ABSTRACT
Generation of coherent monochromatic optical beams with well-defined spatial structure, that is, intensity and phase distributions, is required for various applications in industry, biomedicine, metrology, communications, and research. The propagation of these beams through homogeneous or turbid media or through optical system consisting of lenses, mirrors, prisms, etc., is usually of interest. In most cases, the optical systems possess central symmetry as, for example, widely applied microscopic and telescopic setups. Therefore, the synthesis of the beams with controlled changes or invariance of their spatial structure during propagation in such isotropic systems becomes an important task. The problem of beam synthesis consists of (1) the search of the mathematical solutions of the corresponding propagation equation and (2) physical realization of found complex field amplitudes usually applying the methods of digital holography (Ando et al. 2009, Arrizón et al. 2007, Rodrigo et al. 2011a). In this chapter, we address to the first part of the problem assuming the validity of the paraxial approximation.
