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 2
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 6
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 9
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 10
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 11
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 12
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 14
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 16
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 17
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 21
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 24