Phase Synchronization of Distorted Imaging Antenna Arrays

Diffraction-limited performance of an imaging system is often unattainable without some feedback-controlled compensation built into the image-forming process. Dielectric-constant perturbations due to atmospheric turbulence distort the phasefront of the optical radiation field. Muller and Buffington have discovered a class of integrals of the image intensity which, when maximized by adjustments of a compensating lens or mirror, reduce the error in the image to zero, except for an unknown shift in the optical axis [1]. This is a remarkable theorem. Its success depends upon the spatial incoherence of optical sources. Another approach, due to Gerchberg and Saxton [2], utilizes known properties of the class of expected signals, their autocorrelations or their Fourier transforms. It introduces considerable heuristics into the iterative Fourier transformation process. After each successive transformation, portions of the image or its Fourier transform are retained and portions deleted. Retention or deletion is based on a priori scene information and the physics of the process. Ref. [3] and [4] apply [2] to the optical problem.