To focus a synthetic-aperture radar image that is suffering from phase errors, a phase-error estimate is found that, when it is applied, maximizes the sharpness of the image. Closed-form expressions are derived for the gradients of a sharpness metric with respect to phase-error parameters, including both a point-by-point (nonparametric) phase function and coefficients of a polynomial expansion. Use of these expressions allows for a highly efficient gradient-search algorithm for high-order phase errors. The effectiveness of the algorithm is demonstrated with an example.
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