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We propose a method to recover quantitative phase from a stack of defocused intensity images illuminated with partially coherent light from a source of arbitrary shape in Köhler geometry. The algorithm uses a sparse Kalman filtering approach which is fast, accurate, and robust to noise. The proposed method is able to recover not only the phase, but also the source shape, which defines the spatial coherence of the illumination. We validate our algorithm experimentally in a commercial microscope with biological samples.

Partially coherent phase imaging with source shapes estimation