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"The Ray and Wave Theory of Lenses" by A. Walther

Cambridge Studies in Modern Optics (No. 15)

Calculations on lens systems are often marred by the unjustifiable use of the small-angle approximation. This book describes in detail how the ray and wave pictures of lens behaviour can be combined and developed into a theory capable of dealing with the large angles encountered in real optical systems. A distinct advantage of this approach is that Fourier optics appears naturally, in a form valid for arbitrarily large angles. The book begins with extensive reviews of geometrical optiks, eikonal functions and the theory of wave propagation.

The propagation of waves through lenses is then treated by exploiting the close connection between eikonal function theory and the stationary phase approximation. Aberrations are then discussed, and the book concludes with various applications in lens design and analysis, including chapters on laser beam propagation and diffractive optical elements. Throughout, special emphasis is placed on the intrinsic limitations of lens performance. The many practical insights it contains, as well as the exercises with their solutions, will be of interest to graduate students as well as to anyone working in optical design and engineering.

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Transferred to digital printing 2003. Online Publication - November 2009

• Provides an accurate description of the behaviour of real optical systems

• Contains many problems and solutions

• A valuable reference for professionals in optical design and engineering

Contents

Preface

Part I. Preview:

1. Some consequences of the wave equation

Part II. Geometrical Optics:

2. Fermat's principle

3. Path differentials

4. The structure of image forming pencils

5. Eikonal transformations

6. Perfect images

7. Aberrations

8. Radiometry

Part III. Paraxial Optics:

9. The small angle approximation

10. Paraxial calculations

11. Stops and pupils

12. Chromatic aberrations

Part IV. Waves in Homogeneous Media:

13. Waves

14. Wave propagation I: exact results

15. Wave propagation II: approximations

16. The stationary phase approximation

Part V. Wave Propagation Through Lenses:

17. Toward a wave theory of lenses

18. General propagation kernels

19. Paraxial wave propagation

20. The wave theory of image formation

21. Fourier optics

Part VI. Aberrations:

22. Perfect systems

23. The vicinity of an arbitrary ray

24. Third order aberrations

25. The small field approximation

26. Ray tracing

27. Aberrations and the wave theory

Part VII. Applications:

28. Gaussian beams

29. Concentric systems

30. Thin lenses

31. Mock ray tracing

32. Diffractive optical elements

Appendices

Bibliography

Index.

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