White-light scanning interferometry (WLSI) has been widely in the field of Nano-Micro topography measurement. In this study , to improve accuracy and robust of surface recovery, the Fast Fourier Transform-Levenberg Marquardt Algorithm-Phase Shift Interference (FFT-LMA-PSI) algorithm is first proposed to position zero optical path difference (OPD), and the FFT-LMA-PSI algorithm is a cascaded algorithm that involves FFT and multiple iterative optimization steps. In order to improve the computational efficiency, the GPU-accelerated FFT-LMA-PSI is developed and designed via compute unified device architecture (CUDA) C language. The speedup ratio of the proposed method are 28.6756×, 36.6950×, 41.9732×, 33.1928× for CCD pixel sizes of 128 × 128, 256 × 256, 512 × 512, 1024 × 1024. The standard deviation (σ) error are 7.34 nm and 9.79 nm and the peak-valley (PV) error are 87.04 nm and 90.36 nm for the Step and Sphere, respectively. The experiment shows that the proposed method has good performance in calculation accuracy and efficiency.
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