Background-oriented schlieren sensitivity in terms of geometrical parameters of measurement setup

Background-oriented schlieren imaging is a recently proposed noninvasive optical method for imaging of full ultrasound fields. In this work, the impact of uncertainty in geometrical parameters of a background-oriented schlieren measurement setup for imaging of full ultrasound fields is studied using numerical simulations. The studied parameters are focal length of the camera and positions and orientations of the camera, water tank, and ultrasound field. The results demonstrate that the most sensitive parameters affecting the accuracy of the reconstructed ultrasound fields are the orientations of the camera that change the direction of an effective optical axis. Other sensitive parameters are the focal length of the camera and the position of the ultrasound field in perpendicular directions of an optical axis. This synthetic study demonstrates the accuracy requirements for calibrating the geometrical parameters of a measurement setup that would be required to achieve accuracy comparable to that of hydrophone measurements using the background-oriented schlieren imaging. Explicitly, limits of the variation ranges of the geometrical parameters resulting in relative error ranges of 5% and 10% are given. The results of this study may contribute to help design future background-oriented schlieren measurement setups intended for measurement of full ultrasound fields.