Tolerancing in CODE V

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Kerry Hoover
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1 Tolerancing in CODE V 3280 East Foothill Boulevard Pasadena, California USA (626) Fax (626) service@opticalres.com World Wide Web:

2 About This Presentation This presentation consists of: A PowerPoint show to introduce and describe CODE V s tolerancing features A few demonstrations to show how the features work in CODE V Tolerancing in CODE V, Slide-2

3 What is Tolerancing? Tolerancing is complex interactive process required for any system that will be fabricated, steps include: Definition of fabrication and assembly tolerance budget Definition of fabrication and alignment compensators, and an alignment plan Success requires the ability to accurately predict individual tolerance sensitivities & the as-built performance of the entire system, including the effects of compensation Tolerancing in CODE V, Slide-3

4 What Does Tolerancing Tells Us? Which lens parameters are the most sensitive to manufacture or align Which compensator or compensators are effective for assembly or alignment What is the probability of achieving a given performance level for the fabricated system Cumulative Probability (%) Cooke Triplet f/4.5 Tolerance Analysis ORA Jun-02 Field 1 Field 2 Field 3 80% probability of achieving ~0.88 MTF for Field 1 -or- 80% of built systems will have about 0.88 MTF or better at Field Modulation Transfer Function Typical Cumulative Probability Curve Tolerancing in CODE V, Slide-4

5 Why is Tolerancing Important? Cost reduction! When attacked with the right tools, tolerancing can significantly reduce: Non-recurring costs including designer time, production tool development, and definition of assembly/alignment procedures Recurring costs including system fabrication, assembly, and alignment The design that meets spec with the loosest tolerances and the best compensator set will minimize manufacturing and assembly costs! Tolerancing in CODE V, Slide-5

$tolerancing option, TOR, supports the following performance metrics Diffraction MTF RMS wavefront error Fiber Coupling Efficiency Polarization Dependent Loss Zernike Wavefront Coefficients (command$

6 CODE V s Tolerancing Options Analysis > Tolerancing menu allows you to choose among CODE V s various methods for computing the performance impact of manufacturing and assembly errors CODE V s primary tolerancing option, TOR, supports the following performance metrics Diffraction MTF RMS wavefront error Fiber Coupling Efficiency Polarization Dependent Loss Zernike Wavefront Coefficients (command line only) Tolerancing in CODE V, Slide-6

7 How TOR works TOR uses a fast wavefront differential algorithm to determine the performance impact due to tolerances Required information computed from a real ray trace of the nominal system Includes cross-terms, the impact of interacting tolerances TOR can be 50x to 1000x faster than alternative tolerancing methods This allows TOR to be use early and frequently during the design process Tolerancing in CODE V, Slide-7

8 TOR Modes of Operation Inverse mode - computes the tolerance values so each tolerance has approximately the same impact on performance (default mode) However, tolerances will never violate userdefined minimum & maximum limits Individual tolerance values can be frozen to not change during an Inverse mode analysis if desired Sensitivity mode - computes the effects of specified tolerances on performance CODE V will not try to change the tolerance values Tolerancing in CODE V, Slide-8

9 2-Parameter TOR Demonstration Tolerancing in CODE V, Slide-9

10 What Does This Example Show Us? TOR is easy to use For real systems, compensation is crucial Realistic tolerance limits can be imposed TOR s inverse sensitivity analysis will help reduce system sensitivity by attempting to set each tolerance to contribute equally to the performance degradation of the system Tolerancing in CODE V, Slide-10

11 Assumptions of the Wavefront Differential method Only applicable to a subset of performance metrics that can be adequately described by an exit pupil function Fundamental assumption is that optical path differences induced by tolerance perturbations for each ray in the ray grid vary linearly with tolerance change Valid when tolerance change results in a small degradation of the nominal performance (typically true for tolerances) Wavefront differential equations requires knowledge of how each tolerance affects the system This means that only CODE V pre-programmed tolerance types can be analyzed Tolerancing in CODE V, Slide-11

12 Entry of Tolerances Along with the Surface Properties window you can also use Review > Tolerances Enter specific tolerances using drop-down menu Tolerancing in CODE V, Slide-12

13 Default Tolerances Default tolerances can be generated for a surface or range of surfaces via the Autofill button on the Tolerance Review Tolerancing in CODE V, Slide-13

14 CODE V Tolerance Types Tolerances on single surfaces Radius, thickness, index, etc. Tolerances on elements Wedge Tolerances on components (single elements or cemented elements) Decenter, tilt, etc. Tolerances on polarization properties Retardance, Faraday rotation, etc. CODE V tolerances are used by TOR and a large subset are used by other tolerancing features Tolerancing in CODE V, Slide-14

Single Surface Tolerances: Radius Changes in radius DLR (delta radius) DLC (delta curvature) DLS (delta sag at clear aperture) DLF (delta fringe - test plate fit) DLF S2 IRR (cylindrical irregularity

15 Single Surface Tolerances: Radius Changes in radius DLR (delta radius) DLC (delta curvature) DLS (delta sag at clear aperture) DLF (delta fringe - test plate fit) DLF S2 IRR (cylindrical irregularity in fringes) CYN (cylinder normal - oriented at 0 ) CYD (cylinder diagonal - oriented at 45 ) irregularity Underlined tolerances indicate Default tolerance types Photo of actual test plate fit Tolerancing in CODE V, Slide-15

16 Single Surface Tolerances: Sag Change in surface sag in waves at the fringe wavelength, defined by Standard or Fringe Zernike coefficients (can be applied to any surface type) ZRN Cm (Standard Zernike coefficient) ZFR Cm (Fringe Zernike coefficient) Tolerancing in CODE V, Slide-16

17 Single Surface Tolerances: Index, Thickness Changes in refractive index DLN (delta index) DLV (delta V value) Only used if there are three wavelengths or more HOM (homogeneity) AXG (axial index gradient) RAG (radial quadratic index gradient) DLT (change in thickness) DLT S1 Tolerancing in CODE V, Slide-17

18 Single Surface Tolerances: Shape Change in aspheric coefficients (can be applied to any surface type) DAK (delta conic constant) DAA (delta A - 4th order coefficient) DAB (delta B - 6th order coefficient) DAC (delta C - 8th order coefficient) DAD (delta D -10th order coefficient) DAE (delta E - 12th order coefficient) DAF (delta F - 14th order coefficient) DAG (delta G - 16th order coefficient) DAH (delta H - 18th order coefficient) DAJ (delta J - 20th order coefficient) Cosine ripple and random surface error RPA, RPS (cosine ripple amplitude and slope) RSE (random surface error) Tolerancing in CODE V, Slide-18

19 Single Surface Decenter and Displacement Tolerances Decentration tolerances DEC (decenter) DLX (delta shift in X) DLY (delta shift in Y) DLZ (delta shift in Z) Tilt tolerances TIL (tilt) DLA (delta tilt in alpha in radians) DLB (delta tilt in beta in radians) DLG (delta tilt in gamma in radians) Wedge tolerances TIR (total indicated reading) TRX (TIR in X) TRY (TIR in Y) DLY S1 A DLA S1 TIR S1 = A - B B Tolerancing in CODE V, Slide-19

20 Group Decenter and Displacement Tolerances Group tilt BTI (barrel tilt in radians) BTX (barrel tilt in X in radians) BTY (barrel tilt in Y in radians) BRL (barrel roll about Z in radians) Group displacement DIS (displacement) DSX (displacement in X) DSY (displacement in Y) DSZ (displacement in Z) Group roll (cemented surfaces) ROL (roll) RLX (roll in X) RLY (roll in Y) R = reverse (roll about second surface) DSY S1..2 BTY S1..2 RLY S1..2 R Tolerancing in CODE V, Slide-20

21 Group Tolerances (cont.) DOL (delta overall length - change is divided among each surface) STI (shear tolerance - each surface is independently tilted) STX (shear in X) STY (shear in Y) STY S1..2 Tolerancing in CODE V, Slide-21

22 Polarization Tolerances BMA, BMB, BMG Tolerance on tilt about X, Y, and Z crystal axes, respectively, for birefringent material BMN Tolerance on ordinary and extraordinary refractive index difference for birefringent materials PPA Amplitude transmittance tolerance for a leaky linear polarizer PPF Rotation angle tolerance for Faraday rotator PPR Retardance tolerance for ideal retarder PPO Rotation angle tolerance for polarizing elements Tolerancing in CODE V, Slide-22

23 Typical Tolerancing Example Define tolerances and compensator(s) Or use the CODE V default values Determine the tolerance performance metric of interest Enter required information (e.g., MTF spatial frequency and azimuth values) Modify tolerance limits Or use CODE V default limits Run TOR in inverse sensitivity mode Review results, optionally modify tolerance and compensator set, adjust performance change value, etc. & re-run TOR Tolerancing in CODE V, Slide-23

24 Demonstration - Typical TOR Run Tolerancing in CODE V, Slide-24

25 Wavefront Differential Tolerancing Statistics MTF MTF probability distribution MTF = A ΔP 2 + B ΔP + C σ Probability Nominal MTF (C) 50% change Nominal MTF MTF Nominal parameter value ΔP Impact of single compensated tolerance on MTF at one field "Probable change" Integral of 50% of cases Integral of 84% of cases (1σ) Integral of 98% of cases (2σ) Integral of 99.7% of cases (3σ) MTF performance probability distribution due to all tolerances (and compensation) at one field Tolerancing in CODE V, Slide-25

immediately see the impact on performance and compensator motion Tolerances causing the largest

26 Interactive Tolerancing Interactive Tolerancing is a special spreadsheet interface that leverages the speed of TOR s wavefront differential algorithm Users can interactively change tolerance values and immediately see the impact on performance and compensator motion Tolerances causing the largest performance degradation are automatically put at the top of the list by default Tolerancing in CODE V, Slide-26

27 Interactive Tolerancing - Demonstration Tolerancing in CODE V, Slide-27

28 Other TOR Features Modeling your Optomechanical System accurately for TOR Coupled (Grouped) Tolerances Labeled Tolerances & Compensators Zoomed Tolerances & Compensators Tolerance X, Y, Z offsets TOR Compensation Solution using Singular Value Decomposition TOR Compensation for Magnification and Line-of- Sight Errors TOR Distortion Analysis Tolerancing in CODE V, Slide-28

Other Tolerancing Options Analysis > Tolerancing > Distortion Tolerancing for the performance metric of chief ray distortion (TOD) Also uses the

29 Other Tolerancing Options Analysis > Tolerancing > Distortion Tolerancing for the performance metric of chief ray distortion (TOD) Also uses the fast wavefront differential algorithm Used when distortion or image mapping is the primary performance metric of interest Tolerancing in CODE V, Slide-29

30 Distortion Tolerancing (TOD) Two modes: Listing of change in chief ray locations with tolerances Difference between chief ray positions for two zoom positions Useful for biocular (i.e., two-eye) systems analysis Single zoom chief ray positional changes in X and Y with tolerances Tolerancing in CODE V, Slide-30

31 Other Tolerancing Options (cont.) User - Finite Differences Macro for finite-difference tolerancing using userdefined performance measures with optional userdefined tolerances (TOLFDIF) Useful for determining tolerance drivers, but performance summary does not include cross-terms User - Monte Carlo Macro for Monte Carlo tolerance analysis to simulate production yield using user-defined performance measures with optional user-defined tolerances (TOLMONTE) Useful for predicting system performance but includes no information about performance drivers Tolerancing in CODE V, Slide-31

32 What is Finite Differences Tolerancing? Each parameter is individually varied at the plus & minus limits of its tolerance range, compensation is typically achieved using optimization, and the system performance degradation is predicted on a tolerance-bytolerance basis These individual results are statistically combined to yield a total system performance prediction Tolerancing in CODE V, Slide-32

33 Pros & Cons of Finite Differences Tolerancing +Predicted performance sensitivity for individual tolerances is usually accurate, especially for tolerances that cause a large decrease in performance +Allows determination of performance drivers - Does not include cross-terms (i.e., how multiple tolerances interact), so overall performance prediction is generally optimistic - Accuracy of tolerance sensitivity prediction can be poor for tolerances that cause small performance changes - System must be analyzed (e.g., ray traced) twice for each tolerance (Typical triplet requires 100 ray traces) Tolerancing in CODE V, Slide-33

34 What is Monte Carlo Tolerancing? Simultaneously vary all of the parameters that have an associated tolerance randomly within each tolerance range, with compensation typically achieved using optimization The resulting system performance is analyzed This process is repeated many times with different random perturbations and results are statistically combined to yield a total system performance prediction Each analysis is called a trial Tolerancing in CODE V, Slide-34

35 Pros & Cons of Monte Carlo Tolerancing +Includes cross-terms (the impact of interacting tolerances), so system performance prediction can be accurate - No information about individual tolerance sensitivities - Requires one analysis (e.g., ray trace) per trial - Accurate predictions generally require 100 to 1000 trials! Tolerancing in CODE V, Slide-35

36 User Tolerancing - Demonstration Tolerancing in CODE V, Slide-36

37 Review: Pros of TOR +Provides information about individual tolerance sensitivities Like Finite Differences tolerancing +Provides accurate performance prediction since cross-terms are included Like Monte Carlo tolerancing +Method requires only a single analysis (ray trace) of the nominal system Can be 50x to 1000x faster than Finite Differences or Monte Carlo The speed of the wavefront differential algorithm allows tolerancing to become part of the design process, not just an end-of-the-project analysis Tolerancing in CODE V, Slide-37

38 Summary Tolerancing is a critical step in the optical design of systems that will be built CODE V s wavefront differential tolerancing feature, TOR, is fast and accurate Allows tolerancing to be done early and often during the design process CODE V s finite difference and Monte Carlo based tolerancing are available for performance metrics not handled by TOR Tolerancing in CODE V, Slide-38

CODE V Tolerancing: A Key to Product Cost Reduction

CODE V Tolerancing: A Key to Product Cost Reduction A critical step in the design of an optical system destined to be manufactured is to define a fabrication and assembly tolerance budget and to accurately