Possibility of phase problem solution via a programmable optical signal processor

Abstract

We have considered an original and a simple phase retrieval method using a programmable optical signal processor. The simplest processor allowing one to measure the phase ϕ(x, y) consists of a controlled spatial light modulator (CSLM), lens, photodetector, ADC, and computer. The spatial modulator (for example, liquid crystal modulator) is set immediately in front of the lens. In its focal plane there is a point photodetector which, by means of an ADC, is connected with the computer intended for handling the information obtained and controlling the CSLM. Complex field E(x, y) = |e(x, y)| expiϕ(x, y) belongs to the function class represented by the Fourier series where { mn (y)} is the orthogonal basis. If the CSLM is programmed for generation transmission according to {ψ mn (x, y)}, {ψ pq (x, y) + ψ mn (x, y)} m ≠ p, n ≠ q and {iψ pq (x, y) + ψ mn (x, y)} m ≠ p, n ≠ q [where ψpq(x, y) is a reference function], then, via the point photodetector, exhaustive information about complex array {c mn } can be obtained. In this case the phase retrieval is performed by the computer.