Structured illumination-based transport-of-intensity phase imaging for quantitative diagnostics of high-speed flows.

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, ∂I∂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, ∂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 ∂I∂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.

A novel wavefront measuring camera for quantitative measurement of density in high-speed gas flows.

This paper presents the development of a novel wavefront measuring camera capable of detecting both the amplitude and phase of the captured light wave simultaneously. The main objective of the present work is to develop a simple "aim and shoot" camera system for quantitative estimation of density variations in high-speed gas flow fields. The interrogating beam which is a plane wave used here gets distorted by flow induced change in refractive index gradients. Wavefront distortion is quantitatively measured by inspecting the projected pattern through the embedded mask of a modified CMOS image sensor, which samples the incoming wavefront space continuously. Post-processing of the captured images through Fourier- and windowed Fourier transform schemes reveals the change in phase and amplitude of the captured wave. The captured phase of the wavefront is used in an iterative tomography scheme to estimate the density distribution of the flow field. The utility of the developed camera is demonstrated in the quantitative visualization of the high-speed flow fields around test objects subjected to hypersonic flows at Mach numbers 8.89 and 5.82 in hypersonic shock tunnel facility (HST2) and also to visualize the flow field generated at the exit of a convergent-divergent nozzle (Mach number 2.9). It is observed that the recovered quantitative density values from the experiments match well with the results obtained through computational fluid dynamic simulations demonstrating the proficiency of the proposed wavefront measuring camera for high-speed flow diagnostics.

Shock-wave imaging by density recovery from intensity measurements.

A method for quantitative estimation of density variation in high-speed flow, which uses light as an interrogating tool, is described. The wavefront distortion of the interrogating beam induced by the compressible flow field is estimated quantitatively, in which the density gradient of the flow field is seen as refractive-index gradient by the probing beam. The distorted wavefront is measured quantitatively by using the cross-sectional intensities of the distorted wavefront along the optical axis. Iterative algorithms are developed using both deterministic (Gauss-Newton) and stochastic (ensemble Kalman filter) update strategies to recover unknown parameters such as the phase of the wavefront or the refractive index distribution in the flow directly from the measured intensities. With phase recovered in the first step, a ray tomography algorithm is used to obtain the refractive index and density distributions in the flow from the phase. Experiments are conducted to quantitatively visualize the shock-wave-induced flow field in a shock-tunnel facility. The reconstructed density cross sections, obtained using different reconstruction methods, are presented and compared with those obtained by solving the Navier-Stokes equation using computational fluid dynamic routines. It is observed that the iterative algorithms always outperform those depending on solution of the transport-of-intensity equation. In particular, when using the iterative algorithms, the stochastic search scheme outperforms the Gauss-Newton method.

Improved quantitative visualization of hypervelocity flow through wavefront estimation based on shadow casting of sinusoidal gratings.

A simple noninterferometric optical probe is developed to estimate wavefront distortion suffered by a plane wave in its passage through density variations in a hypersonic flow obstructed by a test model in a typical shock tunnel. The probe has a plane light wave trans-illuminating the flow and casting a shadow of a continuous-tone sinusoidal grating. Through a geometrical optics, eikonal approximation to the distorted wavefront, a bilinear approximation to it is related to the location-dependent shift (distortion) suffered by the grating, which can be read out space-continuously from the projected grating image. The processing of the grating shadow is done through an efficient Fourier fringe analysis scheme, either with a windowed or global Fourier transform (WFT and FT). For comparison, wavefront slopes are also estimated from shadows of random-dot patterns, processed through cross correlation. The measured slopes are suitably unwrapped by using a discrete cosine transform (DCT)-based phase unwrapping procedure, and also through iterative procedures. The unwrapped phase information is used in an iterative scheme, for a full quantitative recovery of density distribution in the shock around the model, through refraction tomographic inversion. Hypersonic flow field parameters around a missile-shaped body at a free-stream Mach number of ∼8 measured using this technique are compared with the numerically estimated values. It is shown that, while processing a wavefront with small space-bandwidth product (SBP) the FT inversion gave accurate results with computational efficiency; computation-intensive WFT was needed for similar results when dealing with larger SBP wavefronts.