Precision of reconstruction of the phase of the spatiai spectrum of an object from its speckle interferograms

An analysis is made of a method for reconstruction of an image uhdistorted by the atmosphere from speckle interferograms (Knox–Thompson method). The quantum effects and the recording noise are allowed for in a modification of the Knox–Thompson method for reconstruction of the phase of the spatial spectrum of an object. A general analytic dependence suitable for estimating the precision of reconstruction of the phase of the spatial spectrum of an object is obtained for the Poisson statistics of the process of recording speckle interferograms and for the Gaussian statistics of their spatial spectra. An analysis of this dependence in the cases of large and small signals from objects is used to obtain relationships for the optimization of the parameters of the process of analysis of speckle interferograms so as to minimize the error in the reconstruction of the phase of the spatial spectrum from these interferograms.