Compressible large-eddy simulations were carried out to study the aero-optical effects caused by the flow field of a transverse hemispherical/cylindrical structure at Mach numbers of Ma=0.5-0.7. Statistic results of density and optical path difference were calculated from the density field, and the laser characteristics in far field were computed based on the phase screen method. It is found that the root-mean-square of density distortion and the root-mean-square of optical path difference increase with free stream velocity and aperture size. The one hand, with Mach number varying from 0.5 to 0.7, the root-mean-square of density distortion gain 90 percent when the aperture diameter is fixed to 0.5m, and the root-mean-square of optical path difference gain 90 percent when the aperture diameter is fixed to 0.25 m. On the other hand, with the free stream velocity fixed to 0.6, the two parameters gain 4 times respectively when aperture diameter increases from 0.25 m to 0.75 m. The laser Strehl Ratio decreases with free stream velocity and aperture size. It decreases from 0.236 to 0.045 when Mach number varies from 0.5 to 0.7 with aperture diameter fixed to 0.25 m, and it reduces 90 percent when aperture diameter increases from 0.25 to 0.75 m at 0.6 Ma.