Compression of periodic images for faster phase retrieval

Abstract

In fringe analysis, or in projected grids for shape-from-shade, deviations from periodicity are used for finding phase changes. In another example, a Hartmann–Shack sensor produces a deformed grid of spots on a camera. The gradients of the original wavefront are calculated from that image by centroiding the spots or by demodulating them. The computation time rises linearly with the number of pixels in the image. We introduce a method to reduce the size of the image without loss of accuracy prior to the calculation to reduce the total processing time. The compressed result is superior to an image measured with reduced resolution. Hence, higher accuracy and speed are obtained by oversampling the image and reducing it correctly prior to calculations. Compression or expansion coefficients are calculated through the requirement to maintain the integrity of the original phase data.