Through-focus phase retrieval and its connection to the spatial correlation for propagating fields

Through-focus phase retrieval methods aim to retrieve the phase of an optical field from its intensity distribution measured at different planes in the focal region. By using the concept of spatial correlation for propagating fields, for both the complex amplitude and the intensity of a field, we can infer which planes are suitable to retrieve the phase and which are not. Our analysis also reveals why all techniques based on measuring the intensity at two Fourier-conjugated planes usually lead to a good reconstruction of the phase. The findings presented in this work are important for aberration characterization of optical systems, adaptive optics and wavefront metrology.