Optimum apodization for speckle imaging of extended sources

Speckle imaging of extended sources such as the Sun has to be performed on small segments to reduce the impact of anisoplanatism. Since speckle techniques typically work in the Fourier domain, these segments are apodized to minimize the influence of edges on the Fourier transformed quantities. While apodization functions have been studied to optimally estimate the amplitudes of the Fourier transform of the true object, the influence of apodization on the Fourier phase estimates has not been studied. Indeed, commonly used apodization functions distort the phase estimates considerably. Here I show how apodization distorts the phase estimates and present a new type of apodization functions that leaves Knox-Thompson phase estimates unaffected. This leads to a substantial improvement of the quality of speckle reconstructions of the solar surface, in particular under mediocre seeing conditions.