Structured Light Projection-based single-shot transport of intensity phase imaging for quantitative diagnostics of high-speed flows

Abstract: A method for quantitative estimation of density in a high-speed flow field is presented, which uses a structured-light beam probe to interrogate the region of interest (ROI). Wavefront distortion suffered by the interrogating beam as it passes through the shock-induced flow field is investigated. Dedicate camera optics is used to measure the cross-sectional intensities of the exiting wavefront at two different planes, simultaneously. A technique is proposed that uses the lateral displacement of the structured light pattern on both the planes to estimate the axial intensity derivative, dI/dz, which is the input for the transport-of intensity equation (TIE) for phase estimation. By doing this, the need for small defocused distance, dz is avoided in experiments and hence the demand for a low f/# imaging system is alleviated, and now larger dz is admissible as the intensity derivative is not estimated through the conventional finite difference (FD) approximation. The recovered phase from TIE is used as an input to phase tomography algorithm to obtain the refractive index followed by density distributions in the flow field quantitatively. The proposed technique is verified through experiments conducted in hypersonic shock tunnel for flow Mach No. of 8.5. Estimated cross-sectional densities of the flow field around the aerodynamic test model are presented and compared with the numerically estimated values, which shows good agreement.