High-accuracy VISAR velocity extraction via spatial phase-shifting and probability density function

In the field of optical measurement, the inherent edge spectral leakage problem of the Fourier method significantly affects the accuracy of phase extraction. For the velocity measurement scenarios of inertial confinement fusion (ICF) research using a one-dimensional velocity interferometer system for any reflector (VISAR), this issue further undermines the reliability of velocity field calculations. To address this, a data processing method for VISAR image based on four-phase shifting and probability density function (PDF) compensation is proposed in this paper. This method first performs spatial phase-shifting on a single frame original VISAR image to obtain four phase-shifted images with successive phase differences of<i>π</i>/2. To compensate for phase-shifting errors introduced during the experimental measurement and phase-shifting process, the standard deviation of the PDF curve is taken as the objective function. An iterative compensation algorithm is employed to adjust the PDF of the wrapped phase to approximate the ideal distribution, thereby determining the compensation amount for phase-shifting errors. Subsequently, the least-squares method is applied to calculate the wrapped phase. Finally, the wrapped phase is unwrapped to obtain the phase distribution of the VISAR image, enabling velocity calculation. The verification results indicate that our method demonstrates robust performance across ideal simulated image, noisy synthetic image, and experimental VISAR image, which is superior to the Fourier method in suppressing edge spectral leakage, providing more reliable data for ICF diagnosis.