Some different image formation models have been proposed for Nomarski's differential interference contrast (DIC) microscope. However, the nature of coherence of illumination in DIC, of key importance in image formation, remains to be elucidated. We present a partially coherent image formation model for DIC and demonstrate that DIC microscope images the coherent difference of shifted replicas of the specimen; but imaging of the each component is partially coherent. Partially coherent transfer functions are presented for various DIC configurations. Plots of these transfer functions and experimental images provide quantitative comparison among various DIC configurations and elucidate their imaging properties. Approximations for weak or slowly varying specimens are also given. These improved models should be of great value in designing phase retrieval algorithms for DIC.