Lens-based phase retrieval under spatially partially coherent illumination - Part I: Theory

We present a novel approach of phase retrieval using a 4f-imaging system, for the specific case of spatially partially coherent illumination. The theoretical investigation presented in Part I is based on scalar diffraction theory in combination with a heuristic approach. We find that the intensity of the de-focused speckle fields across the image plane shows sufficient contrast for phase retrieval, as long as the radius of the point spread function of the imaging system is well below the radius of the correlation area (spatial coherence) in the object plane. We also derive a useful relation, which allows to determine the requirements towards the essential parameters of an experimental setup, such as maximum propagation distance, diameter of the source, illumination distance and the numerical aperture of the imaging system. The consecutive paper, Part II, describes shape measurement based on the present treatise.