A Novel Phase Measuring Deflectometry Based on Spiral Fringes

To address the problems of fringe compression in optical mirror measurement, this article shows a method for phase measuring deflectometry (PMD) of spiral fringes in polar coordinates. This method modulates the phase in two linearly independent directions in polar coordinates. Furthermore, spiral stripes have the unique property of spiral arms increasing with radius. It can solve the fringe compression problem at the convex mirror’s edge. Due to the periodicity of angles in polar coordinates, phase errors occur where the phase is zero. Therefore, this study studies a solution of extracting the wrapped phase boundary instead of the absolute phase boundary and dealing with the phase error points, effectively solving this problem. When the tangential and radial gradient data of the surface under test (SUT) were obtained, we used an accurate calculation for Zernike polynomial surface reconstruction in polar coordinates. This algorithm no longer uses the traditional Cartesian pixel arrangement to obtain the sampling points but reconstructs the horizontal and vertical pixels. The polar pixel matrix is used to obtain the fan pixel arrangement. On that basis, the geometric and numerical errors of traditional pixel arrangements can be avoided using Zernike polynomial surface reconstruction in polar coordinates. The experimental results demonstrate that the proposed method can improve measurement accuracy.