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Enhancing phase retrieval speed for real-time interferometer and ESPI by two-dimensional continuous wavelet transform

A real-time three-dimensional surface profile metrology system was implemented by integrating Fourier Transform (FT) based algorithms to convert interference intensity fringes to wrapped frequency phase maps and then to unwrapped phase maps. The revival of this field can find its roots in recognizing the development of high-resolution high-speed CCD/CMOS over the years. Two-dimensional Continuous Wavelet Transform (2D-CWT), which possesses the ability to construct daughter wavelets of good time and frequency localization according to different fringes conditions from a characteristic mother wavelet, was implemented with an attempt to reduce redundant fitting process of ordinary Short Time Fourier Transform (STFT), also known as Windowed Fourier Transform (WFT), and therefore to accelerate the FT-related algorithms needed. Implemented with the efficient wavelet construction process by using 2D-CWT, Electronic Speckle Pattern Interferometer (ESPI) was adopted to take advantage of this new process. Different from using several phase shifting steps before to solve the direction ambiguity, which takes time to capture multiple intensity maps during measurement, the phase maps needed were retrieved from a single frame interference fringes. It is to be noted that this one-image interference fringe was captured by having a pre-introduced spatial carrier frequency embedded within the experimental setup so as to remove the directional ambiguity. 2D-CWT dealing with different signal-to-noise ratios was also designed by selecting wavelet parameters properly, which is expected to achieve higher accuracy and faster processing speed. For phase unwrapping, Poisson’s equation with Neumann boundary condition was solved by using FFT. The benefit of using 2D-CWTs with different wavelets as compared to WFT was demonstrated experimentally.