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Spie Press Book

Matrix Methods for Optical Layout
Author(s): Gerhard Kloos
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Book Description

This book is intended to familiarize the reader with the method of Gaussian matrices and some related tools of optical design. The matrix method provides a means to study an optical system in the paraxial approximation. This text contains new results such as theorems on the design of variable optics, on integrating rods, on the optical layout of prism devices, etc. The results are derived in a step-by-step way so that the reader might apply the methods presented here to resolve design problems with ease.

Book Details

Date Published: 21 August 2007
Pages: 138
ISBN: 9780819467805
Volume: TT77

Table of Contents
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Preface

Chapter 1 An Introduction to Tools and Concepts

1.1 Matrix Method
1.2 Basic Elements
1.2.1 Propagation in a homogeneous medium
1.2.2 Refraction at the boundary of two media
1.2.3 Reflection at a surface
1.3 Comparison of Matrix Representations Used in the Literature
1.4 Building up a Lens
1.5 Cardinal Elements
1.6 Using Matrices for Optical-Layout Purposes
1.7 Lens Doublet
1.8 Decomposition of Matrices and System Synthesis
1.9 Central Theorem of First-order Ray Tracing
1.10 Aperture Stop and Field Stop
1.11 Lagrange Invariant
1.11.1 Derivation using the matrix method
1.11.2 Application to optical design
1.12 Petzval Radius
1.13 Delano Diagram
1.14 Phase Space
1.15 An Alternative Paraxial Calculation Method
1.16 Gaussian Brackets

Chapter 2 Optical Components

2.1 Components Based on Reflection
2.1.1 Plane mirror
2.1.2 Retroreflector
2.1.3 Phase-conjugate mirror
2.1.4 Cat's-eye retroreflector
2.1.5 Roof mirror
2.2 Components Based on Refraction
2.2.1 Plane-parallel plate
2.2.2. Prisms
2.2.2.1 Two types of prisms
Thin-prism approximation for dispersive prisms
Trigonometric description of dispersive prisms
2.2.2.2 Brewster condition
2.2.2.3 Refracting prism
Relation of incident and exit angle in the case of a single prism
The transfer function for the beam width altered by a single prism
A prism for expansion along one axis
A prism for compression along one axis
Tolerancing
2.2.2.4 Two-prism arrangements
Relation of incident and exit angle in the case of a two-prism arrangement
The transfer function for the beam width altered by two prisms
Expansion or compression
Tolerancing
2.2.2.5 Prism with one internal reflection
2.2.2.6 Prism with two internal reflections
2.2.3. Axicon devices
2.3 Components Based on Reflection and Refraction
2.3.1 Integrating rod
2.3.2 Triple mirror

Chapter 3 Sensitivities and Tolerances

3.1 Cascading Misaligned Systems
3.2 Axial Misalignment
3.3 Beam Pointing Error

Chapter 4 Anamorphic Optics

4.1 Two Alternative Matrix Representations
4.2 Orthogonal and Nonorthogonal Anamorphic Descriptions
4.3 Cascading
4.4 Rotation of an Anamorphic Component with Respect to the Optical Axis
4.4.1 Rotation of an "orthogonal" system
4.4.2 Rotation of a "nonorthogonal" system
4.5 Examples
4.5.1 Rotated anamorphic thin lens
4.5.2 Rotated thin cylindrical lens
4.5.3 Cascading two rotated thin cylindrical lenses
4.5.4 Cascading two rotated thin anamorphic lenses
4.5.5 "Quadrupole" lens
4.5.6 Telescope built by cylindrical lenses
4.5.7 Anamorphic collimation lens
4.6 Imaging Condition
4.7 Incorporating Sensitivities and Tolerances in the Analysis

Chapter 5 Optical Systems

5.1 Single-Pass Optics
5.1.1 Triplet synthesis
5.1.2 Fourier transform objectives and 4f arrangements
5.1.3 Telecentric lenses
5.1.4 Concatenated matrices for systems of n lenses
5.1.5 Dyson optics
5.1.6 Variable single-pass optics
5.1.6.1 Mechanical compensation of the triplet
5.1.6.2 Optical compensation of the triplet
5.1.6.3 Theorem on optically compensated adaptive lens arrangements
5.1.6.4 Adaptive optics
5.2 Double-Pass Optics
5.2.1 Autocollimators
5.3 Multiple-Pass Optics
5.4 Systems with a Divided Optical Path
5.4.1 Fizeau interferometer
5.4.2 Michelson interferometer
5.4.3 Dyson interferometer
5.5 Nested Ray Tracing
Outlook
Bibliography

Preface

This book is intended to familiarize the reader with the method of Gaussian matrices and some related tools of optical design. The matrix method provides a means to study an optical system in the paraxial approximation.

In optical design, the method is used to find a solution to a given optical task, which can then be refined by optical-design software or analytical methods of aberration balancing. In some cases, the method can be helpful to demonstrate that there is no solution possible under the given boundary conditions. Quite often it is of practical importance and theoretical interest to get an overview on the "solution space" of a problem. The paraxial approach might then serve as a guideline during optimization in a similar way as a map does in an unknown landscape.

Once a solution has been found, it can be analyzed under different points of view using the matrix method. This approach gives insight on how degrees of freedom couple in an optical device. The analysis of sensitivities and tolerances is common practice in optical engineering, because it serves to make optical devices or instruments more robust. The matrix method allows one to do this analysis in a first order of approximation. With these results, it is then possible to plan and to interpret refined numerical simulations.

In many cases, the matrix description gives useful classification schemes of optical phenomena or instruments. This can provide insight and might in addition be considered as a mnemonic aid.

An aspect that should not be underestimated is that the matrix description represents a useful means of communicating among people designing optical instruments, because it gives a kind of shorthand description of main features of an optical instrument.

The book contains an introductory first chapter and four more specialized chapters that are based on this first chapter. Sections 1.1-1.14 are intended to provide a self-contained introduction into the method of Gaussian transfer matrices in paraxial optics. The remaining sections of the chapter contain additional material on how this approach compares to other paraxial methods.

The emphasis of Chapters 3 and 4 is on refining and expanding the method of analysis to additional degrees of freedom and to optical systems of lower symmetry. The last part of Chapter 4 can be skipped at first reading.

To my knowledge, the text contains new results such as theorems on the design of variable optics, on integrating rods, on the optical layout of prism devices, etc. I tried to derive the results in a step-by-step way so that the reader might apply the methods presented here to her/his design problems with ease. I also tried to organize the book in a way that might facilitate looking up results and the ways of how to obtain them.

It would be a pleasure for me if the reader might find some of the material presented in this text useful for her/his own engineering work.


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