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.

A remote temperature sensor for an ultrasound hyperthermia system using the acoustic signal derived from the heating signals.

We demonstrate a non-invasive technique, based on the modal frequency shift of a region insonified by a dual-beam ultrasound (US) transducer (region of interest, ROI), to remotely assess the temperature of the region in a tissue-mimicking object. The application is in ultrasound hyperthermia systems for controlled maintenance of tumour temperature during chemotherapy. Towards this, we have characterised the variation of the storage modulus with the temperature of two tissue-mimicking visco-elastic materials. Due to this variation in tissue storage modulus (and viscosity), we have observed a shift in the resonant modes of the ROI, vibrated remotely with a dual-beam focussed ultrasound transducer. A modal analysis of the vibrating ROI is done to identify the modes captured by the detector. A variation in this modal frequency with temperature is computed and matches reasonably well with the experimental measurements. Through this, we demonstrate that an ultrasound hyperthermia system can have a remote temperature sensor without using an additional imaging modality.

Orthotropic elastic moduli of biological tissues from ultrasound-assisted diffusing-wave spectroscopy.

We obtain vibro-acoustic (VA) spectral signatures of a remotely palpated region in tissue or tissue-like objects through diffusing-wave spectroscopy (DWS) measurements. Remote application of force is through focused ultrasound, and the spectral signatures correspond to vibrational modes of the focal volume (also called the ROI) excited through ultrasound forcing. In DWS, one recovers the time evolution of mean-square displacement (MSD) of Brownian particles from the measured decay of intensity autocorrelation of light, adapted also to local particles pertaining only to the ROI. We observe that the plateau of the MSD-versus-time curve has noisy fluctuations when ultrasound is applied, which disappear when forcing is removed. It is shown that the spectrum of fluctuations contains peaks corresponding to some of the modes of vibration of the ROI. This enables us to measure the vibrational modes carried by VA waves. We also show recovery of components of the orthotropic elastic tensor pertaining to the material of the ROI from the measured vibrational modes. We first recover the elastic constants for agar slabs, which are verified to be isotropic. Thereafter, we repeat the exercise on fat recovered from pork back tissue, which, from these measurements, is seen to be orthotropic. We validate some of our present measurements through independent runs in a rheometer. The present work is the first step taken, to the best of our knowledge, to characterize biological tissue on the basis of the anisotropic elasticity property, which may potentially aid in the diagnosis and tracking of the progress of cancer in soft-tissue organs.

Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes.

We demonstrate a simple and computationally efficient method to recover the shear modulus pertaining to the focal volume of an ultrasound transducer from the measured vibro-acoustic spectral peaks. A model that explains the transport of local deformation information with the acoustic wave acting as a carrier is put forth. It is also shown that the peaks correspond to the natural frequencies of vibration of the focal volume, which may be readily computed by solving an eigenvalue problem associated with the vibrating region. Having measured the first natural frequency with a fibre Bragg grating sensor, and armed with an expedient means of computing the same, we demonstrate a simple procedure, based on the method of bisection, to recover the average shear modulus of the object in the ultrasound focal volume. We demonstrate this recovery for four homogeneous agarose slabs of different stiffness and verify the accuracy of the recovery using independent rheometer-based measurements. Extension of the method to anisotropic samples through the measurement of a more complete set of resonant modes and the recovery of an elasticity tensor distribution, as is done in resonant ultrasound spectroscopy, is suggested.

Quantitative photoacoustic tomography by stochastic search: direct recovery of the optical absorption field.

We present, perhaps for the first time, a stochastic search algorithm in quantitative photoacoustic tomography (QPAT) for a one-step recovery of the optical absorption map from time-resolved photoacoustic signals. Such a direct recovery is free of the numerical inaccuracies inherent in conventional two-step approaches that depend on an accurate estimation of the absorbed energy distribution. The absorption profile parameterized as a vector stochastic process is additively updated over time recursions so as to drive the measurement-prediction misfit to a zero-mean white noise. The derivative-free additive update is a welcome departure from the conventional gradient-based methods requiring evaluation of Jacobians at every recursion. The quantitative accuracy of the recovered absorption map from both numerical and experimental data is good with an overall error of less than 10%.

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.

Fully 3D refraction correction dosimetry system.

The irradiation of selective regions in a polymer gel dosimeter results in an increase in optical density and refractive index (RI) at those regions. An optical tomography-based dosimeter depends on rayline path through the dosimeter to estimate and reconstruct the dose distribution. The refraction of light passing through a dose region results in artefacts in the reconstructed images. These refraction errors are dependant on the scanning geometry and collection optics. We developed a fully 3D image reconstruction algorithm, algebraic reconstruction technique-refraction correction (ART-rc) that corrects for the refractive index mismatches present in a gel dosimeter scanner not only at the boundary, but also for any rayline refraction due to multiple dose regions inside the dosimeter. In this study, simulation and experimental studies have been carried out to reconstruct a 3D dose volume using 2D CCD measurements taken for various views. The study also focuses on the effectiveness of using different refractive-index matching media surrounding the gel dosimeter. Since the optical density is assumed to be low for a dosimeter, the filtered backprojection is routinely used for reconstruction. We carry out the reconstructions using conventional algebraic reconstruction (ART) and refractive index corrected ART (ART-rc) algorithms. The reconstructions based on FDK algorithm for cone-beam tomography has also been carried out for comparison. Line scanners and point detectors, are used to obtain reconstructions plane by plane. The rays passing through dose region with a RI mismatch does not reach the detector in the same plane depending on the angle of incidence and RI. In the fully 3D scanning setup using 2D array detectors, light rays that undergo refraction are still collected and hence can still be accounted for in the reconstruction algorithm. It is found that, for the central region of the dosimeter, the usable radius using ART-rc algorithm with water as RI matched medium is 71.8%, an increase of 6.4% compared to that achieved using conventional ART algorithm. Smaller diameter dosimeters are scanned with dry air scanning by using a wide-angle lens that collects refracted light. The images reconstructed using cone beam geometry is seen to deteriorate in some planes as those regions are not scanned. Refraction correction is important and needs to be taken in to consideration to achieve quantitatively accurate dose reconstructions. Refraction modeling is crucial in array based scanners as it is not possible to identify refracted rays in the sinogram space.

A global optimization paradigm based on change of measures.

A global optimization framework, COMBEO (Change Of Measure Based Evolutionary Optimization), is proposed. An important aspect in the development is a set of derivative-free additive directional terms, obtainable through a change of measures en route to the imposition of any stipulated conditions aimed at driving the realized design variables (particles) to the global optimum. The generalized setting offered by the new approach also enables several basic ideas, used with other global search methods such as the particle swarm or the differential evolution, to be rationally incorporated in the proposed set-up via a change of measures. The global search may be further aided by imparting to the directional update terms additional layers of random perturbations such as 'scrambling' and 'selection'. Depending on the precise choice of the optimality conditions and the extent of random perturbation, the search can be readily rendered either greedy or more exploratory. As numerically demonstrated, the new proposal appears to provide for a more rational, more accurate and, in some cases, a faster alternative to many available evolutionary optimization schemes.

Detection and estimation of liquid flow through a pipe in a tissue-like object with ultrasound-assisted diffuse correlation spectroscopy.

Using coherent light interrogating a turbid object perturbed by a focused ultrasound (US) beam, we demonstrate localized measurement of dynamics in the focal region, termed the region-of-interest (ROI), from the decay of the modulation in intensity autocorrelation of light. When the ROI contains a pipe flow, the decay is shown to be sensitive to the average flow velocity from which the mean-squared displacement (MSD) of the scattering centers in the flow can be estimated. While the MSD estimated is seen to be an order of magnitude higher than that obtainable through the usual diffusing wave spectroscopy (DWS) without the US, it is seen to be more accurate as verified by the volume flow estimated from it. It is further observed that, whereas the MSD from the localized measurement grows with time as τ(α) with α≈1.65, without using the US, α is seen to be much less. Moreover, with the local measurement, this super-diffusive nature of the pipe flow is seen to persist longer, i.e., over a wider range of initial τ, than with the unassisted DWS. The reason for the super-diffusivity of flow, i.e., α<2, in the ROI is the presence of a fluctuating (thermodynamically nonequilibrium) component in the dynamics induced by the US forcing. Beyond this initial range, both methods measure MSDs that rise linearly with time, indicating that ballistic and near-ballistic photons hardly capture anything beyond the background Brownian motion.

Internal noise-driven generalized Langevin equation from a nonlocal continuum model.

Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases.

Diffusing-wave spectroscopy in an inhomogeneous object: local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume.

We demonstrate diffusing-wave spectroscopy (DWS) in a localized region of a viscoelastically inhomogeneous object by measurement of the intensity autocorrelation [g(2)(τ)] that captures only the decay introduced by the temperature-induced Brownian motion in the region. The region is roughly specified by the focal volume of an ultrasound transducer which introduces region specific mechanical vibration owing to insonification. Essential characteristics of the localized non-Markovian dynamics are contained in the decay of the modulation depth [M(τ)], introduced by the ultrasound forcing in the focal volume selected, on g(2)(τ). The modulation depth M(τ(i)) at any delay time τ(i) can be measured by short-time Fourier transform of g(2)(τ) and measurement of the magnitude of the spectrum at the ultrasound drive frequency. By following the established theoretical framework of DWS, we are able to connect the decay in M(τ) to the mean-squared displacement (MSD) of scattering centers and the MSD to G*(ω), the complex viscoelastic spectrum. A two-region composite polyvinyl alcohol phantom with different viscoelastic properties is selected for demonstrating local DWS-based recovery of G*(ω) corresponding to these regions from the measured region specific M(τ(i))vsτ(i). The ultrasound-assisted measurement of MSD is verified by simulating, using a generalized Langevin equation (GLE), the dynamics of the particles in the region selected as well as by the usual DWS experiment without the ultrasound. It is shown that whereas the MSD obtained by solving the GLE without the ultrasound forcing agreed with its experimental counterpart covering small and large values of τ, the match was good only in the initial transients in regard to experimental measurements with ultrasound.

Diffraction tomography from intensity measurements: an evolutionary stochastic search to invert experimental data.

We develop iterative diffraction tomography algorithms, which are similar to the distorted Born algorithms, for inverting scattered intensity data. Within the Born approximation, the unknown scattered field is expressed as a multiplicative perturbation to the incident field. With this, the forward equation becomes stable, which helps us compute nearly oscillation-free solutions that have immediate bearing on the accuracy of the Jacobian computed for use in a deterministic Gauss-Newton (GN) reconstruction. However, since the data are inherently noisy and the sensitivity of measurement to refractive index away from the detectors is poor, we report a derivative-free evolutionary stochastic scheme, providing strictly additive updates in order to bridge the measurement-prediction misfit, to arrive at the refractive index distribution from intensity transport data. The superiority of the stochastic algorithm over the GN scheme for similar settings is demonstrated by the reconstruction of the refractive index profile from simulated and experimentally acquired intensity data.

Quantitative estimation of mechanical and optical properties from ultrasound assisted optical tomography data.

We demonstrate quantitative optical property and elastic property imaging from ultrasound assisted optical tomography data. The measurements, which are modulation depth M and phase ϕ of the speckle pattern, are shown to be sensitively dependent on these properties of the object in the insonified focal region of the ultrasound (US) transducer. We demonstrate that Young's modulus (E) can be recovered from the resonance observed in M versus ω (the US frequency) plots and optical absorption (µ(a)) and scattering (µ(s)) coefficients from the measured differential phase changes. All experimental observations are verified also using Monte Carlo simulations.

Ultrasound modulation of coherent light in a multiple-scattering medium: experimental verification of nonzero average phase carried by light.

We demonstrate the phase fluctuation introduced by oscillation of scattering centers in the focal volume of an ultrasound transducer in an optical tomography experiment has a nonzero mean. The conditions to be met for the above are: (i) the frequency of the ultrasound should be in the vicinity of the most dominant natural frequency of vibration of the ultrasound focal volume, (ii) the corresponding acoustic wavelength should be much larger than [Formula: see text], a modified transport mean-free-path applicable for phase decorrelation and (iii) the focal volume of the ultrasound transducer should not be larger than 4 - 5 times [Formula: see text]. We demonstrate through simulations that as the ratio of the ultrasound focal volume to [Formula: see text] increases, the average of the phase fluctuation decreases and becomes zero when the focal volume becomes greater than around [Formula: see text]; and through simulations and experiments that as the acoustic frequency increases from 100 Hz to 1 MHz, the average phase decreases to zero. Through experiments done in chicken breast we show that the average phase increases from around 110° to 130° when the background medium is changed from water to glycerol, indicating that the average of the phase fluctuation can be used to sense changes in refractive index deep within tissue.

Practical fully three-dimensional reconstruction algorithms for diffuse optical tomography.

We have developed an efficient fully three-dimensional (3D) reconstruction algorithm for diffuse optical tomography (DOT). The 3D DOT, a severely ill-posed problem, is tackled through a pseudodynamic (PD) approach wherein an ordinary differential equation representing the evolution of the solution on pseudotime is integrated that bypasses an explicit inversion of the associated, ill-conditioned system matrix. One of the most computationally expensive parts of the iterative DOT algorithm, the reevaluation of the Jacobian in each of the iterations, is avoided by using the adjoint-Broyden update formula to provide low rank updates to the Jacobian. In addition, wherever feasible, we have also made the algorithm efficient by integrating along the quadratic path provided by the perturbation equation containing the Hessian. These algorithms are then proven by reconstruction, using simulated and experimental data and verifying the PD results with those from the popular Gauss-Newton scheme. The major findings of this work are as follows: (i) the PD reconstructions are comparatively artifact free, providing superior absorption coefficient maps in terms of quantitative accuracy and contrast recovery; (ii) the scaling of computation time with the dimension of the measurement set is much less steep with the Jacobian update formula in place than without it; and (iii) an increase in the data dimension, even though it renders the reconstruction problem less ill conditioned and thus provides relatively artifact-free reconstructions, does not necessarily provide better contrast property recovery. For the latter, one should also take care to uniformly distribute the measurement points, avoiding regions close to the source so that the relative strength of the derivatives for measurements away from the source does not become insignificant.

A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography.

PURPOSE: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. METHODS: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed "measurement" equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. RESULTS: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as µ(a) (b)=0.01mm(-1) and µ(s) ('b)=1.0mm(-1), respectively. We also assume µ(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and µ(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown µ(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. CONCLUSIONS: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging.

Ultrasound modulated optical tomography: Young's modulus of the insonified region from measurement of natural frequency of vibration.

We demonstrate a method to recover the Young's modulus (E) of a tissue-mimicking phantom from measurements of ultrasound modulated optical tomography (UMOT). The object is insonified by a dual-beam, confocal ultrasound transducer (US) oscillating at frequencies f0 and f0 + Δf and the variation of modulation depth (M) in the autocorrelation of light traversed through the focal region of the US transducer against Δf is measured. From the dominant peaks observed in the above variation, the natural frequencies of the insonified region associated with the vibration along the US transducer axis are deduced. A consequence of the above resonance is that the speckle fluctuation at the resonance frequency has a higher signal-to-noise to ratio (SNR). From these natural frequencies and the associated eigenspectrum of the oscillating object, Young's modulus (E) of the material in the focal region is recovered. The working of this method is confirmed by recovering E in the case of three tissue-mimicking phantoms of different elastic modulus values.

Pseudo-time particle filtering for diffuse optical tomography.

We recast the reconstruction problem of diffuse optical tomography (DOT) in a pseudo-dynamical framework and develop a method to recover the optical parameters using particle filters, i.e., stochastic filters based on Monte Carlo simulations. In particular, we have implemented two such filters, viz., the bootstrap (BS) filter and the Gaussian-sum (GS) filter and employed them to recover optical absorption coefficient distribution from both numerically simulated and experimentally generated photon fluence data. Using either indicator functions or compactly supported continuous kernels to represent the unknown property distribution within the inhomogeneous inclusions, we have drastically reduced the number of parameters to be recovered and thus brought the overall computation time to within reasonable limits. Even though the GS filter outperformed the BS filter in terms of accuracy of reconstruction, both gave fairly accurate recovery of the height, radius, and location of the inclusions. Since the present filtering algorithms do not use derivatives, we could demonstrate accurate contrast recovery even in the middle of the object where the usual deterministic algorithms perform poorly owing to the poor sensitivity of measurement of the parameters. Consistent with the fact that the DOT recovery, being ill posed, admits multiple solutions, both the filters gave solutions that were verified to be admissible by the closeness of the data computed through them to the data used in the filtering step (either numerically simulated or experimentally generated).

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.