Gradient Index Optics

Gradient Index Optics deals with the application of gradients in optical systems of classical types: gradient index lenses. The emphasis is on the theory and practice related to gradient index lenses. Only isotropic media are considered since they are the ones for which the refractive index at each point is independent of direction. Comprised of 12 chapters, this book begins with a historical background on the use of gradients in astronomy and developments in gradient index lenses, along with the underlying basic theory. The discussion then turns to spherical gradients, paying particular attention to rays, Maxwell's fisheye lens, the Luneburg lens, and astronomical refraction. Subsequent chapters focus on the ray trace in a spherical gradient; axial gradients and their use as an anti-reflection coating; radial gradients and ray tracing in a radial gradient; and fundamentals of aberration theory. The wood lens and ray trace in a general medium are also considered, together with methods for fabrication of gradient elements and measurement of index gradients using an approximate method and interferometric methods. This monograph will be of interest to physicists.

PrefaceChapter 1 Historical Introduction 1.1 Gradients in Astronomy 1.2 Gradient Index Lenses 1.3 Recent Developments 1.4 Basic TheoryChapter 2 Spherical Gradients 2.1 Introduction 2.2 Determining the Rays 2.3 Maxwell's Fisheye Lens 2.4 The Luneburg Lens 2.5 The Generalized Luneburg Lens 2.6 Astronomical RefractionChapter 3 Ray Trace in a Spherical Gradient 3.1 Basic Equations 3.2 Improving the Ray-Trace Formulas 3.3 Finding the Direction of the Ray 3.4 Technical Considerations 3.5 Summary 3.6 Numerical Example 3.7 Other ExamplesChapter 4 Axial Gradients 4.1 Introduction 4.2 Equations of the Rays 4.3 A Special Axial Gradient 4.4 Wave Optics Considerations 4.5 Axial Gradient as an Antireflection CoatingChapter 5 Radial Gradients 5.1 Basic Equations 5.2 Practical Considerations 5.3 A Special Radial Gradient 5.4 The GRIN Rod ProblemChapter 6 Ray Tracing in a Radial Gradient 6.1 Introduction 6.2 Paraxial Ray Trace 6.3 Special Trace for Meridional Rays 6.4 A Perturbation Tracing Method 6.5 Third-Order TraceChapter 7 Aberration Theory 7.1 Basic Concepts 7.2 Total Aberrations 7.3 Buchdahl TheoryChapter 8 The Wood Lens 8.1 Introduction 8.2 The Photographic Wood Lens 8.3 The Thin Wood LensChapter 9 More General Media 9.1 Rotation-Symmetric Gradient 9.2 A Practical Ray-Tracing Routine 9.3 Ray Trace in a General MediumChapter 10 Lens Design with Gradient 10.1 General Comments 10.2 A Simple Axial-Gradient Lens 10.3 Paraxial Rays in a Gradient Singlet 10.4 Designing Gradient Singlets 10.5 A Spherical-Gradient Singlet 10.6 Replacing Aspherics by Gradients 10.7 A Simple Image InverterChapter 11 Fabrication of Gradient Elements 11.1 The Diffusion Method 11.2 Other MethodsChapter 12 Measurement of Index Gradients 12.1 An Approximate Method 12.2 Interferometric MethodsAppendix A Derivation of Equations (1.8)Appendix B Verification of Tracing Formulas for a Spherical GradientAppendix C Derivation of Third-Order Tracing Formulas for a Radial GradientAppendix D Derivation of Equations (10.10) to (10.16)ReferencesIndex