Quantitative background-oriented schlieren (BOS) analysis of density fields around supersonic projectiles using two optical flow techniques

Optical flow is an image processing technique that measures intensity shifts between image pairs. The Horn-Schunk and Lucas-Kanade algorithms were used to produce background-oriented schlieren (BOS) images of supersonic conical projectiles. The optical flow processing methods are compared to each other and other BOS image processing methods for quantitative measurements of the density field around the projectiles. The Horn-Schunk analysis is shown to more accurately reproduce the sharp density jump across the shock wave and had less background noise. Both optical flow methods cause some artificial spreading of the shock wave appearance and density rise which is related to the local averaging of pixel intensities in the image processing analysis. The BOS processing methods show accuracy similar to quantitative schlieren but are limited by the pixel resolution of the images. The reconstruction of the density field requires the application of an Abel inversion to account for the path integration of the light ray deflection through the conical flowfield. Several methods for computation of the inversion are considered and compared. The calculated density fields are compared to the theoretical Taylor-Maccoll conical flow profile.