  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.
