Abstract:
Methods are surveyed for the design of mirror systems which transform, within the geometrical optics approximation, a primary spherical wave into a wave with specified ray structure (namely flat, spherical, or with a specific focal line). The existing approaches to this problem are discussed in detail. Mirror surfaces can be chosen starting from different conditions: (a) the amplitude distribution over the initial wave front is transformed into a specified amplitude distribution over the front of the doubly reflected wave; (b) focusing (without aberrations) of two waves from different directions; (c) the polarization structure of the primary wave is transformed into the specified polarization structure of a doubly reflected wave. For different formulations, the problem boils down to solving equations in second- or first-order partial derivatives, and equations in partial derivatives with delayed argument. In degenerate situations (the flat or the axially symmetric problem), the solution reduces to ordinary differential equations. Boundary conditions providing unique solutions are considered.

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