Table of Contents

Preface

Introduction

1 The Basics

1.1 Ray Calculations

     1.1.1 Law of refraction: Snell's law

     1.1.2 Law of reflection

     1.1.3 The transfer equations

1.2 Lenses

1.3 Imaging

1.4 Types of Images

2 Rays and Ray Sketching

2.1 Collimation

2.2 Thin Lenses

2.3 Ray Sketching

     2.3.1 Finite object distance

     2.3.2 Object at infinity

2.4 Treating Virtual Images

2.5 Mirrors

2.6 Planar Optics

2.7 Multiple Elements

2.8 Beyond Two-Lens Systems

First Hiatus: Ledgers to Laptops

3 How to Put a Lens in a Computer

3.1 System Data

3.2 Prescription Data

3.3 Entering a Single Lens Using Commands

3.4 Entering a Single Lens Using the Lens Design Manager

3.5 Checking the Lens

     3.5.1 Reduction Ratio

3.6 Angle Solves

3.7 Entering Mirrors

4 To First Order…

4.1 Principal Surfaces and Planes

4.2 What Does This Get You

4.3 Cardinal Points

4.4 Immersed Systems

     4.4.1 Nodal points for immersed systems

     4.4.2 The human eye

     4.4.3 Mirrors as immersed systems

     4.4.4 A concluding remark

5 Stop and Pupils and Windows, Oh My!

5.1 Fields

5.2 Some Special Rays

     5.2.1 Meridional rays

     5.2.2 Sagittal rays

     5.2.3 Skew rays

     5.2.4 Axial rays

     5.2.5 Ray for objects at infinity

     5.2.6 Reference rays

5.3 The Aperture Stop and Marginal Rays

5.4 Chief Rays and Pupils of a Lens

5.5 The Field Stop and its Windows

5.6 Pupil and Field Specifications

     5.6.1 Field of view

     5.6.2 f-number and numerical aperture

5.7 A Final Comment

Second Hiatus: Rays and Waves

H2.1 Rayleigh Criterion

H2.2 The Pinhole Camera

6 Spherical Aberration

6.1 Propagating Real Rays

6.2 Third-Order Aberrations

6.3 On-Axis Ray Errors for a Singlet Lens

6.4 Displaying Spherical Aberration

6.5 Transverse Ray Plots

6.6 Seidel Aberrations

6.6 Lens Bending

7 Coma and Astigmatism

7.1 Coma

     7.1.1 Lens modules

     7.1.2 Coma and lens bending

7.2 Aplanatic Lenses

7.3 Astigmatism

8 Aberrations of the Image Surface

8.1 Field Curves

8.2 Petzval Curvature

8.3 Field Curvature and Third-Order Coefficients

8.4 An Astigmatic Lens

8.5 Distortion

9 Chromatic Aberration

9.1 Refraction and Dispersion

9.2 Longitudinal Chromatic Aberration

9.3 Correcting Longitudinal Chromatic Aberration

9.4 An Example

9.5 Secondary Color and Superchromatism

9.6 Lateral Color

10 Reducing Aberrations

10.1 Defocus

10.2 Reducing Spherical Aberration

10.3 Reducing Coma

     10.3.1 Stop shifting

     10.3.2 Flipping a lens

10.4 Reducing Distortion

10.5 Reducing Field Curvature

     10.5.1 Correcting astigmatism

     10.5.2 Correcting Petzval

11 Analyzing the Performance of a Lens

11.1 Sensors

11.2 Spot Diagrams

11.3 Point Spread Function

11.4 Image Simulation

11.5 Modulation Transfer Functions

12 Designing a Lens

12.1 Defining the Problem

12.2 Specifying the System

12.3 Step 0: The Initial Assessment

12.4 Step 1: Fix the Design

12.5 Step 2: Shift the Stop

12.6 Step 3 : Add a Lens

     12.6.1 Fictitious glasses

     12.6.2 Constructing a doublet

     12.6.3 Optimizing the doublet

12.7 Step 4: Add a Field Flattener

     12.7.1 Optimizing the design

     12.7.2 Add more points

12.8 Step 5: Return to Real Glasses

12.9 Step 6: Open Up the Lens

Third Hiatus: Building a Lens

H3.1 Fabricating a Lens

H3.2 Mounting a Lens

H3.3 Testing a Lens

13 Tolerancing

13.1 Assigning Tolerances

     13.2.1 Lens parameter errors

     13.2.2 Lens shape errors

     13.2.3 Lens assembly errors

13.2 An Initial TOR Example: OSDsecureCam2

13.3 Tolerancing the OSDsecureCam2

     13.3.1 Cumulative probability

     13.3.2 A tolerance run in sensitivity mode

     13.3.3 The cumulative probability plot

13.4 Adding a Compensator

13.5 Tightening Tolerances

13.6 The Lens Drawing

13.7 The Design Example: OSDsecureCam6

     13.7.1 TOR run with default tolerances

     13.7.2 Run using assigned tolerances

     13.7.3 Interactive tolerancing

13.8 Interactive Tolerancing

13.9 Some Final Comments

Preface

The purpose of this text is to show you how to design of an optical system, using the optical design program, CODE V^®. The design process from lens definition to the description and evaluation of lens errors and onto the improvement of lens performance will be developed and illustrated using the program. The text is organized so that a student will be able to (1) reproduce each step of the process including the plots for evaluating lens performance and to (2) understand their significance in producing a final design.

We chose CODE V because it is a well-regarded, full-featured optical design program that has a command line interface. This text is not a user's manual for CODE V. Synopsys has a set of books for that. Rather, the text starts with a single lens to demonstrate the laws of optics and illustrate the basic optical errors (aberrations) using CODE V. Then, through a series through the examples, demonstrations and exercises, you can follow each step in the design process using the CODE V commands to analyze and optimize the system to meet the specifications required for the lens to perform correctly. Once the design meets these specs, you can determine if your lens can be manufactured to a set of tolerances that permits a large fraction of them to be usable.

Although it is assumed that readers will follow the examples in the text and reproduce the results, you are encouraged to use them as jumping off points for an exploration of the designs. In addition to exercises with answers, we have added toward the end of the text, what we call, "Explorations": open-ended problems with several possible directions to explore the design space. But this exploration needn't be confined to the final chapters. If there is a design feature or strategy that piques your curiosity and you want to find out what happens when you make a change in the design, go ahead and explore the consequences. You can't break anything. However, remember to save your lens before you begin to tinker with things.

Because it is not possible to demonstrate important optical principles with every worthwhile program in a single text, we use CODE V. This text is written for a student to continually interact with the program. Although any commercial program can provide the tools to enter and modify designs, each program has its own interface and command syntax. For those who do not have immediate access to copies of CODE V, there are two possible ways to use this text. If you're connected with a college or university, there are arrangements for students to use CODE V for a modest fee for a limited time. For those who have access to other design programs, the operations and data entry may differ, but most of them will contain the same plotting, evaluation, and optimization functions as CODE V. So, with some translation, it should be possible to demonstrate the same operations as those used in the text. We hope that this text will engage your curiosity and provide directions that will encourage you to work through all of our examples. Designing optics is much like a game, where the rules are laid down by the laws of physics; where the pieces are surfaces, spaces, and glass; where aberrations are obstacles to be overcome; and where the goals are set by the practical requirements of a design. Have fun playing!

Donald C. O'Shea
Julie L. Bentley
June 2018