The synthesis and identification of layered media is represented as an inverse problem for the wave equation or a related Schroedinger equation. Analytically it can be solved by using a relation between the reflection coefficient and the refractive-index profile, resulting from a Bremmer series solution of the wave equation. With a view to practical synthesis within a given system family three approaches are discussed: complete scanning by means of pattern recognition; investigation of a related Tschebyschev approximation problem; and application of quasi-linearization.
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Kaiser et al. (1981) studied this question.
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