A procedure for calculating the atmospheric mutual coherence function via the statistical Fourier-optical method

An algorithm is presented for computing the atmospheric mutual coherence function at optical and millimeter wavelengths from flux measurements taken at the focal plane of a reflector antenna. The procedure consists of first computing the inverse Abel transform of the flux, taking the Fourier transform of the result, and then dividing by the aperture pupil function. It is shown that when the flux measurements contain additive noise, the Abel inversion is an ill-posed problem. Therefore, calculation of the inverse Abel transform is accomplished by a Kalman filtering algorithm. Results of the mutual coherence function estimator are given for simulated flux measurements