# Tolerancing in Zemax - PowerPoint

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```					Tolerancing in Zemax

OPTI 521 Tutorial
By Stacie Hvisc
December 5, 2006
Outline
• Motivation
• Zemax tolerancing capabilities
– Sensitivity Analysis
– Inverse Sensitivity Analysis
– Monte Carlo
• Zemax Demo
• Conclusion
Motivation
• Once you design a lens, you will want to know how it will
perform once it is built.
• Tolerancing a lens is a very important skill to have.
– We can do this by perturbing each element individually and
reoptimizing the system, which is very slow, but accurate.
• On homework 4, we perturbed each element at a time to find the
sensitivities
– We can 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.
– On the homework, some people hit the sensitivity analysis button and
got numbers that were incorrect – up to two orders of magnitude off!
Zemax tolerancing capabilities
• You can set tolerances in the tolerance data editor for a
wide variety of parameters
– There is a default tolerance generator which can automatically
enter tolerances for: Radius of curvature, fringes, thickness,
position, x and y tilt, x and y decenter, irregularity, wedge, glass
index, Abbe number, and more.
– Other things you can tolerance include: aspheric constants,
decenters/tilts, solve and parameter tolerances, etc
• You can define what compensators you wish to use,
such as focus, tilt, or position of any optical element,
surface, or element group.
– Remember on the homework, we used the final focus position
• You can select the tolerance criteria
– For example, on the homework, we used RMS wavefront
Zemax tolerancing capabilities
• ZEMAX conducts an analysis of the
tolerances using any or all of these three
tools:
– Sensitivity Analysis
– Inverse Sensitivity Analysis
– Monte Carlo Analysis
Sensitivity Analysis
• The sensitivity analysis considers each
defined tolerance independently.
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.
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.
Monte Carlo
• The 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 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 a huge number of lenses and
reports statistics on simulated manufacturing yields.
Zemax Demo
• How to do Homework 4 in Zemax:

• 1st step: open the HW4.zmx file
Zemax demo
 In the Zemax window, go to “Editors” drop
down menu and choose “Tolerance data”
and the Tolerance Data Editor will open.
Zemax demo
 On the Tolerance Data Editor window, go
to the “Tools” drop down menu and select
“Default Tolerances…”
Zemax demo
• …and the following Default Tolerances
window will open.
Zemax demo
 Adjust the perturbations to match what I
used on the homework and click “OK”.
Zemax demo
• …and the following table appears
Zemax demo
• This table is the Tolerance Data Editor
mentioned earlier.
– Here you adjust each of the tolerances.
– Columns:
• 1) Operand number
• 2) 4 letter mnemonic for the tolerance
– see next slide for a list
•   3) Surface number for tolerance
•   4 and 5) Skip for now
•   6) Nominal value (helps me identify surfaces)
•   7 and 8) Minimum and Maximum perturbations
Tolerance mnemonics in Zemax
• Tolerance
operands tell
ZEMAX
which
parameters
in the system
to change.
• ZEMAX uses
4 letter
mnemonics
for the basic
tolerances:
Zemax demo
• After using the generate default tolerances
window, you need to check to make sure all the
numbers are correct.
– For example, the lens spacing between lens 1 and
lens 2, I had a perturbation of 0.2mm on the
homework, but all thicknesses were set to be 0.1mm
perturbations.
– Zemax adds an additional compensator for
thicknesses (in column 4). If you don’t want this,
delete it – possible room for mistakes here!
Zemax demo
 Next go to the “Tools” drop down window
and choose “Tolerancing” and then
“Tolerancing…”
Zemax demo
• Then the following
Tolerancing window opens
up.
– Choose your mode:
(Sensitivity, Inverse
Sensitivity, Inverse
Increment, Skip
Sensitivity). We want
Sensitivity right now, which
is the default already
chosen.
– Choose the Criteria: (RMS
Wavefront, Merit Function,
Boresight Error, MTF and
more). We need to select
RMS Wavefront.
Zemax demo
– Tolerancing window
cont.
• Choose the
Compensator: (Paraxial
focus, Optimize All,
None). We want the
paraxial focus to be the
compensator, which is
• Check “Force Ray
Aiming On” (makes
more accurate, but
slower)
• You can also check
“Show Compensators”
(for example to see
how much focus
changes for example).
Zemax - results
•   Here are the results:
•   Analysis of Tolerances
•   File : C:\Documents and Settings\shvisc\Desktop\HW4.zmx
•
•
Title: Focusing doublet
Date : TUE DEC 5 2006
Numbers needed to calculate the sensitivities:
•   Units are Millimeters.
•   Paraxial Focus compensation only.
•   WARNING: Boundary constraints on compensators will be ignored.                            Perturbations                          Change in merit function
•   Criteria        : RMS Wavefront Error in waves
•   Mode              : Sensitivities
•   Sampling            : 20
•   Nominal Criteria : 0.00065152
•   Test Wavelength : 0.6328
•   Fields: Y Symmetric Angle in degrees
•   #      X-Field      Y-Field     Weight VDX VDY VCX VCY
•   1 0.000E+000 0.000E+000 1.000E+000 0.000 0.000 0.000 0.000
•   Sensitivity Analysis:
•                                        |----------------- Minimum ----------------| |----------------- Maximum ----------------|
•   Type                   Value           Criteria         Change                         Value Criteria           Change
•   TRAD 2             -0.100000000 0.001543200 0.000891675 0.100000000 0.001773699 0.001122174
•   TRAD 3             -0.100000000 0.000721251 6.9726E-005 0.100000000 0.000642781 -8.7431E-006
•   TRAD 4             -0.100000000 0.002301125 0.001649600 0.100000000 0.002559580 0.001908056
•   TRAD 5             -0.100000000 0.000888400 0.000236876 0.100000000 0.000731590 8.0066E-005
•   TTHI 2 0          -0.100000000 0.001036787 0.000385263 0.100000000 0.000845486 0.000193961
•   TTHI 3 0          -0.200000000 0.004974029 0.004322505 0.200000000 0.004698490 0.004046966
•   TTHI 4 0          -0.100000000 0.000693073 4.1548E-005 0.100000000 0.000828411 0.000176886
•   TEDX 2 3            -0.100000000 0.009626142 0.008974618 0.100000000 0.009626142 0.008974618
•   TETX 2 3           -0.100000000 0.005722684 0.005071160 0.100000000 0.005722684 0.005071160
•   TEDX 4 5            -0.100000000 0.009681031 0.009029507 0.100000000 0.009681031 0.009029507
•   TETX 4 5           -0.100000000 0.011549130 0.010897605 0.100000000 0.011549130 0.010897605
•   TIRX 2           -0.100000000 0.017751740 0.017100215 0.100000000 0.017751740 0.017100215
•   TIRX 3           -0.100000000 0.031032656 0.030381132 0.100000000 0.031032656 0.030381132
•   TIRX 4           -0.100000000 0.063785240 0.063133716 0.100000000 0.063785240 0.063133716
•   TIRX 5           -0.100000000 0.034639912 0.033988387 0.100000000 0.034639912 0.033988387
•   TIND 2           -0.000500000 0.000890818 0.000239294 0.000500000 0.000735714 8.4190E-005
•   TIND 4           -0.000500000 0.000814628 0.000163103 0.000500000 0.000998033 0.000346509
Zemax - results cont.
•   Worst offenders:
•   Type                     Value     Criteria Change
•   TIRX 4            -0.100000000 0.063785240 0.063133716
•
•
TIRX 4
TIRX 5
0.100000000 0.063785240 0.063133716
-0.100000000 0.034639912 0.033988387
Worst Offenders
•   TIRX 5              0.100000000 0.034639912 0.033988387
•   TIRX 3            -0.100000000 0.031032656 0.030381132
•   TIRX 3              0.100000000 0.031032656 0.030381132
•   TIRX 2            -0.100000000 0.017751740 0.017100215
•   TIRX 2              0.100000000 0.017751740 0.017100215
•   TETX 4 5             -0.100000000 0.011549130 0.010897605
•   TETX 4 5              0.100000000 0.011549130 0.010897605
•   Estimated Performance Changes based upon Root-Sum-Square method:
•   Nominal RMS Wavefront : 0.000651524
•   Estimated change              : 0.081762126
•   Estimated RMS Wavefront : 0.082413650
•   Compensator Statistics:
•   Change in back focus:
•   Minimum              :      -0.327629
•   Maximum                :     0.327965
•   Mean              :        0.000030
•   Standard Deviation :            0.105018
•   Monte Carlo Analysis:
•
•
Number of trials: 20
Initial Statistics: Normal Distribution                            Monte Carlo
•    Trial      Criteria         Change
•        1 0.045548742 0.044897218
•        2 0.013286277 0.012634752
•        3 0.036228419 0.035576894
•        4 0.009442727 0.008791203
•        5 0.014894832 0.014243307
•        6 0.020252474 0.019600949
•        7 0.047652045 0.047000521
•        8 0.013279680 0.012628156
•        9 0.009529791 0.008878266
•       10 0.088488208 0.087836684
•       11 0.019946472 0.019294947
•       12 0.014766018 0.014114493
•       13 0.008394405 0.007742881
•       14 0.069265579 0.068614055
•       15 0.005727527 0.005076003
•       16 0.026195678 0.025544154
•       17 0.009141888 0.008490364
Zemax - results
 From these numbers, we can calculate the
sensitivities by dividing the change in the
criteria (RMS wavefront) by the
perturbation.

      xi  xi    2
 0
2


xi            xi
Zemax - results
• Paste the results
into Excel and
calculate the
sensitivities
– (A possible place
for error: mixing up
degrees and mm
for the tilt terms.)
Zemax - results
• So, how did we do?
• Not too good, but not too bad either,
nothing is more than an order of
magnitude off.
– Possible differences due to using a
slightly different RMS wavefront error
as the criteria:
• I used on the homework: “RMS (to
centroid) from integration of the rays”
• Zemax used RWCE: “RMS (to
centroid) from integration of the fixed
coefficients”
• The one with the -734% difference is
due to the insensitivity of that
perturbation
• Zemax also calculates the change in
criteria differently (doesn’t do a root
sum square) – see next slide
Zemax - results
   0  1   2   ...
2         2        2
Conclusions
• Zemax is very powerful and has many
tolerancing design capabilities.
• You must understand how Zemax does
the sensitivity analysis before you can
blindly use it.
References
•   http://zemax.com/appnotes/tolerancing_example/index.html
•   http://www.optima-research.com/Software/Optical/Zemax/tolerancing.htm
•   Zemax Users Manual

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