A fundamental analysis of phase aberration correction techniques which use speckle brightness-based image equality factors (QFs) to iteratively reduce phase errors is presented. Phase aberration arises from the spatial inhomogeneity of acoustic velocity in human tissue and degrades the performance of diagnostic ultrasonic imaging systems. A theoretical analysis is presented indicating that the mean speckle brightness decreases with root-mean-square (RMS) phase error. A general definition of QFs is given using the probability of error as a criterion of performance. The QF is optimized through minimization of the probability of error under different conditions. The analysis provides a theoretical framework for the current correction technique using QFs under a variety of conditions, and is a useful tool to evaluate new QFs and correction techniques.