Background-oriented schlieren with image processing based on phase-shifting profilometry

New modification of background-oriented schlieren (BOS) technique using periodic grayscale and color patterns and phase-shifting profilometry (PSP) image processing is proposed. Its accuracy, spatial resolution and robustness with respect to large displacement gradient are analyzed using synthetic images. Comparison with multi-pass direct cross-correlation, wavelet-based optical flow analysis and Fourier transform profilometry (FTP) is performed. Grayscale PSP BOS requires at least three phase-shifted images to be taken with the schlieren object remaining unchanged. Its accuracy improves with growing number of images. The required three grayscale images can also be coded as the channels of a single color image. Thus, single-frame color PSP BOS is realized, which can be used to measure the unsteady flows. The negative effects of the color channels cross-talk and imbalance are corrected. PSP BOS yields reliable results for displacement gradient far above 1 pix/pix, which is the limit for other image processing techniques. However, its accuracy is affected by the camera sensor noise. The ability of color PSP BOS to measure strongly refracting objects is confirmed by experimental measurements of the glycerol mass fraction in glycerol–water diffusion layer. Quantitative comparison between PSP, direct cross-correlation and FTP is also performed for the measurements of natural convection in water near a heated vertical plate.