Normalized quadrature four-frame phase shift algorithm based on crossed fringe patterns

Abstract

In the phase measurement deflectometry, sinusoidal fringe patterns are separately projected on a specular test surface, and the distorted fringes reflected by the surface are recorded by a charge-coupled device (CCD) camera. The phase shift algorithm is used to find the position of the light source on the display corresponding to the pixel point on the CCD, thereby calculating the slope of each point on the element to be tested, and finally retrieving the surface shape of the test element by using the surface reconstruction algorithm. The phase information is usually obtained by traditional 16-step phase-shifting algorithm, which involves certain complicated and time-consuming procedures, for instance, fringe projection in the horizontal and vertical directions. Therefore, to avoid these procedures, a four-step phase shift algorithm based on crossed fringes is proposed. Based on Gram–Schmidt orthonormalization method, only four crossed fringe patterns are needed to determine the phase in both directions simultaneously. Both numerical simulation and experiment are conducted to verify the validity of the algorithm.