Background oriented schlieren based wavefront sensing (BOS-WS) is a new experimental technique for measuring the two-dimensional distribution of optical wavefronts and the optical path differences (OPDs) induced by the flow-field density variations. Background oriented schlieren (BOS) is traditionally used to test the flow-field density distribution, which restricts the obtaining of useful information since the obtained density information is integrated over the optical path. The OPD is very important for predicting the optical distortion when light travels through the flow field and it is tested by BOS-WS. In order to obtain the optical distortion generated by aero-optic effect, and restore the original image from the distortion known information so as to explore a new kind of supersonic imaging guidance method, theory analysis, numerical simulation and experimental methods are used based on BOS-WS. Through theoretical analysis, the wavefront measurement method based on BOS is verified and the calculation methods of using wavefront information known to predict distortion displacement field and using known displacement field to reconstruct wavefront are explored. By numerical simulation, the error sizes and the result rationalities of one stepped integral algorithm and Southwell method on the wavefront reconstruction are compared, and through the error analysis it is proved that the Southwell method is more accurate and reasonable. By a wavefront aberration experiment carried out in the flow field above the candle flame and a lens perturbation experiment, the methods of using OPD known to reconstruct distorted displacement field and correcting image distortion by the field are creatively explored. The verification experiments show the effectiveness of the correction method.