Design rules for Background Oriented Schlieren experiments with least-squares based displacement calculation

Background Oriented Schlieren (BOS) is a non-intrusive optical method used to visualize density variations in fluids. A camera is used to measure the distortion of a background image displaying a random pattern due to the refraction of the light induced by the local gradients in the refractive index of the under study. In contrast to conventional schlieren, for which direct observation is possible, the images obtained with the BOS technique have to be processed. In this contribution, a computationally affordable approach based on linear least-squares minimization and adapted from optical flow techniques is presented in detail and tested in the context of BOS with the Matlab GUI application comBOS. A series of synthetic images are first analyzed to devise design rules for the definition of an optimal random Gaussian dot background pattern. Tests are performed for comBOS, the commercial BOS module included in DaVis 10, and the free PIV tool PIVlab. It is found that the diameter of the dot images on the camera sensor should be at least 3 pixels, but can be larger without affecting the accuracy of the measurement with comBOS and DaVis 10, while PIVlab severely degrades the quality of the results for dots larger than 5 pixels. The contrast and the density of dots must also be sufficient such that a minimum of 75 % of the surface of the background is shaded. If these conditions are met, the maximum systematic error in the measured distortions is 0.006 pixel for comBOS and 0.001 pixel with DaVis 10 when local gradients are small. Similar errors are found with PIVlab for dots smaller than 5 pixels in diameter, but they increase rapidly for larger dots. The random error is typically smaller than 0.004 pixel in optimal conditions, but it increases significantly for images affected by a random noise or local gradients of the distortion. Finally, it is concluded with a realistic test case that both comBOS and DaVis 10 are well suited to capture the main features of a complex compressible flow with Schlieren imaging. Thus, the main advantage of comBOS is its affordability and robustness for researchers and educators willing to implement BOS, for example in educational contexts.