Tolerancing in Zemax

1
Tolerancing in Zemax

• OPTI 521 Tutorial
• By Stacie Hvisc
• December 5, 2006

2
Outline

• Motivation
• Zemax tolerancing capabilities
• Sensitivity Analysis
• Inverse Sensitivity Analysis
• Monte Carlo
• Zemax Demo
• Conclusion

3
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 Zemaxs 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!

4
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

5
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

6
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.

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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.

8
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.

9
Zemax Demo

• How to do Homework 4 in Zemax
• 1st step open the HW4.zmx file downloaded from
  the course website

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Zemax demo

• In the Zemax window, go to Editors drop down
  menu and choose Tolerance data and the
  Tolerance Data Editor will open.

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Zemax demo

• On the Tolerance Data Editor window, go to the
  Tools drop down menu and select Default
  Tolerances

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Zemax demo

• and the following Default Tolerances window will
  open.

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Zemax demo

• Adjust the perturbations to match what I used on
  the homework and click OK.

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Zemax demo

• and the following table appears

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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
• 9) Comments

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Tolerance mnemonics in Zemax

• Tolerance operands tell ZEMAX which parameters in
  the system to change.
• ZEMAX uses 4 letter mnemonics for the basic
  tolerances

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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 dont want
  this, delete it possible room for mistakes here!

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Zemax demo

• Next go to the Tools drop down window and
  choose Tolerancing and then Tolerancing

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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 Spot Radius, RMS
  Wavefront, Merit Function, Boresight Error, MTF
  and more). We need to select RMS Wavefront.

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Zemax demo

• Tolerancing window cont.
• Choose the Compensator (Paraxial focus, Optimize
  All, None). We want the paraxial focus to be the
  compensator, which is already the default.
• 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).

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Zemax - results

• Here are the results
• Analysis of Tolerances
• File C\Documents and Settings\shvisc\Desktop\HW
  4.zmx
• Title Focusing doublet
• Date TUE DEC 5 2006
• Units are Millimeters.
• Paraxial Focus compensation only.
• WARNING Boundary constraints on compensators
  will be ignored.
• 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 0.000E000 0.000E000 1.000E000 0.000
  0.000 0.000 0.000
• Sensitivity Analysis
• ----------------- Minimum
  ---------------- ----------------- Maximum
  ----------------
• Type Value Criteria
  Change Value Criteria
  Change

Numbers needed to calculate the sensitivities
Perturbations
Change in merit function
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Zemax - results cont.

• Worst offenders
• Type Value Criteria
  Change
• TIRX 4 -0.100000000 0.063785240
  0.063133716
• TIRX 4 0.100000000 0.063785240
  0.063133716
• TIRX 5 -0.100000000 0.034639912
  0.033988387
• 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

Worst Offenders
Monte Carlo
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Zemax - results

• From these numbers, we can calculate the
  sensitivities by dividing the change in the
  criteria (RMS wavefront) by the perturbation.

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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.)

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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 (doesnt do a root sum square) see
  next slide

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Zemax - results
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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.

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References

• http//zemax.com/appnotes/tolerancing_example/inde
  x.html
• http//www.optima-research.com/Software/Optical/Ze
  max/tolerancing.htm
• Zemax Users Manual