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ABSTRACT

The performance of a long-baseline optical stellar interferometer is greatly enhanced if the instantaneous atmospheric delay  tau(t), can be tracked to within a fraction of a wavelength, permitting coherent integration of the optical correlation (fringe visibility).  Real-time fringe- tracking involves a control system that servos a rapidly responding path-length compensator in real-time.

However precise delay-tracking can be achieved at somewhat lower signal levels by employing an off-line delay-tracking system, in which the raw data measured by the interferometer is stored for subsequent analysis.  Then the estimate of  tau  at time t, is based on data collected both before and after time t.

An optimum delay-tracking algorithm embraces the a priori statistics of the atmospheric delay process.  Rather than simply estimating tau at a point in time, a superior estimate of tau will be obtained by comparing all possible functions, tau(t), over a time period.  Using Bayes' theorem, the a posteriori probability density of any  tau(t) function can be determined.  An algorithm has been developed which determines one or more functions which maximize that probability.  Even the ambiguous estimates which result at lower signal levels, can be employed for the coherent integration of optical correlation.