Dark-Field Lau Interferometer: Barker-Babinet Gratings

We design a phase rendering technique that exploits the link between the angular deviations of a beam and the optical implementation of cross-correlations. We employ two suitably coded gratings, which are incorporated as part of a new device here called a dark-field, Lau interferometer. To this end, we use a first grating whose unit cell is coded with the white and black versions of a Barker sequence. We employ a second grating that is coded as the Babinet’s complementary of the first grating. We describe the cross-correlation operation by using a compact matrix formulation, which is amenable to numerical evaluation.