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Spie Press Book

Optical Design: Applying the Fundamentals
Author(s): Max J. Riedl
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Book Description

This text is written for engineers and scientists who have some experience in the field of optics and want to know more about the details and derivations of equations used in optical design. Organized by topic, the book begins with the fundamental law of geometrical optics, Snell's law of refraction, and states the paraxial ray trace equations, then moves on to thin lenses and increasingly more sophisticated components and multi-element systems. Each topic is covered in depth and provides comprehensive information on performance and limitations.

While the text is based on general optical laws, special emphasis has been placed on the two major infrared regions--the mid-wave (MWIR) and the long-wave (LWIR). This is particularly important with regard to diffractive hybrids, which have found their place in these long-wavelength areas for the correction of chromatic aberrations and athermalization. Comments relating to single-point diamond turning have also been included because this process is predominantly used to produce optical elements for the infrared regions.


Book Details

Date Published: 23 July 2009
Pages: 190
ISBN: 9780819477996
Volume: TT84

Table of Contents
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Preface
1. Law of Refraction: The Foundation of Geometrical Optics
1.1 Introduction
1.2 Fermat's Principle
  1.2.1 Historic Remarks
  1.2.2 Derivation
1.3 Snell and the Lens
1.4 Graphical Ray Tracing
1.5 Paraxial Ray Tracing
  1.5.1 Equations, symbols, and sign conventions
2. Optics Fundamentals
2.1 Concept of Thin Lens
2.2 Object at Any Position
2.3 Object at Infinity with Added Field of View
  2.3.1 Spherical aberration
  2.3.2 Chromatic aberration
  2.3.3 Coma
  2.3.4 Astigmatism
  2.3.5 Total blur-spot size
2.4 Special Case
3. Best Shapes for Multiple Thin Lenses, Aspherizing, and the Natural Stop Position
3.1 Introduction
3.2 Best Shapes for Minimum Spherical Aberration
3.3 Aspherizing a Singlet to Eliminate Spherical Aberration
3.4 Correcting Coma and Spherical Aberration
  3.4.1 Eliminating Coma
  3.4.2 Eliminating spherical aberration
3.5 Natural Stop Position
4. Transition from a Thin Lens to a Thick Lens
4.1 Introduction
4.2 Adding a Thickness and Changing the Second Surface Radius
  4.2.1 VIS singlet with n = 1.5
  4.2.2 MWIR singlet with n = 3.4
  4.2.3 LWIR singlet with n = 4
4.3 Change of Spherical Aberration with Added Thickness
5. Achromats
5.1 Introduction
5.2 Thin Achromat for the VIS Spectrum, On-Axis Performance
  5.2.1 Adding a field to the on-axis corrected achromat
  5.2.2 Optimizing
5.3 Smith's Method of Determining the Surface Shapes
  5.3.1 Curvatures and inverse object distances
  5.3.2 The K-functions
  5.3.3 The calculations
5.4 Achromat for the MWIR Region
5.5 Achromat for the LWIR Region
5.6 Diamond-Turned Hybrid
  5.6.1 Hybrid for the MWIR region
    5.6.1.1 Basic lens shape
    5.6.1.2 Aspherizing
    5.6.1.3 The diffractive phase profile
    5.6.1.4 Comments
  5.6.2 Useful nomograms
6. Systems with Two Separated Components
6.1 Introduction
6.2 Dialyte - An Air-Spaced Achromat
  6.2.1 Example for the MWIR region
    6.2.1.1 Aspheric deformation coefficients of surface
    6.2.1.2 Phase coefficients
    6.2.1.3 Step height at the zone transition
6.3 Telephoto and Reversed Telephoto
  6.3.1 Examples for the MWIR and LWIR regions
7. From an Air-Spaced Doublet to a Triplet
7.1 Introduction
7.2 Chromatic Aberration
7.3 Example, a Conventional Triplet
7.4 Hybrid Petzval Objective with a Cold Stop
8. A Hybrid for Two Wavelengths
8.1 Introduction
8.2 Basic Lens Shape for the Long Wavelength
8.3 Required Diffractive Profile
9. Athermats
9.1 Introduction
9.2 Focus Shift of a Refractive Element
9.3 Athermalization with a Doublet
9.4 Focus Shift of a Diffractive Lens
9.5 Design Examples
  9.5.1 Athermat with two elements in an aluminum housing
  9.5.2 Hybrid athermat in an aluminum housing
9.6 Impact of Housing Material
9.7 Athermat for the CO2 Laser Line
9.8 Athermalized Achromat
  9.8.1 Three-element athermat in an aluminum housing
  9.8.2 Two-element athermat in an aluminum housing
9.9 Effect of Quarter-Wave Limit without Athermalization
10. The Ball Lens
10.1 Introduction
10.2 Spherical Aberration
10.3 Coma 91
10.4 Astigmatism
11. Seidel and the Pegel Diagrams
11.1 Introduction
11.2 Triplet for the LWIR Region
  11.2.1 Surface contributions
  11.2.2 Pegel diagram for the triplet
  11.2.3 Remarks to field curvature
11.3 Cassegrain Version with a Maksutov-Mangin Mirror Combination for the LWIR Region
  11.3.1 Pegel diagram
12. The Single-Imaging Mirror
12.1 Introduction
12.2 Spherical Mirror
12.3 Toroidal Mirrors
12.4 Examples
  12.4.1 Spherical mirror
    12.4.1.1 Additional comments
  12.4.2 Toroidal mirror
12.5 Parabolic Mirror
12.6 Manufacturing Remarks
12.7 Mangin Mirror
13. Eight Single Optical Elements as Imaging Objectives
13.1 Introduction
13.2 Diffraction Limit
13.3 Eight Chosen Configurations
13.4 Shapes of the Elements
13.5 Aberrations
13.6 Examples
14. A Progression of Performance with an Increase in Lens Complexity
14.1 Objectives
15. Two-Mirror Systems as Telescope and Microscope Objectives
15.1 Introduction
15.2 Basic Cassegrain Telescope Layout
  15.2.1 Equations
15.3 Cassegrain with Two Spherical Mirrors
15.4 Classic Cassegrain System
15.5 Dall-Kirkham Arrangement
15.6 Ritchey-Chretien Configuration
15.7 Examples
15.8 Cassegrain with Mangin as a Secondary Reflector
15.9 Gregorian Telescope
15.10 Gregorian Microscope Objective
15.11 Two Schwarzschild Objectives
  15.11.1 Prescription for the classic configuration for an object at infinity
    15.11.1.1 Brief historic remark about the golden ratio
  15.11.2 Prescription for the inverted configuration for an object at infinity
15.12 Solid Microscope Objective
16. The Plane-Parallel Plate
16.1 Introduction
16.2 Aberrations
  16.2.1 Examples
16.3 Shift of Image
16.4 Tilted Plate
  16.4.1 Lateral Displacement
16.5 Two Tilted Plates
17. MTF, Limits, and Pixel Sizes
17.1 Introduction
17.2 Optical Modulation Transfer Function
17.3 Focal Plane Array
18. Details of a Hybrid Lens
18.1 Introduction
18.2 Hybrid
18.3 Coordinates of the Combined Surface
19. From the Höegh Meniscus to Double Anastigmats
19.1 Introduction
19.2 Höegh Meniscus
  19.2.1 Approach and design method
19.3 Hypergon Lens
19.4 Achromatic Double Lens
  19.4.1 Approach and design method
19.5 Double Anastigmats
  19.5.1 Approach and design method
Index

Preface

This book is written for engineers and scientists who have some experience in the field of optics and want to know more about the details and derivations of equations used in optical design. Such knowledge is especially valuable in the layout stages of an optical system, when the question is "Where shall I begin?" The other question may be "How come?" instead of just using a given equation.

The book begins with the derivation of the fundamental law of geometrical optics, Snell's law of refraction, and states the paraxial ray trace equations. The following discussions are organized by subjects, starting with a thin lens and progressing to increasingly more sophisticated components and multi-element systems. Each subject is covered in depth to provide a good understanding for performance and limitations. The often ignored effects of plane-parallel plates are included as a separate subject.

While the text is based on general optical laws, special emphasis has been placed on the two major infrared regions, the mid-wave (MWIR) and the long-wave (LWIR). This is particularly apparent in the discussion about diffractive hybrids, which have found their place in these long wavelengths areas for the correction of chromatic aberrations and athermalization. Comments relating to single-point diamond turning have been included because this process is predominantly used to produce optical elements for the infrared regions.

The final subject gradually leads the reader from a single element as an imaging objective for the visible spectrum, the historic Höegh, to a four-element anastigmat. This is done by successively adding and shaping elements and selecting suitable glasses for aberration reduction.

Finally, I thank Tim Lamkins, Scott Schrum, and Gwen Weerts of SPIE for their special support and editorial assistance.

Max J. Riedl
July 2009


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