Comparison of Fourier phase spectrum estimation using deconvolution from wavefront sensing and bispectrum reconstruction

Abstract

Atmospheric turbulence limits the resolution of astronomical optical imaging systems. Speckle imaging and deconvolution from wavefront sensing (DWFS) are two post-detection image processing methods for overcoming some turbulence effects which do not require adaptive optics. Both speckle imaging and DWFS create estimates of the object irradiance distribution by first estimating the Fourier transform, or spectrum of the object. Previous work has established the signal-to-noise ratio performance for some of the estimators used in both speckle imaging and DWFS. However, the comparative quality of the object spectrum phase estimation provided by these two techniques has not been studied in detail. In this paper we present the results of a simulation study of the comparative Fourier phase estimation errors for speckle imaging using the bispectrum technique, and DWFS. It is shown that even for good wavefront sampling and bright objects DWFS provides Fourier phase spectrum estimation of lower quality than the phase spectrum estimate provided by the bispectrum technique. When the beacon is not bright enough to provide a good signal-to-noise ratio in the wavefront sensor the bispectrum technique provides much better Fourier phase spectrum estimation than DWFS.