摘要： When aircraft ?ying at a high speed, the density and re?ective index of atmosphere around it become uneven. Thus images or videos observed from the observation window on the aircraft are usually blur or quivering, which is called the aero-optical effect. To recover the images from poor quality, it is necessary to learn about the wavefront distortion of the light, described as optical path difference (OPD). Among the existing methods, the method of computational ?uid dynamics (CFD) simulation followed by ray tracing is very time consuming, and the method of real-time OPD measurement with OPD sensor has a certain lag for OPD with high frequency. In this paper, a reconstructible dimension reduction method based on dictionary learning is employed to map the high-dimensional OPD data into a low-dimensional space, and the OPD data are calculated when rays travel across the supersonic shear layer. All the parameters of training and test datasets remain the same except the convective Mach numbers (Mc number). According to the dimension reduction results of training sets, we ?nd that OPD is obviously periodic and its distribution characteristics have a strong correlation with Mc number. By ?tting the OPD data in the low-dimensional space, every point on the ?tting curve can be reconstructed to the original high-dimensional space, which works as prediction. Compared with the truthful data, the average similarity coef?cient of the prediction for the test datasets is up to 83%, which means that the prediction result is credible.