II Paraxial Theory in Optical Design in Terms of Gaussian Brackets

Publisher Summary This chapter reviews Gaussian brackets defined on the basis of the theory of continued fractions, and summarizes the paraxial theory formulated with these Gaussian brackets for both homogeneous and inhomogeneous optical systems and also for the Gaussian beam optical system. Some examples of the application of the Gaussian brackets formulation to the analysis and synthesis of the optical system are also presented. A summary of one of the useful methods for the analysis or synthesis of an optical system in lens design is presented. The method is based on the concept named “Gaussian brackets”. Gaussian brackets are derived as the denominator of the nth convergent of a continued fraction, whose every partial numerator is equal to unity. The Generalized Gaussian Constants (GGC's) are written with the Gaussian brackets, whose elements consist of constitutional parameters of an optical system. The GGC's have a clear physical meaning, and are useful to formulate paraxial theory. The chapter explores that the Gaussian brackets' formulation can be applied not only to other types of optical systems such as a decentered optical system, but also to the aberration theory.

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