On the application of background oriented schlieren for wavefront sensing

The concept of utilizing a background oriented schlieren (BOS) imaging system to measure the distortion of a wavefront is presented and analyzed. It is shown that the fundamental equations characterizing the image distortion measured using BOS and the distortion of a wavefront are based on the same physical phenomena and can be easily related to one another. An analysis is performed to consider the influence of practical considerations, such as the field-of-view (FOV) and depth-of-field (DOF) on the sensitivity of the BOS measurement. It is found that when the FOV of the schlieren object is held constant and placement of both the medium and background is constrained to the DOF of the imaging system, the sensitivity of the BOS measurement is independent of the focal length of the imaging lens and overall length of the system, both of which are dependent on the FOV and DOF. An equation is derived that expresses the BOS sensitivity as a function of imaging lens f-number and the circle of confusion as these parameters are used in practice to determine the FOV and DOF. It is shown that allowing the background to be slightly out of focus can significantly increase the sensitivity of the measurement. The analysis is tested and confirmed using both computer generated model images and experiments performed to measure the wavefront distortion induced by a plano-convex lens. An uncertainty analysis is performed showing better than 0.1 pixel resolution in the image distortion, which results in an absolute error of the reconstructed wavefront that is better than 5% for the case considered here.