Charles L. Matson

Three-dimensional tumor localization in thick tissue with the use of diffuse photon-density waves

A new approach to three-dimensional tumor localization in turbid media with the use of measurements in a single plane is presented. Optical diffuse photon-density waves are used to probe the turbid medium. Relative amplitudes and phases are measured in the detection plane. Lateral localization is accomplished in the detection plane. With a Fourier optics approach, the scattered wave is reconstructed throughout the volume to provide depth localization. Computer-simulation results that validate this technique are presented. Applications of this technique to multiple tumors and to optical mammography are discussed.

Weighted-least-squares phase reconstruction from the bispectrum

A new weighted-least-squares algorithm for phase estimation from the bispectrum is presented. The algorithm uses phasors instead of phases to avoid modulo-2π ambiguities present in the bispectrum phases. The performance of this algorithm is compared with the performances of several other previously proposed algorithms from both simulated and field data. It is shown that the new algorithm results in more accurate phase-spectrum estimates than the other approaches.

Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects

We report a multiframe blind deconvolution algorithm that we have developed for imaging through the atmosphere. The algorithm has been parallelized to a significant degree for execution on high-performance computers, with an emphasis on distributed-memory systems so that it can be hosted on commodity clusters. As a result, image restorations can be obtained in seconds to minutes. We have compared and quantified the quality of its image restorations relative to the associated Cramér-Rao lower bounds (when they can be calculated). We describe the algorithm and its parallelization in detail, demonstrate the scalability of its parallelization across distributed-memory computer nodes, discuss the results of comparing sample variances of its output to the associated Cramér-Rao lower bounds, and present image restorations obtained by using data collected with ground-based telescopes.

Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing

The use of predetection compensation for the effects of atmospheric turbulence combined with postdetection image processing for imaging applications with large telescopes is addressed. Full and partial predetection compensation with adaptive optics is implemented by varying the number of actuators in the deformable mirror. The theoretical expression for the single-frame power spectrum signal-to-noise ratio (SNR) is reevaluated for the compensated case to include the statistics of the compensated optical transfer function. Critical to this analysis is the observation that the compensated optical transfer function does not behave as a circularly complex Gaussian random variable except at high spatial frequencies. Results from a parametric study of performance are presented to demonstrate improvements in power spectrum estimation for both point sources and an extended object and improvements in the Fourier phase spectrum estimation for an extended object. Full compensation is shown to provide a large improvement in the power spectrum SNR over the uncompensated case, while successively smaller amounts of predetection compensation provide smaller improvements, until a low degree of compensation gives results essentially identical to those of the uncompensated case. Three regions of performance were found with respect to the object Fourier phase spectrum estimate obtained from bispectrum postprocessing: (1) the fully compensated case in which bispectrum postprocessing provides no improvement in the phase estimate over that obtained from a fully compensated long-exposure image, (2) a partially compensated regime in which applying bispectrum postprocessing to the compensated images provides a phase spectrum estimation superior to that of the uncompensated bispectrum case, and (3) a poorly compensated regime in which the results are essentially indistinguishable from those of the uncompensated case. Accurate simulations were used to obtain some parameters for the power spectrum SNR analysis and to obtain the Fourier phase spectrum results.

ANALYSIS OF THE FORWARD PROBLEM WITH DIFFUSE PHOTON DENSITY WAVES IN TURBID MEDIA BY USE OF A DIFFRACTION TOMOGRAPHY MODEL

We extend our previously developed diffraction tomography model of diffuse photon density wave propagation in turbid media to analyze the forward problem associated with detecting and resolving both absorptive and scattering inhomogeneities. Our results assume that detection occurs in a plane but no restrictions are placed on the illumination source geometry. We then specialize these results to plane-wave illumination and derive the turbid media version of the Fourier diffraction theorem. We also develop a shot-noise-limited Fourier-domain signal-to-noise-ratio (SNR) expression to determine how background, system, and inhomogeneity parameters affect one’s ability to detect and resolve inhomogeneities. We show that, in general, scattering inhomogeneities are more easily resolved than absorbing inhomogeneities. We also show that lower temporal modulation frequencies enhance one’s ability to detect and resolve inhomogeneities. These theoretical results are compared with previously published image-domain SNR results, and qualitative agreement is demonstrated.

Backpropagation in turbid media

We extend the backpropagation algorithm of standard diffraction tomography to backpropagation in turbid media. We analyze the behavior of the backpropagation algorithm both for a single-view geometry, as is common in mammography, and for multiple views. The most general form of the algorithm permits arbitrary placement of sources and detectors in the background medium. In addition, we specialize the algorithm for the case of a planar array of detectors, which permits the backpropagation algorithm to be implemented with fast-Fourier-domain noniterative algebraic methods. In this case the algorithm can be used to reconstruct three-dimensional images in a minute or less, depending on the number of views. We demonstrate the theoretical results with computer simulations.

The Aggregate behavior of branch points - measuring the number and velocity of atmospheric turbulence layers

Optical waves propagating through atmospheric turbulence develop spatial and temporal variations in their phase. For sufficiently strong turbulence, these phase differences can lead to interference in the propagating wave and the formation of branch points; positions of zero amplitude. Under the assumption of a layered turbulence model, we show that these branch points can be used to estimate the number and velocities of atmospheric layers. We describe how to carry out this estimation process and demonstrate its robustness in the presence of sensor noise.

Blind deconvolution in optical diffusion tomography

We use blind deconvolution methods in optical diffusion tomography to reconstruct images of objects imbedded in or located behind turbid media from continuous-wave measurements of the scattered light transmitted through the media. In particular, we use a blind deconvolution imaging algorithm to determine both a deblurred image of the object and the depth of the object inside the turbid medium. Preliminary results indicate that blind deconvolution produces better reconstructions than can be obtained using backpropagation techniques. Moreover, it does so without requiring prior knowledge of the characteristics of the turbid medium or of what the blur-free target should look like: important advances over backpropagation.

Reflective tomography using a short-pulselength laser: system analysis for artificial satellite imaging

The Air Force Phillips Laboratory is in the process of demonstrating an advanced space surveillance capability with a heterodyne laser radar (ladar) system. Notable features of this ladar system include its narrow (< 1.5 ns) micropulses, contained in a pulse-burst waveform that allows high-resolution range data to be obtained, and its high power (30 J in a pulse burst), which permits reasonable signal returns from satellites. The usefulness of these range data for use in reflective tomographic reconstructions of satellite images is discussed. A brief review of tomography is given. Then it is shown that the ladar system is capable of providing adequate range-resolved data for reflective tomographic reconstructions in terms of range resolution and sampling constraints. Mathematical expressions are derived which can be used to convert the ladar returns into reflective projections. Image reconstructions from computer-simulated data which include the effects of laser speckle and photon noise are presented and discussed. These reconstructions contain artifacts even in the absence of noise, due to the inadequacies of the standard tomographic problem formulation to accurately model the reflective projections obtained from the ladar system. However, object features can still be determined from the reconstructions when typical noise levels are included in the simulation.

Fourier spectrum extrapolation and enhancement using support constraints

The use of support constraints for improving the quality of Fourier spectra estimates is discussed. It is shown that superresolution is an additive phenomenon that is a function of the correlation scale induced by the support constraint, and it is independent of the bandwidth of the measured Fourier spectrum. It is also shown for power spectra that support constraints, due to the enforced correlation of power spectra, reduce the variance of measured power spectra. These theoretical results are validated via computer simulation in the area of speckle interferometry, with very good agreement shown between theory and simulation. >