. We present a new approach for simulating time-evolving speckle patterns, by combining the shift of a rigid phase screen with its evolution . Thus, the two time-scales associated with speckle boiling and speckle motion can be adjusted independently . The statistical properties of the phase perturbation and the speckle pattern are investigated by using the temporal phase structure function and the temporal intensity correlation . We found a very good agreement with experimental results . . IntroductionThe recent demonstration of the potential of adaptive optics systems in groundbased astronomy [1][2][3][4][5][6][7] has increased the efforts in this field enormously . As the temporal evolution of the turbulent atmosphere is crucial for the specification of the whole system, a computer simulation is very useful for investigating the performance [8][9][10] . In this paper we present an algorithm to simulate evolving speckle patterns by moving a phase screen in front of the telescope aperture . To model the speckle boiling effect the phase screen evolves, using a Markov process .The temporal properties of speckle patterns [11][12][13][14][15][16][17] or the phase perturbation [18,19] in the telescope aperture have been repeatedly measured and it has been demonstrated that a short time scale of the order of 10 milliseconds, associated with an evolution of the wavefront, and a long time-scale of the order of a second, associated with the moving wavefront, can be distinguished . These short time-scales determine how fast an adaptive optics system has to adjust to the changes in the wavefront . In speckle interferometry, the short time-scale determines the exposure time of the speckle frame in order to get the maximum signal to noise ratio . A longer exposure time would smear the speckle image and eventually lead to the long exposure image .The models for the temporal behaviour of the turbulent atmosphere used to interpret the experiments have relied on the shift of one [12,14] or more [20] frozen layers of turbulence . Using one moving layer gives the correct qualitative behaviour of the correlation, but requires unrealistic wind speeds of about 100 m s -1 to give the correct short time-scale . Furthermore, this time constant does not depend on the wavelength, although this has been found experimentally to be important . With the model involving several moving layers with frozen turbulence, the short time-scale has the correct order of magnitude for realistic wind speeds and depends on the wavelength . It is probably sufficient to employ two layers so that the difference and 0950-0340/93 81000

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The conventional way of measuring the average slope of the phase of a wave front is from the centroid of the image formed at the focal plane. We show the limitations of using the centroid and present an optimal estimator along with the derivation of its lower error bound for a diffraction-limited image. The method is extended to slope estimation in the case of a random aberration introduced by atmospheric turbulence. It was found that the variance of the error of the slope estimator can be improved significantly at low turbulence levels by using the minimum mean-square-error estimator instead of the centroid.

The analysis of binary stars has to date been one of the major successes of speckle interferometry. A new technique for estimating the parameters of a binary star is presented. Unlike earlier methods, the system does not require the measurement of a reference star to compensate for the speckle transfer function. The algorithm relies on model fitting to the bispectrum phase and can obtain the separation, position angle, and relative brightness of the two components.