To systematically study the effect of oblique compressible turbulence on inverse synthetic aperture lidar (ISAL) imaging, the atmospheric random phase screen with modified compressible turbulence spectrum is numerically simulated by using FFT spectral inversion method. Using Kirchhoff approximation and convolutional inverse projection algorithm, ISAL imaging of rough surfaces (rough square plates and rough circular plates), rough shapes and rough bodies with different roughness under various compressible turbulence intensities is realized. The analysis shows that the stronger the turbulence, the worse the image quality. The phase gradient self-focusing (PGA) algorithm is used to compensate for the ISAL image resolution caused by compressible turbulence. In the case of weak compressible turbulence, the focusing effect of the image is effectively improved, and the shape of the rough target can be basically distinguishable, thus improving the image quality. However, the image interference and damage caused by medium-strong compressible turbulence are relatively large. The useful information about the target is very small, so the only PGA compensation algorithm can’t recover the image of the target.

In order to better study the imaging characteristics of high-speed moving targets in atmospheric turbulence, it is necessary to solve the optical distortion caused by aerodynamic optical effects, and the optical distortion needs to be described by compressible turbulence spectrum. In order to better understand the spectral characteristics of aero-optical distortion, according to the Maxwell equation, the Boltzmann factor equation is introduced based on the existing compressible turbulence spectrum theory, and the analytical expression of the modified compressible turbulence spectrum is derived and verified. Then, based on the freezing theory, the compressible turbulence spectrum is simulated by the phase screen method of power spectrum inversion. The influence of the distance from the moving target wall and turbulence intensity on the compressible turbulence phase screen is simulated and analyzed. Compared with atmospheric turbulence, it is found that the intensity of turbulence is proportional to the compressible turbulence, but the compressible turbulence is also inversely proportional to the distance of the moving target wall. As the distance from the moving target wall decreases, the phase fluctuation of the compressible turbulence is larger, which also indicates that the aero-optical effect mainly occurs in the boundary layer annex of the moving target, and the nearer the target, the aero-optical effect becomes more serious.

Inverse synthetic aperture LiDAR (ISAL) breaks through the limitations of the diffraction limit and achieves ultra-long-distance radar imaging with centimeter-level resolution. However, because ISAL obtains a high resolution, it is accompanied by a high sampling rate and a large data volume, and the processing process is complicated, which is not conducive to fast real-time imaging of ISAL targets. At the same time, considering that actual non-cooperative targets cannot obtain full-angle ISAL images during movement, in this paper, the Kirchhoff approximation method based on two-dimensional Fourier transform is used to calculate the scattering echo of the rough surface of the target, and then, the rough surface scattering echo of the target coordinate system is obtained through coordinate transformation. After vector superposition, the scattered echo and ISAL image of the rough target are finally obtained, and then the influence of the rotation angle on the ISAL imaging of the rough plate and the rough target is discussed. It is found that a small rotation angle range can also achieve clear ISAL imaging of rough targets, and the influence of different roughness on the ISAL imaging results of different rough targets under a small rotation angle is analyzed. When the roughness is decreased, the target scattering mainly comes from coherent scattering, and the target edge becomes sharper. As the roughness increases, the image energy distribution becomes more uniform. Theoretical and simulation experiments verify the feasibility of ISAL imaging of rough targets under small rotation angles.