Quantitative phase imaging with partially coherent illumination

In this Letter, we formulate a mathematical model for predicting experimental outcomes in quantitative phase imaging (QPI) when the illumination field is partially spatially coherent. We derive formulae that apply to QPI and discuss expected results for two classes of QPI experiments: common path and traditional interferometry, under varying degrees of spatial coherence. In particular, our results describe the physical relationship between the spatial coherence of the illuminating field and the halo effect, which is well known in phase-contrast microscopy. We performed experiments relevant to this common situation and found that our theory is in excellent agreement with the data. With this new understanding of the effects of spatial coherence, our formulae offer an avenue for removing halo artifacts from phase images.