Phase extraction based on iterative algorithm using five-frame crossed fringes in phase measuring deflectometry

In phase measuring deflectometry, two orthogonal sinusoidal fringe patterns are separately projected on the test surface and the distorted fringes reflected by the surface are recorded, each with a sequential phase shift. Then the two components of the local surface gradients are obtained by triangulation. It usually involves some complicated and time-consuming procedures (fringe projection in the orthogonal directions). In addition, the digital light devices (e.g. LCD screen and CCD camera) are not error free. There are quantization errors for each pixel of both LCD and CCD. Therefore, to avoid the complex process and improve the reliability of the phase distribution, a phase extraction algorithm with five-frame crossed fringes is presented in this paper. It is based on a least-squares iterative process. Using the proposed algorithm, phase distributions and phase shift amounts in two orthogonal directions can be simultaneously and successfully determined through an iterative procedure. Both a numerical simulation and a preliminary experiment are conducted to verify the validity and performance of this algorithm. Experimental results obtained by our method are shown, and comparisons between our experimental results and those obtained by the traditional 16-step phase-shifting algorithm and between our experimental results and those measured by the Fizeau interferometer are made.