Abstract

Joint spatial/spatial-frequency energy representations are proposed as a powerful framework, allowing a generalized formulation of stellar speckle interferometry and related imaging techniques. There are four basic functions in this scheme, which are related to each other by Fourier transforms, and all of them being able to keep both high frequency information and phase after averging: The Product Function P_i (x,δx) = i^*(x– δx/2) i(x+δx/2) of the image i(x); the Wigner distribution is W_i (x,u) = FT [P_i(x,δx)δ_{x - >} u; the Spectral Product K_i(u,δu) = I^*(u -δu/2) I(u + δu/2) = FT [W_i(x,u)]_{x- >} δu and the Ambiguity function A_i (δx,δu) = FT [K_i(u, δu)]_{u- >} δx. Within this framework, most speckle imaging techniques appear to be particular implementations of a generalized method. For instance, the Knox-Thompson method consists of taking the average (u,u) of the short exposure frames i(x), for small values of u. However, in this joint formulation it seems to be more natural and direct to take the average < P_i(x,δx) > avoiding the computation of typically hundreds or even thousands Fourier transforms. Results of a realistic computer simulation of this particular implementation of stellar speckle interferometry are included showing good reconstructions.

© 1990 Optical Society of America