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Monte Carlo Simulation and Analysis in Modern Optical Tolerancing
Author(s): Ronian Siew
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Book Description

This Spotlight offers a perspective on the role of Monte Carlo simulation in the analysis and tolerancing of optical systems. The book concisely explores two overarching questions: (1) What principles can we adopt from a variety of statistical methods - such as the analysis of variance (ANOVA), "root sum of squares" (RSS), and Monte Carlo simulation - to analyze variability in complex optical systems? (2) When we assign perturbations to component variables (such as tilts and radii of curvatures) subject to arbitrary probability distributions, are the resulting distributions of system parameters (such as EFL, RMS spot size, and MTF) necessarily normal?

These questions address the problem of analyzing and managing variability in modern product development, where many functions integrate to produce a complete instrument. By discussing key concepts from optics, multivariable calculus, and statistics, and applying them to two practical examples in modern technology, this book highlights the role Monte Carlo simulations play in the tolerancing of optical systems that comprise many components of variation.

Book Details

Date Published: 15 October 2019
Pages: 54
ISBN: 9781510631656
Volume: SL53

1 Introduction
1.1 What is "modern" about modern optical tolerancing?
1.2 What is a Monte Carlo simulation?
1.3 Significance of functions of random variables

2 Prelude to Monte Carlo
2.1 Systematic versus random variability
2.2 Standard deviation as error, uncertainty, and variability
2.3 Error of the mean (why averaging reduces variability)
2.4 Error of the error (why variability also varies)
2.5 Sample variance: why we divide by "n - 1"
2.6 Concept of variance components and sensitivity analysis

3 Monte Carlo Approach
3.1 Influence of compensators on variability: correlations and covariances
3.2 Sensitivity analysis by way of statistical tests of effects on distributions
3.3 Do normal component distributions yield normal system distributions?
3.4 When is the central limit theorem applicable?
3.5 Example: miniature multifunctional relay lens system with liquid element
3.6 Example: geometric optical fiber coupling efficiency
3.7 Role of Monte Carlo simulation in Six Sigma, quality, and reliability
3.8 Random numbers and the subtle art in the science of modern optical tolerancing

References

## Preface

This Spotlight offers my perspective on the role of the Monte Carlo simulation in the analysis and tolerancing of optical systems. In this concise Spotlight, I explore two overarching questions: (1) What principles can we adopt from a variety of statistical methods - such as the analysis of variance, "root sum of squares," and Monte Carlo simulation - to analyze variability in complex optical systems? (2) When we assign perturbations to component variables (such as tilts and radii of curvatures) subject to arbitrary probability distributions, are the resulting distributions of system parameters (such as effective focal length, root mean square spot size, and modulation transfer function) necessarily normal? The questions above address the problem of analyzing and managing variability in modern product development, where many functions integrate to produce a complete instrument. By discussing key concepts from optics, multivariable calculus, and statistics, and applying them to two practical examples in modern technology, this Spotlight highlights the role Monte Carlo simulations play in the tolerancing of optical systems that comprise many components of variation.

I am grateful to the editors of the SPIE Spotlight series, and in particular, Craig Olson and Scott McNeill, for their encouragement and patience in receiving my manuscript. Without their support, this Spotlight would not have been possible. I thank two anonymous referees for their valuable comments. I thank Richard N. Youngworth (Riyo, LLC) for his early critique of my ideas. I thank Sanjay Gangadhara (Zemax, LLC), Vladimir Smagley (Zemax, LLC), and Michael Humphreys (Zemax, LLC) for helpful correspondence regarding tolerancing using OpticStudio. Finally, I thank my wife, Claire, for her support and patience while I sit and write, yet again.

Ronian Siew
September 2019