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Spie Press Book

Optimization in Lens Design
Author(s): Akira Yabe
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Book Description

Interested in developing a lens design system that can produce the best solutions without special considerations or a lot of trial and error? This Spotlight explains the process of lens design optimization with a collection of previously published techniques and new methods inspired by practical design tasks. It also includes guidelines for designers who want to develop their own design code.

Book Details

Date Published: 26 April 2018
Pages: 53
ISBN: 9781510619838
Volume: SL36

Table of Contents
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1 Overview
1.1 Design requirements and independent variables
1.2 Problem of sensitivity and tolerances

2 Lens Design Optimization Principles
2.1 Merit function
2.2 Problem of nonlinear optimization
2.3 Metric in the parameter space
2.4 Control of boundary conditions
2.5 Local and global optimization
2.6 Damped least-squares method for local optimization
2.7 Effective use of the escape function for global optimization

3 Special Independent Variables
3.1 Fictitious glass model
3.2 Asphere model
3.3 Freeform model
3.4 Traveling asphere and traveling freeform model

4 Evaluation and Optimization
4.1 Ray aiming
4.2 Aberration control
4.3 Efficient method of MTF optimization
4.4 Sensitivity control
4.5 Control of the Monte Carlo simulation result

5 Design Process
5.1 Outline of the initial design of zoom lenses
5.2 Design example

6 Cost-Based Optimization of Tolerances
6.1 Concept
6.2 Minimization of tolerance cost
6.3 Tolerance optimization

7 Future Development
7.1 Treatment of patents
7.2 Application of deep learning
7.3 Common framework of program development


I started working in lens design in 1980, the same year that the International Lens Design Conference was held in Oakland, California. The session titles included:

  • Lens design using large computers,
  • Lens design using small computers,
  • Lens design using microcomputers,
  • Optimization techniques,
  • Optimization and aberration theory,
  • Aberration theory and computational techniques, and so on.

The optimization techniques had been already established, and the race among various commercial software companies had just started.

Over the past four decades, the improvement of the calculation speed and the decrease in cost of computers have been remarkable. Calculation speed changed from megaflops to gigaflops. The price of computers changed from a million dollars to a thousand dollars. Under these circumstances, the most important viewpoint of the programmer was to make the best use of the improved calculation speed and reduced cost. The purpose of a lens design program is to produce the best design within the shortest time. My early work assumed that the intervention of the lens designer needs to be reduced as much as possible to make the best use of the improved calculation speed. Before optimization, lens designers needed to determine the pattern of the positive and negative elements. To improve the performance, they repeated the small adjustment of targets and tried many different starting points for the optimization. Many tasks, such as the choice of glasses, the choice of surfaces to be aspherized, the reduction of the tolerance sensitivity, and the control of manufacturing feasibility, needed to be determined and controlled. The problems of the choice of glasses and the choice of aspheric surfaces are discrete and combinatorial, and they seemed to be difficult to treat in the ordinary optimization scheme. My design program was developed to control such complicated tasks.

The development of global optimization in the 1990s created a drastic change. Global optimization found a lot of patterns of positive and negative elements automatically. Many functions, intended to reduce the intervention of the lens designer, were used to produce useful solutions.

When I explained global optimization, a specialist of metrology asked me, "If commercial software gives different solutions to the same problem, is it defective?" I did not immediately understand his question, but the result of the optimization strongly depends on the character of the software, contrary to software for analysis or simulation. On the other hand, every time the level of control is raised, a question comes to mind: "Are lens designers losing their roles?"

I wonder how many designers in the world are using their own personal design codes. The implementation of raytracing and optimization algorithms is not very difficult. It would be exciting if lens designers could use their own code and be fully responsible for the design result without relying on black-box commercial software. This Spotlight consists of the concepts that other researchers established and I accepted, original design methods that I have published, and previously unpublished concepts. I intend to offer guidelines to novice lens designers who wish to develop their own design code.

Akira Yabe
March 2018

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