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The fusion of a velocity interferometer system for any reflector with compressed ultrafast photography systems in recent literature can achieve two-dimensional spatiotemporal diagnosis of shock wave velocities. Addressing the limitations posed by 7 × 7 coded aperture sampling, this study introduces an enhanced three-dimensional reconstruction algorithm grounded in fractional-order total variation regularization (E-3DFOTV). Simulated reconstructions and analysis were conducted on 80 frames of 350 × 800 fringes. The results show that compared with TWIST, ADMM, and E-3DTV, the average PSNR of the E-3DFOTV algorithm is increased by 16.81 dB, 14.46 dB, and 2.98 dB, respectively, and the average SSIM of the E-3DFOTV algorithm is increased by 53.20%, 27%, and 3.19%, respectively. Moreover, the reconstruction time consumption of E-3DFOTV is reduced by 33.48% compared with the E-3DTV algorithm and 2.94% compared with the ADMM algorithm. The two-dimensional distribution of shock wave velocity fields reconstructed using E-3DFOTV exhibits minimal errors, with percentages within 1.67%, 1.00%, and 2.14% at different slices, respectively. Moreover, the experiment was conducted on the ShenGuang-III prototype laser facility and VISAR data has been reconstructed in 1.25 ns range. Reconstruction results from experimental data demonstrate that the percentage errors at maximum velocity location for ADMM, E-3DTV, and E-3DFOTV are 12.08%, 19.27%, and 3.59%, and the maximum percentage error for E-3DFOTV is 6.65%, underscoring the feasibility of the algorithm.
Li et al. (Mon,) studied this question.