The Ray And Wave Theory Of Lenses (cambridge Studies In Modern Optics)

This book describes techniques used to predict the quality of images formed by optical systems, such as telescopes, camera lenses, and microscope objectives. It covers in detail how the ray and wave pictures of lens behavior can be combined and developed to produce a theory capable of dealing with the large angles encountered in real optical systems. Several applications are considered, including the propagation of a Gaussian beam along a skew ray, a clear and convincing demonstration that diffractive optical elements are subject to the same fundamental limitation as conventional lenses, a thorough discussion of the "cosine-to-the-fourth law," and a detailed example of mock ray tracing. Containing many practical insights, as well as exercises and solutions, this book will be of great interest to graduate students taking courses in this field, and to anyone working in optical design and engineering. Pt. 1. Preview. 1. Some Consequences Of The Wave Equation -- Pt. 2. 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 -- Pt. 3. Paraxial Optics. 9. The Small Angle Approximation. 10. Paraxial Calculations. 11. Stops And Pupils. 12. Chromatic Aberrations -- Pt. 4. Waves In Homogeneous Media. 13. Waves. 14. Wave Propagation I: Exact Results. 15. Wave Propagation Ii: Approximations. 16. The Stationary Phase Approximation -- Pt. 5. 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 -- Pt. 6. 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 -- Pt. 7. Applications. 28. Gaussian Beams. 29. Concentric Systems. 30. Thin Lenses. 31. Mock Ray Tracing. 32. Diffractive Optical Elements -- Appendix 1: Fourier Transforms -- Appendix 2: Third Order Calculations -- Appendix 3: Ray Tracing -- Appendix 4: Eikonals And The Propagation Kernels -- Appendix 5: Paraxial Eikonals -- Appendix 6: Hints And Problem Solutions. A. Walther. Includes Bibliographical References (p. 392-395). 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 The analysis of practical imaging systems is often marred by the use of poor approximations, particularly the small-angle approximation. This book describes clearly how the ray and wave pictures of lens behaviour can be combined and developed to produce a theory capable of dealing with the large angles encountered in real optical systems.Introductory chapters describe the properties of eikonal functions. The wave theory of lenses is then developed, following a discussion of wave behaviour in homogeneous media. A detailed description of aberrations is then given, and the book concludes with applications of the theory in lens design and analysis. Containing many practical insights, as well as exercises and solutions, this book will be of great interest to graduate students taking courses in this field, and to anyone working in optical design and engineering. This book describes clearly how the ray and wave pictures of lens behaviour can be combined and developed, to produce a theory capable of dealing with the large angles encountered in real optical systems. It will be invaluable to graduate students and professionals in optical design and engineering.