Advanced Fourier transform analysis method for phase retrieval from a single-shot spatial carrier fringe pattern

An advanced Fourier transform analysis (AFTA) method is proposed in this study for phase retrieval from a single-shot spatial carrier fringe pattern (SCFP). It firstly extracts four phase-shifted fringe patterns (FP) from the SCFP with one pixel malposition, and then performs Fourier transform to each of them for their Fourier spectrums. The innovation of AFTA is making a subtraction in frequency domain directly to calculate the spectrum difference, which can generally eliminate the direct current component, thus it could mitigate the spectrum leakage problem and the edge error of traditional Fourier transform analysis (FTA) method significantly. After that, by making an inverse Fourier transform to the spectrum difference and a simple average operation, the phase information could be reconstructed conveniently. The time cost is approximately twice of FTA, which is still highly efficient and time-saving for dynamic or real-time measurement. AFTA is adequately validated as a promising method in fringe analysis by various simulations and comparative experiments, with emphasis of this study on its performance in terms of accuracy, noise-tolerance, carrier frequency, time cost, etc.