The signatures of moving targets with synthetic aperture radar (SAR) imagery are typically smeared primarily in the radar cross-range direction. For such endoclutter targets, the time interval between adjacent radar pulses along the synthetic aperture is sufficiently small that the collection of the target signature does not experience aliasing. If a mobile target is moving sufficiently fast during the SAR collection interval, then the signature exhibits a smearing that lies along a diagonal in the SAR image space of down-range versus cross-range. In the present analysis, the properties of such diagonal signatures are investigated for constant velocity targets. The research further includes the development of new and advanced mathematics and algorithms that yield finely refocused SAR imagery for automatic detection and recognition, even for relatively fast exoclutter targets with non-uniform rotation. This proposal develops and applies two algorithms to detect and refocus fast-moving exoclutter surface targets within SAR imagery: (1) _Rapid �xoclutter E_ocus Transformation (REFT) algorithm to transform input SAR imagery into a form conducive for the detection of fast-moving exoclutter targets, and (2) _Arbitrary _Rigid Object Motion Autofocus (AROMA) algorithm for automatic focus of moving targets with non-uniform rotation and translation.