Abstract

A method for quantitative estimation of density in a high-speed flow field is presented, which uses structured illumination 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. Customized camera optics is used to measure the cross-sectional intensities of the exiting wavefront at two different planes, concurrently. A technique is proposed that uses the displacement of the structured light pattern to estimate the axial intensity derivative, $\frac{{\partial I}}{{\partial z}}$, which is the input to the transport-of-intensity equation (TIE) for phase estimation. The proposed method allows the use of images with larger defocused distances, $\partial z$, as it does not follow the conventional recipe of finite-difference (FD) approximation for intensity derivative estimation. This flexes two requirements of conventional TIE imaging: first, it brings flexibility in imaging optics, not restricted to small $f$-number objectives; second, use of a sensitive camera is optional, as $\frac{{\partial I}}{{\partial z}}$ estimation does not use absolute intensities but information from the distorted pattern of structured light. The recovered phase from the TIE is used as an input to the phase tomography algorithm to obtain the refractive index followed by density distributions in the flow field quantitatively. The proposed phase estimation technique is verified through simulations first and then is implemented in experiments conducted in a hypersonic shock tunnel for flow Mach No. of 8.8. 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.

© 2022 Optical Society of America

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