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Abstract: We demonstrate a Kalman filtering method to recover the phase of a thin object illuminated by partially coherent light. Our method is fast, efficient, robust to noise, and able to handle arbitrary source shapes when used in a microscope with Köhler illumination. 2013 Optical Society of America OCIS codes: (100.5070) Phase retrieval; (110.1758) Computational imaging. Quantitative phase imaging has become an important tool in biology and surface metrology [1,2], since objects of interest often do not absorb much light, but cause phase delay. Phase retrieval methods [3-5] that use a stack of intensity images taken through focus are particularly attractive because they are experimentally simple. We have previously shown that Kalman filtering can be used in such schemes [6], providing information theoretic near-optimal phase solution. However, this method was computationally expensive and could only handle fully coherent (laser) illumination. By using a sparse Kalman filter [7], the computational complexity was reduced to ( log ), where is the number of pixels in the phase construction. Here, we extend this method to the case of spatially partially coherent illumination [8]. The new Kalman filtering method is fast, efficient, robust to noise, and able to handle arbitrary source distribution whe