Cover

Half-title

Title

Copyright

Contents

Preface

Part one: Preview

1 Some consequences of the wave equation

1.1 Plane wave expansions

1.2 The Fourier lens

1.3 Perfect imaging

1.4 Stationary phase

Part two: Geometrical optics

2 Fermat's principle

2.1 Introduction

2.2 Refraction by a curved surface

2.3 Cartesian surfaces

Exercises

3 Path differentials

3.1 Characterizing a lens

3.2 Path differentials

3.3 The point eikonal

3.4 A reciprocity theorem

3.5 Symmetric camera lenses

Exercises

4 The structure of image forming pencils

4.1 The theorem of Malus and Dupin

4.2 Pinhole projection

4.3 Wavefronts

4.4 Narrow pencils

4.5 Caustics

4.6 The case of axial symmetry

Exercises

5 Eikonal transformations

5.1 The point angle eikonal

5.2 The angle and angle point eikonals

5.3 Reciprocity relations

5.4 Shifts of the reference planes

5.5 Compounding eikonals

5.6 The angle eikonal of a single refracting surface

Exercises

6 Perfect images

6.1 The cosine rule

6.2 Abbe's sine rule

6.3 Herschel's rule

6.4 The perfect imaging of a plane

6.5 The perfect imaging of two planes

6.6 Example: afocal imaging

Exercises

7 Aberrations

7.1 Introduction

7.2 The point angle eikonal for an imperfect lens

7.3 The wavefront aberration

7.4 The angle eikonal

7.5 Which eikonal?

7.6 Example

Exercises

8 Radiometry

8.1 Terminology

8.2 Radiance invariance

8.3 Phase space

8.4 Image plane irradiance

Exercises

Part three: Paraxial optics

9 The small angle approximation

9.1 Axial symmetry

9.2 The small angle approximation

9.3 Imaging

9.4 Other paraxial eikonals

Exercises

10 Paraxial calculations

10.1 Introduction

10.2 Notation and sign rules

10.3 Refraction

10.4 Translation

10.5 The system matrix

10.6 Imaging relations

10.7 Connections with projective geometry

10.8 Cardinal points

10.9 Example

10.10 Thin lenses

10.11 Magnifying power

10.12 Afocal systems

10.13 Tracing paraxial rays

Exercises

11 Stops and pupils

11.1 Entrance and exit pupil

11.2 Instruments for visual use

11.3 Depth of focus

11.4 Perspective

11.5 Pupil distortion

Exercises

12 Chromatic aberrations

12.1 Dispersion

12.2 Thin doublets

12.3 Apochromats

12.4 Airspaced doublets

12.5 The general case

Exercises

Part four: Waves in homogeneous media

13 Waves

13.1 Energy conservation

13.2 Monochromatic waves

13.3 An integral equation

13.4 The radiation condition

13.5 Partial coherence

14 Wave propagation I: exact results

14.1 The Rayleigh-Sommerfeld integral

14.2 Plane wave expansions

14.3 Loss of information

14.4 The field at infinity

14.5 The total energy flow

14.6 Waves in media with n?1

14.7 Cylinder waves

Exercises

15 Wave propagation II: approximations

15.1 The Fraunhofer approximation

15.2 The Fresnel approximation

15.3 The small angle approximation

16 The stationary phase approximation

16.1 Introduction

16.2 The stationary phase approximation

16.3 The Jo Bessel function

16.4 A case of wave propagation

16.5 The angular spectrum representation

16.6 Light rays

16.7 Energy considerations

Exercises

Part five: Wave propagation through lenses

17 Toward a wave theory of lenses

17.1 Introduction

17.2 The stationary phase approximation

17.3 The amplitude function

17.4 A single thin lens

17.5 Where do we go from here?

18 General propagation kernels

18.1 The point angle kernel

18.2 Other kernels

18.3 Further correspondences

18.4 Example1: Free space propagation

18.5 Example2: A plane interface

18.6 Example3: A Fourier lens

18.7 Cylinder lenses

18.8 Appendix: Proof of an equality

Exercises

19 Paraxial wave propagation

19.1 Mathematical preliminaries

19.2 Translation

19.3 Refraction

19.4 Lens systems

19.5 A thin lens in air

Exercises

20 The wave theory of image formation

20.1 The point angle kernel

20.2 A perfect lens in air

20.3 The Airy disk

20.4 Defocussing

20.5 Natural amplitude variations

20.6 Calculations with the point eikonal

20.7 Object or image at infinity

Exercises

21 Fourier optics

21.1 Introduction

21.2 A pair of Fourier lenses

21.3 Other imaging systems

21.4 Incoherent objects

21.5 The modulation transfer function

21.6 Transfer function calculations

Exercises

Part six: Aberrations

22 Perfect systems

22.1 Perfect imaging

22.2 Flat object, curved image

22.3 Curved object, curved image

22.4 Satisfying additional conditions

22.5 Fortuitous perfection

Exercises

23 The vicinity of an arbitrary ray

23.1 Point eikonal relations

23.2 Angle eikonal relations

23.3 More on symmetry relations

23.4 Moving the reference planes

23.5 Imaging

23.6 Moving the object point

23.7 Implementation

23.8 The orthogonal case

23.9 Numerical example

23.10 Appendix: Derivation of the refraction matrices

Exercises

24 Third order aberrations

24.1 Introduction

24.2 Ray intercept errors

24.3 The five third order aberrations

24.3.1 Distortion

24.3.2 Spherical aberration

24.3.3 Coma

24.3.4 Astigmatism and field curvature

24.4 Imaging with a Fourier lens

24.5 Object and stop shifts

24.6 Example: shifting the pupil

24.7 Exchange of object and pupil

24.8 Shifting the object

24.9 Axis imaged perfectly

24.10 Outlook

Exercises

25 The small field approximation

25.1 Small fields and large apertures

25.2 Spherical aberration

25.3 Object points near the axis

25.4 Diapoints

Exercises

26 Ray tracing

26.1 Introduction

26.2 Mathematical procedures

26.3 Interpreting the ray trace results

26.4 Third order aspects

26.5 Fifth order aberrations

26.6 Lens design

27 Aberrations and the wave theory

27.1 Introduction

27.2 Strehl definition

27.3 The circle polynomials of Zernike

27.4 Examples

27.5 Larger aberrations

27.6 The transfer function

27.7 Bounds on the transfer function

Exercises

Part seven: Applications

28 Gaussian beams

28.1 Gaussian beams in free space

28.2 The passage through lenses I

28.3 Three examples

28.4 The passage through lenses II

28.5 Generalized Gaussian beams

28.6 Numerical example

29 Concentric systems

29.1 Basic properties

29.2 A ray invariant

29.3 Paraxial properties

29.4 Aplanatic systems I

29.5 Ray tracing

29.6 Aplanatic systems II

29.7 Third order aberrations

Exercises

30 Thin lenses

30.1 Basic properties

30.2 Meridional and sagittal image curvature

30.3 More third order theory

30.4 Calculation of fi and y

30.5 Aplanatic doublets

30.6 Eyeglasses

Exercises

31 Mock ray tracing

31.1 Introduction

31.2 Lenses perfect for one magnification

31.3 Mock ray tracing with the angle eikonal

31.4 Mock ray tracing: an example

31.5 Mock lens design: Imaging a small volume

31.6 Outlook

32 Diffractive optical elements

32.1 Introduction

32.2 Self imaging

32.3 Zone plates

32.4 Generalized zone plates

32.5 Holograms

32.6 Curved interfaces

32.7 DOE aspherics

Appendix1 Fourier transforms

Appendix2 Third order calculations

Appendix3 Ray tracing

Appendix4 Eikonals and the propagation kernels

Appendix5 Paraxial eikonals

Appendix6 Hints and problem solutions

Bibliography

Index