Performance evaluation of a phase retrieval algorithm from sequences of interferograms with unknown phase shifts using generalized N-dimensional Lissajous figures

摘要

Phase retrieval is a basic step for most interferometric techniques. Both spatial and temporal approaches are frequently used. Temporal methods require a sequence of images with very well know phase shifting increments to produce accurate results. Sometimes environmental disturbances can add random phase values that can result in a sequence of images with virtually unknown phase shift increments. This paper presents and evaluates an approach to retrieve phase values from a sequence of five or more phase shifted images by unknown quantities. The phase shifting increments are determined from Lissajous ellipsis. This paper introduces the use of N-dimensional Lissajous figures to determine phase shifting increments. The use of additional dimensions makes the phase shifting increment determination more robust and less dependent of the pixel choices. The mathematical background is detailed and discussed. The paper presents and evaluates simulations and real world examples using fringe projection and speckle interferometry.