Optical Systems Design
with Zemax
OpticStudio
Lecture 1
Why Optical Systems Design
Optical system design is no longer a skill
reserved for a few professionals. With
readily available commercial optical design
software, these tools are accessible to the
general optical engineering community and
rudimentary skills in optical design are now
expected by a wide range of industries who
utilize optics in their products.
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Course Aims
To introduce the design principles of
lens and mirror optical systems and the
evaluation of designs using modern
computer techniques. The lectures will
cover lens design, aberrations,
optimization, tolerancing and image
quality metrics.
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ZEMAX Optics Studio
The ZEMAX optical design program is a
comprehensive software tool. It integrates all
the features required to conceptualize,
design, optimize, analyze, tolerance, and
document virtually any optical system. It is
widely used in the optics industry as a
standard design tool. This course will
introduce the basics of ZEMAX using the
recently released (2014) OpticStudio
interface.
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Other Optical Design Software
• Code-V (Optical Research Associates)
• OSLO (Sinclair Optics)
• OpTaliX (Optenso Ltd)
• ASAP (Breault Research)
• TracePro (Lambda Research)
• FRED (Photon Engineering)
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Course Outline
• Lecture 1: Introduction
• Lecture 2: Sequential Systems
• Lecture 3: Optimization
• Lecture 4: Tolerancing
• Lecture 5: Non-sequential & other stuff
Web page: http://astro.dur.ac.uk/~rsharp/opticaldesign.html
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Objectives: Lecture 1
At the end of this lecture you should:
1. Be able to install a version of the Zemax optical
design programme on a Windows PC
2. Understand the main tasks involved in optical
systems design with Zemax
3. Be aware of Zemax notation for the 5 main Seidel
aberrations
4. Know the relevance of the terms: optical axis,
stop, pupil, chief ray, marginal ray, point spread
function for Zemax
5. Use the Zemax lens data editor to enter the
specifications of a simple lens
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Recommended Texts
• OpticStudio User Manual and Getting Started Using
OpticStudio (access from programme help)
• Introduction to Lens Design with Practical Zemax
Examples, Joseph M Geary (Willmann-Bell Inc.)
• Optical Systems Design, Robert Fischer & Bijana
Tadic(SPIE Press)
• Practical Computer-Aided Design, Gregory HallockSmith (Willmann-Bell Inc.)
• Astronomical Optics, Dan Schroeder (Academic Press;
GoogleBooks)
• Optics, Jeff Hecht (Addison Wesley)
Also the Zemax knowledge base:
http://www.zemax.com/support/knowledgebase
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Optical Systems Design
‘Science or art of developing optical systems to
image, direct, analyse or measure light.’
• Includes camera lenses, telescopes, microscopes,
scanners, photometers, spectrographs,
interferometers, …
• Systems should be as free from geometrical optical
errors (aberrations) as possible.
• Correcting and controlling aberrations is one of the
main tasks of the optical designer (includes
performance evaluation and fabrication/tolerancing
issues).
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Historical Note
• Lens design has changed significantly since
~1960 with the introduction of digital computers
and numerical optimisation.
• Equations describing aberrations of lens/mirror
systems are very non-linear functions of system
parameters (curvatures, spacings, refractive
indices, dispersions, …)
• Only a few specialised systems can be derived
analytically in exact closed-form solutions.
• Analytical design methods (Petzval, Seidel) were
historically based on a mathematical treatment
of geometrical imagery and primary aberrations
– still useful for initial designs.
• Numerical evaluation methods ray trace many
light rays from object to image space.
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Seidel (3rd order) Aberrations
1.
2.
3.
4.
5.
Spherical aberration
Coma
Astigmatism
Field curvature
Distortion
6. Longitudinal chromatic aberration
7. Lateral chromatic aberration
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Numerical Evaluation Methods
• Assume only trigonometry, law of reflection and
Snell’s law
• n1 sin θ1 = n 2 sin θ 2
• For each ray calculate new ray parameters at each
surface
• Sequential ray-tracing assumes that light travels
from surface to surface in adefined order.
• Non-sequential ray-tracing does not assume a predefined path for the rays, but when a ray hits a
surface in its path, it may then reflect, refract,
diffract, scatter or split into child rays (scattered
light).
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Numerical Optimisation
Methods
• Given a starting configuration, the computer
can be used to optimise a design by an
iterative process.
• Final image quality is ‘best’ that can be
achieved under constraints of basic
configuration, required focal length, f/
number, field of view, wavelength etc.
• Programs are still ‘dumb’. Designer must
supply intelligence through selection of
starting configuration, control of
optimization parameters, understanding of
underlying optical theory, etc.
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Objects, Light Rays & Wavefronts
• Objects composed of self-luminous (radiant) points of
light
• Trajectories of photons from each of these points
define the light rays
• Neglecting diffraction, these physical rays become
geometrical rays (ray bundles)
• Wavefronts are surfaces normal to rays
• Light travel times along all rays to the wavefront from
an object point are the same (for a fixed wavelength)
• Neglecting diffraction, physical wavefronts become
geometrical wavefronts (good approximation except
near boundaries or edges)
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Objects, Light Rays & Wavefronts
Optical axis
Wavefronts
Image
Plane
Object
Plane
Ray bundles
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The Optical Axis
• Most optical systems are collections of rotationally
symmetric surfaces whose centres of curvature are
all located along a common axis (Optical Axis)
• Plane surfaces have infinite radius of curvature
• Intersection of the optical axis and a surface is at
the surface vertex
• Longitudinal cross-section defines a meridional
plane (all equivalent)
• Ray in this plane are meridional rays. Rays out of
plane are skew rays.
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Stops & Pupils
• Every optical system contains one physical aperture that
limits the extent of the wavefront for the ray bundle which is
transmitted through the system to the on-axis image point
(aperture stop or stop)
• If optics are large enough then this will also be true for off-axis
image points
• In many cases this is not true leading to mechanical
vignetting of off-axis image points
• Size and location of the aperture stop can have important
impact on system performance through its effects on
geometrical aberrations
• Image of the stop in object space is the entrance pupil.
Image of the stop in image space is the exit pupil.
• Focal ratio (e.g. f/5.6) is ratio of effective focal length (EFL) to
entrance pupil diameter (EPD)
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Stops & Pupils
Entrance pupil
Exit pupil
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Marginal & Chief Rays
• Marginal ray originates at the object point on axis
and goes to the edge of the stop of the system.
• Chief ray (principal ray) originates at the object
point at the edge of the field of view and passes
through the centre of the stop of the system.
Axial height (transverse distance away from the
optical axis) of the marginal ray is zero at the object
and all images of the object. At these locations the
axial height of the chief ray determines the size
(semi-diameter) of the object and its images
(magnification). These roles are reversed when
considering the aperture stop and its images (pupils).
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Marginal & Chief Rays
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Point Spread Function (PSF)
• Impossible to image a point object as
a perfect point image.
• PSF gives the physically correct light
distribution in the image plane
including the effects of aberrations
and diffraction.
• Errors are introduced by design
(geometrical aberrations), optical and
mechanical fabrication & alignment.
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Co-ordinate Systems and Sign
Conventions
• No standardization between different
codes!
• Zemax uses a right-handed cartesian
co-ordinate system, where the Z-axis is
the optical axis and light initially moves
in the direction of +Z.
• Co-ordinate breaks (rotations) are
defined in a right-handed sense.
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Optical Prescriptions
• An optical design is described by a set of
surfaces through which the light passes
sequentially.
• Surfaces are tabulated in the lens data
editor and are numbered sequentially from
the object surface (surface 0) and ending
with the image surface.
• A minimum of 3 surfaces is required (object,
stop, image).
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Surface Parameters
•
•
•
•
•
•
•
Surface number
Radius of curvature (R)
Thickness to the next surface (t)
Glass type in the next medium (or Air if blank)
Aspheric data (if any)
Aperture size (semi-diameter D)
Tilt and decenter data (if any)
One surface is designated the stop surface.
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Using the Lens Data Editor
Setup tab -> System Explorer:
• Aperture: define entrance pupil diameter (50mm)
• Fields: define field angle(s) (FoV) (0 deg)
• Wavelengths: define wavelength(s) of rays (632.8nm)
Singlet lens prescription:
(,(''"(,('" ,+" $(,)*
),$(''"), $- $ "" $),)*
% & % ,*'&#
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ZEMAX Lens Data Editor
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ZEMAX System Viewers
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System Properties
• Optical Systems Design
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Summary: Lecture 1
• Optical design has changed radically since
the introduction of modern ray-tracing
software packages
• ZEMAX is a comprehensive software tool
which integrates all the features required to
design an optical system
• The optical design process involves
developing a conceptual optial design, raytracing an optical layout and varying
parameters of the specification to improve
performance
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Exercises: Lecture 1
• Install Zemax Optic Studio(or the
OpticStudio demo) on your PC
• Use the lens data editor to input the
optical prescription of the biconvex
singlet from the lecture
• Investigate how the focus depends
on wavelength and lens curvatures
• Investigate how the image quality
depends on the thickness of the lens
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Sequential Ray Tracing
Lecture 2
Sequential Ray Tracing
• Rays are traced through a pre-defined sequence of
surfaces while travelling from the object surface to
the image surface.
• Rays hit each surface once in the order
(sequence)in which thesurfaces are defined.
Particularly well-suited to imaging systems (including
spectrometers).
• Numerically fast and extremely useful for the
design, optimization and tolerancing of such
systems.
• Aberrations evaluated using spot diagrams, ray fan
plots, OPD plots, geometrical image analysis and
MTF (physical optics) calculations.
February 15, 2016
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Example Imaging Systems
Double Gauss lens
February 15, 2016
Schmidt-Cassegrain telescope
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Objectives: Lecture 2
At the end of this lecture you should:
1. Be able to use ZEMAX to design and optimise a
simple singlet lens to specified parameters.
2. Understand the use of meridional plane layouts,
spot diagrams, and ray fan plots to evaluate
performance.
3. Design and optimise a Cassegrain reflecting
telescope to specified parameters.
4. Understand the way that conic and higher order
surfaces are specified in ZEMAX.
5. Understand how to achromatise a doublet lens.
February 15, 2016
Optical Systems Design
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Lens Data Editor (LDE)
Surf: Type
the type of surface (Standard, Even
Asphere, Diffraction Grating, etc)
Comment
an optional field fortyping in surface
specific comments
Radius
surface radius of curvature (the inverse of
curvature) in lens units
Thickness
the thickness in lens units separating the
vertex of the current surface to the vertex of
the following surface
Material
the material type (glass, air, etc.) which
separates the current surface and the next
surface listed in the LDE
Coating
any (anti-reflection) coating on surface
Semi-Diameter
February 15, 2016
the half-size of the surface in lens units
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Singlet Lens Parameters
Focal ratio is F/4.
Glass is N-BK7.
Effective focal length = 100mm.
Field-Of-View = 10 degrees.
Wavelength =632.8nm (HeNe).
Centre thickness of lens: 3mm to 12mm .
Edge thickness of lens: minimum 2mm.
Lens should be optimized for smallest RMS spot size
averaged over the field of view at the given
wavelength.
• Object is at infinity.
•
•
•
•
•
•
•
•
February 15, 2016
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System Settings
• Entrance Pupil Diameter (EPD) is the diameter of the
pupil in chosen lens units as seen from object
space.
• Effective focal length (efl) is distance along optical
axis from the effective refracting surface (principal
plane) to the paraxial focus.
• So EPD = 25mm.
February 15, 2016
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System Explorer (Setup)
February 15, 2016
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Lens Data & Solves
Optimize -> Quick
Focus
[Ctrl+Shift+Q]
N.B. use of comments field
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Optical Systems Design
Performance Evaluation (Analyze)
Spots
Layout
Ray
Fan
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Optical
Path
Difference
10
Variables for Optimisation
• Thickness of lens
• Front radius of curvature
• Back focal distance (from Surface 2 to
IMA plane)
February 15, 2016
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Optimize Wizard (Default Merit Function)
February 15, 2016
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Final System Results (Optimize)
February 15, 2016
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More Optical Concepts
• Effective Refracting Surface
– Virtual surface at which entering and exiting rays meet.
A plane for paraxial (first order) rays close to the axis.
• Zones
– Annular regions of constant distance from the optical
axis. Can apply to lens surfaces, stops, pupils, objects &
images.
• Paraxial rays
– Rays close to the optical axis for which first order (linear)
equations can be used for the ray transport calculations.
February 15, 2016
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More Optical Concepts
February 15, 2016
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Tangential & Sagittal Planes
• Tangential plane is identical to the
meridional plane for an axially symmetric
system. Tangential rays lie within the
tangential plane.
• Sagittal plane is orthogonal to the
tangential plane and intersects it along
the chief ray. All sagittal rays are skew
rays. The sagittal pane changes its tilt
after each surface to follow the direction
of the chief ray.
February 15, 2016
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Tangential & Sagittal Planes
February 15, 2016
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Back Focal Length &
Effective Focal Length
• Back focal length (BFL) is the distance along the
optical axis from the vertex of the rear lens
surface to the on-axis paraxial focus for an
object at infinity.
• Effective focal length (EFL) is the distance along
the optical axis from the vertex of the effective
refracting surface to the on-axis paraxial focus
for an object at infinity.
• BFL controls the longitudinal location of the focus
• EFL controls the transverse image scale at focus
February 15, 2016
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BFL, EFL & Aberrations
Dependence
BFL
EFL
With wavelength
Longitudinal chromatic
aberration
Lateral chromatic
aberration
With pupil zone
Spherical aberration
Coma
With field zone
Astigmatism & field
(focal plane) curvature
Distortion
February 15, 2016
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Basic Zemax Analysis Tools
• Layout plots (cross-section/shaded)
• Spot diagrams
• Ray-aberration plot
•
•
•
•
•
Optical path plot (OPD)
Field curvature & distortion plot
Point Spread Function (diffraction PSF)
Modulation transfer funtion (MTF)
Enclosed energy plot
February 15, 2016
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I: Layout
• Good for basic check of obvious
mistakes (e.g. data entry sign errors)
• Sanity check after optimisation e.g.
excessive surface curvatures,
inappropriate glass/air thicknesses,
negative edge thicknesses etc
• Check on mechanical vignetting
February 15, 2016
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I: Layout
February 15, 2016
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II: Spot Diagram
• Analog of the geometrical PSF
• Shows the intersection points where a
ray bundle which fills the entrance
aperture meets the image plane
• For polychromatic (white light) systems
these must be generated at
representative wavelengths
February 15, 2016
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II: Spot Diagram
February 15, 2016
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III: Ray Aberration Plots
• Spot diagrams give little information about which
parts of the entrance pupil particular rays pass
through
• A given ray passes through the entrance pupil at
a particular height P (-1<P<+1) and intercepts
the image plane at a separation Δh from the
chief ray
• Ray aberration plots (ray fan plots) present the
transverse ray height errors Δh as a function of
pupil zone height P
• Customary to present these separately for the
tangential (meridional) fan and the sagittal fan
February 15, 2016
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III: Ray Fan Plots
February 15, 2016
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III: Ray Fan Plots
• Slope of ray fan plot reflects whether image
plane is close to focus (inside focus → positive
slope and vice versa)
• If effective refractive surface is curved or image
surface is curved then ray fan plot also curved
• Behavior close to origin reflects whether image
plane is close to the paraxial focus
• Each Seidel aberration has a characteristic
appearance in the ray fan plot
February 15, 2016
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III: Ray Fan Plots
February 15, 2016
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Spherical Aberration
February 15, 2016
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Coma
February 15, 2016
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Astigmatism
0 deg
February 15, 2016
5 deg
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Field Curvature
0 deg
February 15, 2016
5 deg
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Distortion
0 deg
February 15, 2016
5 deg
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Longitudinal Colour
February 15, 2016
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Lateral Colour
February 15, 2016
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Glass Dispersion Curve
Dispersion:
Vd =
n d −1
n 2 − n1
d=587.6 nm
1=486.1 nm
2=656.3 nm
[Abbé number]
February 15, 2016
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Abbé Diagram
Crown glass – low
dispersion
Flint glass – high
dispersion
Use easily
available glasses
when possible:
BK7, LLF1, F2,
SF2, SF57, SK16,
KzFSN4. CaFl
often used as
crown. Large Δn is
good.
Final optimization
is usually done on
actual melt data.
February 15, 2016
37
Optical Systems Design
Aspheric Surfaces
• Most optical surfaces are spherical
• By far the easiest surfaces to manufacture using
conventional polishing techniques
• General rotationally symmetric optical surface has
departure from plane (sag) given by:
z=
ch 2
+ Ah 4 + Bh 6 + Ch8 + Dh10
2 2 1/2
1+[1−[(1+ k)c h ]
where h2=x2+y2 is the axial height, c=1/R is the
surface curvature at the vertex, and k the conic
constant. A,B,C,D are 4th, 6th, 8th, 10th order coeffs.
k=0
-1<k<0
k=-1
k<-1
k>0
sphere
prolate
paraboloid
hyperboloid
oblate
February 15, 2016
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Cassegrain Telescope
• Start with a 30cm diameter F/2 spherical
primary (RoC=120cm) and a spherical
secondary. Adjust the radius of curvature of the
secondary to put the focus in the plane of the
primary
• Glass Type = MIRROR for reflecting surfaces;
distances change sign after each reflection
• Use a Quick-focus or M-solve to locate paraxial
focus and single variables in any optimization
• Now make primary a parabola (K=-1)
• Adjust conic constant on secondary to get best
on-axis performance
February 15, 2016
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Summary: Lecture 2
• Sequential ray tracing is the main mode of Zemax
for the design of optical systems.
• Zemax has a range of optimising tools to improve
the performance of the basic design.
• The major tools for assessing performance are the
layout plots, the spot diagrams and the ray fan
plots.
• All the main Seidel aberrations have
characteristic forms in these plots which can be
used to decide how to improve the design.
• Careful choice of glasses is required to remove
longitudinal and lateral colour effects.
February 15, 2016
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Exercises: Lecture 2
• Input the parameters of a 50mm diameter F/10
optimised (R1=265mm) achromatic doublet from
Lecture 4 of the Optical Engineering Course (Dr
Rolt). Take the lens thicknesses as 8mm (crown)
and 4mm (flint). Investigate the axial colour over
the wavelengths 0.486, 0.587 and 0.656 µm. Can
you improve the performance • Investigate the performance of the Cassegrain
telescope for off-axis (1 deg) field points. What is
the main off-axis aberration • Try to minimize this aberration by making both the
primary and secondary hyperbolic.
February 15, 2016
Optical Systems Design
Optimisation
Lecture 3
41
Objectives: Lecture 3
At the end of this lecture you should:
1. Understand the use of Petzval curvature to
balance lens components
2. Know how different aberrations depend on
field angle or pupil zone
3. Understand the basics of the Zemax merit
function and the Zemax operands
4. Be able to progressively optimise a
complex lens system to achieve the final
performance requirements
March 10, 2015
Optical Systems Design
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Petzval Surface & Petzval
Curvature
• Theoretical best image surface which
exhibits no astigmatism
φ
• Petzval sum P = −∑ n n where φ = n2 − n1 is the
1 2
r
optical power of each surface
φ
• For simple lenses P = −∑ n where φ is the
power of each lens (reciprocal of focal
length) and n is the refractive index
• Minimizing Petzval curvature produces a
flat, anastigmatic image plane
March 10, 2015
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Aberration Dependance on
Aperture and Field
Aperture Exponent
Field Exponent
Longitudinal colour
1
0
Lateral colour
0
1
Spherical aberration
3
0
Coma
2
1
Astigmatism
1
2
Field curvature
1
2
Distortion
0
3
• Stopping down a lens can make a big difference on spherical aberration
• Stopping down a lens wont improve the distortion
• For wide-angle lenses, astigmatism is harder to control than coma
• Symmetrical systems (about stop) minimise lateral colour, coma & distortion
March 10, 2015
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Optimisation Process
• Enter a starting lens configuration
• Allow Zemax to change lens
parameters to improve performance
• Requires a measure of performance –
merit function (error function)
• Optimisation tries to minimise merit
function (gradient search or Hammer)
March 10, 2015
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Constituents of Merit Function
Measures of:
1. How well first-order properties are
satisfied (e.g. paraxial focus, locations of
pupils and images)
2. How well special constraints are satisfied
(e.g. element centre or edge thickness,
curvatures, glass properties)
3. How well aberrations are controlled (e.g.
image sharpness and distortion)
March 10, 2015
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Image Sharpness metrics
1. Spot size measured by ray-intercept
errors in image plane
2. Wavefront imperfections measured
by optical path difference (OPD)
errors in the exit pupil
3. Modulation transfer function (MTF) in
the image plane
(Start with [1], moving to [2] or [3] only in final
optimisation stages)
March 10, 2015
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Optimization Operands
• Individual components of the merit function
which are assigned a target value and
weights
• Number of operands often greatly exceeds
the number of independent lens variables
• Apply iterative least squares optimisation to
minimise the (weighted) deviations between
operands and their target values
March 10, 2015
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Zemax Operands
March 10, 2015
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Zemax Operands
• Zemax has over 300 user-selectable operands (see
OpticStudio manual, p. 259)
• Mostly used to supplement a default merit function
(now called Sequential Merit Function)
• Weights = 0 ignored, weights < 0 treated as a
Lagrangian multiplier (∞ weight)
• OptimizationWizard adds the default merit
function
• Can also have user-defined operands (ZPL)
Spherical
Coma
SPHA,
REAY
COMA, ASTI,
TRAY
TRAX,TRAY
March 10, 2015
Astigmatism Field
Curvature
FCUR
Distortion
Long.
Colour
Lateral
Colour
DIMX,
DIST
AXCL
LACL
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Optimisation Techniques
• Choose starting design carefully (e.g.
scale from existing lens catalogue)
• Develop optimisation approach that is
systematic & rationale
• Sheperd design in direction intended
• Do continuous sanity checks
• Discard poor solutions as they arise
March 10, 2015
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Optimisation Wizard
March 10, 2015
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Early Optimisations
• Reduce number of independent
variables
• Freeze glass types and use pickup solves
to symmetrise configurations
• Replace large RoC surfaces with planes
• Include first order (paraxial) properties
and boundary conditions (e.g. back focal
length) in merit function
March 10, 2015
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Intermediate Optimisations
• Start to control on-axis and off-axis
aberrations
• Chromatic aberrations using only two
extreme wavelengths
• Monochromatic aberrations using single
central wavelength
• Typically: longitudinal & lateral colour,
spherical & distortion
• Keep image plane at paraxial focus
March 10, 2015
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Final Optimisations
• Shrink polychromatic spots for all field angles
• Use several wavelengths across the band
• Re-optimise using wavefront OPDs in exit
pupil rather than transverse ray errors (spots)
on image surface
• Allow small amount of paraxial defocussing
• Include any deliberate mechanical
vignetting
• Take a critical look at the final lens & its
performance
March 10, 2015
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Potential Problem Areas
• Avoid systems which attempt to balance lenses
with large amounts of positive and negative
power
• Avoid highly curved surfaces and grazing rays
• Look out for designs which have individual
elements which stand out as either very strong
(split) or very weak (eliminate)
• Watch for variables that are only weakly effective
• Avoid aspherics unless really necessary
• Avoid glasses with undesirable properties (e.g. low
transmission, softness)
March 10, 2015
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Example: Cooke Triplet (1983)
• One of 1st fast, wide-field photographic lenses.
• Consists of two positive singlets and one negative
singlet (all thin lenses)
• Negative element located about halfway
between positive elements to maintain a large
amount of symmetry
• 8 major variables (6 radii, 2 spacings).
10/03/2015
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Early Optimisation
10/03/2015
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Intermediate Optimisation
10/03/2015
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Final Optimisation
10/03/2015
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Balancing Aberrations
Analyse –> Aberrations –> Seidel Diagram
10/03/2015
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Summary: Lecture 3
• Minimising the Petzval sum can give a good
starting point for lens optimisation
• Proper use of the Zemax optimisation tools is the
key to successful lens design
• Optmisation using spot size (ray intercept errors) is
more stable than OPD errors and should normally
be used first
• Whilst the Zemax default merit function gives a
good starting point, in many cases it will need
supplementing with individual user-selected
operands to achieve the desired constraints
March 10, 2015
Optical Systems Design
22
Exercises: Lecture 3
• Repeat the analysis of a Cooke triplet to work at
F/3.5 which has a 52mm focal length, starting
from COOKE-LECT3-EARLY.ZMX on course www
page (Lecture 3).
• Assume wavelengths of 0.45,0.50,0.55,0.60 & 0.65
µm and field angles of 0o,9o,16o & 22o
• Place the aperture stop between the 2nd and 3rd
lenses and use LaFN21 & SF53 for the glass types
• Optimize the performance on the paraxial focal
plane, so that the lens still performs well when
stopped down
March 10, 2015
Optical Systems Design
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Tolerancing in Zemax
Lecture 4
Objectives: Lecture 4
At the end of this lecture you should:
1. Understand the reason for tolerancing and
its relation to typical manufacturing errors
2. Be able to perform a Sensitivity Analysis
and Inverse Sensitivity Analysis on a new
design
3. Be able to interpret the data from a Monte
Carlo tolerancing analysis of a new design
March 16, 2015
Optical Systems Design
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Motivation
• Having designed a lens, it is important to
know how it will perform once it is built.
• Tolerancing a lens is a very important skill to
have.
• Two approaches:
– Perturbing each element individually and
reoptimizing the system each time. Slow but
accurate. Determines the sensitivities of each
element.
– Find all the sensitivities at once by using Zemax’s
tolerancing function. This method is very fast, but
there is a lot of room for mistakes with complex
systems.
March 16, 2015
Optical Systems Design
3
Optical System Tolerancing
1. Define quantitative figures of merit for the
requirements
2. Estimate component manufacturing
tolerances
3. Define assembly/alignment procedure and
estimate mechanical alignment tolerances
4. Calculate sensitivities, estimate
performance
5. Adjust tolerances, keeping cost and
schedule in mind
March 16, 2015
Optical Systems Design
4
System Figure of Merit
• Keep this as simple as possible
• Must propagate all performance specs
through to assembly
• Typical requirements:
–
–
–
–
–
–
–
RMSWE (root mean square wavefront error)
MTF at particular spatial frequencies
Distortion
Fractional encircled energy
Beam divergence
Geometric RMS image size
Dimensional limits
March 16, 2015
Optical Systems Design
5
Dimensional Tolerances for
Machined Parts
• Depends on fabrication methods and
equipment
• Rules of thumb for machined parts:
– ± 1 mm for coarse dimensions that are not
important
– ± 0.25 mm for typical machining without
difficulty
– ± 0.025 mm precision machining, readily
accessible
– < ± 0.002 mm high-precision, requires special
tooling
March 16, 2015
Optical Systems Design
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Dimensional Tolerances for
Optical Elements
•
•
•
•
Diameter
Clear aperture
Thickness
Wedge Angles
– wedge or optical deviation for lenses
– angles for prisms
• Bevels
• Mounting surfaces
Start with nominal tolerances from lens fabricator
March 16, 2015
Optical Systems Design
7
Tolerancing Surface Shape
• Specifications are based on measurement:
– Inspection with test plate:
• Typical spec: 0.5 fringe
– Measurement with phase shift interferometer:
• Typical spec: 0.05 λ rms
• For most diffraction-limited systems, rms surface gives
a good figure of merit
• Special systems require a Power Spectral Density
(PSD) spec
• Aspheric systems really need a slope spec, but this is
uncommon. Typically, assume the surface
irregularities follow low order forms and simulate them
using Zernike polynomials
March 16, 2015
Optical Systems Design
8
Rules of Thumb for Optical
Assemblies
Base: Typical, no cost impact for reducing tolerances beyond this.
Precision: Requires special attention, but easily achievable in most
shops, may cost 25% more
High precision: Requires special equipment or personnel, may cost
100% more
March 16, 2015
Optical Systems Design
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Rules of Thumb for Lens
Tolerances
Base: Typical, no cost impact for reducing tolerances beyond this.
Precision: Requires special attention, may cost 25% more
High precision: Requires special equipment may cost 100% more
March 16, 2015
Optical Systems Design
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Rules of Thumb for Glass
Tolerances
Base: Typical, no cost impact for reducing tolerances beyond this.
Precision: Requires special attention, may cost 25% more
High precision: Requires special equipment, may cost 100% more
March 16, 2015
Optical Systems Design
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Zemax Tolerancing Capabilities
• Can set tolerances in the tolerance data editor for
a wide variety of parameters
– The default tolerance generator can
automatically enter tolerances for: radius of
curvature, surface form, lens thickness, position, x
and y tilt, x and y decentre, irregularity, wedge,
glass index, Abbe number, and more.
• Must define what compensators to use (e.g. focus,
tilt, position of any optical element) in sensitivity
analysis
• Can select the tolerance criteria (e.g. RMS
wavefront, RMS spot radius)
March 16, 2015
Optical Systems Design
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Zemax Tolerancing Tools
• ZEMAX conducts an analysis of the
tolerances using any or all of these
three tools:
– Sensitivity Analysis
– Inverse Sensitivity Analysis
– Monte Carlo Analysis
March 16, 2015
Optical Systems Design
13
I: Sensitivity Analysis
• The sensitivity analysis considers each
defined tolerance sequentially
(independent).
• Parameters are adjusted to the limits of
the tolerance range, and then the
optimum value of each compensator is
determined.
• A table is generated listing the
contribution of each tolerance to the
performance loss.
March 16, 2015
Optical Systems Design
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II: Inverse Sensitivity Analysis
• The inverse sensitivity analysis
iteratively computes the tolerance
limits on each parameter when the
maximum or incremental degradation
in performance is defined.
• Limits may be overall or specific to
each field or configuration.
March 16, 2015
Optical Systems Design
15
III: Monte Carlo
• Monte Carlo analysis is extremely powerful and useful
because all tolerances are considered at once.
• Random systems are generated using the defined
tolerances.
• Every parameter is randomly perturbed using
appropriate statistical models, all compensators are
adjusted, and then the entire system is evaluated
with all defects considered.
• User defined statistics based upon actual fabrication
data is supported.
• ZEMAX can quickly simulate the fabrication of large
numbers of lenses and reports statistics on simulated
manufacturing yields.
March 16, 2015
Optical Systems Design
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Zemax Example
•
•
•
•
Open the file DOUBLET-LECT4.ZMX
Go to the Tolerance tab
Remove all variables/solves
Open the Tolerance Wizard
• Adjust default tolerances as required
March 16, 2015
Optical Systems Design
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Tolerance Data Editor
• Here you adjust each of the tolerances
March 16, 2015
Optical Systems Design
18
Tolerance Mnemonics
• Tolerance
operands
tell ZEMAX
which
parameters
in the
system to
change.
• ZEMAX uses
four letter
mnemonics
for the basic
tolerances
March 16, 2015
Optical Systems Design
19
Zemax Tolerancing
•
•
•
•
•
•
•
Choose Tolerancing from the
menu bar
Select the mode: Sensitivity
(default)
Check Force Ray Aiming On
(slower but more accurate)
Select the Criteria: RMS Spot
Radius
Set the Compensator: Paraxial
focus (default)
Select Monte-Carlo to check
number of runs (20 OK)
Check Display -> Show
Compensators (to see how
much focus changes for
example).
March 16, 2015
Optical Systems Design
20
Tolerancing Results
Numbers needed to calculate the sensitivities:
Perturbations
Change in merit function
Focus compensation
Radius tolerance for surface 2
March 16, 2015
Optical Systems Design
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Tolerancing Results
Worst Offenders
Monte Carlo
March 16, 2015
Optical Systems Design
22
Summary: Lecture 4
• Tolerancing is a critical step to ensure that
a lens design can be manufactured and
to predict its expected performance
• Difficult because it involves complex
relationships across different disciplines
• Zemax has many very powerful design
tolerancing capabilities
• Important to understand how Zemax
does the sensitivity analysis before you
can blindly use it.
March 16, 2015
Optical Systems Design
23
Exercises: Lecture 4
• Perform tolerance analysis of the Cooke
triplet lens designed in the exercise for
Lecture 3
• Use precision mechanical dimensional
tolerances and λ/20 RMS surface form error
• What is the mean increase in RMS spot
radius from the Monte Carlo simulation ?
• Which are the three most critical
dimensional tolerances ?
March 16, 2015
Optical Systems Design
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Other Stuff
Lecture 5
Objectives: Lecture 5
At the end of this lecture you should:
1. Be aware of the Zemax capability to
approximate a lens design with catalogue
components
2. Be familiar with the use of co-ordinate breaks in
Zemax to model off-axis systems
3. Understand the use of non-sequential ray-tracing
to model scattered light
4. Appreciate the capabilities of Zemax to model
physical optics wave propagation
5. Be able to use Zemax to model the performance
of imaging systems using realistic images
March 17, 2015
Optical Systems Design
2
COTS Lens Substitution
•
•
•
•
•
•
•
Zemax can take a custom design and substitute real
lenses
As an example start from paraxial lens model (DOUBLETELECENTRIC-PARAXIAL-LECT5.ZMX)
Select Libraries -> Lens Catalogue
Use Vendor(s) drop-down menu to search standard
manufacturers catalogues
Search on lens type, EFL, pupil size
Select best match and Insert (delete paraxial surface)
(DOUBLE-TELECENTRIC-EDMUNDOPTICS-LECT5.ZMX)
May need to reverse some lens elements to improve
performance, since convex surface of doublets always
optimised for ∞ conjugate (there is a convenient icon
above the lens data streadsheet to do this)
17/03/2015
Optical Systems Design
3
Co-ordinate Breaks
• Non-axially symmetric systems where surfaces are
tilted or decentered require the use of co-ordinate
breaks
• Rotate/shift local co-ordinate frame
• Positive rotation (in ZEMAX) is clockwise as viewed
along +ve axis direction
• Subsequent co-ordinate breaks refer to the newly
defined axis orientations
• If a co-ordinate break is placed immediately before
an optical surface, it can be useful to put another
one with opposite sign immediately after, thus
undoing the tilt etc
• There are now simple tools in the Lens Data icon bar
to tilt/decentre surfaces and add fold mirrors
March 17, 2015
Optical Systems Design
4
Nasmyth Field Derotator
FIELDROTATOR-LECT5.ZMX
March 17, 2015
Optical Systems Design
5
Non-Sequential Systems
• No predefined sequence of surfaces
• Objects encountered determined solely by physical
positions of surfaces and directions of rays
• Co-ordinate system is global
• Can deal with Total Internal Reflection (TIR), stray
light and illumination systems
• Required for prisms, beamsplitters, light pipes,
faceted (array) objects etc
• In some cases need mixed sequential/nonsequential ray tracing
March 17, 2015
Optical Systems Design
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Non-Sequential Systems
Sequential
Non-Sequential
[PRISM-SEQ-LECT5.ZMX]
[PRISM-NONSEQ-LECT5.ZMX]
March 17, 2015
Optical Systems Design
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Non-Sequential Systems
PENTAPRISM-NONSEQ-LECT5.ZMX
Can convert from sequential design using Tools -> Miscellaneous -> Convert to
NSC Group (need to first move STOP to front surface)
March 17, 2015
Optical Systems Design
8
Physical Optics Propagation
• Geometrical ray tracing is an incomplete
description of light propagation
• POP uses diffraction calculations to propagate a
light modelled as a wavefront through an optical
system
• Wavefront is modeled by an array of complex
amplitudes which is user-definable in terms of its
dimension, sampling and aspect ratio
• Applications include fibre coupling, diffraction by
apertures and beam irradiance calculations
March 17, 2015
Optical Systems Design
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Gibbs Phenomenon
March 17, 2015
GIBBS-LECT5.ZMX
Optical Systems Design
10
Fibre Coupling
March 17, 2015
FIBRE-LECT5.ZMX
Optical Systems Design
11
Array Elements
•
•
•
March 17, 2015
Optical Systems Design
Rectangular array
of spherical lenses
Modelled as a userdefined surface
(DLL)
LENSLET-LECT5.ZMX
12
Image Simulation
• For an optical designer the lens
performance is specified in terms of spot
diagrams, ray-fan plots, vignetting, field
curvature, astigmatism etc
• In some cases its much more effective to
demonstrate what images will look like when
viewed through the lens
• Zemax now has a nice feature called Image
Simulation to demonstrate this on an input
image
March 17, 2015
Optical Systems Design
13
Image Simulation
• Object scene is represented by a source bitmap
(.BMP or .JPG)
• Rays traced using the defined object through
the lens to the image plane
• At detection surface place a pixellated detector
which receives the rays and builds up an image
of the source bitmap as seen through the lens
March 17, 2015
Optical Systems Design
14
Design for Fabrication
• Primary considerations: optical
material, component size, shape, and
manufacturing tolerances
• Minimize cost and delivery time by
using COTS items whenever possible
• Minimize risk through prototyping and
pre-production models
March 17, 2015
Optical Systems Design
15
Optical Materials
•
•
•
•
•
•
•
Over 100 optical glasses available worldwide
Each manufacturer has a list of “preferred” glasses that are
most frequently melted and usually available from stock
Generally can substitute similar glasses from different
manufacturers (and re-optimise)
Material quality defined by tolerances on spectral transmission,
index of refraction, dispersion, striae grades (AA/A/B),
homogeneity (H1-H4), and birefringence (NSK/NSSK)
Tighter than standard optical tolerances require additional
cost and time
May be more economical to add a lens to the design in order
to avoid expensive glasses
Some glasses (e.g. SF-59) made much less frequently than
others (e.g. BK-7)
March 17, 2015
Optical Systems Design
16
Fabrication
• Mechanical properties: hardness &
abrasion resistance (manufacture)
• Chemical properties: resistance to
humidity, acids, alkalis
• Thermal properties: expansion
coefficients from 4 -16 x 10-6/°K.
March 17, 2015
Optical Systems Design
17
Some Other Zemax Examples
ZMX/SES files on course website:
• Cassegrain Telescope (WHT)
• Ritchey Chretien Telescope (AAT)
• Off-axis parabola
• Melles Griot ball lens
• Shack-Hartmann wavefront sensor
• Palomar triple spectrographs
March 17, 2015
Optical Systems Design
18
Summary: Lecture 5
• Co-ordinate breaks allow Zemax to model
arbitrarily complex off-axis systems in a local coordinate system
• Need care in use to avoid over-complication
• Non-sequential mode allows complex objects to
be defined using a global co-ordinate system
• Can also be used to model scattered light and
illumination systems
• Physical optics propagation in Zemax includes the
effects of diffraction
• Fabrication issues need to be thought about early
in the instrument design phase
March 17, 2015
Optical Systems Design
19
Exercises: Lecture 5
• Work your way through some
of the example Zemax files,
evaluating their performance
and making sure that you
understand the prescription
data.
March 17, 2015
Optical Systems Design
20
Homework Problem
• Design a very simple telephoto lens with the following
first-order properties:
,%&$
,)$
",%$
,($
,$!&!'!
,$)+*μ
• Design goal: maintain all first-order properties and
achieve rms spot sizes ≤ 20 μm. Start from two paraxial
lenses with focal lengths 75mm and -75mm.
• Final solutions should include a layout diagram, spot
diagram and system prescription data (also email the
Zemax file).
• Hand in the solutions to my pigeon hole by Friday 17th
April.
17/03/2015
Optical Systems Design
21