We model differential interference contrast (DIC) for microscopes with residual aberrations. The model presented allows to predict the DIC performance of objectives directly from its bright field point spread function. We numerically simulate partially coherent illumination and discuss the influence of individual aberrations on the image quality. For the recently proposed PlasDIC setup, that comes without any condenser prism, we find that under coherent illumination the contrast reaches the performance of DIC. We present a rule for objective correction to drastically improve PlasDIC contrast also for partially coherent illumination.