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In this letter, we present an autofocus routine for backprojection imagery from spotlight-mode synthetic aperture radar data. The approach is based on maximizing image sharpness and supports the flexible collection and imaging geometries of BP, including wide-angle apertures and the ability to image directly onto a digital elevation map. While image-quality-based autofocus approaches can be computationally intensive, in the backprojection setting, we demonstrate a natural geometric interpretation that allows for optimal single-pulse phase corrections to be derived in closed form as the solution of a quartic polynomial. The approach is applicable to focusing standard backprojection imagery, as well as providing incremental focusing in sequential imaging applications based on autoregressive backprojection. An example demonstrates the efficacy of the approach applied to real data for a wide-aperture backprojection image.