Differential interference contrast (DIC) microscopy is an inherently qualitative phase-imaging technique. What is obtained is an image with mixed phase-gradient and amplitude information rather than a true linear mapping of actual optical path length (OPL) differences. Here we investigate an approach that combines the transport-of-intensity equation (TIE) with DIC microscopy, thus improving direct visual observation. There is little hardware modification and the computation is noniterative. Numerically solving for the propagation of light in a series of through-focus DIC images allows linear phase information in a single slice to be completely determined and restored from DIC intensity values.