The authors propose an iterative method for in situ optical testing under partially coherent illumination that relies on the rapid computation of aerial images. In this method, a known pattern is imaged with the test optics at several planes through focus. A model is created that iterates through possible aberration maps until the through-focus series of aerial images matches the experimental result. The computation time of calculating the through-focus series is significantly reduced by reduced optimized coherent sum, an adapted form of the sum of coherent systems decomposition. In this method, the Hopkins formulation is described by an operator S, which maps the space of pupil aberrations to the space of aerial images. This operator is well approximated by a truncated sum of its spectral components.