa although the
edge shows relatively high internal stresses but it is outside of the clear aperture.
Hence, microinjection molding is also demonstrated to be an effective tool to precisely
replicate micro features in optical mass production to correct color aberrations. Besides
its improved optical performance and easy mechanical alignment, the hybrid lenses are
also chemical corrosion resistant. These lenses also have reduced weight, compact size
and robust thermal stability (Doushkina, 2010).
83
Chapter 6. Modeling of Optical Performance of Molded Freeform
Optics
Injection molding processes are ideal for high-volume production, and can work with a
wide range of materials including optical grade polymer materials. However injection
molded freeform optical components have several major issues. These issues include, for
example, large geometric shrinkage, refractive index variation and birefringence. Hence,
it is of great interest to utilize numerical modeling to investigate and predict the
manufacturing process. Kim and Turng used a finite element method (FEM) to model the
filling phase of the injection molding process for an optical lens and verified the filling
pattern experimentally (Kim & Turng, 2006). Park and Joo applied FEM analysis results
of an injection molded lens to a ray tracing simulation (Park & Joo, 2008) and concluded
that inhomogeneous distribution of refractive index could occur if molding conditions
were not carefully controlled. Besides the simulations for refractive index distribution,
Huang (Huang C. , 2008) and Yang et al. (Yang, et al., 2011) discussed the refractive
index variation of injection molded precision optical lenses using two different
experimental setups. Suhara constructed the refractive index distribution of an injection
molded lens by using computed tomography technique (Suhara, 2002). Furthermore, Su
et al. compensated the refractive index change and geometric deviation during glass
molding process to improve lens forming quality (Su, et al., 2014).
84
Based on the aforementioned research, geometric deformation induced by cooling
shrinkage can be minimized in the production of precision freeform optics. In addition,
uniform refractive index distribution also plays a crucial role in high quality optical
elements. Therefore, in this chapter we focus on modeling of the injection molding
process, including how geometric deformation and refractive index variation are related
to wavefront of molded freeform optics.
6.1
FEM modeling for precision molding
Figure 6.1. Meshed FEM model of a Progressive Addition Lens (PAL). Node(i,1) is
numbered along number i line at the bottom surface of PAL, and Node(i,N) is the node
along number i line at its top surface.
After the geometric model was constructed, a 3D model example was generated using
HyperMesh (www.altair.com) as shown in Figure 6.1. The meshed model was then
imported to a commercial software package Moldex3D (http://www.moldex3d.com/en/)
to complete the FEM simulation. The entire lens model was divided into 12 surface
85
layers of prism elements, and each element layer could be considered as a lens surface. In
addition to the lens itself, the mold base and cooling pipes were also included in the
model to ensure accuracy but were omitted from Figure 6.1 for clarity.
Table 6.1. Material parameters of PMMA.
PVT Tait Model
Parameters
Values
b1L (cc/g)
0.85982
b1S (cc/g)
0.860702
b2L (cc/g·k)
0.0005697
b2S (cc/g·k)
0.0001995
2
b3L (dyne/cm )
2.09×109
2
b3S (dyne/cm )
2.73×109
b4L (1/K)
0.0049083
b4s (1/K)
0.003394
b5 (K)
383
b6 (cm2·K/dyne)
2×10-8
0.0894
C
Viscosity Cross WLF Model
Parameters
Values
0.21
n
6
*
2
1.48×10
 (dyne/cm )
B (g/cm·s)
1×10-16
Tb (K)
24294
In this simulation, three stages of the injection molding process were analyzed: filling,
packing and cooling. An optical grade polymethylmethacrylate (PMMA, trade name
Plexiglas V825) was selected for molding the freeform lens. The PVT properties of the
PMMA are expressed by the modified Tait Model as follows,
V  V0 1  Cln 1  P / B 
(11)
b  b2 ST , if T  Tt
V0   1S
b1L  b2 LT , if T  Tt
(12)
b3S exp  b4 ST  , if T  Tt
B
b3Lexp  b4 LT  , if T  Tt
(13)
T  T  b5
(14)
86
Tt  b5  b6 P
(15)
where V is specific volume in cm2, P is pressure in dyne/cm2, T is temperature in kelvin,
and the remaining parameters are constants listed in the left half part of Table 6.1. The
modified Cross WLF model describes the viscosity behavior of the PMMA material used
in this study in the following equations,

0
(16)
1 n
  
1   0* 
 
 Tb 

T 
0  Bexp 
(17)
where  is viscosity in g/cm·s,  is shear rate in dyne/cm2, and the remaining parameters
are shown in the right half of Table 6.1. These material properties were directly taken
from the Moldex3D database. Additionally, Table 6.2 also summarizes the values of the
molding condition used in this work.
Table 6.2. Injectin molding condition.
Molding parameters
Melt temperature (ºC)
Mold temperature (ºC)
Injection velocity (mm/s)
Maximum injection pressure (MPa)
Velocity/pressure switch (vol %)
Packing pressure (MPa)
Packing time (s)
Cooling time (s)
Coolant temperature (ºC)
Values
250
75
200
100
90
80
6
25
65
As mentioned previously, the computed geometric deformation and refractive index
distribution were exported from the FEM calculation for later discussion. The geometric
87
deformation primarily has an impact on optical refraction, so the nodes’ positions on the
top and bottom surface meshes were extracted for numerical analysis of its optical
aberrations in next section. Furthermore, uneven cooling as well as the polymer’s
rheological properties could result in an unevenly distributed density that consequently
causes variation in refractive index (Yang, et al., 2011). Therefore refractive index
information at each node was also collected for optical aberration analysis. It should be
noted here that birefringence is defined as a variation in refractive index with polarization
angle at any point inside the lens. Previously, Isayev investigated the refractive index
through birefringence approach with consideration of flow-induced stress and relaxation
effect (Isayev, 1983). Different from Isayev’s work, refractive index in this study is
considered to be a scalar, which can vary with lens location.
6.2
Prediction of optical performance influenced by molding process
After the FEM computation is completed, the geometric deformation and refractive index
variation were exported for later analysis. The geometric deformation primarily affects
refraction at the surface, while refractive index variation affects internal propagation.
As for the surface warpage, in this study it was defined as the geometric deformation in
lens thickness. The coordinate positions of the nodes on both top and bottom surfaces
were recorded. For example, the original thickness at the coordinates (xi, yi) line is
defined as,
ti  z  i, N   z i,1
88
(18)
where z(i, 1) and z(i, N) are z coordinate positions of the Node (i, 1) on the nominal
bottom and top surfaces, respectively. The deformed thickness between top and bottom
surface at the coordinates (xi, yi) line was calculated using the following equation,
ti'  z  i, N   z i,1
(19)
where z’(i, 1) and z’(i, N) are z coordinate positions of Node (i, j) on the fitted deformed
bottom surface and Node (i,N) on the fitted deformed top surfaces, respectively.
Due to non-uniform cooling rate at different locations of the microinjection molded
Alvarez lens, uneven density distribution is formed inside the lens. This density deviation
leads to refractive index variation. It should be noted that in this study refractive index is
considered to be a scalar, varying with location inside the lens. In order to simplify the
problem of refractive index variation, one index value over the xy plane corresponds to
the refractive index information on one vertical line at certain xy coordinates.
More specifically, the index value along the vertical lines at coordinates (xi, yi) is the
average of the refractive index values of all the nodes along this line in the thickness
direction of the Alvarez lens, or,
 N

ni   n  i, j   / N
 j 1

(20)
where ni is the average refractive index value along the line at coordinates (xi, yi) in the
thickness direction, n (i, j) is the refractive index of the Node (i, j) or the jth node on the
line, N is the number of the nodes on the Number i line. Figure 6.1 illustrates the
numbering scheme. Hence, the refractive index variation at coordinates (xi, yi) can be
obtained by
89
NV
ni  ni  n j / NV
(21)
j 1
where NV is the number of the vertical lines along the z direction in the mesh model.
Therefore, the optical path when both inhomogeneous refractive index and geometric
deformation were considered can be calculated depending on the specific cases.
90
Chapter 7. Optical Metrology of Molded Freeform Optics
Traditionally, the freeform optics measurement is challenging because of its nonaxisymmetric nature as compared with conventional optics. Savio et al. reviewed general
freeform surfaces measurement for various applications (Savio, et al., 2007). The
measurement methods are divided into two types, i.e., contact and non-contact
techniques. Coordinate measuring machines (CMM) are the most widely used contact
measurement tool for large measurement range, although its uncertainty is at the micron
level (Schellekens, et al., 1998). For non-contact methods, optical imaging and
interferometry techniques can provide fast measurement with low uncertainty, but they
are sensitive to ambient influences such as surface roughness, defects, light transmission,
dust, oil or water coats (Fang, et al., 2013). Fringe Reflection Technique (FRT) is another
non-contact robust system for measuring freeform surfaces by converting fringe spacing
variations to local surface gradients (Bothe, et al., 2004). An interferometry based setup
is an ideal way to evaluate flat, spherical surfaces with nanometer resolution. If
interferometers are used to measure an aspheric or freeform surface with large deviation,
a null lens or some type of wavefront modulator must be added to the optical setup.
The techniques mentioned above require either expensive equipment or complex
procedures, so we present two simple approaches to quantifying freeform wavefront
patterns. One is realized by customized Shack-Hartmann sensor (Lane & Tallon, 1992),
while the other one is achieved by a wet cell based interferometer.
91
7.1
Shack-Hartmann wavefront sensing measurement
Progressive addition lenses (PALs) have been widely accepted for the compensation of
presbyopia (i.e. the decline in ocular accommodation with age) over the past 60 years.
Compared with conventional bifocal lenses, PALs provide users a continuous change in
spherical optical power through different regions of the lenses. PALs are typically
manufactured using a casting process. In this process, a monomer is injected into the
mold cavity, and then either an initiator is injected, or ultraviolet (UV) exposure is turned
on to cure the monomer. However, manufacturing cost for the traditional methods is high
due to limited production rate. Therefore, in recently years, new more affordable molding
techniques have been proposed to produce PALs, such as glass molding (Lochegnies, et
al., 2013) and plastic injection molding (Hsu, et al., 2010; Cheung, et al., 2012).
Comprehensive methods for evaluating and measuring their optical properties have been
developed. Castellini et al. modified the Hartmann test to accurately measure the
prismatic deviation and spherical power of PALs (Castellini, et al., 1994). Villegas and
Artal set up a Shack-Hartmann wavefront sensor system to perform spatially revolved
aberration measurement of PALs either isolated or in combination with the eye (Villegas
& Artal, 2003). Huang compared the wavefront sensing method with a moiré
interferometer-based method and a coordinate measuring machine (CMM) method, and
discovered that those three methods were comparable for measuring optical powers of
PALs (Huang, et al., 2012). This research utilized a custom optical measurement system
based on a Shack-Hartmann wavefront sensor to evaluate second order wavefront
aberrations of injection molded PALs, to verify FEM simulated results (Li, et al., 2013).
92
7.1.1
PAL design
The front convex surface of the PAL in this research is a spherical shape, and its
geometry can be described by the radially symmetric second order Zernike term
.
z  0.462  3   2 x 2  2 y 2  1
(22)
where z is surface height in mm, x and y are normalized coordinate positions ranging
from -1 to +1, and the nominal radius is 20 mm. The front surface has a peak-valley
difference of approximately 1.6 mm and a radius of curvature of 125 mm. Assuming a
refractive index of 1.49, this surface has a dioptric power of approximately 3.9 D.
The back concave surface height, in mm, is a freeform surface described by Zernike
polynomials:
z  0.462  3   2 x 2  2 y 2  1  0.015  2 2  3x 2 y  y 3 
0.046  2 2  3x 2 y  3 y 3  2 y   0.007  2 2  3x 3  3xy 2  2 x 
(23)
0.007  2 2  x 3  3xy 2   0.0064  2 3 10 x 4 y  20 x 2 y 3  12 x 2 y  10 y 5  12 y 3  3 y 
Figure 7.1 shows the freeform surface of the backside of the PAL where the first
polynomial term representing the spherical shape is removed for clarity to show the
freeform pattern. The center thickness of the PAL is 2.285 mm. In terms of Zernike
polynomials, this freeform surface is the sum of third order coma and trefoil, and fifth
order secondary vertical coma.
93
Figure 7.1. Freeform surface of the backside of the PAL. The first polynomial term was
removed to show the freeform geometry.
7.1.2
PALs fabrication
For the mold fabrication process, the mold insert with the convex freeform surface was
also machined on the Freeform Generator 350 (Moore Nanotechnology, Inc., Keene,
New Hampshire) using ultraprecision diamond slow tool servo to optical quality. In this
study, a diamond tool with a controlled radius of 2.6055 mm was utilized. The tool path
trajectory was compensated offline by the tool radius. On the finishing machining path
for the convex freeform optical surface, the cutting depth was 5 m and the feedrate was
20 mm/min. 6061 aluminum alloy was used as the material of the mold inserts. Figure
7.2 shows the finished aluminum mold inserts for the PAL. The surface roughness of the
convex surface was approximately 10 nm measured using the Wyko NT9100 optical
profilometer. The concave spherical mold surface was machined by conventional
94
ultraprecision diamond turning and its surface roughness was measured to be about 8 nm.
No post-polishing was performed on the inserts.
Figure 7.2. Finished ultraprecision diamond turned mold inserts for PAL injection
molding.
Figure 7.3. PALs manufactured by microinjection molding.
The diamond turned mold inserts were then installed in the microinjection molding
machine (LD30EH2, Sodick Plustech) for molding test. The microinjection molding
machine employed in this study can generate up to 250 mm/s maximum injection
95
velocity with a 30 ton maximum clamping force. The special injection system of this
machine has separated screw plasticizing unit and plunger injection unit to precisely
manage the micro feature replication by their independent controls. Same as the material
modeled in the simulation, the optical grade PMMA, Plexiglas V825, was used in the
experiment. The experimental molding conditions were the same as in the simulations
listed in Table 6.2. The injection molded PALs are shown in Figure 7.3.
7.1.3
Simulated wavefront pattern of PALs
With the exported FEM results obtained in Chapter 6, the optical path difference (OPD)
when both inhomogeneous refractive index and geometric deformation were considered
can be calculated by:
OPD   ni  n0  1  (di'  t0 )
(24)
where n0 is the nominal refractive index of the PMMA material, which is 1.49, t0 is the
center thickness of the PAL, which is 2.285 mm in this study.
The calculated OPD was fitted to a Zernike polynomial up to the 8th order, or 45 terms
using a least square method. The Zernike coefficients of the 45 terms were annotated as a
column vector cc. Moreover, if a subaperture was translated within the original aperture
of the lens, the Zernike coefficient vector for the newly translated subaperture could be
calculated by the following equation

cc'  TZ   ZT  x, y   cc  .*rs j

(25)
where, cc' is transformed Zernike coefficient vector, TZ and ZT(x,y) are matrices for
Taylor-to-Zernike and Zernike-to-Taylor transform respectively, rsj is a column vector of
96
size rescaling terms, and ‘.*’ represents element-by-element multiplication. The detailed
explanation of this method for calculating transformed Zernike coefficients can be found
in (Raasch, 2011). In this fashion, the spherocylindrical power with this subaperture can
be obtained according to the second order Zernike polynomial coefficients:
c20 4 3
M
r2
(26)
J0 
c22 2 6
r2
(27)
J 45 
c22 2 6
r2
(28)
where M, J0, J45, in units of diopters, are spherical defocus, orthogonal astigmatism and
oblique astigmatism, respectively (Thibos, et al., 2004). In Equations (26)~(28), these
second order Zernike coefficients C2m have meridional frequency m, and have units of
µm. The radius of the subaperture, r, has a unit of mm. Finally, the calculated
spherocylindrical powers of all the arrayed subapertures or pupils are assembled in their
corresponding positions to plot the figures of the optical powers for the entire PAL.
7.1.4
Wavefront measurement of PALs
Figure 7.4 shows a schematic of the wavefront sensor measuring system. A small, distant
white light source produces a nearly flat wavefront in the plane of the tested PAL. The
refracted wavefront traverses two relay lenses, and arrives at the Shack-Hartmann sensor.
The two relay lenses (elements 3 and 4 in Figure 7.4) are positioned such that the PAL
and the microlens array are in optically conjugate planes. To position any given location
of the PAL along the measurement axis, the lens is pivoted around horizontal and vertical
97
axes, the intersection of which represents the center of rotation of an eye 27 mm behind
the lens. Lens positioning is performed with stepper-motors that pivot the lens mount
around the horizontal and vertical rotation axes (not shown in the figure).
150 mm
1
2
300 mm
3
150 mm
4
5
Figure 7.4. Schematic of the wavefront measuring system. 1: Distant source; 2: PAL
under test; 3 and 4: 150 mm fl lenses; 5: Shack-Hartmann sensor.
The Shack-Hartmann sensor consists of a microlens array and a CCD camera. A 3.5 mm
virtual stop is placed at the microlens array, and since it is conjugate with the lens plane
at unit magnification, it represents a 3.5 mm eye pupil centered at that lens position. Each
microlens is 0.36 mm on a side, and with a 3.5 mm diameter pupil, approximately 70
lenslet spot images are contained in the camera image. When a wavefront enters the
sensor, it is partitioned by the microlens array. The local tilt of the wavefront within each
subaperture causes a displacement of the focal spot from the reference central position.
Thus, these deviations can be assembled to reconstruct the wavefront variation (Shack &
Platt, 1971). Wavefront aberration arises from the freeform nature of the PAL, the nonuniform refractive index distribution, and geometric deformation of the lens surfaces.
98
7.1.5
Results and discussions
Figure 7.5. Simulated refractive index variation of an injection molded PAL.
As discussed in Chapter 6, the rheological phenomenon and uneven cooling lead to the
refractive index variation of the injection molded PAL. The FEM results show that the
refractive index on one surface layer varies in the scale of 10-4, whereas the variation
scale among the multiple surface layers along the thickness direction is 10-3. Figure 7.5
illustrates the refractive index variation of the molded PAL calculated by Equation (21).
The location of the injection gate is at the bottom of this picture. Although the upper limit
of the injection pressure was set as 100 MPa, the actual maximum injection pressure was
about 80 MPa indicated by the FEM simulation which was almost equal to the packing
pressure. This is an effective packing with high packing pressure and long packing time.
Thus, compared with previous studies (Park & Joo, 2008; Yang, et al., 2011), the
99
distribution variation is relatively small with a maximum deviation of 6×10-4. In addition
to the small deviation, because higher packing pressure occurs closer to the injection
gate, the general trend of the distribution decreases along the flow direction.
Despite of the dominant effects by the sufficient packing, the uneven cooling may
outweigh the packing effects. For example, the material at the region farther away from
the center in the radial direction cools and shrinks faster than the central region. This
causes denser material formation resulting in a higher refractive index. More specifically,
as an example, some region at the top may have higher refractive index than the lower
part although the top region is farther away from the injection gate. Additionally, since a
thinner area cools faster than a thicker area, this analysis can also apply to the thinner top
region when compared with the thicker bottom. In Figure 7.5, the index variation is
similar to the freeform geometry pattern illustrated in Figure 7.1, which suggests that
regional thickness discrepancies may be more important than radial position differences
for refractive index variation in terms of thermal transportation. So, with all of these
effects combined, the highest refractive index happens at the bottom half of the PAL
surrounded by an ox-horn-shaped transition region from the bottom to the top.
Geometric deformation is another important factor that influences the PAL’s optical
performance. As defined before, the geometric deformation is the thickness deviation
between the design and the molded parts. The simulated thickness for the molded lens
between the top and bottom surfaces can be calculated by Equation (19). If similar
derivations are applied to the original design, the thickness deviation is the discrepancy
between the design and simulation. Figure 7.6 shows the simulated thickness deviation
between the design and the molded PAL. As seen in this figure, the thicker bottom part of
100
the PAL has more shrinkage in thickness, although it is closer to the injection gate or the
highest packing pressure location. Consistent with the analysis above, the larger
shrinkage in the thicker region may also result in higher refractive index. In this situation,
the regional thickness difference largely contributes to the thickness change of the
molded PAL.
Figure 7.6. Simulated thickness change in xy plane of the molded PAL.
Considering both the refractive index variation and geometric deformation, each
component of the optical aberrations of the injection molded PAL can be determined by
the derivations developed in Section 7.1.3. Figure 7.7 ~ Figure 7.9 show the PAL’s
spherical power M, and the two cylindrical components J0 and J45 respectively, in terms of
the design, simulation and measurement results. It can be seen that the variation scales of
the simulated optical powers and aberrations are slightly larger than the design.
101
Figure 7.7(b) shows that the magnitude of the simulation is smaller than the design. In
addition the optical aberration patterns were also slightly changed when the injection
molding process was taken into consideration. For instance, as the simulated spherical
power in Figure 7.7(b), a round corner appears at the left side of the bottom red area in
contrast to the flat slope at the transition area between red and yellow region in Figure
7.7(a). There is a falling tip pattern on the right side of the blue area though smooth
progression in design. Additionally, as can be observed in Figure 7.8(b), the top area in
the red zone is larger than the blue area at the bottom while the overall pattern is
rotational symmetric in the original design as shown in Figure 7.8(a). Moreover, the
simulated cylindrical aberration component J45 in Figure 7.9(b) displays the sagging blue
area and red area, but these two areas are symmetric about the horizontal direction in the
design as illustrated in Figure 7.9 (a). Finally, the Shack-Hartmann sensor measurements
(Figure 7.7(c), Figure 7.8(c), Figure 7.9c), appear to be in relatively good agreement
with the simulations.
(a)
(b)
(c)
Figure 7.7. Spherical power M of the molded PAL (a) design (b) simulation (c)
measurement
102
(a)
(b)
(c)
Figure 7.8. Cylindrical component J0 of the injection molded PAL (a) design (b)
simulation (c) measurement
(a)
(b)
(c)
Figure 7.9. Comparison of (a) design, (b) simulated and (c) measured cylindrical
component J45 of the injection molded PAL.
There are many other possible reasons that can potentially affect the accuracy of the
evaluation process. For example, in ophthalmic applications, the distance between the
lens and the entrance pupil of the eye is typically about 15 mm. The wavefront will, in
103
general, change shape as it travels that distance. However, in this instance, curvatures are
not high enough for this difference to be clinically meaningful. In addition, meshing
strategies, materials models and boundary conditions also have an influence on the final
simulated results. Furthermore, in the optical measurement apparatus, the PAL was
rotated around an ocular center of rotation 27 mm behind the lens to select each
measurement area. This was done to imitate a rotating eye as it views through different
locations on the lens. Nevertheless, large oblique incidence will affect wavefront shape,
which is not yet accounted for in this modeling. Finally, precision of centering and
positioning the PAL could be improved.
Table 7.1. Injection molding conditions for design of experiment
Process number Packing pressure (Kg/cm2) Packing time (s) Injection time (s)
800
3
0.125
1
1,200
3
0.125
2
1,200
6
0.125
3
800
6
0.125
4
800
3
0.1
5
800
6
0.1
6
1,200
3
0.1
7
1,200
6
0.1
8
In this research, the goal was to search for a preferred injection molding condition for the
PALs. Specifically, packing pressure, packing time, and injection time, were investigated.
Two levels of each parameter were investigated, as listed in Table 7.1. Our conclusions
can be summarized as: (a) neither the packing time nor the injection time has a significant
impact on the optical properties of the PALs, (b) higher packing pressure results in
smaller refractive index variation and smaller thickness change (refractive index variation
104
-1.5×10-4 ~ 3.5×10-4, thickness change -15.5 ~ -11 µm), (c) the patterns and the scales of
the second order optical powers and aberrations do not change dramatically when the
injection molding process conditions are varied.
The first conclusion can be explained by the fact that packing times were adequate to
offset shrinkage. Further, the higher packing pressure reduced the absolute amount of
thickness deformation. However, deformation patterns plotted in the same way as Figure
7.6 were still quite similar between the two packing pressure levels. From the test
conditions, the No. 2 process condition was adopted for future production of PALs
because of its shorter cycle time, less power requirement, more uniform refractive index
distribution and less geometric deformation.
This research presents a new approach to fabricate PALs using the combination of
ultraprecision diamond turning and precision injection molding. This approach has wide
industrialization potential due to its affordability. Also, it is demonstrated that the
modeling of the injection molded PALs can be used to successfully predict their optical
aberrations. The numerical modeling can also be utilized to optimize manufacturing
processes.
7.2
Interferometer measurements
A simple approach to quantifying freeform wavefront patterns with large deviation is
accomplished by reducing the lens’s surface powers. The power reduction is realized by
immersing the freeform lens in a wet cell containing an optical liquid with controlled
refractive index (Li, et al., 2014). By comparing the collected wavefront patterns with the
nominal values, the differences can be obtained and evaluated by comparing to the FEM
105
simulation. This also improves the understanding of the quality control of microinjection
molded freeform optics.
7.2.1
Optical design
Alvarez lens is used as an example in the wet cell based interferometer study. The
purpose of Alvarez lens is to realize variable refraction powers by a simple and compact
approach. Previous studies showed that the optical refraction power of Alvarez lens pair
could be varied by shifting the two freeform surfaces perpendicular to the optical axis
(Simonov, et al., 2006; Barbero, 2009). In this study, the bottom surface of the Alvarez
lens is flat while its top surface height, in mm, can be described by the polynomial below:
z  a1 x 2 y  a2 y 3
(29)
where x and y are coordinate positions ranging within a 6 mm diameter circular aperture,
and a1 and a2 are 0.019583063 and 0.0062879497 respectively. The deviation from the
actual value of a2/a1 to the standard ratio of 1/3 is due to a compensation of spherical
aberrations by means of the freeform surface (Sieber, 2014). More details of the optical
design can be found in (Sieber, 2014). Figure 7.10 shows the color map of the top
freeform surface. The surface pattern is axisymmetric about y axis and negatively
rotationally symmetric with respect to x axis. The maximum (peak-valley) deviation is
493.4 µm.
106
Figure 7.10. Top freeform surface of Alvarez lens.
7.2.2
Manufacturing of Alvarez lenses
Ultraprecision diamond machining can be utilized to directly fabricate Alvarez lens pair
for either infrared light (Smilie, et al., 2011) or visible light (Barbero & Rubinstein,
2013). Furthermore, in order to achieve high volume production, molding techniques
have to be employed. For the mold fabrication process, the mold insert with the freeform
surface was machined using ultraprecision diamond fast tool servo (FTS) machining for
its capability of delivering optical quality surfaces with high precision. Nickel alloy was
used as the material of the mold inserts. Figure 7.11(a) shows the finished mold for the
Alvarez lens. The arithmetic average surface roughness Ra of the optical surface was
approximately 6 nm as measured by a Wyko NT9100 optical profilometer. No postpolishing was performed on the inserts. Some mechanical features were machined into
the stainless steel mold housing the mold insert. These features were used to assemble the
lens into an automatic driven system. The 3D model of the lens with mechanical features
107
is shown in Figure 7.11(b). The performance of this molded lens will be discussed in a
different publication (Sieber, 2014).
(a)
(b)
Figure 7.11. (a) Finished ultraprecision diamond machined mold for injection molding.
(b) 3D model of the molded Alvarez lens with small straight pins and flats designed for
assembly.
The diamond machined mold inserts were then mounted in the microinjection molding
machine (LD30EH2, Sodick Plustech) for freeform lens fabrication. The same optical
grade polymethylmethacrylate (PMMA), Plexiglas V825, was used in the experiment.
The experimental molding conditions are listed in Table 7.2. The inlet of plastic melt is
located at the lower right side of the lens shown in Figure 7.11(b). The thickness of the
Alvarez lens ranges from 100 µm to 594 µm. A microinjection molded miniature Alvarez
lens is shown in Figure 7.12. Not only was the optical surface quality successfully
achieved, the small mechanical features were also precisely replicated.
108
Table 7.2. Microinjection molding conditions
Molding parameters
Values
Melt temperature C)
250
Mold temperature C)
35
Injection velocity (mm/s)
220
Maximum injection pressure (MPa)
150
Velocity/pressure switch (vol %)
89
Packing pressure (MPa)
120
Packing time (s)
3
Cooling time (s)
50
Coolant temperature C)
25
Figure 7.12. An injection molded Alvarez lens.
7.2.3
Wavefront prediction and simulation
A 3D FEM model for the freeform Alvarez lens was established using HyperMesh
(http://www.altair.com) as shown in Figure 7.13. The meshed model was then imported
into a commercial FEM software package Moldex3D (http://www.moldex3d.com/en/) to
perform the FEM simulation. The entire lens model was meshed, based on a layer-bylayer structure (Li, et al., 2013). There are 10 total surface layers of prism elements, with
each layer considered to be a lens surface. Besides the lens itself, the runner, mold base
and cooling pipes were also included in the model to ensure accuracy but were omitted
109
from Figure 7.13 for clarity. The material properties of the selected PMMA Plexiglas
V825, such as PVT properties and viscosity behaviors, can be found in the Chapter 6.
The conditions for the molding simulation were the same as in the experiments listed in
Table 7.2.
Figure 7.13. FEM mesh model of the Alvarez lens. Node (i, 1) is numbered along the
vertical line at coordinates (xi, yi) at the bottom surface, and Node (i, N) is the node along
the vertical line at coordinates (xi, yi) at its top surface.
One approach to evaluating the optical performance of an Alvarez lens is to measure a
wavefront passing through the lens. The Shack-Hartmann sensor system can be used for
measuring wavefront deviations in ophthalmic applications (Liang, et al., 1994).
However, if large wavefront deviations are involved, the large displacement of the focal
spots will result in overlap on the sensor. On the other hand, if interferometers are used,
as mentioned previously, a freeform null lens or light modulator has to be added, which
significantly increases complexity of this freeform lens measurement system. Therefore,
110
in order to reduce the optical power, such that the entire wavefront variation can be
measured using the interferometer, we immersed the lens in one optical liquid with
controlled refractive index close to the lens’ nominal refractive index (Joo & Jung, 2012;
Barbero, et al., 2003; Tayag & Bachim, 2010). The phase delay was reduced by a
conversion factor (Jeong, et al., 2005):
CF 
nlens  nliquid
nlens  nair
(30)
where nlens is the nominal surface refractive index of the lens, nliquid is the refractive index
of the optical liquid, and nair is the refractive index of air. Reliable and repeatable
measurement of wavefront aberrations using a wet cell technique was demonstrated in
previous studies, for example (Jeong, et al., 2005). In this study, the wet cell technique
was introduced to measure the wavefront pattern of the microinjection molded freeform
optics compared with conventional axisymmetric optics, and Shack-Hartmann sensor
based metrology system was replaced by an interferometer in order to increase accuracy
and resolution.
Figure 7.14 shows the interferometry setup for the wavefront map measurement of the
microinjection molded Alvarez lens. The proposed setup is similar to a previously used
scheme studied in (Yun, et al., 1998) except in the current layout the previous double
pass setup was modified to a single pass arrangement to accommodate the large deviation
in freeform lens geometry. If double pass setup is adopted, the freeform characteristics of
the lens, such as freeform surface power and uneven refractive index distribution will be
coupled with the measured wavefront.
111
If the controlled refractive index of the optical liquid matches the lens’ refractive index at
the lens surface, the measured wavefront deviation reflects the information of refractive
index variation (Suhara, 2002; Yang, et al., 2011). This is because with a matching index
immersion fluid the surface power of the lens is eliminated.
Figure 7.14. Interferometry setup for measuring wavefront pattern of microinjection
molded Alvarez lens immersed in a wet cell. 1: He-Ne laser light source; 2: optical pin
hole; 3: collimation lens; 4: beam splitter A; 5: flat mirror A; 6: flat mirror B; 7: Alvarez
lens immersed in a wet cell; 8: beam splitter B; 9: CCD camera; 10: PZT stage.
Next, the measured wavefront pattern due to refractive index variation can be compared
with the simulated results. Back to the FEM simulated results, the optical path located at
the (xi, yi) line passing through the microinjection molded lens can be computed by
OPi  ni  ti'  nliquid  Tchamber  ti' 
(31)
where Tchamber is the thickness of the wet cell housing the molded lens. Consequently, the
simulated optical path deviation can be simply obtained using:
112
NV
OPi  OPi  OPj / NV
(32)
j 1
In addition, if the controlled refractive index of the optical liquid is not equal but close to
the nominal refractive index of the lens, the number of interference fringes can be
decreased to a number recognizable to the computer. In this scenario, the surface power
of the freeform lens in the air can be reconstructed by multiplying the measured
wavefront by the conversion factor:
Wair  xi , yi   CF  Wliquid  xi , yi 
(33)
where Wair(xi, yi) is the wavefront aberration at coordinates (xi, yi) if lens is placed in the
air, Wair(xi, yi) is the wavefront aberration at coordinates (xi, yi) if the lens is immersed in
the optical matching liquid.
The microinjection molded Alvarez lenses are immersed into two optical liquids from
Cargille Labs (http://www.cargille.com/): one with refractive index 1.4917 for PMMA’s
nominal refractive index and the other one with 1.5167 for BK7 glass.
Once the measured wavefront patterns were obtained, a mask for locating the effective
area was manually placed within the aperture region. The positioning of the effective
measured wavefront was also manually iterated to achieve minimum deviation from the
simulated results by a MATLAB program.
7.2.4
Results and discussions
Surface deformation has its primary impact on refraction at the lens surface/air interface.
The deformation in injection molding is due to the polymer’s rheological properties and
thermal history of the molding process. According to the FEM simulation mentioned in
113
Chapter 6, the surface displacements of the top freeform surface and bottom flat surface
are very similar. Therefore, in order to assess the surface deformation of the Alvarez lens,
only the bottom surface displacement was selected as evaluation parameter to study the
geometry deformation of the microinjection molded Alvarez lenses. Figure 7.15 shows
the (a) simulated and (b) measured bottom surface deformations. The injection direction
is from the top of the plot to the bottom. The surface measurement was conducted by the
stitching program of the Wyko NT9100 optical profilometer.
(a)
(b)
Figure 7.15. (a) Simulated and (b) measured bottom surface deformations of the
microinjection molded Alvarez lens.
The simulated and measured surfaces have very closely matched variation tendency and
range. As can be seen in Figure 7.15, the positive (red) areas are on the left and right
corners of the bottom half, where the thinnest areas and two assembly pins are located.
But the top areas with higher thickness have an opposite deformation trend compared
114
with the bottom corners. Moreover, the transition region exists between the top half and
bottom corners. So the deformation is affected by the freeform surface variation and the
surrounding mechanical assemble features. Generally speaking, the deformation is
mainly influenced by the geometric structure of the Alvarez lens. Figure 7.16 shows the
deformed Alvarez lens with a magnification scale of 50X.
Figure 7.16. Simulation plot of the deformed microinjection molded Alvarez lens with a
magnification scale of 50X.
The residual stresses of the molded Alvarez lenses were measured using a polariscope
(PS-100-SF, Strainoptics, Inc), and its value was below 3 MPa, small enough to be safely
neglected in this experiment. The maximum residual stress occurred in the thinnest
region of the molded lens.
Injection molding process has three stages including filling, packing and cooling. The
refractive index inside the microinjection molded Alvarez lenses vary with the location of
115
the point of interest. The refractive index variation is a result of the uneven cooling rate at
different locations, Figure 7.17 show the refractive index variation maps of simulation
and measurement results. Again, the gate of the lens mold is at the top of the plot. For
both results, most of the areas have less than 1 λ wavefront deviation. The small deviation
is contributed by the effective packing indicated by the simulation. The general trend of
the simulation and measured deviations is in good agreement with each other. The peak
to valley value of the simulated wavefront deviation is about 1 λ while the value is about
0.5 λ for the measurement. The RMS value of the measured wavefront is 0.082 λ.
(a)
(b)
Figure 7.17. (a) Simulated and (b) measured wavefront pattern describing refractive
index distribution of the microinjection molded Alvarez lenses.
The highest values occur at the bottom left and right corners, because these are the
thinnest parts of the freeform lens leading to the fastest cooling rate. Faster cooling
causes denser material formation and then produces higher refractive index. In contrast,
116
the top left and right corners are thicker, which slows the cooling process, so these two
areas have lower refractive index. This refractive index effect is relatively small, so the
regional thickness distortion tends to have the larger effect on the refractive properties of
the lens.
Although from Figure 7.10 the center portion of the Alvarez lens has a relatively uniform
thickness, for both the simulation and measurement plots, the wavefront deviation
decreases from the top center to the bottom center. This is because the top center area is
closer to the gate where higher packing pressure is expected, and higher packing pressure
yields denser material structure. This pattern may help explain the astigmatism observed
in injection molded optics. So the combined effects mentioned above are responsible for
the refractive index deviation within the aperture of the microinjection molded Alvarez
lens as illustrated in Figure 7.17.
(a)
(b)
(c)
Figure 7.18. (a) Nominal and (b) measured wavefront pattern describing surface power
distribution of the microinjection molded Alvarez lenses. (c) Difference between the
simulated and the measured results.
117
However, there are still some differences between the simulations and measurements for
the above two factors. These differences may be due to reasons that can affect the
evaluation accuracy. For example, in the FEM calculation, the simulation parameters and
boundary conditions may not be accurate enough, such as the materials properties,
boundary conditions, and mesh strategies. Moreover, in the wavefront measurement, the
position of the lens, the mirror flatness, and the refractive index accuracy of the optical
liquids at the current wavelength may also need to be enhanced in the future.
When the optical liquid is switched to higher refractive index of 1.5167, the wavefront
pattern from the surface power can be measured. Figure 7.18 show the nominal
wavefront pattern of an undeformed Alvarez lens with uniform refractive index, the
measured wavefront pattern of the microinjection molded Alvarez lens and their
difference map, respectively. The nominal wavefront deviation is 15.89 λ while the
measured wavefront deviation is 15.8 λ, so the deviation values are close, and were
normalized for comparison in Figure 7.18. The maximum local difference of these two
wavefront patterns is less than 5%. In addition, as can be seen in Figure 7.18 (c), the
major differences come from the center and corner areas. The deviation trend of the
wavefront differences between the nominal and the measurement is a combined result of
surface deformation and refractive index variation.
It can be observed in Figure 7.16 that the overall shape of the top half of the lens in the
positive y axis is concave, and the shape of the bottom half is convex. Nevertheless, when
taking the geometric deformation into account, the absolute values of the radii of both the
concave and convex curvature are increased. In another words, the top concave surface
becomes slightly more concave while the bottom convex surface becomes more convex.
118
This leads to the larger optical path for the light traveling through the top region since the
ambient optical liquid has higher refractive index, as illustrated in Figure 7.19. In
addition to the surface deformation, the refractive index variation factor shown in Figure
7.17(b) further increases the optical path difference between the central top half and the
central bottom half.
Figure 7.19. Optical path change on the freeform surface.
In addition, the positive optical path difference in the top center results in the phase delay
at the top left and top right corners, and the opposite trend occurs at the two bottom
corners. The described patterns can be confirmed by the surface deformation and
refractive index variation at the local corners. Thus, the combined effects of the surface
deformation and refractive index variation largely result in the differences between the
nominal and the measured wavefront patterns in Figure 7.18.
Injection molding has its own intrinsic advantages over conventional glass materials for
its capability of providing affordable freeform optics in high volume. This research
119
combined the techniques of ultraprecision diamond machining and microinjection
molding to fabricate miniature Alvarez lenses. However, the geometric deformation and
uneven density distribution caused by the microinjection molding process complicates its
application to precision freeform optics. Therefore, we present an FEM simulation
approach to visualize how both the surface deformation and refractive index variation
affect the wavefront change. Moreover, a simple and fast wavefront measurement
technique by using an optical matching wet cell for injection molded freeform optics is
proposed to validate the simulation.
120
Chapter 8. Conclusions
This dissertation discusses the fundamental understanding of the freeform optical lens
fabrication and its related freeform optical design, ultraprecision mold machining,
numerical modeling, and optical metrology.
At the first part of this dissertation, a freeform microlens array, which was made of
PMMA and had 32 freeform microlenses, was fabricated using the combination of
ultraprecision diamond machining and microinjection molding. This method was
demonstrated in manufacturing high volume and low cost beam shaping freeform
microlens arrays. The design, fabrication, simulation and measurement of a specific
freeform microlens were discussed.
Ultraprecision slow tool servo diamond machining provides the mold with optical quality
without the need for post-polishing. The diamond machining on both of regular materials
and brittle materials were evaluated to achieve optical finish. A computer code was
programmed to visualize the development of micro fractures distribution on diamond
machined silicon surface in 3D. In addition, the novel compression molding and
microinjection molding processes were developed to fabricate axisymmetric and
asymmetric affordable achromatic optics with high precision. The molding method was
selected according to the specific design requirements. By performing the measurement
of chromatic focal shifts, these two novel molding processes have been demonstrated as
121
effective approaches for manufacturing affordable and highly flexible optical
components.
If injection molding is employed, refractive index variation and geometric deformation of
injection molded optics influence its optical performance. Finite element modeling were
used to calculate the above two factors. Two freeform optics applications were studied as
examples: progressive addition lens and Alvarez lens. The wavefront refracted through
the injection molded PALs could be measured by Shack-Hartmann sensor, and the
Alvarez lens’s wavefront can be evaluated by wet cell based interferometer. The
measurement results successfully verified the simulated manufacturing influences to their
optical performances.
122
References
Aoki, M., Kuribayashi, K., Monji, H., Okinaka, H., Sakai, M., & Torii, H. (1987). Patent
No. 4,685,948. US.
Autodesk Moldflow Insight. (2011). Retrieved from http://www.moldflow.com/
Barbero, S. (2009). The Alvarez and Lohmann refractive lenses revisited. Optics Express,
17(11), 9376-9390.
Barbero, S., & Rubinstein, J. (2013). Power-adjustable sphero-cylindrical refractor
comprising two lenses. Optical Engineering, 52(6), 063002.
Barbero, S., Marcos, S., & Jiménez-Alfaro, I. (2003). Optical aberrations of intraocular
lenses measured in vivo and in vitro. JOSA A, 20(10), 1841-1851.
Belousov, A. A., Doskolovich, L. L., & Kharitonov, S. I. (2008). A gradient method of
designing optical elements for forming a specified irradiance on a curved surface.
Journal of Optical Technology, 75(3), 161-165.
Blackley, W. S., & Scattergood, R. O. (1991). Ductile-regime machining model for
diamond turning of brittle materials. Precision Engineering, 13(2), 95-103.
Blake, P. N., & Scattergood, R. O. (1990). Ductile‐Regime Machining of Germanium and
Silicon. Journal of the American Ceramic Society, 73(4), 949-957.
Bothe, T., Li, W., von Kopylow, C., & Juptner, W. P. (2004). High-resolution 3D shape
measurement on specular surfaces by fringe reflection. In Photonics Europe (pp.
411-422). International Society for Optics and Photonics.
123
Brinksmeier, E., & Autschbach, L. (2004). Ball-end milling of free-form surfaces for
optical mold inserts. In Proc. of the ASPE Annual Meeting.
Buttner, A., & Zeitner, U. D. (2002). Wave optical analysis of light-emitting diode beam
shaping using microlens arrays. Optical Engineering, 41(10), 2393-2401.
Castellini, C., Francini, F., & Tiribilli, B. (1994). Hartmann test modification for
measuring ophthalmic progressive lenses. Applied Optics, 33(19), 4120-4124.
Chaves, J. (2008). Introduction to nonimaging optics. CRC Press.
Chen, Y., Yi, A. Y., Su, L., Klocke, F., & Pongs, G. (2008). Numerical simulation and
experimental study of residual stresses in compression molding of precision glass
optical components. Journal of Manufacturing Science and Engineering, 130(5),
051012.
Cheng, D., Wang, Y., Hua, H., & Talha, M. M. (2009). Design of an optical see-through
head-mounted display with a low f-number and large field of view using a
freeform prism. Applied Optics, 48(14), 2655-2668.
Cheung, C. F., Kong, L. B., Ho, L. T., To, S., Wang, B., & Lai, K. T. (2012). An
integrated approach for design, ultraprecision polishing, and measurement of
freeform progressive lenses. In 6th International Symposium on Advanced Optical
Manufacturing and Testing Technologies (AOMATT 2012) (p. 84160C).
International Society for Optics and Photonics.
Ding, Y., Liu, X., Zheng, Z. R., & Gu, P. F. (2008). Freeform LED lens for uniform
illumination. Optics Express, 16(17), 12958-12966.
Dobson, S. L., Sun, P. C., & Fainman, Y. (1997). Diffractive lenses for chromatic
confocal imaging. Applied Optics, 36(20), 4744-4748.
124
Dorrer, C. (2004). Temporal van Cittert-Zernike theorem and its application to the
measurement of chromatic dispersion. JOSA B, 21(8), 1417-1423.
Doushkina, V. (2010). Innovative hybrid optics: combining the thermal stability of glass
with low manufacturing cost of polymers. International Society for Optics and
Photonics (pp. 778809-778809). In SPIE Optical Engineering+ Applications.
Fang, F. Z., Wu, H., & Liu, Y. C. (2005). Modelling and experimental investigation on
nanometric cutting of monocrystalline silicon. International Journal of Machine
Tools and Manufacture, 45(15), 1681-1686.
Fang, F. Z., Zhang, X. D., Weckenmann, A., Zhang, G. X., & Evans, C. (2013).
Manufacturing and measurement of freeform optics. CIRP Annals-Manufacturing
Technology, 62(2), 823-846.
Fernández, E., Unterhuber, A., Prieto, P., Hermann, B., Drexler, W., & Artal, P. (2005).
Ocular aberrations as a function of wavelength in the near infrared measured with
a femtosecond laser. Optics Express, 13(2), 400-409.
Firestone, G. C., & Yi, A. Y. (2005). Precision compression molding of glass microlenses
and microlens arrays--an experimental study. Applied Optics, 44(29), 6115-6122.
Firestone, G. C., Jain, A., & Yi, A. Y. (2005). Precision laboratory apparatus for high
temperature compression molding of glass lenses. Review of Scientific
Instruments, 76(6), 063101.
Fischbach, K. D., Georgiadis, K., Wang, F., Dambon, O., Klocke, F., Chen, Y., et al.
(2010). Investigation of the effects of process parameters on the glass-to-mold
sticking force during precision glass molding. Surface and Coatings Technology,
205(2), 312-319.
125
Hagerty, R. J., Kingsbury, P. I., & Shafer Jr, H. G. (1988). Patent No. 4,747,864. US.
He, P., Li, L., Li, H., Yu, J., Lee, L. J., & Yi, A. Y. (2014). Compression molding of
glass freeform optics using diamond machined silicon mold. Manufacturing
Letters, 2(2), 17-20.
He, P., Li, L., Yu, J., Huang, W., Yen, Y. C., Lee, L. J., et al. (2013). Graphene-coated Si
mold for precision glass optics molding. Optics Letters, 38(14), 2625-2628.
He, P., Wang, F., Li, L., Georgiadis, K., Dambon, O., Klocke, F., et al. (2011).
Development of a low cost high precision fabrication process for glass hybrid
aspherical diffractive lenses. Journal of Optics, 13(8), 085703.
Herzberger, M., & McClure, N. R. (1963). The design of superachromatic lenses. Applied
Optics, 2(6), 553-560.
Hirabayashi, K., Ikoma, K., Kurihara, N., Taniguchi, Y., & Yamamoto, K. (1991). Patent
No. 5,026,415. US.
Hsu, W. Y., Liu, Y. L., Cheng, Y. C., & Su, G. D. (2010). Design and fabrication of the
progressive addition lens. In Frontiers in Optics. Optical Society of America.
Huang, C. (2008). Investigation of injection molding process for high precision polymer
lens manufacturing. Doctoral dissertation. The Ohio State University.
Huang, C. Y., Raasch, T. W., Yi, A. Y., Sheedy, J. E., Andre, B., & Bullimore, M. A.
(2012). Comparison of three techniques in measuring progressive addition lenses.
Optometry & Vision Science, 89(11), 1564-1573.
Isayev, A. I. (1983). Orientation development in the injection molding of amorphous
polymers. Polymer Engineering & Science, 23(5), 271-284.
126
Jasinevicius, R. G., Duduch, J. G., Cirino, G. A., & Pizani, P. S. (2013). Diamond turning
of small Fresnel lens array in single crystal InSb. Journal of Micromechanics and
Microengineering, 23(5), 055025.
Jeong, T. M., Menon, M., & Yoon, G. (2005). Measurement of wave-front aberration in
soft contact lenses by use of a Shack-Hartmann wave-front sensor. Applied
Optics, 44(21), 4523-452.
Joo, W.-D., & Jung, M.-S. (2012). A study of optical properties of intraocular lenses and
of measurement of the index of reflection for an unknown liquid. Journal of the
Optical Society of Korea, 16(3), 236-242.
Juang, Y. J., Lee, L. J., & Koelling, K. W. (2002). Hot embossing in microfabrication.
Part II: Rheological characterization and process analysis. Polymer Engineering
& Science, 42(3), 551-566.
Juskaitis, R., & Wilson, T. (1999). A method for characterizing longitudinal chromatic
aberration of microscope objectives using a confocal optical system. Journal of
Microscopy, 195(1), 17-22.
Kempe, M., & Rudolph, W. (1993). Impact of chromatic and spherical aberration on the
focusing of ultrashort light pulses by lenses. Optics Letters, 18(2), 137-139.
Kim, S. W., & Turng, L. S. (2006). Three‐dimensional numerical simulation of injection
molding filling of optical lens and multiscale geometry using finite element
method. Polymer Engineering & Science, 46(9), 1263-1274.
Klocke, F., Dambon, O., & Georgiadis, K. (2010). Comparison of nitride and noble metal
coatings for precision glass molding tools. Key Engineering Materials, 438, 9-16.
127
Kozubek, M., & Matula, P. (2000). An efficient algorithm for measurement and
correction of chromatic aberrations in fluorescence microscopy. Journal of
Microscopy, 200(3), 206-217.
Kubala, K., Dowski, E., & Cathey, W. (2003). Reducing complexity in computational
imaging systems. Optics Express, 11(18), 2102-2108.
Laikin, M. (2010). Lens design. CRC Press.
Lane, R. G., & Tallon, M. (1992). Wave-front reconstruction using a Shack—Hartmann
sensos. Applied Optics, 31(32), 6902-6908.
Lee, B. K., Kim, D. S., & Kwon, T. H. (2004). Replication of microlens arrays by
injection molding. . Microsystem Technologies, 10(6-7), 531-535.
Leung, T. P., Lee, W. B., & Lu, X. M. (1998). Diamond turning of silicon substrates in
ductile-regime. Journal of Materials Processing Technology, 73(1), 42-48.
Li, L., & Yi, A. Y. (2011). Design and fabrication of a freeform microlens array for
uniform beam shaping. Microsystem Technologies, 17(12), 1713-1720.
Li, L., & Yi, A. Y. (2013). An affordable injection-molded precision hybrid glass–
polymer achromatic lens. The International Journal of Advanced Manufacturing
Technology, 69(5-8), 1461-1467.
Li, L., Collins, S. A., & Yi, A. Y. (2010). Optical effects of surface finish by
ultraprecision single point diamond machining. Journal of Manufacturing Science
and Engineering, 132(2), 021002.
Li, L., He, P., Wang, F., Georgiadis, K., Dambon, O., Klocke, F., et al. (2011). A hybrid
polymer–glass achromatic microlens array fabricated by compression molding .
Journal of Optics, 13(5), 055407.
128
Li, L., Raasch, T. W., & Yi, A. Y. (2013). Simulation and measurement of optical
aberrations of injection molded progressive addition lenses. Applied Optics,
52(24), 6022-6029.
Li, L., Raasch, T. W., Sieber, I., Beckert, E., Steinkopf, R., Gengenbach, U., et al. (2014).
Fabrication of microinjection molded miniature freeform alvarez lenses. Applied
Optics, 53(19), 4248–4255.
Liang, J., Grimm, B., Goelz, S., & Bille, J. F. (1994). Objective measurement of wave
aberrations of the human eye with the use of a Hartmann-Shack wave-front
sensor. JOSA A, 11(7), 1949-1957.
Lim, J., Choi, M., Kim, H., & Kang, S. (2008). Fabrication of hybrid microoptics using
UV imprinting process with shrinkage compensation method. Japanese Journal of
Applied Physics, 47(8S1), 6719.
Lochegnies, D., Moreau, P., Hanriot, F., & Hugonneaux, P. (2013). 3D modelling of
thermal replication for designing progressive glass moulds. New Journal of Glass
and Ceramics,, 3, 34.
Lohmann, A. W. (1989). Scaling laws for lens systems. Applied Optics, 28(23), 49964998.
Lu, X., & Khim, L. S. (2001). A statistical experimental study of the injection molding of
optical lenses. Journal of Materials Processing Technology, 113(1), 189-195.
Luo, Y., Feng, Z., Han, Y., & Li, H. (2010). Design of compact and smooth free-form
optical system with uniform illuminance for LED source. Optics Express, 18(9),
9055-9063.
129
Ma, K. J., Chien, H. H., Chuan, W. H., Chao, C. L., & Hwang, K. C. (2008). Design of
protective coatings for glass lens molding. Key Engineering Materials, 364, 655661.
Michaelis, D., Kudaev, S., Steinkopf, R., Gebhardt, A., Schreiber, P., & Bräuer, A.
(2008). Incoherent beam shaping with freeform mirror. In Optical Engineering+
Applications (pp. 705905-705905). International Society for Optics and
Photonics.
Michaelis, D., Schreiber, P., & Bräuer, A. (2011). Cartesian oval representation of
freeform optics in illumination systems. Optics Letters, 36(6), 918-920.
Mirkhalaf, M., Tor, S. B., Murukeshan, V. M., Loh, N. H., & Lye, S. W. (2010).
Optimization of compression molding of stand‐alone microlenses: Simulation and
experimental results. Polymer Engineering & Science, 50(11), 2216-2228.
Naples, N. (2014). Novel Ultra-precision Machining processes with optical applications
by use of single crystal diamond tools. PhD Candidacy Proposal.
Narayanaswamy, O. S. (1971). A model of structural relaxation in glass. Journal of The
American Ceramic Society, 54(10), 491-498.
Oliker, V. (2005). Geometric and variational methods in optical design of reflecting
surfaces with prescribed irradiance properties. In Optics & Photonic (p. 594207).
International Society for Optics and Photonics.
Oliker, V. (2006). Freeform optical systems with prescribed irradiance properties in nearfield. In Contract Proceedings (p. 634211). International Society for Optics and
Photonics.
130
Oliva, E., & Gennari, S. (1998). Achromatic lens systems for near infrared instruments.
Astron. Astrophys. Supplement Series, 128, 599-603.
Park, K., & Joo, W. (2008). Numerical evaluation of a plastic lens by coupling injection
molding analysis with optical simulation. Japanese Journal of Applied Physics,
47(11R), 8402.
Parkyn, B., & Pelka, D. (2006). Free-form illumination lenses designed by a pseudorectangular lawnmower algorithm. In SPIE Optics+ Photonics (p. 633808).
International Society for Optics and Photonics.
Patten, J. A., & Gao, W. (2001). Extreme negative rake angle technique for single point
diamond nano-cutting of silicon. Precision Engineering, 25(2), 165-167.
Piegl, L., & Tiller, W. (1997). The NURBS Book. Monographs in Visual Communication.
Plummer, W. T. (1982). Unusual optics of the Polaroid SX-70 Land camera. Applied
Optics, 21(2), 196-208.
Raasch, T. (2011). Aberrations and spherocylindrical powers within subapertures of
freeform surfaces. JOSA A, 28(12), 2642-2646.
Reichelt, S., & Zappe, H. (2007). Design of spherically corrected, achromatic variablefocus liquid lenses. Optics Express, 15(21), 14146-14154.
Rempfer, G. F., Desloge, D. M., Skoczylas, W. P., & Griffith, O. H. (1997).
Simultaneous correction of spherical and chromatic aberrations with an electron
mirror: an electron optical achromat. Microscopy and Microanalysis, 3(01), 1427.
Ries, H., & Muschaweck, J. (2002). Tailored freeform optical surfaces. JOSA A, 19(3),
590-595.
131
Ries, H., & Rabl, A. (1994). Edge-ray principle of nonimaging optics. JOSA A, 11(10),
2627-2632.
Savio, E., De Chiffre, L., & Schmitt, R. (2007). Metrology of freeform shaped parts.
CIRP Annals-Manufacturing Technology, 56(2), 810-835.
Scheiding, S., Yi, A. Y., Gebhardt, A., Li, L., Risse, S., Eberhardt, R., et al. (2011).
Freeform manufacturing of a microoptical lens array on a steep curved substrate
by use of a voice coil fast tool servo. Optics Express, 19(24), 23938-23951.
Schellekens, P., Rosielle, N., Vermeulen, H., Vermeulen, M. M., Wetzels, S. F., & Pril,
W. (1998). Design for precision: current status and trends. CIRP AnnalsManufacturing Technology, 47(2), 557-586.
Schreiber, P., Kudaev, S., Dannberg, P., & Zeitner, U. D. (2005). Homogeneous LEDillumination using microlens arrays. In Optics & Photonics (p. 59420K).
International Society for Optics and Photonics.
Seong, K., & Greivenkamp, J. E. (2008). Chromatic aberration measurement for
transmission interferometric testing. Applied Optics, 47(35), 6508-6511.
Shack, R. V., & Platt, B. C. (1971). Production and use of a lenticular Hartmann screen.
JOSA, 61(5), 656.
Shibata, T., Fujii, S., Makino, E., & Ikeda, M. (1996). Ductile-regime turning mechanism
of single-crystal silicon. Precision Engineering, 18(2), 129-137.
Sieber, I. Y. (2014). Design of freeform optics for an ophthalmological application. In
Proc. of SPIE, (pp. 9131, 913108-1).
Sigler, R. D. (1990). Apochromatic color correction using liquid lenses. Applied Optics,
29(16), 2451-2459.
132
Silicon. (2013). Retrieved from Wikipedia: http://en.wikipedia.org/wiki/Silicon
Simonov, A. N., Vdovin, G., & Rombach, M. C. (2006). Cubic optical elements for an
accommodative intraocular lens. Optics Express, 14(17), 7757-7775.
Smilie, P. J., Dutterer, B. S., Lineberger, J. L., Davies, M. A., & Suleski, T. J. (2011).
Freeform micromachining of an infrared Alvarez lens. In SPIE MOEMS-MEMS
(p. 79270K). International Society for Optics and Photonics.
Stoebenau, S., & Sinzinger, S. (2009). Ultraprecision machining techniques for the
fabrication of freeform surfaces in highly integrated optical microsystems . In
SPIE Optical Engineering+ Applications (pp. 742608-742608). International
Society for Society for Optics and Photonics.
Stone, T., & George, N. (1998). Hybrid diffractive-refractive lenses and achromats.
Applied Optics, 27(14), 2960-2971.
Su, L., Chen, Y., Yi, A. Y., Klocke, F., & Pongs, G. (2008). Refractive index variation in
compression molding of precision glass optical components. Applied Optics,
47(10), 1662-1667.
Su, L., Wang, F., He, P., Dambon, O., Klocke, F., & Yi, A. Y. (2014). An integrated
solution for mold shape modification in precision glass molding to compensate
refractive index change and geometric deviation. Optics and Lasers in
Engineering, 53, 98-103.
Suhara, H. (2002). Interferometric measurement of the refractive-index distribution in
plastic lenses by use of computed tomography. Applied Optics, 41(25), 53175325.
133
Sun, L., Jin, S., & Cen, S. (2009). Free-form microlens for illumination applications.
Applied Optics, 48(29), 5520-5527.
Tao, B., He, P., Shen, L., & Yi, A. Y. (2014). Quantitatively measurement and analysis of
residual stresses in molded aspherical glass lenses. The International Journal of
Advanced Manufacturing Technology.
Tayag, T. J., & Bachim, B. L. (2010). Simulation of an interferometric computed
tomography system for intraocular lenses. In SPIE Optical Engineering
Applications (p. 77910K). International Society for Optics and Photonics (SPIE).
Thibos, L. N., Hong, X., Bradley, A., & Applegate, R. A. (2004). Accuracy and precision
of objective refraction from wavefront aberrations. Journal of Vision,, 4(4), 9.
Tiziani, H. J., Wegner, M., & Steudle, D. (2000). Confocal principle for macro-and
microscopic surface and defect analysis. Optical Engineering, 39(1), 32-39.
Tohme, Y. E., & Lowe, J. A. (2003). Machining of freeform optical surfaces by slow
slide servo method. In Proceedings of ASPE.
Van Ligten, R. F., & Venkatesh, V. C. (1985). Diamond grinding of aspheric surfaces on
a CNC 4-axis machining centre. CIRP Annals-Manufacturing Technology, 34(1),
295-298.
Verstegen, E. J., Faasen, J. H., Stapert, H. R., Duineveld, P. C., & Kloosterboer, J. G.
(2003). Influence of the reaction mechanism on the shape accuracy of optical
components obtained by photoreplication. Journal of Applied Polymer Science,
90(9), 2364-2376.
134
Villegas, E. A., & Artal, P. (2003). Spatially resolved wavefront aberrations of
ophthalmic progressive-power lenses in normal viewing conditions. Optometry &
Vision Science, 80(2), 106-114.
Wach, H. B., Dowski Jr, E. R., & Cathey, W. T. (1998). Control of chromatic focal shift
through wave-front coding. Applied Optics, 37(23), 5359-5367.
Wang, K., Chen, F., Liu, Z., Luo, X., & Liu, S. (2010). Design of compact freeform lens
for application specific light-emitting diode packaging. Optics Express, 18(2),
413-425.
Wang, W., Morrison, J., & Paliwal, J. (2006). Correcting axial chromatic aberration in a
fixed focal plane near-infrared imaging system. In Annual Conference (p. 06127).
CSBE/SCGAB.
Winston, R., Miñano, J. C., & Benitez, P. (2005). Nonimaging Optics. Academic Press.
Yan, J., Asami, T., Harada, H., & Kuriyagawa, T. (2009). Fundamental investigation of
subsurface damage in single crystalline silicon caused by diamond machining.
Precision Engineering, 33(4), 378-386.
Yang, C., Su, L., Huang, C., Huang, H. X., Castro, J. M., & Yi, A. Y. (2011). Effect of
packing pressure on refractive index variation in injection molding of precision
plastic optical lens. Advances in Polymer Technology, 30(1), 51-61.
Yi, A. Y., & Jain, A. (2005). Compression molding of aspherical glass lenses–a
combined experimental and numerical analysis. Journal of the American Ceramic
Society, 88(3), 579-586.
Yi, A. Y., & Li, L. (2005). Design and fabrication of a microlens array by use of a slow
tool servo. Optics letters, 30(13), 1707-1709.
135
Yi, A. Y., & Raasch, T. W. (2005). Design and fabrication of a freeform phase plate for
high-order ocular aberration correction. Applied Optics, 44(32), 6869-6876.
Yi, A. Y., Chen, Y., Klocke, F., Pongs, G., Demmer, A., Grewell, D., et al. (2006). A
high volume precision compression molding process of glass diffractive optics by
use of a micromachined fused silica wafer mold and low Tg optical glass. Journal
of Micromechanics and Microengineering, 16(10), 2000.
Yi, A. Y., Huang, C., Klocke, F., Brecher, C., Pongs, G., Winterschladen, M., et al.
(2006). Development of a compression molding process for three-dimensional
tailored free-form glass optics. Applied Optics, 45(25), 6511-6518.
Yu, D. P., Wong, Y. S., & Hong, G. S. (2011). A novel method for determination of the
subsurface damage depth in diamond turning of brittle materials. International
Journal of Machine Tools and Manufacture, 51(12), 918-927.
Yu, D. P., Wong, Y. S., & Hong, G. S. (2011). Ultraprecision machining of microstructured functional surfaces on brittle materials. Journal of micromechanics and
microengineering, 21(9), 095011.
Yun, Z., Liu, Z., & Li, Y. (1998). Aspheric surface testing with a liquid compensatory
interferometer. Optical Engineering, 37(4), 1364-1367.
Zwiers, R. J., & Dortant, G. (1985). Aspherical lenses produced by a fast high-precision
replication process using UV-curable coatings. Applied Optics, 24(24), 44834488.
136
Appendix A: Replicated Microoptical Arrays for Multiple 3D Optical
Trapping
A.1 Introduction
Conventional laser optical tweezers require a high magnification microscope objective
lens with high numerical aperture (N.A.) to achieve adequate 3D manipulation. In
addition to high cost, limited depth of field, and limited field of view associated with
such lenses, the conventional design only allows a single laser trapping spot for
manipulating individual micro object. Since the ultimate goal is to process large number
of cancer cells simultaneously and these cells have to be manipulated in a specific
fashion, a low cost, microlens array based trapping system has been developed. Here we
describe our program involving in replicated microoptical lenses fabricated using a
combination of diamond machining and microinjection molding.
A.2 Competitive analysis
Simultaneous multiple trapping of micro objects is of great interest to the state-of-the-art
biomedical research since it provides maximum flexibility and capacity for cell
manipulation and is also non-invasive to living cells. There are three major solutions
available today, namely, time-sharing laser beam, holographic optical elements and
microoptics array. The first two methods are expensive and complicated because the
delicate optical components used in the system. The third method using microoptics can
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be made more economic with the combination of ultraprecision machining and molding
processes.
Ultraprecision diamond machining provides a means to produce arbitrary array patterns
for the microlens array in addition to lower optical aberrations. High volume productivity
by molding processes makes the devices very affordable. After individual parts are
fabricated, the optical devices can be inserted into the conventional optical trapping setup
utilizing the proper mechanical alignment features to obtain the precise focal spots for
multiple trapping, providing a unique solution to biomedical and medical research.
Our work is one of the first attempts to use replicated optical devices made by combining
ultraprecision diamond machining and proper replication processes to create multiple
trapping, and it will also represent the first affordable integrated device with future
commercialization potential thus establishing the foundation for lost cost multiple
trapping using microlens arrays.
A.3 Experiment setup and results
Figure A.1 shows the optical layout of the integrated multiple trapping system
constructed for this research. In this design, the collimated infrared laser beam passes
through the microlens array (MLA) forming an array of “beamlets”. Assuming proper
optical alignment is established, these beamlets are then transferred by the field lens
again to form a set of laser traps at the focal plane of the microscope objective (MO). The
resulting optical traps can be utilized to manipulate multiple micro objects (in this case
living cells) as shown in the figure. Additionally, the fabricated device can be integrated
with NEP chip in the future. As illustrated at the bottom of Figure A.1, multiple
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nanochannels allow multiple cells to be placed in required areas for high efficiency
multiple trapping.
Figure A.1. Optical setup of the integrated multiple trapping system.
Ultraprecision diamond machining has many advantages over more conventional
cleanroom based technologies since it can eliminate complicated process steps, avoid
high lab maintenance expense and provide more flexibility in 3D pattern manipulation. In
addition, ultraprecision machining of freeform optics provides a unique solution to
eliminate many optical aberrations that are associated with the optics made with
conventional lithography, such as spherical aberration. Once the optical mold is finished,
replication processes are utilized for high volume manufacturing while maintaining high
precision and quality. One of the replication process options here is microinjection
molding which provides an economic way to produce high volume and low cost devices.
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A couple of designs for the polymer microlens array have been manufactured to evaluate
their optical performance. However, because of the high energy laser required in this
study, glass microlens array may be desired to avoid the "burn out" issue involved in the
experiment. To this end, glass microlens arrays were fabricated to demonstrate their
manufacturing feasibility as shown in Figure A.2.
Figure A.2. Compression molded glass microlens array used in hybrid glass-polymer
microlens assmely.
Figure A.3(a) shows the multiple trapping spots obtained by using the combination of a
glass microlens array and a microscope objective. The intensity of the laser spots was not
completely uniform, and typically brighter spots lead to higher trapping force. Moreover,
as shown in Figure A.3(b) the multiple polystyrene beads with approximate 3 m
diameter were successfully trapped by this design.
The formation pattern of trapped micro objects are determined by the arrangement of the
microlens array, therefore the trapping pattern layout can be adjusted according to the
need of the specific applications. In addition to multiple trapping, these micro objects can
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be positioned, such as moved or rotated, to the desired locations by steering the incoming
laser beam.
(a)
(b)
Figure A.3. (a) Multiple laser focal spots generated by the optical setup discussed before
(b) trapped polystyrene beads
A.4 Summary and future work
Precision replicated microoptics with high quality provide a low cost alternative for
multiple optical trapping, because they can be manufactured by using the combination of
ultraprecision diamond machining and molding replication processes. In addition to cost,
they offer the advantages of more flexibility of trapping formation pattern and reducing
common optical aberrations.
The future focus will include the evaluating the performance of optical design,
optimizing the optical setup, fabricating suitable microlens arrays with low cost and
integrating the device with the NEP chip system. Our ultimate goal is to realize
disposable assembled multiple optical trapping devices by replacing the microscope
objective with affordable molded precision optical components.
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