Optical phase retrieving employing differentiation of a couple of two-beam π/2 phase-shifted projected interference patterns

Abstract

An approach to retrieve the 3D surface map of an estimated (i.e., digitally generated) object by projection of a couple of differentiated two-beam interference patterns is presented. A couple of two-beam interference patterns of a certain spatial frequency, shifted by a phase angle (π/2), are produced. Each one of these patterns is differentiated with respect to the carrier’s phase angle. The four obtained interference patterns are projected onto two estimated objects. Each object’s phase variations are retrieved utilizing the definition of the mathematical differentiation of the intensity distribution of the projected patterns. The inclination of the projected interference pattern on the object’s topography caused a redistribution of the intensity according to Lambert’s “cos” law of illumination. This effect is considered when the object’s phase map is retrieved. The limitations of the presented approach are discussed.