Cross-spectrum Techniques Applied To Astronomical Speckle Interferometry

A cross spectrum analysis technique, which makes it possible to compute an unbiased estimate of the speckle pattern Wiener spectrum, has been developed at the Nice University Astrophysics Department. The technique is based upon the use of a dual channel experiment, each of the channels giving a record of the image intensity with its specific noise. A cross spectrum analysis between the two channels gives an estimate of the Wiener spectrum free of background noise bias. Using a one-dimensional interferometer, the technique has given results on several subjects such as the study of atmospheric MTF including anisotropies due to the geometry of the telescope aperture, the time-space properties of speckles, the angular structure of Betelgeuse and the convective motions of solar photospheric microstructures. The cross spectrum analysis technique has been applied also to the speckle spectroscopy technique and to the differential speckle interferometry technique. A theoretical study of the bichromatic cross spectrum has been elaborated and the first experimental results are shown, they are in good agreement with the theory. Expressions are given for the signal-to-noise ratio on the amplitude and the uncertainty on the phase of the cross-spectrum of two speckle images in the presence of photon shot noise. They are applied to the very promising differential speckle interferometry technique which already permitted us to measure angular micro-displacements, due to atmospheric dis-persion, into the submilliarcsecond range.