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Articles 1651 - 1680 of 5600
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Improving The Cybersecurity Of Cyber-Physical Systems Through Behavioral Game Theory And Model Checking In Practice And In Education, Seth T. Hamman
Improving The Cybersecurity Of Cyber-Physical Systems Through Behavioral Game Theory And Model Checking In Practice And In Education, Seth T. Hamman
Theses and Dissertations
This dissertation presents automated methods based on behavioral game theory and model checking to improve the cybersecurity of cyber-physical systems (CPSs) and advocates teaching certain foundational principles of these methods to cybersecurity students. First, it encodes behavioral game theory's concept of level-k reasoning into an integer linear program that models a newly defined security Colonel Blotto game. This approach is designed to achieve an efficient allocation of scarce protection resources by anticipating attack allocations. A human subjects experiment based on a CPS infrastructure demonstrates its effectiveness. Next, it rigorously defines the term adversarial thinking, one of cybersecurity educations most important …
Optical Theory Improvements To Space Domain Awareness, Tyler J. Hardy
Optical Theory Improvements To Space Domain Awareness, Tyler J. Hardy
Theses and Dissertations
This dissertation focuses on increasing the ability to detect space objects and increase Space Domain Awareness (SDA) with space surveillance sensors through image processing and optical theory. SDA observations are collected through ground-based radar and optical systems as well as space based assets. This research focuses on a ground-based optical telescope system, the Space Surveillance Telescope (SST). By increasing the number of detectable Resident Space Objects (RSOs) through image processing, SDA capabilities can be expanded. This is accomplished through addressing two main degrading factors present in typical SDA sensors; spatial undersampling in the collected data and noise models and assumptions …
Data Driven Device Failure Prediction, Paul L. Jordan
Data Driven Device Failure Prediction, Paul L. Jordan
Theses and Dissertations
As society becomes more dependent upon computer systems to perform increasingly critical tasks, ensuring those systems do not fail also becomes more important. Many organizations depend heavily on desktop computers for day to day operations. Unfortunately, the software that runs on these computers is still written by humans and as such, is still subject to human error and consequent failure. A natural solution is to use statistical machine learning to predict failure. However, since failure is still a relatively rare event, obtaining labeled training data to train these models is not trivial. This work presents new simulated fault loads with …
Absolute Positioning Using The Earth's Magnetic Anomaly Field, Aaron J. Canciani
Absolute Positioning Using The Earth's Magnetic Anomaly Field, Aaron J. Canciani
Theses and Dissertations
Achieving worldwide alternatives to GPS is a challenging engineering problem. Current GPS alternatives often suffer from limitations such as where and when the systems can operate. Navigation using the Earth's magnetic anomaly field, which is globally available at all times, shows promise to overcome many of these limitations. We present a navigation filter which uses the Earth's magnetic anomaly field as a navigation signal to aid an inertial navigation system (INS) in an aircraft. The filter utilizes highly-accurate optically pumped cesium (OPC) magnetometers to make scalar measurements of the Earth's magnetic field and compare them to a map using a …
Experimental Testing Of A Van De Graaff Generator As An Electromagnetic Pulse Generator, John S. Leahy
Experimental Testing Of A Van De Graaff Generator As An Electromagnetic Pulse Generator, John S. Leahy
Theses and Dissertations
The purpose of this research was to evaluate an existing Van de Graaff generator facility for use as an EMP research tool. In order to assess the Van de Graaff, the unclassified Military Standard 464, which specifies a testing free field wave as having an intensity of 50 kV/m with a time-to-peak, of no more than 5 ns, was used as a baseline for free field analysis and this temporal standard used as a basis for generated currents. Unfortunately, the free field measurements were subject to substantial electronic interference from electromagnetic coupling from internal wall reflections, invalidating the assessment. Therefore …
Evaluation Of Hydrothermally Synthesized Uranium Dioxide For Novel Semiconductor Applications, Christopher M. Young
Evaluation Of Hydrothermally Synthesized Uranium Dioxide For Novel Semiconductor Applications, Christopher M. Young
Theses and Dissertations
Neutron radiation detection is an important part of the national strategy for nonproliferation efforts worldwide. Key to the success of these programs is detector material development which establishes the limits of efficiency, sensitivity, and power usage for a detector of practical use. This research focused upon the study of neutron detection using single crystal actinide compounds, specifically UO2, taking advantage of the successful hydrothermal synthesis of UO2 at the Air Force Research Laboratories. Initial indications are that this material may be of sufficient quality for semiconductor application.
Non-Linear Metamodeling Extensions To The Robust Parameter Design Of Computer Simulations, Joseph P. Bellucci
Non-Linear Metamodeling Extensions To The Robust Parameter Design Of Computer Simulations, Joseph P. Bellucci
Theses and Dissertations
Robust parameter design (RPD) is used to identify a systems control settings that offer a compromise between obtaining desired mean responses and minimizing the variability about those responses. Two popular combined-array strategies the response surface model (RSM) approach and the emulator approach are limited when applied to simulations. In the former case, the mean and variance models can be inadequate due to a high level of non-linearity within many simulations. In the latter case, precise mean and variance approximations are developed at the expense of extensive Monte Carlo sampling. This research combines the RSM approach's efficiency with the emulator approach's …
Improving Real-World Performance Of Vision Aided Navigation In A Flight Environment, Donald T. Venable
Improving Real-World Performance Of Vision Aided Navigation In A Flight Environment, Donald T. Venable
Theses and Dissertations
The motivation of this research is to fuse information from an airborne imaging sensor with information extracted from satellite imagery in order to provide accurate position when GPS is unavailable for an extended duration. A corpus of existing geo-referenced satellite imagery is used to create a key point database. A novel algorithm for recovering coarse pose using by comparing key points extracted from the airborne imagery to the reference database is developed. This coarse position is used to bootstrap a local-area geo-registration algorithm, which provides GPS-level position estimates. This research derives optimizations for existing local-area methods for operation in flight …
Application Of Executable Architecture In Early Concept Evaluation Using The Dod Architecture Framework, Zhongwang Chua
Application Of Executable Architecture In Early Concept Evaluation Using The Dod Architecture Framework, Zhongwang Chua
Theses and Dissertations
The increasing complexity in the development of today's modern warfighting systems demands a systematic evaluation approach in the assessment of the envisaged capability and estimating the cost effectiveness, especially in the early stages of Concept Development. This research focused on the development of early Concept evaluation methodology through the use of Executable Architecture (EA) through the System Architecting process. Particularly, the methodology was applied in the assessment of a proposed Multi-tiered Unmanned Aircraft System System-of-System that is designed provide target acquisition and conduct dynamic strike on Theater Ballistic Missile launchers. Through the implementation of the evaluation methodology using dynamic modeling …
Adaptive Estimation And Heuristic Optimization Of Nonlinear Spacecraft Attitude Dynamics, Joshuah A. Hess
Adaptive Estimation And Heuristic Optimization Of Nonlinear Spacecraft Attitude Dynamics, Joshuah A. Hess
Theses and Dissertations
For spacecraft conducting on-orbit operations, changes to the structure of the spacecraft are not uncommon. These planned or unanticipated changes in inertia properties couple with the spacecraft's attitude dynamics and typically require estimation. For systems with time-varying inertia parameters, multiple model adaptive estimation (MMAE) routines can be utilized for parameter and state estimates. MMAE algorithms involve constructing a bank of recursive estimators, each assuming a different hypothesis for the systems dynamics. This research has three distinct, but related, contributions to satellite attitude dynamics and estimation. In the first part of this research, MMAE routines employing parallel banks of unscented attitude …
Time Domain Analysis Of Electromagnetic Scattering From Multiple Cavities Embedded In A Ground Plane, Richard P. Uber
Time Domain Analysis Of Electromagnetic Scattering From Multiple Cavities Embedded In A Ground Plane, Richard P. Uber
Theses and Dissertations
This work examines the scattered fields produced when a transient wave is reflected from an infinite perfect electric conductor (PEC) ground plane with multiple embedded cavities. Incident and reflected waves will be decomposed into transverse magnetic to the z direction (TMz) and transverse electric to the z direction (TEz) polarizations, with primary focus given to the TMz. Cavities may be unfilled, partially filled, or fully filled with non-magnetic dielectric material and no assumptions are made regarding similarity, regularity, or periodicity. The Newmark method is used to discretize time and a variational formulation is presented for each time step. The principle …
Orbit Determination Using Vinti's Solution, Steven P. Wright
Orbit Determination Using Vinti's Solution, Steven P. Wright
Theses and Dissertations
Orbital altitudes congested with spacecraft and debris combined with recent collisions have all but negated the Big Sky Theory. As the sheer number of orbital objects to track grows unbounded so does interest in prediction methods that are rapid and minimally computational. Claimed as the \other solvable solution, the recently completed solution too orbital motion about the earth, based on Vinti's method and including the major effects of the equatorial bulge, opens up the prospect of much more accurate analytical models for space situational awareness. A preliminary examination of this solution is presented. A numerical state transition matrix is found …
A Novel Machine Learning Classifier Based On A Qualia Modeling Agent (Qma), Sandra L. Vaughan
A Novel Machine Learning Classifier Based On A Qualia Modeling Agent (Qma), Sandra L. Vaughan
Theses and Dissertations
This dissertation addresses a problem found in supervised machine learning (ML) classification, that the target variable, i.e., the variable a classifier predicts, has to be identified before training begins and cannot change during training and testing. This research develops a computational agent, which overcomes this problem. The Qualia Modeling Agent (QMA) is modeled after two cognitive theories: Stanovich's tripartite framework, which proposes learning results from interactions between conscious and unconscious processes; and, the Integrated Information Theory (IIT) of Consciousness, which proposes that the fundamental structural elements of consciousness are qualia. By modeling the informational relationships of qualia, the QMA allows …
Physical Layer Defenses Against Primary User Emulation Attacks, Joan A. Betances
Physical Layer Defenses Against Primary User Emulation Attacks, Joan A. Betances
Theses and Dissertations
Cognitive Radio (CR) is a promising technology that works by detecting unused parts of the spectrum and automatically reconfiguring the communication system's parameters in order to operate in the available communication channels while minimizing interference. CR enables efficient use of the Radio Frequency (RF) spectrum by generating waveforms that can coexist with existing users in licensed spectrum bands. Spectrum sensing is one of the most important components of CR systems because it provides awareness of its operating environment, as well as detecting the presence of primary (licensed) users of the spectrum.
Synergistic Effects Of Phase Folding And Wavelet Denoising With Applications In Light Curve Analysis, Andrew M. Armstrong
Synergistic Effects Of Phase Folding And Wavelet Denoising With Applications In Light Curve Analysis, Andrew M. Armstrong
Theses and Dissertations
The growing size of cosmological data sets is causing the current human-centric approach to cosmology to become impractical. Autonomous data analysis techniques need to be developed in order to advance the field of cosmology. This research examines the benefits of combining two signal analysis techniques, namely phase folding and wavelet denoising, into a newly-developed suite of autonomous light curve analysis tools which includes aspects of component extraction and period detection. The improvements these tools provide, with respect to autonomy and signal quality, are demonstrated using both simulated and real-world light curve data. Although applied to light curve data, the suite …
Fusion Of Renewable Ring Resonator Lasers And Ultrafast Laser Inscribed Photonic Waveguides, Hengky Chandrahalim, Stephen C. Rand, Xudong Fan
Fusion Of Renewable Ring Resonator Lasers And Ultrafast Laser Inscribed Photonic Waveguides, Hengky Chandrahalim, Stephen C. Rand, Xudong Fan
Faculty Publications
We demonstrated the monolithic integration of reusable and wavelength reconfigurable ring resonator lasers and waveguides of arbitrary shapes to out-couple and guide laser emission on the same fused-silica chip. The ring resonator hosts were patterned by a single-mask standard lithography, whereas the waveguides were inscribed in the proximity of the ring resonator by using 3-dimensional femtosecond laser inscription technology. Reusability of the integrated ring resonator – waveguide system was examined by depositing, removing, and re-depositing dye-doped SU-8 solid polymer, SU-8 liquid polymer, and liquid solvent (toluene). The wavelength reconfigurability was validated by employing Rhodamine 6G (R6G) and 3,3′-Diethyloxacarbocyanine iodide (CY3) …
Estimation Of Temporal Variations In Path-Averaged Atmospheric Refractive Index Gradient From Time-Lapse Imagery, Santasri Basu, Jack E. Mccrae, Steven T. Fiorino, Jared Przelomski
Estimation Of Temporal Variations In Path-Averaged Atmospheric Refractive Index Gradient From Time-Lapse Imagery, Santasri Basu, Jack E. Mccrae, Steven T. Fiorino, Jared Przelomski
Faculty Publications
The sea level vertical refractive index gradient in the U.S. Standard Atmosphere model is −2.7×10−8 m−1 at 500 nm. At any particular location, the actual refractive index gradient varies due to turbulence and local weather conditions. An imaging experiment was conducted to measure the temporal variability of this gradient. A tripod mounted digital camera captured images of a distant building every minute. Atmospheric turbulence caused the images to wander quickly, randomly, and statistically isotropically and changes in the average refractive index gradient along the path caused the images to move vertically and more slowly. The temporal variations of …
Direct Bandgap Cross-Over Point Of Ge1-YSnY Grown On Si Estimated Through Temperature-Dependent Photoluminescence Studies, Thomas R. Harris, Mee-Yi Ryu, Yung Kee Yeo, Buguo Wang, C. L. Senaratne
Direct Bandgap Cross-Over Point Of Ge1-YSnY Grown On Si Estimated Through Temperature-Dependent Photoluminescence Studies, Thomas R. Harris, Mee-Yi Ryu, Yung Kee Yeo, Buguo Wang, C. L. Senaratne
Faculty Publications
Epitaxial Ge1-ySny (y = 0%–7.5%) alloys grown on either Si or Ge-buffered Si substrates by chemical vapor deposition were studied as a function of Sn content using temperature-dependent photoluminescence (PL). PL emission peaks from both the direct bandgap (Γ-valley) and the indirect bandgap (L-valley) to the valence band (denoted by ED and EID, respectively) were clearly observed at 125 and 175 K for most Ge1-ySny samples studied. At 300 K, however, all of the samples exhibited dominant ED emission with either very weak or no measureable EID emission. At 10 K, …
A Hybrid Optimization Technique Applied To The Intermediate-Target Optimal Control Problem, Clay J. Humphreys, Richard G. Cobb, David R. Jacques, Jonah A. Reeger
A Hybrid Optimization Technique Applied To The Intermediate-Target Optimal Control Problem, Clay J. Humphreys, Richard G. Cobb, David R. Jacques, Jonah A. Reeger
Faculty Publications
The DoD has introduced the concept of Manned-Unmanned Teaming, a subset of which is the loyal wingman. Optimal control techniques have been proposed as a method for rapidly solving the intermediate-target (mid-point constraint) optimal control problem. Initial results using direct orthogonal collocation and a gradient-based method for solving the resulting nonlinear program reveals a tendency to converge to or to get `stuck’ in locally optimal solutions. The literature suggested a hybrid technique in which a particle swarm optimization is used to quickly find a neighborhood of a more globally minimal solution, at which point the algorithm switches to a gradient-based …
Quantum Key Distribution: Boon Or Bust, Logan O. Mailloux, Douglas D. Hodson, Michael R. Grimaila, Colin V. Mclaughlin, Gerald B. Baumgartner
Quantum Key Distribution: Boon Or Bust, Logan O. Mailloux, Douglas D. Hodson, Michael R. Grimaila, Colin V. Mclaughlin, Gerald B. Baumgartner
Faculty Publications
Quantum Key Distribution (QKD) is an emerging cybersecurity technology which provides the means for two geographically separated parties to grow “unconditionally secure” symmetric cryptographic keying material. Unlike traditional key distribution techniques, the security of QKD rests on the laws of quantum mechanics and not computational complexity. This unique aspect of QKD is due to the fact that any unauthorized eavesdropping on the key distribution channel necessarily introduces detectable errors (Gisin, Ribordy, Tittel, & Zbinden, 2002). This attribute makes QKD desirable for high-security environments such as banking, government, and military applications. However, QKD is a nascent technology where implementation non-idealities can …
Predictive Coupled-Cluster Isomer Orderings For Some SiNCM (M, N ≤ 12) Clusters: A Pragmatic Comparison Between Dft And Complete Basis Limit Coupled-Cluster Benchmarks, Jason N. Byrd, Jesse J. Lutz, Duminda S. Ranasinghe, Yifan Jin, Ajith Perera, Xiaofeng F. Duan, Larry W. Burggraf, John A. Montgomery Jr.
Predictive Coupled-Cluster Isomer Orderings For Some SiNCM (M, N ≤ 12) Clusters: A Pragmatic Comparison Between Dft And Complete Basis Limit Coupled-Cluster Benchmarks, Jason N. Byrd, Jesse J. Lutz, Duminda S. Ranasinghe, Yifan Jin, Ajith Perera, Xiaofeng F. Duan, Larry W. Burggraf, John A. Montgomery Jr.
Faculty Publications
The accurate determination of the preferred Si12C12 isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC3 to Si12C12. It is found that post-MBPT(2) correlation energy plays a …
Nitrogen Rate And Landscape Impacts On Life Cycle Energy Use And Emissions From Switchgrass-Derived Ethanol, Eric G. Mbonimpa, Sandeep Kumar, Vance N. Owens, Rajesh Chintala, Heidi L. Sieverding, James J. Stone
Nitrogen Rate And Landscape Impacts On Life Cycle Energy Use And Emissions From Switchgrass-Derived Ethanol, Eric G. Mbonimpa, Sandeep Kumar, Vance N. Owens, Rajesh Chintala, Heidi L. Sieverding, James J. Stone
Faculty Publications
Switchgrass-derived ethanol has been proposed as an alternative to fossil fuels to improve sustainability of the US energy sector. In this study, life cycle analysis (LCA) was used to estimate the environmental benefits of this fuel. To better define the LCA environmental impacts associated with fertilization rates and farm-landscape topography, results from a controlled experiment were analyzed. Data from switchgrass plots planted in 2008, consistently managed with three nitrogen rates (0, 56, and 112 kg N ha−1), two landscape positions (shoulder and footslope), and harvested annually (starting in 2009, the year after planting) through 2014 were used as input into …
Wartime Construction Project Outcomes As A Function Of Contract Type, Ryan M. Hoff, Gregory D. Hammond, Peter P. Feng, Edward D. White
Wartime Construction Project Outcomes As A Function Of Contract Type, Ryan M. Hoff, Gregory D. Hammond, Peter P. Feng, Edward D. White
Faculty Publications
The United States has spent more than $23 billion on construction in Afghanistan since 2001. The dynamic security situation created substantial project uncertainty, and many construction projects used cost-plus-fixed-fee contracts (CPFF) instead of the firm-fixed-price (FFP) norm. Using a dataset of 25 wartime construction projects managed by the Air Force Civil Engineer Center, the authors sought to confirm that both contract types yield project outcomes consistent with the established literature. As expected, they found CPFF contracts had greater cost and schedule growth than FFP. However, they did not find differences regarding as-built quality. Additionally, the authors sought to determine whether …
Benefits Of Considering More Than Temperature Acceleration For Gan Hemt Life Testing, Ronald A. Coutu Jr., Robert A. Lake, Bradley D. Christiansen, Eric R. Heller, Christopher A. Bozada, Brian S. Poling, Glen D. Via, James P. Theimer, Stephen E. Tetlak, Ramakrishna Vetury, Jeffrey B. Shealy
Benefits Of Considering More Than Temperature Acceleration For Gan Hemt Life Testing, Ronald A. Coutu Jr., Robert A. Lake, Bradley D. Christiansen, Eric R. Heller, Christopher A. Bozada, Brian S. Poling, Glen D. Via, James P. Theimer, Stephen E. Tetlak, Ramakrishna Vetury, Jeffrey B. Shealy
Faculty Publications
The purpose of this work was to investigate the validity of Arrhenius accelerated-life testing when applied to gallium nitride (GaN) high electron mobility transistors (HEMT) lifetime assessments, where the standard assumption is that only critical stressor is temperature, which is derived from operating power, device channel-case, thermal resistance, and baseplate temperature. We found that power or temperature alone could not explain difference in observed degradation, and that accelerated life tests employed by industry can benefit by considering the impact of accelerating factors besides temperature. Specifically, we found that the voltage used to reach a desired power dissipation is important, and …
A Multi-Objective Approach To Tactical Maneuvering Within Real Time Strategy Games, Christopher D. Ball
A Multi-Objective Approach To Tactical Maneuvering Within Real Time Strategy Games, Christopher D. Ball
Theses and Dissertations
The real time strategy (RTS) environment is a strong platform for simulating complex tactical problems. The overall research goal is to develop artificial intelligence (AI) RTS planning agents for military critical decision making education. These agents should have the ability to perform at an expert level as well as to assess a players critical decision-making ability or skill-level. The nature of the time sensitivity within the RTS environment creates very complex situations. Each situation must be analyzed and orders must be given to each tactical unit before the scenario on the battlefield changes and makes the decisions no longer relevant. …
Synaptic Annealing: Anisotropic Simulated Annealing And Its Application To Neural Network Synaptic Weight Selection, Justin R. Fletcher
Synaptic Annealing: Anisotropic Simulated Annealing And Its Application To Neural Network Synaptic Weight Selection, Justin R. Fletcher
Theses and Dissertations
Machine learning algorithms have become a ubiquitous, indispensable part of modern life. Neural networks are one of the most successful classes of machine learning algorithms, and have been applied to solve problems previously considered to be the exclusive domain of human intellect. Several methods for selecting neural network configurations exist. The most common such method is error back-propagation. Backpropagation often produces neural networks that perform well, but do not achieve an optimal solution. This research explores the effectiveness of an alternative feed-forward neural network weight selection procedure called synaptic annealing. Synaptic annealing is the application of the simulated annealing algorithm …
Meeting The Dod’S Tactical Weather Needs Using Cubesats, Shayna K. Mckenney
Meeting The Dod’S Tactical Weather Needs Using Cubesats, Shayna K. Mckenney
Theses and Dissertations
This thesis investigates a CubeSat design that uses Commercial-Off-The-Shelf (COTS) components to capture, store, process, and downlink collected terrestrial weather data at resolutions near stat-of-the-art. The weather phenomena to be detected and transmitted in a timely manner are cloud formations, wind profiles, ocean currents, sea state, lightning, temperature profiles, and precipitation. It is hypothesized and shown that the proposed design will provide an improvement on the current U.S. tactical weather collection satellites because of the anticipated increased reliability and lowered cost to build and maintain the proposed CubeSat constellation. The methodology employed a multi-phase approach through the collective research of …
Design, Manufacturing, And Testing Of A Small Through-Flow Wave For Use Within The Brayton Cycle, Micahel J. Mcclearn
Design, Manufacturing, And Testing Of A Small Through-Flow Wave For Use Within The Brayton Cycle, Micahel J. Mcclearn
Theses and Dissertations
With the ever growing popularity of drones and other unmanned aerial vehicles for military, commercial, and private usage, there is a desire to improve performance in terms of range, altitude, and flight speed. Current technology uses either electric motors or internal combustion engines: both piston and jet engine types. These sorts of engines undergo significant efficiency degradation as their size decreases. While some efficiency may be recovered via intensive design studies, the cycles are approaching the limit to their operating physics. A possible solution to this is to change the operating physics to something more immune to scaling losses; a …
Test And Verification Of A Cubesat Attitude Determination And Control System In Variable Magnetic Fields, Eric A. Bassett
Test And Verification Of A Cubesat Attitude Determination And Control System In Variable Magnetic Fields, Eric A. Bassett
Theses and Dissertations
The Center for Space Research and Assurance (CSRA) at the Air Force Institute of Technology (AFIT) continues to explore CubeSat initiatives for solving many current space security issues. Regardless of the mission requirements, the success of the Cube- Sat on orbit frequently depends on the Attitude Determination and Control System (ADCS) functioning correctly. Previous research at AFIT has demonstrated single axis control on a spherical air bearing test bed incorporated within a Helmholtz cage utilizing artificially strong magnetic fields for better signal to noise ratios which are not experienced on orbit. This research explores the process of redesigning, testing, and …
Microfacet Wavelength Scaling Of The Brdf, Samuel E. Freda
Microfacet Wavelength Scaling Of The Brdf, Samuel E. Freda
Theses and Dissertations
The bidirectional reflectance distribution function (BRDF) describes realistic scattering of light off materials by relating incident irradiance to outbound radiance. One popular class of BRDF models assumes a surface is comprised of tiny microfacets. The drawback of microfacet BRDFs is that they often no not contain specific material parameters and neglect wavelength effects. Wave optics BRDF expressions, however, can describe wavelength effects at the expense of being more computationally cumbersome. Previous work of following a Beckmann-Kirchhoff derivation of BRDF, then relating wave optics BRDF coordinates to microfacet coordinates led to a complicated, but versatile, BRDF. In this work, the infinite …