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2011

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Articles 31 - 60 of 87

Full-Text Articles in Optics

Estimating Anthropometric Marker Locations From 3-D Ladar Point Clouds, Matthew J. Maier Jun 2011

Estimating Anthropometric Marker Locations From 3-D Ladar Point Clouds, Matthew J. Maier

Theses and Dissertations

An area of interest for improving the identification portion of the system is in extracting anthropometric markers from a Laser Detection and Ranging (LADAR) point cloud. Analyzing anthropometrics markers is a common means of studying how a human moves and has been shown to provide good results in determining certain demographic information about the subject. This research examines a marker extraction method utilizing principal component analysis (PCA), self-organizing maps (SOM), alpha hulls, and basic anthropometric knowledge. The performance of the extraction algorithm is tested by performing gender classification with the calculated markers.


Saturated Absorption For A Magneto-Optical Atom Trap As A Step Toward Atomic Dipole Traps In A Diffraction Pattern From A Circular Aperture, Andrew Ferdinand Jun 2011

Saturated Absorption For A Magneto-Optical Atom Trap As A Step Toward Atomic Dipole Traps In A Diffraction Pattern From A Circular Aperture, Andrew Ferdinand

Physics

Neutral atom quantum computing is a promising avenue toward the realization of a physical quantum computer. The diffraction pattern formed by laser light immediately behind a circular aperture can be used as optical atomic dipole traps, and has the potential to be scaled up to create a two dimensional array of individually addressable qubit sites. In working towards experimental demonstration of the dipole traps, we are constructing a MOT. The function of the MOT is to cool and trap 87Rb in a localized cloud in our vacuum chamber, which will be used to load the dipole traps. One critical …


Laser-Induced Breakdown Spectroscopy, Connor Drake Jun 2011

Laser-Induced Breakdown Spectroscopy, Connor Drake

Physics

The goal of this work is to use a Neodymium-Doped Yttrium Aluminum Garnet (Nd:YAG) Laser, spectrometer, and computer to create a Laser Induced Breakdown Spectroscopy (LIBS) system. LIBS utilizes a focused, high-powered, pulsed laser whose peak electric field ionizes materials at the beam focal point, creating localized plasma.  The plasma state includes broken molecular bonds, atom/electron-ionization, and excited electrons, which on the macroscopic level is a loud “snap” and a bright spark. In this project, a fiber optic cable is used to capture light emitted from the spark, and direct it into a spectrometer which tallies the number of photons …


Projected Pinhole Diffraction, David Moore Jun 2011

Projected Pinhole Diffraction, David Moore

Physics

The goal of this experiment was to observe the effects of passing light through a pinhole, more specifically, to observe the interference and diffraction that occurs due to the pinhole and to successfully achieve CCD camera recording of a projected diffraction pattern from a pinhole. This experiment involved the diffraction of a laser incident upon a 100-mm diameter circular aperture. The diffraction pattern is then projected using a 100-mm focal length plano-convex lens. The lens allows for the pattern to be magnified and stretched a few focal lengths past the lens where it can be then viewed using a CCD …


Principal Angles And Principal Azimuths Of Frustrated Total Internal Reflection And Optical Tunneling By An Embedded Low-Index Thin Film, R. M.A. Azzam, F. F. Sudradjat May 2011

Principal Angles And Principal Azimuths Of Frustrated Total Internal Reflection And Optical Tunneling By An Embedded Low-Index Thin Film, R. M.A. Azzam, F. F. Sudradjat

Electrical Engineering Faculty Publications

The condition for obtaining a differential (or ellipsometric) quarter-wave retardation when p- and s-polarized light of wavelength λ experience frustrated total internal reflection (FTIR) and optical tunneling at angles of incidence ϕ≥ the critical angle by a transparent thin film (medium 1) of low refractive index n1 and uniform thickness d, which is embedded in a transparent bulk medium 0 of high refractive index n0 takes the simple form: −tanh2x=tanδptanδs , in whichx=2πn1(d/λ)(N2sin2ϕ−1)1/2 , N=n0/n1 , and δp , δs are 01 interface Fresnel reflection phase shifts for the pand s polarizations. From this condition, the …


Quantum Ghost Imaging Through Turbulence, John C. Howell May 2011

Quantum Ghost Imaging Through Turbulence, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We investigate the effect of turbulence on quantum ghost imaging. We use entangled photons and demonstrate that for a specific experimental configuration the effect of turbulence can be greatly diminished. By decoupling the entangled photon source from the ghost-imaging central image plane, we are able to dramatically increase the ghost-image quality. When imaging a test pattern through turbulence, this method increases the imaged pattern visibility from V=0.15±0.04 to 0.42±0.04.


Studies Of Shrinkage As A Result Of Holographic Recording In Acrylamide Based Photopolymer Film, Mohesh Moothanchery, Izabela Naydenova, Vincent Toal May 2011

Studies Of Shrinkage As A Result Of Holographic Recording In Acrylamide Based Photopolymer Film, Mohesh Moothanchery, Izabela Naydenova, Vincent Toal

Articles

We studied the shrinkage in acrylamide-basedphotopolymer by measuring the Bragg detuning of transmission diffraction gratings recorded at different slant angles and at different intensities. Transmission diffraction gratings of spatial frequency 1000 lines/mm were recorded in an acrylamide-based photopolymer film having 60 ± 5 μm thickness. We have obtained the grating thickness and the final slant angles from the Bragg curve and hence calculated the shrinkage caused by holographic recording. The shrinkage of the material was evaluated for three different recording intensities 1, 5 and 10 mW/cm2, while the total exposure energy was kept constant at 80 mJ/cm2. From the experimental …


Examination Of Chaotic Signal Encryption And Recovery For Secure Communication Using Hybrid Acousto-Optic Feedback, Monish Ranjan Chatterjee, Mohammed A. Al-Saedi May 2011

Examination Of Chaotic Signal Encryption And Recovery For Secure Communication Using Hybrid Acousto-Optic Feedback, Monish Ranjan Chatterjee, Mohammed A. Al-Saedi

Electrical and Computer Engineering Faculty Publications

Generation of chaos from acousto-optic (A-O)Bragg cell modulators with an electronic feedback has been studied for over 3 decades. Since an acousto-optic Bragg cell with zeroth- and first-order feedback exhibits chaotic behavior past the threshold for bistability, such a system was recently examined for possible chaotic encryption of simple messages (such as a low-amplitude sinusoidal signal) applied via the bias input of the sound cell driver. Subsequent recovery of the message signal was carried out via a heterodyne-type strategy employing a locally generated chaotic carrier, with threshold parameters matched to the transmitting Bragg cell.

In this paper, we present numerical …


Impact Of Dispersion On Amplitude And Frequency Noise In A Yb-Fiber Laser Comb, Lora Nugent-Glandorf, Todd A. Johnson, Yohei Kobayashi, Scott A. Diddams May 2011

Impact Of Dispersion On Amplitude And Frequency Noise In A Yb-Fiber Laser Comb, Lora Nugent-Glandorf, Todd A. Johnson, Yohei Kobayashi, Scott A. Diddams

Physics Faculty Publications

We describe a Yb-fiber-based laser comb, with a focus on the relationship between the net-cavity dispersion and frequency noise on the comb. While tuning the net-cavity dispersion from anomalous to normal, we measure the relative intensity noise, offset frequency (fCEO) linewidth, and the resulting frequency noise spectrum on the fCEO. We find that the laser operating at zero net-cavity dispersion has many advantages, including an approximately 100× reduction in free-running fCEO linewidth and frequency noise power spectral density when compared to the normal-dispersion regime. At the zero-dispersion point, we demonstrate a phase-locked fCEO …


Prioritizing Investment In Residential Energy Efficiency And Renewable Energy: A Case Study For The U.S. Midwest, Robert J. Brecha, Austin Mitchell, Kevin P. Hallinan, J. Kelly Kissock May 2011

Prioritizing Investment In Residential Energy Efficiency And Renewable Energy: A Case Study For The U.S. Midwest, Robert J. Brecha, Austin Mitchell, Kevin P. Hallinan, J. Kelly Kissock

Physics Faculty Publications

Residential building energy use is an important contributor to greenhouse gas emissions and in the United States represents about 20% of total energy consumption. A number of previous macro-scale studies of residential energy consumption and energy-efficiency improvements are mainly concerned with national or international aggregate potential savings. In this paper we look into the details of how a collection of specific homes in one region might reduce energy consumption and carbon emissions, with particular attention given to some practical limits to what can be achieved by upgrading the existing residential building stock. Using a simple model of residential, single-family home …


Potassium Ion Fluxes In Corneal Epithelial Cells Exposed To Uvb, John L. Ubels, Rachel E. Van Dyken, Julienne R. Louters, Mark P. Schotanus May 2011

Potassium Ion Fluxes In Corneal Epithelial Cells Exposed To Uvb, John L. Ubels, Rachel E. Van Dyken, Julienne R. Louters, Mark P. Schotanus

University Faculty Publications and Creative Works

The goal of this study was to investigate the efflux of K+ from human corneal limbal epithelial cells (HCLE) exposed to ambient levels of UVB, which is known to cause apoptosis, and to examine the effect of K+ channel blockers on loss of potassium induced by UVB. HCLE cells were exposed to 100-200 mJ/cm2 UVB, followed by incubation in culture media with 5.5-100 mM K+, BDS-1, Ba2+ or ouabain. To measure intracellular cations, cells were washed in 280 mM sucrose and lysed in DI water. K+ and Na+ levels in lysates were measured by ion chromatography. HCLE cells showed maximal …


Potassium Ion Fluxes In Corneal Epithelial Cells Exposed To Uvb, John L. Ubels, Rachel E. Van Dyken, Julienne R. Louters, Mark P. Schotanus May 2011

Potassium Ion Fluxes In Corneal Epithelial Cells Exposed To Uvb, John L. Ubels, Rachel E. Van Dyken, Julienne R. Louters, Mark P. Schotanus

University Faculty Publications and Creative Works

The goal of this study was to investigate the efflux of K+ from human corneal limbal epithelial cells (HCLE) exposed to ambient levels of UVB, which is known to cause apoptosis, and to examine the effect of K+ channel blockers on loss of potassium induced by UVB. HCLE cells were exposed to 100-200 mJ/cm2 UVB, followed by incubation in culture media with 5.5-100 mM K+, BDS-1, Ba2+ or ouabain. To measure intracellular cations, cells were washed in 280 mM sucrose and lysed in DI water. K+ and Na+ levels in lysates were measured by ion chromatography. HCLE cells showed maximal …


Optimization Of The Nanolens Consisting Of Coupled Metal Nanoparticles: An Analytical Approach, Greg Sun, Jacob B. Khurgin Apr 2011

Optimization Of The Nanolens Consisting Of Coupled Metal Nanoparticles: An Analytical Approach, Greg Sun, Jacob B. Khurgin

Physics Faculty Publications

Using a simple and intuitive analytical approach, we perform optimization of a nanolens composed of coupled metal nanoparticles capable of subwavelength focusing of light inside the narrow gap separating the particles. Specifically, we optimize the structure of two nanospheres of different sizes to achieve maximum field enhancement at an off-center position in the gap. We demonstrate that the nanolens of two or more spheres acts simultaneously as an efficient antenna with large dipole and an efficient cavity with small effective volume.


Scalar Em Beam Propagation In Inhomogeneous Media, John M. Jarem, Partha P. Banerjee Apr 2011

Scalar Em Beam Propagation In Inhomogeneous Media, John M. Jarem, Partha P. Banerjee

Electrical and Computer Engineering Faculty Publications

In the previous chapter, we reviewed some of the mathematical preliminaries that will be useful later on in the text. In this chapter, we discuss some of the basic concepts of scalar wave propagation, and discuss an important numerical method, called the beam propagation method (BPM), to study propagation in linear media and in media with induced nonlinearities. Furthermore, we also discuss propagation through induced gratings, both transmission and reflection type, in order to assess energy coupling between participating waves. Finally, we introduce readers to an important characterization method, called the z-scan method, which is often used to determine the …


Binary And Core-Shell Nanoparticle Dispersed Liquid Crystal Cells For Metamaterial Applications, George Nehmetallah, Rola Aylo, Partha P. Banerjee Apr 2011

Binary And Core-Shell Nanoparticle Dispersed Liquid Crystal Cells For Metamaterial Applications, George Nehmetallah, Rola Aylo, Partha P. Banerjee

Electrical and Computer Engineering Faculty Publications

We theoretically explored the feasibility of a tunable metamaterial using binary as well as core-shell nanoparticle dispersed liquid crystal cells in the infrared and optical regimes. Owing to the spatial variation of the permittivity of the liquid crystal host upon the application of a bias voltage, the host was decomposed into a layered medium and the effective refractive index recalculated for each layer due to the distribution of polaritonic and plasmonic nanoparticles.

The scattering, extinction, and absorption of such a nanoparticle dispersed liquid crystal cell were also found. Depending on the applied voltage bias across the liquid crystal host, the …


Ultrafast High-Energy Electron Diffraction Study Of Photoexcited Bismuth Nanoclusters By Femtosecond Laser Pulses, Ahmed R. Esmail Apr 2011

Ultrafast High-Energy Electron Diffraction Study Of Photoexcited Bismuth Nanoclusters By Femtosecond Laser Pulses, Ahmed R. Esmail

Electrical & Computer Engineering Theses & Dissertations

The advancement in ultrafast electron crystallography (UEC) over the past few decades facilitated the study of structural dynamics in all phases of matter induced by femtosecond laser pulses. This technique became very powerful when the spatial resolution was combined with the temporal resolution, and succeeded in studying chemical reactions by ultrafast electron diffraction, bulk crystal phonons and melting by X-ray diffraction.

In this dissertation, I demonstrate the uniqueness of UEC and its potential in monitoring in real time the structural dynamics of bismuth (Bi) nanoclusters and islands induced by femtosecond laser pulses. Our approach to accomplish this task includes building …


Diffusion Of Rubidium Vapor Through Hollow-Core Fibers For Gas-Phase Fiber Lasers, Eric M. Guild Mar 2011

Diffusion Of Rubidium Vapor Through Hollow-Core Fibers For Gas-Phase Fiber Lasers, Eric M. Guild

Theses and Dissertations

This work examines the diffusion of rubidium through a small diameter tube alone and in the presence of noble gases. A fluid dynamics analysis is investigated to aid in choosing a method for transferring atomic rubidium vapor that is reliable and efficient. Solutions to the time dependant ordinary differential equation describing the experimental flow properties of the system reveal more precise outcomes than previously practiced routines. Resolved viscosities and Poiseuille flow theory velocity profile distributions are characterized for noble gas carriers of the rubidium vapor. Applying Reynolds Numbers to the flow experiments provides pressure differential boundaries that are employed in …


Branch Point Mitigation Of Thermal Blooming Phase Compensation Instability, Mark F. Spencer Mar 2011

Branch Point Mitigation Of Thermal Blooming Phase Compensation Instability, Mark F. Spencer

Theses and Dissertations

Thermal blooming can have a major impact on high-energy laser (HEL) beam propagation in the atmosphere. In theory, an adaptiveoptics (AO) system can mitigate the nonlinear optical effects induced by thermal blooming; however, when a single deformable mirror is used for phase-only compensation, analysis predicts the possibility of instability. This instability is appropriately termed phase compensation instability (PCI) and arises with the time-dependent development of spatial perturbations found within the HEL beam. These spatial perturbations act as local hot spots that produce negative-lens-like optical effects in the atmosphere. An AO system corrects for the hot spots by applying positive-lens-like phase …


Optical And Electrical Characterization Melt-Grown Bulk Ingaas And Inasp, Jean W. Wei Mar 2011

Optical And Electrical Characterization Melt-Grown Bulk Ingaas And Inasp, Jean W. Wei

Theses and Dissertations

A new method to determine semiconductor bandgap energy directly from the easily measured transmission spectra was developed. The method was verified using many binary semiconductors with known properties and utilized to determine the unknown ternary semiconductors were determined at various wavelengths and temperatures. Photoluminescence and Hall-effect measurement were performed to identify various electronic transitions, as well as sample quality. The determination of electrical and optical properties of the material will provide important addition to the database of material properties for future optoelectronic device applications. In the near future, newer materials and their applications need to be developed, and often binary …


A Multispectral Bidirectional Reflectance Distribution Function Study Of Human Skin For Improved Dismount Detection, Bradley M. Koch Mar 2011

A Multispectral Bidirectional Reflectance Distribution Function Study Of Human Skin For Improved Dismount Detection, Bradley M. Koch

Theses and Dissertations

In 2008, the Sensors Exploitation Research Group at the Air Force Institute of Technology began using spectral properties of skin for the detection and classification of humans. Since then a multispectral skin detection system was developed to exploit the optical properties of human skin at wavelengths in the visible and near infrared region of the electromagnetic spectrum. A rules-based detector, analyzing an image spectrally, currently bases its skin pixel selection criteria on a diffuse skin reflectance model. However, when observing skin in direct view of the sun, a glint of light off skin is common and indicates specularity. The areas …


Shack-Hartmann And Interferometric Hybrid Wavefront Sensor, Troy R. Ellis Mar 2011

Shack-Hartmann And Interferometric Hybrid Wavefront Sensor, Troy R. Ellis

Theses and Dissertations

This document reports results of wave-optics simulations used to test the performance of a hybrid wavefront sensor designed to combine the self-referencing interferometer and Shack-Hartmann wavefront sensors in an optimal way. Optimal hybrid-wavefront sensor design required a thorough analysis of the noise characteristics of each wavefront sensor to produce noise models that assist in the design of an optimal phase-estimation algorithm. Feasible architectures and algorithms for combining wavefront sensors were chosen, and the noise models of the individual wavefront sensors were combined to form a model for the noise-induced error of the resulting hybrid sensor. The hybrid wavefront sensor and …


A Statistical Approach To Fusing 2-D And 3-D Ladar Systems, Paul F. Dolce Mar 2011

A Statistical Approach To Fusing 2-D And 3-D Ladar Systems, Paul F. Dolce

Theses and Dissertations

LADAR (LAser Detection and Ranging) systems can be used to provide 2-D and 3-D images of scenes. Generally, 2-D images possess superior spatial resolution but without range data due to the density of their focal plane arrays. A 3-D LADAR system can produce range to target data at each pixel, but lacks the 2-D system's superior spatial resolution. The 3-D system is limited by its hardware, specifically its imaging array. Currently developers are investigating ways to change the pixel size in the 3-D LADAR imaging array, but the costs of this research is quite expensive and technically robust. It is …


Development Of An Interference Lithography Capability Using A Helium Cadmium Ultraviolet Multimode Laser For The Fabrication Of Sub-Micron-Structured Optical Materials, Stanley D. Crozier Mar 2011

Development Of An Interference Lithography Capability Using A Helium Cadmium Ultraviolet Multimode Laser For The Fabrication Of Sub-Micron-Structured Optical Materials, Stanley D. Crozier

Theses and Dissertations

The goal of this work is to develop unique holograms on a semiconductor-metal thin films to characterize as potential metamaterials. This is achievable by developing a fabrication recipe to include exposure methods, exposure dosages, and material development. This study developed an interference lithography capability at AFIT for the first time with period resolution below 230nm. It also identified initial acceptable photoresist materials and exposure dosages, and a path to follow to optimize this process. The potential impact of this is to make IL a standard in optical meta-material fabrication, which decreases manufacturing time and allows for less error in production. …


Simulating The Effects Of An Extended Source On The Shack-Hartmann Wavefront Sensor Through Turbulence, Jeffery S. Dennison Mar 2011

Simulating The Effects Of An Extended Source On The Shack-Hartmann Wavefront Sensor Through Turbulence, Jeffery S. Dennison

Theses and Dissertations

Perspective elongation in Shack-Hartmann wavefront sensor (SHWFS) spots is a phenomenon caused by an extended three-dimensional scattering beacon in the mesosphere (80-100km). Elongated spots cause errors in wavefront sensor measurements, which leads to poor turbulence compensation and decreased image resolution of the optical system. In order to compensate for elongated spots, a proper beacon model must be developed to simulate the error. In this paper, a documented theory for modeling an elongated sodium beacon and elongated SHWFS spots using sodium layer slices was tested. It was found that nine evenly-spaced slices were adequate to model the elongated beacon in the …


Polarimetric Enhancements To Electro-Optical Aided Navigation Techniques, Jeremiah D. Johnson Mar 2011

Polarimetric Enhancements To Electro-Optical Aided Navigation Techniques, Jeremiah D. Johnson

Theses and Dissertations

Navigation in indoor and urban environments by small unmanned systems is a topic of interest for the Air Force. The Advanced Navigation Technology Center at the Air Force Institute of Technology is continually looking for novel approaches to navigation in GPS deprived environments. Inertial sensors have been coupled with image aided concepts, such as feature tracking, with good results. However, feature density in areas with large, flat, smooth surfaces tends to be low. Polarimetric sensors have been used for surface reconstruction, surface characterization and outdoor navigation. This thesis combines aspects of some of these algorithms along with a realistic, micro-facet …


Optical Metamaterial Design, Fabrication And Test, Jack P. Lombardi Mar 2011

Optical Metamaterial Design, Fabrication And Test, Jack P. Lombardi

Theses and Dissertations

Metamaterials, materials that make use of naturally occurring materials and designed structures to create materials with special properties not found in nature, are a fascinating new area of research, combining the fields of physics, microfabrication, and material science. This work will focus on the development of metamaterials operating in the visible and infrared which will be constructed and tested for basic optical properties. Possible applications for these materials will not be investigated. The this work will go into the fabrication and test of layered metal-dielectric structures, called layered metamaterials, as these structures hold potential for applications in advanced optical systems. …


Effect Of Coudé Pupil Rotation On Sodium Laser Beacon Perspective Elongation, Russell J. Mcguigan Mar 2011

Effect Of Coudé Pupil Rotation On Sodium Laser Beacon Perspective Elongation, Russell J. Mcguigan

Theses and Dissertations

This research models a sodium laser guide star and its measurement by a Shack-Hartmann wavefront sensor. By predicting the extent of beacon elongation and Coude rotation, reference images are produced for each subaperture throughout an engagement scenario. These reference sources are then used to continuously recalibrate the system as it changes orientation. This model measures the effect of perspective elongation and Coude on SHWFS measurements to quantitatively determine the extent of degradation that occurs.


Single-Beam Holographic Tomography Creates Images In Three Dimensions, George Nehmetallah, Partha P. Banerjee, Nickolai Kukhtarev Mar 2011

Single-Beam Holographic Tomography Creates Images In Three Dimensions, George Nehmetallah, Partha P. Banerjee, Nickolai Kukhtarev

Electrical and Computer Engineering Faculty Publications

In digital holography (DH), the interference between light scattered from an object and a reference wave is recorded using a CCD camera. DH has various advantages over analog holography: no film processing is needed, reconstruction is performed using numerical methods, and no further experimental setup is necessary. However, one of the disadvantages of DH is that current CCDs have a resolution of approximately 1,000 lines/mm, which is less than that of photographic film.


Anisotropic Electrical Properties Of Nanostructured Metallic Thin Films, Mo Ahoujja, Piyush Shah, Andrew Saragan, Said Elhamri, Elena A. Guliants Mar 2011

Anisotropic Electrical Properties Of Nanostructured Metallic Thin Films, Mo Ahoujja, Piyush Shah, Andrew Saragan, Said Elhamri, Elena A. Guliants

Electrical and Computer Engineering Faculty Publications

High surface area, porous, metallic (Ti, Cr) nanorod thin ¯lms with columnar microstructure can be deposited using conventional physical vapor deposition technique of E-beam evaporation. The technique relies on the physical vapor deposition onto a static substrate oriented in a position where °ux from the source material (Ti, Cr) arrives at oblique angle. The adatoms provides geometrical shadowing which results in growth of nanorod columns in the direction of vapor source. Deposition conditions such as angle of the incoming vapor °ux, substrate temperature, surface di®usion etc. have strong in°uence on the shape and arrangement of the columnar thin ¯lms. In …


Shock Wave Dynamics Of Novel Aluminized Detonations And Empirical Model For Temperature Evolution From Post-Detonation Combustion Fireballs, Joe Motos Gordon Mar 2011

Shock Wave Dynamics Of Novel Aluminized Detonations And Empirical Model For Temperature Evolution From Post-Detonation Combustion Fireballs, Joe Motos Gordon

Theses and Dissertations

This research characterizes the blast wave and temperature evolution of an explosion fireball in order to improve the classification of aluminized conventional munitions based on a single explosive type such as RDX. A drag model fit to data shows initial shock velocities of 1.6-2.8 km/s and maximum fireball radii ranging from 4.3-5.8 m with most of the radii reached by 50 ms upon detonation. The Sedov-Taylor point blast model is fitted to data where a constant release (s=1) of energy upon detonation suggests shock energies of 0.5-8.9 MJ with blast dimensionalities indicative of the spherical geometry (n3) observed in visible …