Fringe tracking analysis in background oriented Schlieren for strongly refracting fluids

Background oriented Schlieren (BOS) is a quantitative method for measuring the density distribution of fluid fields. The current commonly used methods such as cross-correlation and Fourier transform encounter challenges when measuring fluids with strong refraction, manifesting as the indistinct distortion of the background patterns. This issue is caused by the rapid changes in density gradients associated with the pattern displacement. To address this problem, we develop the fringe tracking analysis method for BOS based on periodic fringe patterns. We establish a quantitative theoretical relationship between the fringe shape and the density distribution by tracking each complete fringe in the background pattern and calculating their deformation. This method is applied in the laboratory to measure the density of stable and dynamic fields with internal waves. Comparisons with conductivity probe measurements and internal wave theory confirm the method’s accuracy in measuring fluids with large displacement gradients. By establishing an imaging numerical simulation, the performance and limitations of this method in image processing are evaluated. The results show that this method achieves an accuracy exceeding 5% within its effective range for measuring density fields and exhibits robustness against noise. Finally, we provide guidelines for designing fringes in measuring different density fields. This work presents an effective method for measuring density variations in fluids with large refractive index, such as strong stratified fluids, as well as burning and shock waves.