  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.
