Calibration of a background-oriented schlieren (BOS) imaging based on the light deflection angle of a wedge prism

Abstract

The background oriented schlieren (BOS) imaging relies on measuring the light deflection angle in proportion to the refractive index gradient due to the change in the density of a medium. BOS imaging is sensitive to light deflection, and the quantitative measurement requires a reliable calibration method. It is convenient to calibrate the BOS based on the measurement of light deflection. All current BOS calibrations use the random dot as the background and digital image correlation (DIC) as the processing algorithm. Such calibrations can induce an inaccurate measurement. This paper proposes a new method to calibrate the BOS based on measuring a known light deflection angle of a wedge prism. The proposed method uses a fringe pattern instead of the random-dot and works based on phase demodulation. The fringe patterns are phase modulated by the wedge prism (the schlieren object). The demodulation utilizes the Hilbert transform (HT) on the BOS images, giving the phase difference of the images. The BOS converts the phase difference into the deflection angle. The calibration relies on the deviation of the angle measured by the BOS with the known angle of a wedge prism. The results show that the measurement accuracy of the BOS can achieve more than 95%. This result shows high accuracy in measuring the light deflection angle. Also, the proposed method is more accurate than other methods, and fringe patterns outperform random dot patterns in BOS imaging. Soon, this proposed calibration method can be adopted to validate the instruments for measuring the physical properties of a transparent medium in two-dimensional (2-D) visualization, in a contactless and non-intrusive manner.