ICT-7-215280 HELIUM3D
HELIUM Template V1.0
ICT-7-215280 : HELIUM3D
HELIUM Template
V1.0
1/25/2008
ICT-7-215280 HELIUM3D
HELIUM Template V1.0
Document Control
Author1
Eero Willman, Sally Day
2
UCL
Client3
PSC
Owner
Document number
4
Approval status
- draft, -pending, -approved
Purpose
draft
Description of design for the transfer screen and spatial
light modulator.
Change Records5
Version
Date
Reason for Change
Author
V.0.1
Dissemination
Version
V.0.1
Level6 PU, PP,
RE, CO7, WD
WD
Notes
CO
Distribution if not public8
Name
1
Organisation
Version
Date
Author: primary author(s) of the core document. Authors of changes are identified elsewhere.
Owner: WorkPackage leader organisation
3 Client: Organisation requiring this product as input to their own work or Project Steering
Committee (PSC)
4 Document number: see Project Quality Plan
5 Change records: Changes in Major Version are the responsibility of the HELIUM3D Configuration
Management Administrator. Changes in Minor Version are the responsibility of the Document
Owner
6 PU = Public, PP = Restricted to other programme participants (including the Commission
Services), RE = Restricted to a group specified by the consortium (including the Commission
Services), CO = Confidential, only for members of the consortium (including the Commission
Services), WD = Working Draft, only for members of the Work Team producing the document
7 If marked CO, or WD, then the document is deemed to be CONFIDENTIAL and Section 10 of the
HELIUM3D Consortium Agreement applies, IF the Dissemination Level of the document changes
to PP or RE, change the document’s Custom Property ‘Disposition’ to RESTRICTED AND
CONFIDENTIAL. If the document changes to PU, then set Disposition to PUBLIC.
8 Distribution: This is a cumulative record showing all external recipients of all released non-public
versions.
2
ICT-7-215280 HELIUM3D
HELIUM Template V1.0
Sub-documents9
Number
Version
Title
Relevance
Contents
1
2
3
Introduction.......................................................................................................... 1
The Diffuser D1 .................................................................................................... 2
The Pupil Control Module ................................................................................... 3
3.1
Single Spherical Plano-Convex Lens. ................................................................ 5
3.2
Single Aspherical Plano-Convex Lens ............................................................... 7
3.3
Single Meniscus ................................................................................................. 7
3.4
Single Aspherical bi-convex Lens ...................................................................... 8
3.5
Cooke Triplets.................................................................................................. 10
3.5.1
Simple Spherical Cooke Triplet .................................................................... 10
3.5.2
Improved Cooke Triplet ................................................................................ 11
3.6
Comparison of Images ..................................................................................... 12
3.7
The Spatial Light Modulator ............................................................................. 13
4
ZEMAX Modelling of the Transfer Screen ........................................................ 14
4.1
Fresnel Lenses ................................................................................................ 14
4.1.1
Fresnel Lens surface Profiles ....................................................................... 15
4.2
The Superlens Screen ..................................................................................... 16
4.3
Overall considerations of the Superlens Screen............................................... 16
4.3.1
Maximum Incident Angle .............................................................................. 16
4.3.2
Layer 1 (Objective Lens) .............................................................................. 17
4.3.3
Layer 2 (Field Lens) ..................................................................................... 17
4.3.4
Layer 3 (Eyepiece Lens) .............................................................................. 17
4.4
A Preliminary off-the-Shelf Superlens Screen .................................................. 19
4.5
Designing an Improved Superlens Screen ....................................................... 20
5
Preliminary Ray-Tracing Results ...................................................................... 22
5.1
An improved Light Source for Ray-Tracing ...................................................... 24
5.2
Crosstalk Between Right and Left Eyes ........................................................... 26
5.3
Effect of the SLM Opening Width ..................................................................... 28
6
Microlens Array Manufacturers ........................................................................ 31
6.1
SUSS-MicroOptics ........................................................................................... 31
6.2
MEMS Optical .................................................................................................. 31
6.3
Holographix ..................................................................................................... 32
6.4
Epigem ............................................................................................................ 32
6.5
Nihon Tokushu Kogaku Jushi Co., Ltd ............................................................. 32
9
Sub-documents: separate files, each subject to its own approval cycle and version control that
form an integral part of this document
ICT-7-215280 HELIUM3D
HELIUM Template V1.0
1 Introduction
The overall system specification for the display system has been described in D4.1. This
deliverable is concerned with the design of mainly two parts of the system, namely the
microlens arrays at the transfer screen at the output and the Spatial Light Modulator (SLM)
which will select the view to be seen by the observers at the location found from the head
tracking system. However in order to design these components successfully modelling of
other components in the system need to be included and to be specified. In addition a
model of the optical engine is required because the optical engine provides the input light
to the rest of the system. As a result this report should be read in conjunction with D6.1,
as well of course as D4.1.For convenience Figure 1 from D4.1 has been reproduced here:
Figure 1 Display Hardware
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The components that have been considered for this deliverable are: the Horizontal diffuser
after L2: the pupil control module, which consists of the imaging lens L3, the SLM: the
transfer screen, which consists of the combined lenses L4, the Gabor superlens screen
and L5. A full model requires a clear description of the light coming from the light engine,
shown in a circle in figure 1. This is still under development as the overall design
progresses. An issue that has become apparent in testing the light engine is the output
polarisation. To ensure maximum light efficiency it will be necessary to add polarisation
compensation optics with the SLM. This will be in the form of a film and so will not change
the ray tracing optical design, but will require careful design because the compensation
will need to be dichroic since is seems likely that the polarisation output from the light
engine will depend on the RGB colour. In addition during the last few months an
intermediate prototype has been proposed and design work for the lenses for the
prototype has been included in this report.
2 The Diffuser D1
It has been suggested that a cylindrical microlens array is to be used as the horizontal
diffuser. One such component is identified at DMU. Some of the parameters characterising
this component are unknown but it was found to operate in a satisfactory manner by
shining a beam of collimated light onto it, see report “WP4 Components for Optical System
Modelling” (the divergence angle of transmitted light was found to be suitable for
illuminating the whole width of L3). The pitch of the array was measured to be 0.385 mm
with a radius of 0.72mm. However, this is larger than the size of the pixels imaged onto L2
(302 mm / 800 pixels = 0.3775 mm/pixel). This means that in some cases a pixel may be
imaged between two adjacent microlenses. The result of this may be “gaps” or dark
vertical bands appearing in the final image.
The “gaps” introduced by the diffuser can be seen in Figure 2, where a close-up of 6
adjacent pixels (rays of different colours emerging from the left) imaged onto L2 (black
vertical bar) and a cross section of the cylindrical microlens screen used as a horizontal
diffuser are shown. It can be seen how the regions between the microlenses result in nonuniform diffusion of the light.
It is then necessary to use a cylindrical microlens array with a pitch much smaller than the
size of the pixels imaged onto L2, but with an angular spread of at least 20 degrees in
order to resolve this issue. Microlens arrays and diffusers are standard components that
can be purchased from a number of manufacturers (see section 6).
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Figure 2 Non-uniform diffuser D1
3 The Pupil Control Module
The Pupil Control Module (PCM) stage is located between the Intermediate Image Stage
(IIS) and the Front Screen (FS). A schematic diagram of this can be seen in figure 3. The
PCM serves two functions:
1. Projecting the image of the IIS onto the FS.
2. Controlling the directions of beams exiting the FS (i.e. choosing the location of
the exit pupil).
The PCM comprises a projection lens L3, and a linear SLM for selecting the beam
direction. The operation of the display relies on the PCM imaging the IIS onto the correct
location with the correct angle of incidence. If these two requirements are not
simultaneously satisfied, the location of the exit pupil will be incorrect. Both of these
requirements are affected by the imaging quality of L3.
It has been initially suggested that L3 can be a single spherical or possibly Fresnel lens.
However, single lenses perform poorly at imaging over wide angles due to field curvature.
In practice, compound lenses consisting of several elements need to be used for high
quality imaging onto a plane.
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Figure 3 Layout of the Pupil Control Module
The initial prototype is to use a single plano-spherical lens of 325 mm focal length as L3.
This lens is because such a lens is currently available at DMU.
Spherical aberrations due to imaging with a spherical lens can be reduced by using a
small SLM aperture. However, this will not correct the fact that light will be focused on a
“wrong” position on the FS when the open SLM aperture is far from the centre of the SLM.
This in turn means that the angle of incidence will also be incorrect and that the location of
the exit pupil will be off. Using a non-spherical lens for L3 removes the spherical
aberrations but does not correct for the field curvature.
Problems caused by field curvature:
The image projected on L4 will be out of focus at the edges of the screen. This may be
further worsened by the fact that the scanning beam will probably be wider than initially
planned: A wide scanning beam will illuminate several columns of pixels on the LCOS, and
these will be blurred into a single wide column on L4.
The size of the SLM aperture can be used to reduce aberrations to some degree.
However, it has been observed both experimentally as well as through ray tracing
simulations that the imaging quality of the initially planned lens is poor and an alternative
solution may be needed.
ZEMAX ray-tracing has been used to investigate various alternatives for the L3 lens. The
image qualities produced by some simple lenses are compared in the following sections.
First, various single lenses with different aperture stops are considered and finally a simple
compound projection lens consisting of three individual lenses is tried. In all cases, it is
assumed that the Fresnel lenses specified in the document “WP4 Components for Optical
System Modelling V.0.2” (available on the HELIUM3D extranet) are used for L2 and L4.
This fixes the distances in front of and after L3 to 567 and 762 mm respectively (f = 325).
Additionally, L3 is assumed to be of 200 mm diameter (F# = 1.625), and the refractive
index of the lens material is taken as 1.549, unless specified otherwise.
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3.1
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Single Spherical Plano-Convex Lens.
A spherical plano-convex lens, currently available at DMU, is to be used in preliminary
prototypes.
R1
Thickness
178.55
35
Spherical aberrations are a problem with this lens. The situation can be improved by using
only a fraction of the lens area. Table 1 shows ray traces for 80, 60 and 30 mm apertures.
Table 1 L3 with 80, 60 and 30 mm aperture stops
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Table 2 Object and images using single plano-convex lens with various aperture stop sizes.
Figure 5 Image, 80mm aperture
Figure 4 Object
Figure 6 Image, 60 mm aperture
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Figure 7 Image, 30 mm aperture
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Single Aspherical Plano-Convex Lens
Using the ZEMAX optimisation features, the surface radius and conic constant are
optimised to minimise the RMS spot size at the image plane when the aperture stop is
80mm.
R1
Conic1
Thickness
192.228
-0.9963
35
Table 3
Figure 9 Image, 80 mm aperture
Figure 8 Spot diagram, aspherical plano-convex
3.3
Single Meniscus
Single meniscuses give an improved image as compared to a spherical plano-convex
lens.
Thickness
R1
R2
Conic1
Conic2
40
151.0
690.0
-2.044516
-243.828047
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Figure 11 Spot diagram for meniscus
Figure 10 Meniscus
Figure 12 Single meniscus, with 80 mm aperture stop
3.4
Single Aspherical bi-convex Lens
A single aspherical biconvex lens was optimised for radii and conic constatnts
Thickness
R1
R2
Conic1
Conic2
30
389.370
-351.034
3.685
-10.184
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Figure 13 image, single aspheric biconvex lens with 80 mm aperture stop
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3.5
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Cooke Triplets
To achieve good performance both on- and off-axis, more complex lens forms are
required. Cooke triplet is a well-know lens form that provides good imaging performance
over a field of view of +/- 20-25 degrees. Many consumer grade film cameras use lenses
of this type.
3.5.1 Simple Spherical Cooke Triplet
A simple triplet consisting of three spherical lenses (two of which are identical) made of
BK7 glass was modeled first. Only the spacing between the lenses was optimized
(thicknesses of surfaces 3 and 5 in table 2 ).
Table4
Surface Curvature Thickness Glass
SemiDiameter
Conic
OBJ
0
567
159
0
1
200
40
100
0
2
-450
0
100
0
42.092
80
0
90
0
90
0
100
0
STO
Figure 14
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BK7
4
-205
15
BK7
5
205
31.56
6
450
40
7
-200
762
100
0
IMA
0.00E+00
-
250
0
BK7
Figure 15
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Figure 16
3.5.2 Improved Cooke Triplet
Zemax was then used to optimise all lens parameters of the triplet:
Table 5
Surface Curvature Thickness Glass
SemiDiameter
Conic
OBJ
Inf
567
150
0
1
181
83.98
100
0.05197
2
-552.66
0
100
-38.91
42.049
80
0
90
2.665
90
-1.368
100
2.377
STO
BK7
4
-237.64
17.95
BK7
5
183.11
33.11
6
490.54
43.11
7
-193.72
762
100
-0.1228
IMA
Inf
-
208
0
BK7
Table 6
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Comparison of Images
Table 7
Figure 17 Original object
Figure 18 spherical plano-convex 80 mm aperture
Figure 19 spherical plano-convex 30 mm aperture
Figure 21 Aspheric meniscus 80 mm aperture
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Figure 20 aspherical plano-convex 80 mm aperture
Figure 22 apheric biconvex 80 mm aperture
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Figure 24 aspherical triplet 80 mm aperture
Figure 23 spherical triplet 80mm aperture
The comparison of the imaging action of the different lenses show (as expected), that the
performance of the triplet lens is superior to the other. The next stage for this work will be
to find out whether such lenses can be sourced; it is large in size and so may be too
expensive, but should be considered if the image quality is not sufficiently good when
using a singlet.
3.7
The Spatial Light Modulator
The SLM has a number of important properties for the project. It must be relatively large
estimated to be 25cm (from D4.1) and have sufficient pixels to select the exit pupil without
significant cross talk. In addition the switching time must be such as to change the exit
pupil as the frame is scanned to maintain the exit pupil position. It has been agreed that
prototype I will present the same image pairs to four viewers because at present the
optical engine displays do not switch sufficiently fast to present different images. This
means that the rate to scan a single view is 120Hz, i.e. 8ms. The line width illuminating
the displays is to be 200m and the display size is about 8mm, which means that each
line will be illuminated for about 200s. This should give an estimate for the response
time of the SLM. However if the optical engine displays are to be run faster in the future
then the switching will need to be 4 times faster than this, i.e. a response time of 50s. It
is difficult to achieve this with a nematic liquid crystal effect and so it is probably necessary
to use a ferroelectric liquid crystal SLM. There are therefore a limited number of suppliers
for the SLM. Three have been identified Qinetiq, Hong Kong University, Prof. Chigrinov
and Cambridge University.
The number of pixels must be specified with consideration of the cross talk at different
viewing positions. This will also depend on the properties of the superlens transfer screen.
One important factor is the degree to which transmitted beams of light are collimated after
passing through the front screen. Preliminary ray-tracing results presented in section 8
suggest that a resolution of 512 pixels (resulting in a minimum aperture of 200mm/512 =
0.39 mm) in the horizontal direction should be enough.
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4 ZEMAX Modelling of the Transfer Screen
4.1
Fresnel Lenses
The preliminary prototype transfer screen incorporates at least three Fresnel lenses: L2,
L4 and L5 (and possibly additionally L3). Aspheric off-the-shelf Fresnel lenses
manufactured by Fresnel Optics are to be used.
The available models and their properties are listed in Table 1 in “WP4 Components for
Optical System Modelling”. The lenses are characterized by their focal lengths, facet
spacing, thickness and refractive index. However, the surface profiles of the lenses are not
given.
In ZEMAX, Fresnel lenses can be modelled by the non-sequential “Fresnel 1” components
or the sequential “Fresnel” surfaces. The relevant parameters, besides position, thickness
and refractive index, are:
1. depth/frequency (non-sequential only)
2. lens radial height
3. lens sag expression (actually, several parameters)
4. pitch. (non-sequential only)
The depth/frequency parameter determines the dimensions and separation of the lens
grooves. If this parameter is chosen positive, the value fixes the depth of the grooves but
the radial distance may vary. If negative, the (absolute) value corresponds to the number
of grooves per radial unit, but with a variable depth.
The lens radial height determines the external size of the cylindrically symmetric lens.
The lens sag expression gives the surface profile of the equivalent (non-Fresnel,
standard) aspheric lens:
z (r ) 
cr 2
1  1  (1  k )c r
2
r
  1 r 2   2 r 4 ... 3 r 16 ,
(1)
Where r is the radial distance from the centre of the lens, c is related by the spherical lens
radius R by c=1/R, k is the conic constant and the alphas (ranging from 2 to 8) are
polynomial coefficients. In practice, the user sets the values of R, k and  2 -  8 .
When a spherical Fresnel lens is modelled, the conic constant k and the alphas are all set
to zero and only R need to be chosen. However, if R < lens radial height, expression (1)
becomes complex valued, causing an error. In the case of aspheric lenses, in addition to
R, the values of k and alphas are non-zero. This makes it possible to model short focal
length lenses (R < lens radial height) without expression (1) becoming complex valued.
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Figure 25 Lens surface profile when R = 0.5 x lens radial height, for different values of
k (all alphas = 0). When k = 0, z becomes imaginary resulting in an error.
The pitch is the angle in degrees of the “inactive faces” of the Fresnel lens. Ideally this is
zero, but apparently it is typically a few degrees in real Fresnel lenses in order to make the
manufacturing process by molding easier.
4.1.1
Fresnel Lens surface Profiles
Initially, the surface profiles for the Fresnel lenses were estimated by using the ZEMAX
optimisation feature to adjust the coefficients of expression (1) to focus collimated light to a
distance equal to the focal length specified by the manufacturer:
Table 8 Estimated Fresnel lens profiles
Lens (Part #)
Focal length
RoC
Cc
A6
L2 (SC208)
279.4
137.716225
-0.914104
-2.725582e-14
L3 (SC240)
317.5
156.550686
-0.912974
-1.569266e-14
L4 (SC213)
762
376.133148
-0.913285
-1.952196e-16
L5 (SC214)
609.6
300.846041
-0.913381
-5.852377e-16
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The manufacturer later provided the actual parameters for L2, L4 and L5. Entering these
into ZEMAX result in slightly different focal lengths (calculated from front surface) to those
specified by the manufacturer. The actual parameters and the calculated focal lengths are
given in table 2
Table 9 Fresnel Lens surface parameters (as provided by the manufacturer) and calculated focal
lengths
Lens (#)
Calculated
Focal length
L2
(SC208)
Cc
A2
A4
A6
A8
279.2740250 137.935
-1.0
0
4.206759
E-9
-1.9365
E-14
5.53375
E-20
L4
(SC213)
763.707177
376.95
-1.0
0
2.0091
E-10
-1.2855
E-16
5.0528
E-23
L5
(SC214)
607.979827
300.156
-1.0
0
4.07925
E-10
-4.140167
E-16
3.366375
E-22
4.2
RoC
The Superlens Screen
The superlens screen (SS) consists of three layers of cylindrical microlens arrays. The
purpose of these screens is to magnify the angle of the collimated light incident θi on the
first layer.
Design considerations include three properties: maximum angle of incidence θmax, angular
magnification A and degree of collimation of transmitted light.
The angular magnification A scales the angle of θi by some scalar value less than -1
(negative due to reversal of direction) increasing the effective viewing angle of the display.
The direction of rays exiting the superlens screen is then θo = A*θi. For large viewing
angles, the magnitude of A needs to be high.
Degree of collimation. Light transmitted through the SS should remain well (enough)
collimated in order to avoid cross-talk between the left and the right eyes.
4.3
4.3.1
Overall considerations of the Superlens Screen
Maximum Incident Angle
The angle of incidence of incoming rays of light depends on the position of the SLM
aperture opening and the distance between the SLM and the collimating Fresnel lens L4.
This is illustrated in figure 26, where rays for two scanning angles and two SLM aperture
opening positions are shown.
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Figure 26 Angle of incidence θ, of incoming chief rays at the superlens screen. Dashed lines correspond
to chief rays emerging from an SLM opening at 100 from centre and solid lines to SLM opening at the
centre (both for two scanning angles).
The distance between the SLM and L4 is currently fixed at 762 mm due to the focal length
of L4. The dimensions of the SLM are not yet fixed, but assuming a width of about 200
mm, the maximum incident angle θ is atan(100 / 762) = 7.48 degrees. This is the angle of
incidence of the chief rays and in practice θmax will be greater due to a finite width of the
SLM aperture opening. This means that it is reasonable to expect θmax to be at least ±8
degrees (it has earlier been suggested to be less than 5 degrees, see e.g. “D4.1 Overall
System Integration Architecture V0.9”, p33).
4.3.2 Layer 1 (Objective Lens)
The focal lengths of the lenses comprising layer 1 (objective lens) of the superlens
screens is determined by θmax. The focal length must be short enough to focus the
incoming light within the same lenslet through which it emerges. The effect of θi > θmax can
be seen in figure 27. The first point of focus is then within an adjacent lenslet resulting in a
reversal of the angle θo (i.e. the rays exit in the wrong direction).
4.3.3 Layer 2 (Field Lens)
The function of the second layer is to refract the rays from layer 1 to the centre of layer 3.
The properties of this layer are then determined by those of Layer1 and Layer3, and can
be chosen chosen last in the design phase.
4.3.4 Layer 3 (Eyepiece Lens)
The ratio of focal lengths of the first and third layers of lenses determines the angular
magnification of the screen. The magnification A is given by A = f1 / f3 ≈ R1 / R3, where fi
and Ri are the focal lengths and radii of layers 1 and 3 respectively.
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Figure 27 Three beams of different angles of incidence. Blue, θi = 0. Red, θi < θmax. Green, θi > θmax.
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A Preliminary off-the-Shelf Superlens Screen
An initial superlens screen can be made by modifying off-the-shelf cylindrical microlens
arrays. Screen 2 and 3 are of 3.32mm thickness with a radius of 1.219 whereas screen1 is
a 7.04 mm thick screen with 2.584 mm radii. The thickness of screen1 can be cut down so
that incident light is focused on the surface of screen2.
The optimum thickness is found using zemax to minimise the D/d ratio as a function of
screen1 thickness, where d and D are the incident and transmitted beamwidths
respectively. The optimum thickness was found to be 3.715 mm. See figure 28.
The range of operation of the preliminary transfer screen is limited to incident angles θi of
less than about 3.6 degrees. When the incident angle is larger than this, light is focused by
Layer1 onto an adjacent lenslet in Layer2. This means that only a fraction of the SLM
width can be used. The magnification of the superlens screen is about 2 within the allowed
range of operation. The transmitted radiance in angle space as a function of incident angle
is plotted in figure 3.
Figure 28 Optimum thickness of Screen 1 of preliminary superlens screen
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Figure 29 Transmission angle as a function of incident angle, for preliminary superlens screen
Figure 29 shows the intensity of transmitted light in angular space w.r.t. the angle of
incidence for the preliminary superlens screen. In this case, the range of allowed incidence
angles is limited to about ± 4 degrees and the magnification is about 2. As the angle of
incidence is increased to more than θmax, light enters adjacent lenses and a reversal of the
magnification occurs along with multiple transmitted beams (e.g. at 8 degree incidence,
light is transmitted at ~0 and ~12 degrees). Furthermore, as the angle of incidence is
increased, the transmitted beams become less collimated as can be seen from the
increased widths of the lines.
4.5
Designing an Improved Superlens Screen
The preliminary superlens screen consisting of off-the shelf components does not offer a
large viewing field. In order to improve this, a different design is needed.
The optimisation feature of the ZEMAX ray-tracing software is used to devise a superlens
screen with improved characteristics compared to those of the intermediate one presented
in the previous section.
A number of parameters need to be provided as a starting point for the optimisation tool.
These can be obtained e.g. by making a paraxial approximation, as in “D4.1 Overall
System Integration Architecture V0.9”, page 31. The optimisation tool is then used to
adjust these in order to minimise the value of a chosen “merit function”.
The initial assumptions used are:
1. Choosing a material/refractive index for the screens. In practice, it may be that
different materials can/need to be used for the different layers. Here, a refractive
index of n=1.58 (typical to styrene) is chosen for all layers.
2. Assume that θmax needs to be at least 8 degrees (see section 5.3.1). A microlens
array of 0.5mm pitch with a 1mm radius of curvature and thickness of 1.69 mm will
be sufficient for Layer1.
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3. Choosing the radius of curvature of Layer3 as 0.3 mm will result in a magnification
of A≈ - 1 / 0.3, providing a viewing field of approximately ±26.7 degrees. The
starting thickness is set to 0.6mm
4. Layer2 is set to a thickness of 1mm and the radius to 0.5mm.
The merit function is selected to minimise the angular spread of the output beams, while
three collimated beams at 0, 4 and 8 degrees of angle of incidence are used as input. This
means that the optimisation tool is used to find the superlens screen coefficient values
such that on average the output beams remain collimated (it would be easy to design a
screen that would maintain a perfect collimation at a single angle of incidence, but here we
are looking for one that performs equally well for all angles of incidence between 0 and 8
degrees).
While keeping the parameters of Layer1 fixed and allowing for aspherical surfaces in
layers 2 and 3, but fixing spherical part of the radius of Layer3 as 0.3mm, the optimisation
tool results in the following design:
Layer
Radius/mm
Thickness/mm
Conic coeff.
1
1.0
1.69
0
2
0.462913
1.152587
0.786627
3
0.3
0.628433
-2.927232
This corresponds to a local minimum in the chosen merit function. Different starting
conditions typically result in slightly different designs, and the one presented here may not
be the best of all the possible choices (a global minimum).
A closeup of a ray-trace with beams of light incident at 0, 4 and 8 degrees is shown in
figure 30. It can be seen that the first point of focus is in fact before the lens surface of
Layer2, not at the surface as previously expected. This is a result of requiring that the
degree of collimation at the output should be equal for all three incident angles (as
specified in the merit function).
Figure 30 Closeup of a section of a superlens screen designed using the ZEMAX optimisation tool. Blue
rays θi = 0, green rays θi = 4 degrees and red rays θi = 8 degrees.
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The angular magnification of the screen is found to be about -3.69 resulting in a viewing
angle of ±29.3 degrees.
The screen presented above is not intended to be a final one, it may e.g. be
impossible/too expensive to manufacture. Instead, the outlined procedure can later be
used in order to quickly find a design adhering to some given restrictions, once the
limitations, capabilities and manufacturing costs of various microlens manufacturers have
been explored (see section 7).
5 Preliminary Ray-Tracing Results
The components from the previous sections are combined and raytracing used to simulate
the overall system (intermediate prototype).
Selected angles were used as a source and are shown in red, green and blue. The other
components were as specified in deliverable 4.1 and section 4 of this document. The SLM
aperture non-blocking width is set to 2 mm and its position is moved. Results for this (in
plan view) are shown in figures 31-34.
L1
L2 and D1
L3 and SLM
L4, superlens
screen, D2 and L5
Figure 31 Plan view. SLM is non-blocking in centre only.
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Figure 32 SLM non-blocking 30 mm from centre
Figure 33 SLM non-blocking 50 mm from centre
Figure 34 SLM non-blocking 60 mm from centre
It can be seen that the design works for small angles (figures 31 and 32) but not for large
ones (figures 33 and 34). The lens used for L3 is the spherical plano-convex available at
DMU, so not ideal as discussed in section 3. In addition the angular performance of the
superlens screen is limited, as discussed in section 4.4.
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An improved Light Source for Ray-Tracing
A model for L1 is unavailable due to the lens used being a proprietary projector lens (see
deliverable 6.1). Non-seqential ray-tracing was used as follows:

The LCOS-L1-L2 components are replaced by large light sources (source
rectangles) representing the LCOS pixels imaged onto L2 a Fresnel lens of focal
length 567 mm.

For a 800 x 600 pixel display, and L2 intermediate image size of 302 x 227 mm,
pixel width and height at L2 is 0.378333 and 0.3775 mm respectively. Gaps
between the pixels are neglected.

Scanning beamwidth at LCOS is estimated at 100-200 microns, resulting in about
6 – 12 pixel columns being illuminated at any time.
Figure 35 from left to right: Alternating on-off pixels, Lens L2 and diffuser D1. The colours
correnspond to different on-pixels, separated by off-pixels.
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Figure 36 Pixel columns at two scanning angles, SLM open at centre location
The ray aiming feature does not exist in the non-sequential mode of ZEMAX, so raytracing of full system will be slow. This is because ~99% of rays will be blocked by the
SLM and only very few pass through, as shown in figure 36. This makes it very slow to
predict the performance at the exit pupil. A way of overcoming this is by setting the radii of
the microlenses of D1 so that more rays pass through the SLM (by decreasing the
diffusing action of D1). However, this will limit the possibility of predicting the efficiency of
the overall system.
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Crosstalk Between Right and Left Eyes
The position of the open SLM slit, of 1 mm width, is moved in steps of 1 cm between 0 and
90 mm. The irradiance at distances of 75, 100cm, 200cm and 300 cm from the screen are
recorded and plotted in figures 38-41. The superlens screen used in this simulation is
designed using the procedure described in section 4.5, but with a smaller magnification.
SLM position = 90 mm
SLM position = 0 mm
Figure 37
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Figure 38
Figure 39
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Figure 40
5.3
Effect of the SLM Opening Width
Using the same front screen as above, ray tracing was performed to assess the effect of
varying the SLM aperture size between 1 and 4 mm widths (with the open aperture
position only considered in the centre of the SLM). The normalised irradiance at 75, 100,
200 and 300 cm distances from the front screen are plotted in figures 42-45.
A larger SLM opening allows for more light to pass though to the screen. This causes a
widening of the beam at the exit pupil location, but also an increase in the perceived
brightness of the screen. The transmitted beam is also divergent and becomes wider with
distance.
The optimum widths of the beams at the exit pupils are not yet exactly known, but the
beam widths should be narrow enough to limit crosstalk between the left and right eyes (or
multiple viewers). However, it may be beneficial not to make the beams too narrow in
order to combat errors/inaccuracies in the exit pupil location (e.g. introduced due to
aberrations of lens L3).
The beam width at the exit pupil location could then be around 10 cm or slightly less
(assuming that the distance between the right and left eye is about 5 cm). It is probable
that the SLM opening width is not fixed, but should vary depending on the distance
between the viewer and the screen. This is possible by combining several adjacent pixel
columns to form a single aperture.
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An SLM of 200 mm width consisting of 512 pixels in the horizontal dimension would allow
for changes in the open aperture width in increments of less than 0.4 mm. This resolution
seems sufficient, considering that the ray tracing suggests that the widest beam at 300 cm
distance (figure 45) with a 4 mm aperture is about 10 cm wide. In cases when the viewer
is closer, the aperture could be considerably larger. Furthermore, figures 38-41 suggest
that the beams become narrower off axis, allowing for an even wider SLM aperture.
However this may be highly dependent on the exact design of the superlens screen.
Figure 41
Figure 42
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Figure 43
Figure 44
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6 Microlens Array Manufacturers
A number of microlens manufacturers have been identified. They are listed below and
work is ongoing to identify the best microlens array for the different components of the
system. It is very likely that custom microlenses need to be ordered. This work will
continue as part of deliverable 5.2.
6.1
SUSS-MicroOptics
Refractive Microlens Arrays:
Features






Bulk material: Fused Silica, Silicon, Borofloat
Wavelength range: DUV (193nm) to IR (5µm)
Maximum array size: 180 mm, 120 mm x 120 mm
Lens size: 10 μm – 2 mm
Lens profiles: Plano-convex, bi-convex, spheres, aspheres
Double sided lens arrays with precise front-to-back alignment
Comments: Array dimensions are too small for the front screen The company also
manufactures 1-D diffusers, however the dimensions are not given and may again be too
small.
6.2
MEMS Optical
Fused silica and silicon and newer materials such as Gallium Phosphide and Calcium
Fluoride a wide variety of lenses can be made.Molded plastic spherical/aspherical
microlenses of various sizes are possible. Both stock and custom designs are available.
Features:









Refractive
Diffractive
Anamorphic
Aspherical
Spherical
Convex/Concave
Front-to-Back alignment within 1 micron
Surface roughness 20-80 Å
Antireflective coatings
Comments: Dimensions not given, so need to find out if sufficiently large arrays can be
manufactured. They might be able to manufacture Layer1 and Layer2 as a single sheet.
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Holographix
Based on information on the website, Holographics might not be into the right kind of
business for our needs. Holographics manufactures:





Mirrors
Micro-optics
Aspheric surfaces
Membranes
Antireflection surfaces
However, they state that they can assemble large tiled micro-optic arrays by recombining
from smaller master patterns. This might be an option in the case of a company that can
manufacture the required lens arrays, but on a smaller substrate.
6.4
Epigem
www.epigem.co.uk
Product description: Customised replicated microlens arrays on flexible or rigid substrates.
Typical design and manufacturing parameters:
 Focal length: 0.2 to 20 mm
 Lens diameter: 0.05 to 3 mm
 Array size: up to 80 mm x 80 mm standard ; larger sizes on request.
 Packing arrangement: orthogonal, hexagonal, linear etc.
 Lens materials: acrylate or epoxy resins, acrylic Substrate materials: rigid or
flexible including (but not limited to) glass, quartz, silicon, polycarbonate, polyester
(Mylar), PEN (Teonex)
 Operating temperature range: -30°C to +70°C
 Operating wavelength range: 370 to 2000 nm
 Substrate sizes: Up to 80 mm x 80 mm standard for rigid. Flexible substrates up to
300 mm wide. Larger sizes on request.
Comments: It is not clear whether aspherics are possible.
6.5
Nihon Tokushu Kogaku Jushi Co., Ltd
http://www.ntkj.co.jp/index_en.html
“NTKJ manufactures and sells not only Lenticular lens products on the catalog, but also
manufactures custom made Lenticular lens products according to our customers'
requirements in sizes and design. Please contact us for more details.
Our machining systems are ready to produce plastic optical products of practically
any size, including Fresnel, lenticular, linear Fresnel, fly's-eye and aspheric lenses and flat
prisms. Maximum machining dimensions: 200inches.
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Our manufacturing expertise and equipment can accommodate a broad range of
customer needs, from prototype development to mass production.
Our uniquely designed lens machining equipments can craft lenses to microscopic
tolerances, satisfying diverse requests and stringent specifications.”
Comments: They seem to be promising to be able to do what we want and we are in
contact with them at the moment.
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