Computational Aspects of Bispectral Analysis in Interferometric Imaging

Abstract

Although many approaches to phase recovery in the techniques of speckle interferometry and discrete-element optical interferometry are now being currently used, the most promising are those which make use of the closure phase principle (Jennison 1957; Rogstad 1968), which provides an observable phase which is immune to atmospheric corruption, and contains the desired object phases. The general mathematical support for the closure phase quantity is provided by the bispectrum function (Hoffmann et al. 1983), which is a third moment of the complex visibility of the observed (and therefore atmospherically corrupted) source distributions. Specifically, triple products of all visibility elements which can be mapped onto a triangle of discrete interferometer elements, are included in the bispectrum. This constraint implies that the bispectrum volume spans four dimensions, since it is effectively a vector product of the aperture plane with itself, corresponding to the two independent legs of the baseline triangles.