Inverse synthetic aperture ladar (ISAL) can achieve high-resolution images for long-range moving targets, while its performance is affected by atmospheric turbulence. In this paper, the dynamic evolution of atmospheric turbulence is studied by using an infinitely long phase screen (ILPS), and the atmospheric coherent time is defined to describe the variation speed of the phase fluctuation induced by atmospheric turbulence. The simulation results show that the temporal decoherence of the echo induced by turbulence causes phase fluctuation and introduces an extra random phase, which deteriorates the phase stability and makes coherent synthesis impossible. Thus, we evaluated its effects on ISAL imaging and found a method to mitigate the impact of turbulence on ISAL images. The phase compensation algorithm could correct the phase variation in different pulses instead of that within the same pulse. Therefore, the relationship between the atmospheric coherent time and pulse duration time (rather than that between the atmospheric coherent time and ISAL imaging time) ultimately determines the ISAL imaging quality. Furthermore, these adverse effects could be mitigated by increasing the atmospheric coherent time or decreasing the pulse duration time, which results in an improvement in the ISAL imaging quality.

This study presents a comprehensive numerical framework for Background-Oriented Schlieren (BOS) to systematically evaluate its performance and reconstructive capabilities under complex flow conditions. This framework integrates two stages: forward modeling, using ray tracing to simulate image degradation, and inverse processing, using optical flow and a conjugate gradient algorithm to extract displacements and reconstruct phase information. This method is first validated using turbulent flow fields in the Johns Hopkins Turbulence Database, where the reconstructed phase screens closely match the original data, with relative errors below 4% and structural similarity indices above 0.75 in all cases, providing a possible restoration method for degraded flow field images. It is then applied to shock wave fields with varying Mach numbers; this method achieves meaningful reconstruction at short ranges but fails under long-range imaging due to severe wavefront distortions. However, even in degraded conditions, the extracted optical flow fields preserve structural features correlated with the underlying shock patterns, indicating potential for BOS-based target recognition. These findings highlight both the capabilities and limitations of BOS and suggest new pathways for extending its use beyond traditional flow visualization.