On the Efficient Evaluation of the Azimuthal Fourier Components of the Green\u27s Function for the Helmholtz\u27s Equation in Cylindrical Coordinates

In this dissertation, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green’s function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green’s function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green’s function become computationally intractable when the source and target are close or when the wavenumber is large. Furthermore, most of the state of the art methods cannot easily be parallelized. In this work, we present an algorithm for evaluating the modal Green’s function that has performance independent of both source-to-target proximity and wavenumber, and whose cost grows as O(m). Furthermore, our algorithm is embarrassingly parallelizable

On the Efficient Evaluation of the Azimuthal Fourier Components of the Green's Function for Helmholtz's Equation in Cylindrical Coordinates

In this manuscript, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green's function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green's function become computationally intractable when the source and target are close or when the wavenumber is large. Furthermore, most state of the art methods cannot be easily parallelized. In this manuscript, we present an algorithm for evaluating the modal Green's function that has performance independent of both source-to-target proximity and wavenumber, and whose cost grows as $O(m)$, where $m$ is the Fourier mode. Furthermore, our algorithm is embarrassingly parallelizable.Comment: 58 pages, 9 tables, 11 figure

THz and mm-Wave Sensing of Corneal Tissue Water Content: Electromagnetic Modeling and Analysis.

Terahertz (THz) spectral properties of human cornea are explored as a function of central corneal thickness (CCT) and corneal water content, and the clinical utility of THz-based corneal water content sensing is discussed. Three candidate corneal tissue water content (CTWC) perturbations, based on corneal physiology, are investigated that affect the axial water distribution and total thickness. The THz frequency reflectivity properties of the three CTWC perturbations were simulated and explored with varying system center frequency and bandwidths (Q-factors). The modeling showed that at effective optical path lengths on the order of a wavelength the cornea presents a lossy etalon bordered by air at the anterior and the aqueous humor at the posterior. The simulated standing wave peak-to-valley ratio is pronounced at lower frequencies and its effect on acquired data can be modulated by adjusting the bandwidth of the sensing system. These observations are supported with experimental spectroscopic data. The results suggest that a priori knowledge of corneal thickness can be utilized for accurate assessments of corneal tissue water content. The physiologic variation of corneal thickness with respect to the wavelengths spanned by the THz band is extremely limited compared to all other structures in the body making CTWC sensing unique amongst all proposed applications of THz medical imaging

THz and mm-Wave Sensing of Corneal Tissue Water Content: Electromagnetic Modeling and Analysis.

Terahertz (THz) spectral properties of human cornea are explored as a function of central corneal thickness (CCT) and corneal water content, and the clinical utility of THz-based corneal water content sensing is discussed. Three candidate corneal tissue water content (CTWC) perturbations, based on corneal physiology, are investigated that affect the axial water distribution and total thickness. The THz frequency reflectivity properties of the three CTWC perturbations were simulated and explored with varying system center frequency and bandwidths (Q-factors). The modeling showed that at effective optical path lengths on the order of a wavelength the cornea presents a lossy etalon bordered by air at the anterior and the aqueous humor at the posterior. The simulated standing wave peak-to-valley ratio is pronounced at lower frequencies and its effect on acquired data can be modulated by adjusting the bandwidth of the sensing system. These observations are supported with experimental spectroscopic data. The results suggest that a priori knowledge of corneal thickness can be utilized for accurate assessments of corneal tissue water content. The physiologic variation of corneal thickness with respect to the wavelengths spanned by the THz band is extremely limited compared to all other structures in the body making CTWC sensing unique amongst all proposed applications of THz medical imaging

THz and MM-Wave Sensing of Corneal Tissue Water Content: In Vivo Sensing and Imaging Results

A pulsed terahertz (THz) imaging system and millimeter-wave reflectometer were used to acquire images and point measurements, respectively, of five rabbit cornea in vivo. These imaging results are the first ever produced of in vivo cornea. A modified version of a standard protocol using a gentle stream of air and a Mylar window was employed to slightly dehydrate healthy cornea. The sensor data and companion central corneal thickness (CCT) measurements were acquired every 10-15 min over the course of two hours using ultrasound pachymmetry. Statistically significant positive correlations were established between CCT measurements and millimeter wave reflectivity. Local shifts in reflectivity contrast were observed in the THz imagery; however, the THz reflectivity did not display a significant correlation with thickness in the region probed by the 100 GHz and CCT measurements. This is explained in part by a thickness sensitivity at least 10 × higher in the mm-wave than the THz systems. Stratified media and effective media modeling suggest that the protocol perturbed the thickness and not the corneal tissue water content (CTWC). To further explore possible etalon effects, an additional rabbit was euthanized and millimeter wave measurements were obtained during death induced edema. These observations represent the first time that the uncoupled sensing of CTWC and CCT have been achieved in vivo

Methods for Registering and Calibrating in Vivo Terahertz Images of Cutaneous Burn Wounds

A method to register THz and visible images of cutaneous burn wounds and to calibrate THz image data is presented. Images of partial and full thickness burn wounds in 9 rats were collected over 435 mins. = 7.25 hours following burn induction. A two-step process was developed to reference the unknown structure of THz imaging contrast to the known structure and the features present in visible images of the injury. This process enabled the demarcation of a wound center for each THz image, independent of THz contrast. Threshold based segmentation enabled the automated identification of air (0% reflectivity), brass (100% reflectivity), and abdomen regions within the registered THz images. Pixel populations, defined by the segmentations, informed unsupervised image calibration and contrast warping for display. The registered images revealed that the largest variation in THz tissue reflectivity occurred superior to the contact region at ~0.13%/min. Conversely the contact region showed demonstrated an ~6.5-fold decrease at ~0.02%/min. Exploration of occlusion effects suggests that window contact may affect the measured edematous response

Optical System Design for Noncontact, Normal Incidence, THz Imaging of in Vivo Human Cornea

Reflection-mode terahertz (THz) imaging of corneal tissue water content (CTWC) is a proposed method for early accurate detection and study of corneal diseases. Despite promising results from ex vivo and in vivo cornea studies, interpretation of the reflectivity data is confounded by the contact between corneal tissue and dielectric windows used to flatten the imaging field. Herein, we present an optical design for noncontact THz imaging of cornea. A beam-scanning methodology performs angular normal incidence sweeps of a focused beam over the corneal surface while keeping the source, detector, and patient stationary. A quasi-optical analysis method is developed to analyze the theoretical resolution and imaging field intensity profile. These results are compared to the electric field distribution computed with a physical optics analysis code. Imaging experiments validate the optical theories behind the design and suggest that quasi-optical methods are sufficient for designing of THz corneal imaging systems. Successful imaging operations support the feasibility of noncontact in vivo imaging. We believe that this optical system design will enable the first, clinically relevant, in vivo exploration of CTWC using THz technology