Transport model for the propagation of partially coherent, partially polarized, polarization-gradient vector beams.

Recently we predicted and experimentally validated a new physical mechanism for altering the propagation path of a monochromatic beam [Opt. Express30, 38907 (2022)OPEXFF1094-408710.1364/OE.467678]. Specifically, we showed that by properly tailoring the spatial distribution of the linear state of polarization transverse to the direction of propagation, the beam followed a curved trajectory in free space. Here we extend the model to the partially coherent and partially polarized polychromatic case by redefining the beam amplitude, phase, and polarization angle as appropriate statistical quantities. In particular, the definition of polarization angle represents a fundamentally new quantity in modeling beam propagation and is shown to be consistent with recent works on energy and momentum flow. In the new model, the beam curvature matches that of our previous work in the fully coherent case but is predicted to vanish for an unpolarized, spatially incoherent beam. Simulated beam trajectories are shown for varying levels of initial partial coherence and for different polarization profiles. A new class of non-diffracting beams is also suggested by way of example.

Assessing Postconcussive Reaction Time Using Transport-Based Morphometry of Diffusion Tensor Images.

BACKGROUND AND PURPOSE: Cognitive deficits are among the most commonly reported post-concussive symptoms, yet the underlying microstructural injury is poorly understood. Our aim was to discover white matter injury underlying reaction time in mild traumatic brain injury DTI by applying transport-based morphometry. MATERIALS AND METHODS: In this retrospective study, we performed DTI on 64 postconcussive patients (10-28 years of age; 69% male, 31% female) between January 2006 and March 2013. We measured the reaction time percentile by using Immediate Post-Concussion Assessment and Cognitive Testing. Using the 3D transport-based morphometry technique we developed, we mined fractional anisotropy maps to extract the common microstructural injury associated with reaction time percentile in an automated manner. Permutation testing established statistical significance of the extracted injuries. We visualized the physical substrate responsible for reaction time through inverse transport-based morphometry transformation. RESULTS: The direction in the transport space most correlated with reaction time was significant after correcting for covariates of age, sex, and time from injury (Pearson r = 0.44, P < .01). Inverting the computed direction using transport-based morphometry illustrates physical shifts in fractional anisotropy in the corpus callosum (increase) and within the optic radiations, corticospinal tracts, and anterior thalamic radiations (decrease) with declining reaction time. The observed shifts are consistent with biologic pathways underlying the visual-spatial interpretation and response-selection aspects of reaction time. CONCLUSIONS: Transport-based morphometry discovers complex white matter injury underlying postconcussive reaction time in an automated manner. The potential influences of edema and axonal loss are visualized in the visual-spatial interpretation and response-selection pathways. Transport-based morphometry can bridge the gap between brain microstructure and function in diseases in which the structural basis is unknown.

Transport-based model for turbulence-corrupted imagery.

A new model for turbulence-corrupted imagery is proposed based on the theory of optimal mass transport. By describing the relationship between photon density and the phase of the traveling wave, and combining it with a least action principle, the model suggests a new class of methods for approximately recovering the solution of the photon density flow created by a turbulent atmosphere. Both coherent and incoherent imagery are used to validate and compare the model to other methods typically used to describe this type of data. Given its superior performance in describing experimental data, the new model suggests new algorithms for a variety of atmospheric imaging and wave propagation applications.

Localizing and extracting filament distributions from microscopy images.

Detailed quantitative measurements of biological filament networks represent a crucial step in understanding architecture and structure of cells and tissues, which in turn explain important biological events such as wound healing and cancer metastases. Microscopic images of biological specimens marked for different structural proteins constitute an important source for observing and measuring meaningful parameters of biological networks. Unfortunately, current efforts at quantitative estimation of architecture and orientation of biological filament networks from microscopy images are predominantly limited to visual estimation and indirect experimental inference. Here, we describe a new method for localizing and extracting filament distributions from 2D microscopy images of different modalities. The method combines a filter-based detection of pixels likely to contain a filament with a constrained reverse diffusion-based approach for localizing the filaments centrelines. We show with qualitative and quantitative experiments, using both simulated and real data, that the new method can provide more accurate centreline estimates of filament in comparison to other approaches currently available. In addition, we show the algorithm is more robust with respect to variations in the initial filter-based filament detection step often used. We demonstrate the application of the method in extracting quantitative parameters from confocal microscopy images of actin filaments and atomic force microscopy images of DNA fragments.

Localizing and extracting filament distributions from microscopy images.

Detailed quantitative measurements of biological filament networks represent a crucial step in understanding architecture and structure of cells and tissues, which in turn explain important biological events such as wound healing and cancer metastases. Confocal microscope images of biological specimens marked for different structural proteins constitute an important source for observing and measuring meaningful parameters of biological networks. Unfortunately, current efforts at quantitative estimation of architecture and orientation of biological filament networks from microscopy images are predominantly limited to visual estimation and indirect experimental inference. Here we describe a new method for localizing and extracting filament distributions from 2D confocal microscopy images. The method combines a filter-based detection of pixels likely to contain a filament with a constrained reverse diffusion-based approach for localizing the filaments centrelines. We show with qualitative and quantitative experiments, using both simulated and real data, that the new method can provide more accurate centreline estimates of filament in comparison to other approaches currently available. In addition, we show the algorithm is more robust with respect to variations in the initial filter-based filament detection step often used. We demonstrate the application of the method in extracting quantitative parameters from an experiment that seeks to quantify the effects of carbon nanotubes on actin cytoskeleton in live HeLa cells. We show that their presence can disrupt the overall actin cytoskeletal organization in such cells.

Chaotic signal detection and estimation based on attractor sets: applications to secure communications.

We consider the problem of detection and estimation of chaotic signals in the presence of white Gaussian noise. Traditionally this has been a difficult problem since generalized likelihood ratio tests are difficult to implement due to the chaotic nature of the signals of interest. Based on Poincare's recurrence theorem we derive an algorithm for approximating a chaotic time series with unknown initial conditions. The algorithm approximates signals using elements carefully chosen from a dictionary constructed based on the chaotic signal's attractor. We derive a detection approach based on the signal estimation algorithm and show, with simulated data, that the new approach can outperform other methods for chaotic signal detection. Finally, we describe how the attractor based detection scheme can be used in a secure binary digital communications protocol.

Comprehensive approach for correction of motion and distortion in diffusion-weighted MRI.

Patient motion and image distortion induced by eddy currents cause artifacts in maps of diffusion parameters computed from diffusion-weighted (DW) images. A novel and comprehensive approach to correct for spatial misalignment of DW imaging (DWI) volumes acquired with different strengths and orientations of the diffusion sensitizing gradients is presented. This approach uses a mutual information-based registration technique and a spatial transformation model containing parameters that correct for eddy current-induced image distortion and rigid body motion in three dimensions. All parameters are optimized simultaneously for an accurate and fast solution to the registration problem. The images can also be registered to a normalized template with a single interpolation step without additional computational cost. Following registration, the signal amplitude of each DWI volume is corrected to account for size variations of the object produced by the distortion correction, and the b-matrices are properly recalculated to account for any rotation applied during registration. Both qualitative and quantitative results show that this approach produces a significant improvement of diffusion tensor imaging (DTI) data acquired in the human brain.