Modulo-2pi phase determination from individual ESPI images

A family of correlation methods is presented that enables a modulo-2 pi phase map to be evaluated from a single ESPI fringe image and at least two phase-stepped reference images. The requirement for only a single fringe image is useful when making ESPI measurements on moving surfaces, where the time interval between the acquisition of multiple phase-stepped fringe images is not acceptable. The phase computation method involves correlating an image area within a small box around each pixel of the fringe image to the corresponding areas within the reference images. With careful arrangement of the computation sequence and the storage of some intermediate results it is possible to achieve computation times only double that of the classical 4+4 stepped image method, independent of correlation box size. The performance of the proposed phase calculation scheme is demonstrated using experimentally measured speckle images acquired from a Mach-Zehnder interferometer. It is also shown that the phase map evaluation quality can be enhanced by subtracting the mostly uncorrelated phase-average component of the incident light. The correlation box size provides a simple means of controlling spatial filtering, with a small box size giving good spatial resolution with high noise, and a large box size giving smoother results but with slightly reduced spatial resolution. (C) 2012 Elsevier Ltd. All rights reserved.