PHASELESS INVERSE SCATTERING AND THE PHASE PROBLEM IN OPTICS

Two related problems are considered: (1) the inverse scattering problem for a potential V(x) supported on the half-line{x greater-than-or-equal-to 0}, when the given data is \R-(k)\, the amplitude of the reflection coefficient and (ii) determination of a function g(t) supported on the half-line {t greater-than-or-equal-to 0} when the given data is \g(k)\, the amplitude of the Fourier transform of g. Under certain conditions on V or g, uniqueness theorems are proved and computational methods are developed. A numerical example of recovery of V(x) from \R-(k)\ is given.