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This book is intended to familiarize the reader with the method of Gaussian matrices and some related tools of optical design. The matrix method provides a means to study an optical system in the paraxial approximation.
In optical design, the method is used to find a solution to a given optical task, which can then be refined by optical-design software or analytical methods of aberration balancing. In some cases, the method can be helpful to demonstrate that there is no solution possible under the given boundary conditions. Quite often it is of practical importance and theoretical interest to get an overview on the “solution space” of a problem. The paraxial approach might then serve as a guideline during optimization in a similar way as a map does in an unknown landscape.
Once a solution has been found, it can be analyzed under different points of
view using the matrix method. This approach gives insight on how degrees of freedom couple in an optical device. The analysis of sensitivities and tolerances is common practice in optical engineering, because it serves to make optical devices or instruments more robust. The matrix method allows one to do this analysis in a first order of approximation. With these results, it is then possible to plan and to interpret refined numerical simulations.
In many cases, the matrix description gives useful classification schemes of
optical phenomena or instruments. This can provide insight and might in addition be considered as a mnemonic aid.
An aspect that should not be underestimated is that the matrix description represents a useful means of communicating among people designing optical instruments, because it gives a kind of shorthand description of main features of an optical instrument.
The book contains an introductory first chapter and four more specialized chapters that are based on this first chapter. Sections 1.1–1.14 are intended to provide a self-contained introduction into the method of Gaussian transfer matrices in paraxial optics. The remaining sections of the chapter contain additional material on how this approach compares to other paraxial methods.
The emphasis of Chapters 3 and 4 is on refining and expanding the method of analysis to additional degrees of freedom and to optical systems of lower symmetry. The last part of Chapter 4 can be skipped at first reading.
To my knowledge, the text contains new results such as theorems on the design of variable optics, on integrating rods, on the optical layout of prism devices, etc. I tried to derive the results in a step-by-step way so that the reader might apply the methods presented here to her/his design problems with ease. I also tried to organize the book in a way that might facilitate looking up results and the ways of how to obtain them.
t would be a pleasure for me if the reader might find some of the material
presented in this text useful for her/his own engineering work.
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