In this sequel to his book, "The Optics of Rays, Wavefronts, and Caustics," Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k-function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussing such topics as the Cartesian oval, the modern Schiefspiegler, Huygen's principle, and Maxwell's model of Gauss' perfect lens.
The book introduces university undergraduates to the fascinating world of the science of light. Contemporary physics programmes are under increasing pressure to provide a balance between coverage of several traditional branches of physics and to expose students to emerging research areas. It is therefore important to provide an in depth introduction to some branches of physics, such as optics, to students who may not become professional physicists but will need physics in their chosen professions. Some Universities offer optics as semester courses while others offer it as modules within general physics courses in the degree programme. The book meets the needs of both approaches. Optics has three major branches: Geometrical optics, Physical optics and Quantum optics. Chapter 1 is about the nature of light. Geometrical optics is covered in chapters 2 to 5, Physical optics in chapters 6 to 8, and Quantum optics in chapter 9, and lays a foundation for advanced courses in applied quantum optics. The language of physics is universal, and the book is suited to students globally. However, the book recognises certain peculiarities in Africa, and is written to meet the specific needs of students in African Universities. Some students come from well equipped schools while other students come from less well equipped schools. These two groups of students attending the same course have different needs. The well prepared students need challenge, while the others need to be taught in fair detail. The book has therefore detailed discussions and explanations of difficult-to-grasp topics with the help of simple but clearly drawn and labeled diagrams. The discussions and conclusions are presented pointwise, and key words, definitions, laws, etc., are highlighted. There are a large number of problems and exercises at the end of each chapter.
This monograph provides concise and clear coverage of modern ray theory without the need of complicated mathematics. Comprehensive coverage is given to wave problems in engineering physics, considering rays and caustics as physical objects.
Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.
A basic optics textbook that integrates relevant visual and ophthalmic optics material with basic geometric and physical optics. Dr. Keating's book uses the vergence approach to optics as well as the wavefront approach to vergence as an aid to developing optics intuition.
It is by no means easy for the applied mathematician to decide how much importance he should attach to the more abstract and aesthetic side of his work ... To all appearances, Sir William Rowan Hamilton (1850-1865) attached little importance to the practical applications of his method, and it was only with the publication of his Mathematical Papers that it was possible to form a more correct and balanced judgement of Hamilton as an applied mathematician.
The Optics of Rays, Wavefronts, and Caustics presents the fundamental principles of geometrical optics and its unique role in modern technology. It also discusses the procedures used in optical design, which are based on geometrical optics. Organized into 16 chapters, this volume begins with an overview of the underlying general mathematical facts, which constitute the substance of geometrical optics. It then presents the various techniques used to solve the ray and wavefront problems in general inhomogeneous medium. Other chapters consider the concept of ray tracing as a tool for calculating the principal curvatures of a wavefront as it propagates through a lens. In addition, the book tackles several topics, including the aspects of lens design, as well as a system of equations that are similar to the Maxwell equations. The last chapter deals with orthotomic systems of rays. Optical designers, optical physicists, theoretical physicists, and mathematicians will find the information and methods in this book extremely useful.
