Biomedical subjects
Publications and source records attributed to Kevin J Webb.
It is shown that a waveguide mode, which exists between metal dimer particles and does not cut off, produces an enhanced electric field and hence a mechanism for surface-enhanced Raman scattering. Structures can thus be designed that provide large average field enhancement over significant length scales.
Irregular waveguide elements in a silicon-on-insulator platform that allow new device concepts are introduced. Specific designs are achieved using a multiresolution optimization strategy where the waveguide width is varied in stepwise increments. Simulation results are given for high-efficiency waveguide mode converters, power splitters, and waveguide transitions operating at 1.55 microm. The degrees of freedom available permit these functions and small dimensions, making these devices candidates for optical integrated circuits.
Optical vortices are shown to be generated in the near-field through interference between a propagating wave and the amplified evanescent field in a slab of lossy left-handed material. While small loss adversely impacts the sub-wavelength performance in the lens application, the vortex character shown relies on some degree of imperfection. These vortices can be controlled by means of gain/loss and the incident field.
A multiresolution direct binary search iterative procedure is used to design small dielectric irregular diffractive optical elements that have subwavelength features and achieve near-field focusing below the diffraction limit. Designs with a single focus or with two foci, depending on wavelength or polarization, illustrate the possible functionalities available from the large number of degrees of freedom. These examples suggest that the concept of such elements may find applications in near-field lithography, wavelength-division multiplexing, spectral analysis, and polarization beam splitters.
A multigrid inversion approach that uses variable resolutions of both the data space and the image space is proposed. Since the computational complexity of inverse problems typically increases with a larger number of unknown image pixels and a larger number of measurements, the proposed algorithm further reduces the computation relative to conventional multigrid approaches, which change only the image space resolution at coarse scales. The advantage is particularly important for data-rich applications, where data resolutions may differ for different scales. Applications of the approach to Bayesian reconstruction algorithms in transmission and emission tomography with a generalized Gaussian Markov random field image prior are presented, both with a Poisson noise model and with a quadratic data term. Simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed-grid iterative coordinate descent method and a multigrid method with fixed-data resolution.
Second- and third-order frequency correlations of speckle intensity patterns are used to characterize scattering media for multiple polarization states. The polarized temporal responses thus obtained are sensitive to the degree of scatter, with results being predictable by a diffusion model with sufficiently strong scatter. Experimental data are used to reconstruct various transfer functions.
A power analysis of the lossy negative refractive index or left-handed slab lens is described. The presence of vortices in the image plane is revealed with small loss or gain, and these are attributed to the influence of field growth in the evanescent spectrum.
We present a method for detecting and localizing a fluorescing tumor obscured underneath several millimeters of a multiply scattering, homogeneous medium from fluorescence measurements made above the surface. Using a statistical model of the measurement system, we develop approaches for detection by use of a binary hypothesis testing approach and localization by use of maximum-likelihood estimation. We also compute the probability of tumor detection and the Cramér-Rao lower bound for the localization estimate error, which are performance metrics that could potentially be optimized in an experimental design. We validate the methods in an experimental study involving an excised mouse tumor tagged with a new folate-indocyanine dye and obscured under a tissue-simulating lipid suspension.
A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction is particularly difficult because the forward problem is both nonlinear and computationally expensive to evaluate. In this paper, we propose a general framework for nonlinear multigrid inversion that is applicable to a wide variety of inverse problems. The multigrid inversion algorithm results from the application of recursive multigrid techniques to the solution of optimization problems arising from inverse problems. The method works by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid inversion algorithm efficiently computes the solution to the desired fine-scale inversion problem. Importantly, the new algorithm can greatly reduce computation because both the forward and inverse problems are more coarsely discretized at lower resolutions. An application of our method to Bayesian optical diffusion tomography with a generalized Gaussian Markov random-field image prior model shows the potential for very large computational savings. Numerical data also indicates robust convergence with a range of initialization conditions for this nonconvex optimization problem.
We present a technique for reconstructing the spatially dependent dynamics of a fluorescent contrast agent in turbid media. The dynamic behavior is described by linear and nonlinear parameters of a compartmental model or some other model with a deterministic functional form. The method extends our previous work in fluorescence optical diffusion tomography by parametrically reconstructing the time-dependent fluorescent yield. The reconstruction uses a Bayesian framework and parametric iterative coordinate descent optimization, which is closely related to Gauss-Seidel methods. We demonstrate the method with a simulation study.
An interferometric technique is utilized to measure both the time- and frequency-domain optical fields scattered by a random medium. The method uses a tunable continuous-wave laser source to make frequency-resolved measurements within a fixed-path-length interferometer. Measured frequency-domain field statistics, with a linearly polarized input, are shown to be zero-mean, circular complex Gaussian for both co- and cross-polarization states. With decreasing scatter, the extracted average impulse responses for co- and cross-polarized states show distinct differences, thereby providing insight into the scattering domain.
A method is presented for fluorescence optical diffusion tomography in turbid media using multiple-frequency data. The method uses a frequency-domain diffusion equation model to reconstruct the fluorescent yield and lifetime by means of a Bayesian framework and an efficient, nonlinear optimizer. The method is demonstrated by using simulations and laboratory experiments to show that reconstruction quality can be improved in certain problems through the use of more than one frequency. A broadly applicable mutual information performance metric is also presented and used to investigate the advantages of using multiple modulation frequencies compared with using only one.
A nonlinear, Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the diffusion coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and the emission wavelengths to reconstruct all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental data from a tissue phantom containing the fluorescent agent Indocyanine Green.
We reconstruct the temporal response of a random medium by using speckle intensity frequency correlations. When the scattered field from a random medium is described by circular complex Gaussian statistics, we show that third-order correlations permit retrieval of the Fourier phase of the temporal response with bispectral techniques. Our experimental results for random media samples in the diffusion regime are in excellent agreement with the intensity temporal response measured directly with an ultrafast pulse laser and a streak camera. Our speckle correlation measurements also demonstrate sensitivity to inhomogeneous samples, highlighting the potential application for imaging within a scattering medium.
Optical diffusion tomography is a method for reconstructing three-dimensional optical properties from light that passes through a highly scattering medium. Computing reconstructions from such data requires the solution of a nonlinear inverse problem. The situation is further complicated by the fact that while reconstruction algorithms typically assume exact knowledge of the optical source and detector coupling coefficients, these coupling coefficients are generally not available in practical measurement systems. A new method for estimating these unknown coupling coefficients in the three-dimensional reconstruction process is described. The joint problem of coefficient estimation and three-dimensional reconstruction is formulated in a Bayesian framework, and the resulting estimates are computed by using a variation of iterative coordinate descent optimization that is adapted for this problem. Simulations show that this approach is an accurate and efficient method for simultaneous reconstruction of absorption and diffusion coefficients as well as the coupling coefficients. A simple experimental result validates the approach.