Phase shifting through the diffraction orders of spatial coherence

A dynamic diffractive optical element like a moving grating introduces phase shift in the diffraction orders of the field under coherent illumination. We explore the possibility of introducing phase shifts when the illumination is spatially incoherent, utilizing the diffraction of optical coherence. A phase shift to the diffraction order of spatial coherence corresponds to an equivalent phase shift between two non-local points in the stochastic field propagated from the source. Under stationarity, it can lead to a phase shift in the sheared copies of the stochastic optical field. This phase shifting requires no additional splitting or distinguishability of the field, enabling a common-path design for the interferometer schemes. Furthermore, the shear values matching with higher orders of diffraction of spatial coherence are shown to introduce a larger phase shift. Experimental validation and application of the technique in phase-gradient measurement are demonstrated using common-path Sagnac radial and lateral shearing interferometers, respectively, with the added advantage of mitigation of coherence effects.