Spatial coherence measurement and partially coherent diffractive imaging

The complete characterization of spatial coherence is difficult because the mutual coherence function is a complex-valued function of four independent variables. This difficulty limits the ability of controlling and optimizing spatial coherence in a broad range of key applications. Here we propose a method for measuring the complete mutual coherence function, which does not require any prior knowledge and can be scaled to measure arbitrary coherence properties for any wavelength. Our method can also be used to retrieve objects illuminated by partially coherent beam with unknown coherence properties. This study is particularly useful for coherent diffractive imaging of nanoscale structures in the X-ray or electron regime. Our method is not limited by any assumption about the illumination and hence lays the foundation for a branch of new diffractive imaging algorithms.