Visiting Astronomer from the Dept. of Astronomy

In many cases the speckle maxima required for the our realization of the Shift-and- Add method1 are not well defined. This is due mainly to Poisson noise, inherent in the detection process, which obliterates the shape of faint speckles. The problem is aggravated for extended objects with local peaks, such as binary stars. As a remedy, we use a filter that smoothes out each speckle and at the same time defines its location. The best filter should be very close to the mean speckle itself: a matched filter. The initial guess for this filter is a bell function, slightly wider than the expected mean speckle. This initial guess is used to locate filtered speckle maxima which are then used to produce a better mean speckle estimate by shift-and add. The procedure is iterated until the mean speckle converges. We find that the iterative speckle estimate is not the optimum matched filter. The most suitable filter must suppress the variable background created by coalescing speckles in a large speckle cloud as well as smooth the single-photon event noise. Thus we combine the mean speckle with a band-pass filter into a matched filter. Local speckle maxima are thus enhanced, whereas single photons are discriminated against by using a comparison low-pass filtered frame, since they do not contain much power. The combined process, speckle identification and weighted-shift-and-add, can be carried out in the image plane or in the Fourier plane. We have experimented in both domains. Shift-and-Add methods Recent efforts in the field of stellar speckle interferometry2'3 are directed towards achieving true images of the observed objects. A great deal has been done to reconstruct the phases of these objects to combine with their power spectra in order to obtain the true image. Other approaches, known as the Shift-and-Add techniques, try to retain the phases as they appear in the original specklegram. Bates and Cady4 realized that at least one Fourier-plane phase is easy to find: that corresponding to the strongest intensity in the specklegram frame. If the displacement of this point is known, then the frame can be shifted to place this maximum at its center. Adding many such shifted frames will yield the average intensity around the brightest spots in all the specklgrams. This is known as the Shift-and-Add routine. Lynds, Worden and Harvey5 (LWH) devised an approach that locates not just the absolute maximum in each frame, but also the brightest local maximum (after some initial smoothing). A set of equal-amplitude delta-functions is created, corresponding to the coordinates of these maxima. A cross-correlation of this set with the original frame shifts all the local maxima to the center, producing a similar result to the Shift-and- Add technique (though with higher efficiency). The natural continuation to these two methods is the seeing calibrated Weighted Shift-and-Add 1. Like the LWH method, all the local maxima are found, and a set of delta-functions is created according to their locations. Each one of these delta functions is multiplied (or weighted) by the intensity of the corresponding maximum. Each frame is correlated in the Fourier plane with its set of weighted delta functions and the correlations averaged. Finally the average cross-correlation is deconvolved by the average power spectrum of the delta functions in order to reduce the atmospheric seeing effects on the final result.