Search NASA⌕ Search

SEARCH · Search NASA

Results for “Shifted Boundary Method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

2D Quantum Transport Modeling in Nanoscale MOSFETs

With the onset of quantum confinement in the inversion layer in nanoscale MOSFETs, behavior of the resonant level inevitably determines all device characteristics. While most classical device simulators take quantization into account in some simplified manner, the important details of electrostatics are missing. Our work addresses this shortcoming and provides: (a) a framework to quantitatively explore device physics issues such as the source-drain and gate leakage currents, DIBL, and threshold voltage shift due to quantization, and b) a means of benchmarking quantum corrections to semiclassical models (such as density- gradient and quantum-corrected MEDICI). We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions, oxide tunneling and phase-breaking scattering are treated on equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Quantum simulations are focused on MIT 25, 50 and 90 nm "well- tempered" MOSFETs and compared to classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. These results are quantitatively consistent with I D Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and sub-threshold current has been studied. The shorter gate length device has an order of magnitude smaller current at zero gate bias than the longer gate length device without a significant trade-off in on-current. This should be a device design consideration.

Svizhenko, Alexei↗
NASA NTRS2000

2D Quantum Mechanical Study of Nanoscale MOSFETs

With the onset of quantum confinement in the inversion layer in nanoscale MOSFETs, behavior of the resonant level inevitably determines all device characteristics. While most classical device simulators take quantization into account in some simplified manner, the important details of electrostatics are missing. Our work addresses this shortcoming and provides: (a) a framework to quantitatively explore device physics issues such as the source-drain and gate leakage currents, DIBL, and threshold voltage shift due to quantization, and b) a means of benchmarking quantum corrections to semiclassical models (such as density-gradient and quantum-corrected MEDICI). We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. We present the results of our simulations of MIT 25, 50 and 90 nm "well-tempered" MOSFETs and compare them to those of classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. Surprisingly, the self-consistent potential profile shows lower injection barrier in the channel in quantum case. These results are qualitatively consistent with ID Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and subthreshold current has been studied. The shorter gate length device has an order of magnitude smaller current at zero gate bias than the longer gate length device without a significant trade-off in on-current. This should be a device design consideration.

Svizhenko, Alexei↗
DOE OSTI2026

Scattering phase shift in quantum mechanics on quantum computers

Here, we investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in the work by Guo and Gasparian [Phys. Rev. D 108, 074504 (2023)] that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral. The system is first discretized in a finite box with periodic boundary conditions, and the formalism in real time is verified by employing a contact interaction potential with exact solutions. Quantum circuits are then designed and constructed to implement the formalism on current quantum computing architectures. To overcome the fast oscillatory behavior of the integrated correlation functions in real-time simulation, different methods of postdata analysis are proposed and discussed. Test results on IBM hardware show that good agreement can be achieved with two qubits, but complete failure ensues with three qubits due to two-qubit gate operation errors and thermal relaxation errors.

Guo, Peng [Dakota State Univ., Madison, SD (United↗
NASA NTRS2000

Numerical Simulation of Receptivity for a Transition Experiment

The cost of fuel to overcome turbulence induced viscous drag on a commercial airplane constitutes a significant fraction of the operating cost of an airline. Achieving laminar flow and maintaining it over a large portion of the wing can significantly reduce the viscous drag, and hence the cost. Design of such laminar-flow-control wings and their practical operation requires the ability to accurately and reliably predict the transition from laminar to turbulent flow. The transition process begins with the conversion of environmental and surface disturbances into the instability waves of the flow by a process called receptivity. The goal of the current research project has been to improve the prediction of transition through a better understanding of the physics of receptivity. The initial objective of this work was to investigate the specific stability and receptivity characteristics of a particular experimental investigation of boundary layer receptivity at NASA Langley. Some simulation results using direct solutions of the linearized Navier-Stokes equations which modeled this experiment where presented in the 1999 APS DFD meeting. However, based on these initial investigations, it became clear that to cover the vast receptivity parameter space required for a practical transition prediction tool, more efficient methods would be required. Thus, the focus of this research was shifted from modeling this particular experiment to formulating and developing new techniques that could efficiently yet accurately predict receptivity for a wide range of disturbance conditions.

Collis, S. Scott↗
NASA NTRSDate not supplied

Rational Design of Nanoplasmonic Array Geometries for Biosensing

Background: Molecular diagnostics provide early and accurate diagnosis, which is essential for the prevention and treatment of infectious as well as chronic diseases. These tests are designed to detect disease-specific bioanalytes such as nucleic acid (DNA or RNA) or protein (antigens, antibodies) biomarkers. In the context of infectious disease diagnosis, nucleic acid-based detection methods are known to provide more specific and sensitive results. Here, the presence of a unique sequence belonging to the pathogenic genomic material is targeted to identify species, organism, genera and/or antimicrobial resistant gene markers. The majority of the common nucleic acid based diagnostic techniques require amplification (polymerase chain reaction, isothermal amplification etc.) of the pathogenic genetic material prior to detection impacting diagnostic speed, complexity, and cost thereby limiting ease of use. Thus, the development of simplified nucleic acid-based diagnostics that can be even used in resource-poor settings may hugely benefit patients across the globe. Nanopath is a molecular diagnostics company utilizing a solid-state nanosensor to enable sequence-specific detection of target nucleic acids without the need of amplification. These nanostructures enable ultra-sensitive biomarker detection using geometric, feature-dependent properties highly dependent on the local dielectric environment, allowing them to be sensitive to low concentration binding events. This paper describes an application of this approach to provide highly relevant clinical information within a single doctor’s office visit. Intro: The Nanopath team is in collaboration with NASA (National Aeronautics and Space Administration) and NIST (National Institute of Standards and Technology) to push the bounds of the fundamental physics associated with their biosensing platform. The ability of metals to support electromagnetic surface waves gives rise to surface plasmons when optically illuminated. This property, and its strong sensitivity to changes in the local refractive index, allows for the use of metal nanoparticles as ultra-sensitive transducers. In prior work by members of this team, ensembles of randomly oriented nanoparticles (i.e., colloidal nanorods dispersed on chip) were employed for sequence-specific nucleic acid sensing (1-3). While these particle sensors have the advantage of rapid fabrication, they suffer from low sensitivity and quality factor due to the random particle dispersity. In contrast, in this study we employ ordered array nanoparticle ensembles which can be used to improve sensor sensitivity and figure-of-merit. Study Methods Overview: In this talk, we detail the results of sensing experiments and computational simulations to outline a rational design of the structure of these plasmonic nanoparticle arrays for biomolecular sensing. Through simulation and experiment, we iteratively tailor nanostructure dimension to provide high quality signal and large resonance shifts upon modeled nucleic acid binding. In particular, full-wave electromagnetic simulations were conducted using Lumerical photonic simulation software in which periodic boundary conditions were applied in the x- and y- dimensions for each of the nanoplasmonic sensor geometries. To simulate the resonance response to changes in the bulk solution in contact with the sensor surface, the refractive index of the surrounding media was changed appropriately. Nucleic acid hybridization events were modeled using either using spherical structures approximating the relevant radius of genomic material as estimated by polymer models, or as conformal layers with the known refractive indices for nucleic acids. On the basis of initial simulations, nanosensors were fabricated using traditional electron-beam lithography protocols at NIST. To evaluate consensus between simulations and experiments, bulk sensing experiments were carried out in which the resonance peaks were obtained by submerging the sensors in refractive index standards. Key nanosensor characteristics including resonance peak locations, resonance peak shifts as a function of refractive index, and figure of merit (FOM) of extinction curves were examined between the experimental and simulation results prior to proceeding with simulations on additional geometries and more complex solution conditions, and further device fabrication. This iterative process is repeated toward a rational design of nanoplasmonic array geometries for biosensing optimizing response for targeted disease detection. In summary, this study puts forth a methodology for rational design and characterization of regularly spaced nanoparticle arrays for optics-based biosensing. The results of this study will allow for more informed design of nanostructure geometries towards sequence-specific nucleic acid detection. These improved designs have the potential to improve clinical sensitivity and limit-of-detection across disease indication.

sensor↗
NASA NTRS2006

Innovative Trajectory Designs to meet Exploration Challenges

This document is a viewgraph presentation of the conference paper. Missions incorporated into NASA's Vision for Space Exploration include many different destinations and regions; are challenging to plan; and need new and innovative trajectory design methods to enable them. By combining proven methods with chaos dynamics, exploration goals that require maximum payload mass or minimum duration can be achieved. The implementation of these innovative methods, such as weak stability boundaries, has altered NASA's approach to meet exploration challenges and is described to show how exploration goals may be met in the next decade. With knowledge that various perturbations play a significant role, the mission designer must rely on both traditional design strategies as well as these innovative methods. Over the past decades, improvements have been made that would at first glance seem dramatic. This paper provides a brief narrative on how a fundamental shift has occurred and how chaos dynamics improve the design of exploration missions with complex constraints.

Folta, David C.↗
NASA NTRS2000

Abrupt Changes at the Permian/Triassic Boundary: Tempo of Events from High-Resolution Cyclostratigraphy

The Permian/Triassic (P/Tr) boundary (251.4 +/- 3 Myr) is marked by the most severe mass extinction in the geologic record. Recently, precise absolute dating has bracketed the marine extinctions and associated carbon-isotope anomaly within less than 1 Myr. We improve this resolution through high-resolution stratigraphy across the P/Tr boundary in the 331-m Gartnerkofel-1 core and nearby Reppwand outcrop section (Carnic Alps, Austria) utilizing FFT and wavelet timeseries analyses of cyclic components in down-hole core logs of density and natural gamma-ray intensity, and carbon-isotopic ratios of bulk samples. The wavelet analysis indicates continuity of deposition across the P/Tr boundary interval, and the timeseries analyses show evidence for persistent cycles in the ratio of approximately 40: 10: 4.7: 2.3 meters, correlated with Milankovitch-band orbital cycles of approximately 412: 100: 40: 20 kyr (eccentricity 1 and 2, obliquity, and precession), and giving a consistent average sedimentation rate of approximately 10 cm/1,000 yr. Milankovitch periods in delta C-13 and density in these shallow-water carbonates were most likely the result of climatically induced oscillations of sea level and climate, coupled with changes in ocean circulation and productivity, that affected sedimentation. Fluctuations in gamma radiation reflect varying input of clay minerals and the presence of shaly interbeds. Throughout the P/Tr boundary interval in the core, the 100,000-year eccentricity cycle seems to be dominant. Weaker obliquity and precession cycles are in line with the location of the Austrian section in the latest Permian, close to the Equator in the western bight of the Tethys, where obliquity and precessional effects on seasonal contrast might be subdued. Using the improved resolution provided by cycle analysis in the GK-1 core, we find that the dramatic change in the faunal record that marks the P/Tr boundary takes place over less than 6m, or less than 60,000 years. In the nearby Reppwand outcrop section, the same faunal changes occurs over only 0.8 m or about 8,000 years, close to the limit of time-resolution induced by bioturbation and reworking in these sediments. The sharp negative global carbon-isotope shift took place within less than or equal to 40,000 yr, and the isotope excursions persisted for approximately 480,000 yr into the Early Triassic. The results indicate that the severe marine faunal event that marks the P/Tr boundary was very sudden, perhaps less than the resolution window in the GK-1 core, and suggest a catastrophic cause. The wavelet-analysis approach to high-resolution cyclostratigraphy can be applied to other P/Tr boundary sections, and when combined with precise absolute dating and magnetostratigraphic methods promises a significant increase in resolution in determining the correlation and tempo of the end-Permian extinctions and related events worldwide.

Rampino, M. R.↗
DOE OSTI2025

A Comparative Analysis of Waste-as-a-Feedstock Accounting Methods in Life Cycle Assessments

Global waste generation is a ubiquitous challenge, driving a paradigm shift towards viewing waste as a valuable resource for a circular economy across diverse sectors. While innovative waste-to-resource pathways are crucial, rigorous Life Cycle Assessment (LCA) is essential to ensure the pathways are an important part of current practices. However, LCA application to waste valorization varies, leading to incomparable results due to differing methodological choices. This paper examines three key nuances in waste-as-resource LCAs: the zero-burden assumption, the biogenic carbon neutrality assumption, and the benchmark assumption for emissions avoidance. Using a waste gasification to hydrogen case study, we demonstrate how these methodological decisions impact LCA outcomes. Our findings reveal that waste composition significantly influences the results and highlight challenges associated with biogenic carbon accounting under various system boundary assumptions. Emissions avoidance accounting requires multi-functional unit perspectives and robust benchmark selection. This paper clarifies these accounting approaches, empirically illustrates their influence, and discusses broad implications for accurate sustainability assessment, emphasizing the critical role of transparent LCA choices for effective policy and investment in circular economy solutions.

LCA method↗
NASA NTRS1993

Turbulence and transition modeling for high-speed flows

Research conducted during the past three and a half years aimed at developing and testing a turbulence/transition model applicable to high-speed turbulent flows is summarized. The first two years of the project focused on fully turbulent flows, while emphasis shifted to boundary-layer development in the transition region during the final year and a half. A brief summary of research accomplished during the first three years is included and publications that describe research results in greater detail are cited. Research conducted during the final six months of the period of performance is summarized. The primary results of the last six months of the project are elimination of the k-omega model's sensitivity to the freestream value of omega and development of a method for triggering transition at a specified location, independent of the freestream turbulence level.

Wilcox, David C.↗
DOE OSTI2025

Uniform field in microwave cavities through the use of effective magnetic walls

Wire medium (WM) resonators have emerged as a promising realization for plasma haloscopes—devices designed to detect axions, a potential component of dark matter. Key factors influencing the detection probability include cavity volume, resonance quality factor, and form factor. While the form factor has been explored for resonant frequency tuning, its optimization for axion detection remains unexplored. Here, in this work, we present an approach to significantly enhancing the form factor of WM plasma haloscopes. By shifting the metal walls of the resonator by a quarter wavelength, we effectively convert an electric wall boundary condition into a magnetic wall one, allowing for an almost uniform mode. Theoretical analysis and numerical simulations confirm that this modification improves the electric field profile and boosts the form factor, while also slightly enhancing the quality factor. We validate these findings through experimental results from two prototype resonators: one with a standard geometry and another with a quarter-wave air gap between the WM and the walls. Additionally, our method provides a simple way to control the field profile within WM cavities, which can be explored for further applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

An assessment of ocean alkalinity enhancement using aqueous hydroxides: kinetics, efficiency, and precipitation thresholds

Abstract. Ocean alkalinity enhancement (OAE) is a promising approach to marine carbon dioxide removal (mCDR) that leverages the large surface area and carbon storage capacity of the oceans to sequester atmospheric CO2 as dissolved bicarbonate (HCO3-). One OAE method involves the conversion of salt in seawater into aqueous alkalinity (NaOH), which is returned to the ocean. The resulting increase in seawater pH and alkalinity causes a shift in dissolved inorganic carbon (DIC) speciation toward carbonate and a decrease in the surface ocean pCO2. The shift in the pCO2 results in enhanced uptake of atmospheric CO2 by the seawater due to gas exchange. In this study, we systematically test the efficiency of CO2 uptake in seawater treated with NaOH at aquarium (15 L) and tank (6000 L) scales to establish operational boundaries for safety and efficiency in advance of scaling up to field experiments. CO2 equilibration occurred on the order of weeks to months, depending on circulation, air forcing, and air bubbling conditions within the test tanks. An increase of ∼0.7–0.9 mol DIC per mol added alkalinity (in the form of NaOH) was observed through analysis of seawater bottle samples and pH sensor data, consistent with the value expected given the values of the carbonate system equilibrium calculations for the range of salinities and temperatures tested. Mineral precipitation occurred when the bulk seawater pH exceeded 10.0 and Ωaragonite exceeded 30.0. This precipitation was dominated by Mg(OH)2 over hours to 1 d before shifting to CaCO3,aragonite precipitation. These data, combined with models of the dilution and advection of alkaline plumes, will allow the estimation of the amount of carbon dioxide removal expected from OAE pilot studies. Future experiments should better approximate field conditions including sediment interactions, biological activity, ocean circulation, air–sea gas exchange rates, and mixing zone dynamics.

Ringham, Mallory C. (ORCID:0000000348020185)↗
DOE OSTI2025

Modeling MTS pyrolysis and SiC deposition kinetics using principal component analysis and neural networks

Accurate chemical kinetics modeling is crucial for improving the efficiency of chemical processing and synthesis of ceramic matrix composites. Detailed kinetic models are computationally expensive due to the large number of transported chemical species, while the simplified physics-based models, such as single-step global mechanisms, are efficient but often overlook key chemical intermediates and pathways. Recent deep learning approaches promise accurate and cost-effective models. Yet, they require additional closures for the transported nonlinear latent variables, complicating integration with existing solvers. In this work, we develop a hybrid linear—nonlinear reduced model for silicon carbide deposition from methyltrichlorosilane precursor by combining principal component analysis (PCA) and autoencoder (AE) neural network (NN) approaches. PCA is used to identify a smaller set of linear transport variables, enabling direct reuse of conventional transport solvers. NNs then reconstruct the full chemical state from these reduced variables. We demonstrate the method on a chemical vapor deposition reactor—comprising a gas-phase pyrolysis plug flow reactor and a heterogeneous surface reactor—over a wide range of temperatures, pressures, and residence times. Our PCA–AE model achieves high accuracy with only five transported scalars, achieving an eightfold cost reduction compared to detailed mechanisms, in both a priori (using data from the test set only) and a posteriori (coupled with a differential equation solver). In conclusion, notable errors arise primarily near training domain boundaries and for long residence times, indicating the need for domain shift indicators and better long-horizon predictions in future reduced chemistry model development.

autoencoder neural networks↗
NASA NTRS1999

Direct Detection Doppler Lidar for Spaceborne Wind Measurement

The theory of double edge lidar techniques for measuring the atmospheric wind using aerosol and molecular backscatter is described. Two high spectral resolution filters with opposite slopes are located about the laser frequency for the aerosol based measurement or in the wings of the Rayleigh - Brillouin profile for the molecular measurement. This doubles the signal change per unit Doppler shift and improves the measurement accuracy by nearly a factor of 2 relative to the single edge technique. For the aerosol based measurement, the use of two high resolution edge filters reduces the effects of background, Rayleigh scattering, by as much as an order of magnitude and substantially improves the measurement accuracy. Also, we describe a method that allows the Rayleigh and aerosol components of the signal to be independently determined. A measurement accuracy of 1.2 m/s can be obtained for a signal level of 1000 detected photons which corresponds to signal levels in the boundary layer. For the molecular based measurement, we describe the use of a crossover region where the sensitivity of a molecular and aerosol-based measurement are equal. This desensitizes the molecular measurement to the effects of aerosol scattering and greatly simplifies the measurement. Simulations using a conical scanning spaceborne lidar at 355 nm give an accuracy of 2-3 m/s for altitudes of 2-15 km for a 1 km vertical resolution, a satellite altitude of 400 km, and a 200 km x 200 km spatial.

Korb, C. Laurence↗
NASA NTRS1975

Computational study of nonlinear plasma waves. I - Simulation model and monochromatic wave propagation. II - Sideband instability and satellite growth

A hybrid plasma simulation model is described and applied to the study of electrostatic wave propagation in a one-dimensional Maxwellian plasma with periodic boundary conditions. The model employs a cloud-in-cell scheme which can drastically reduce the fluctuations in particle simulation models and greatly ease the computational difficulties of the Vlasov equation approach. A grid in velocity space is introduced and the particles are represented by points in the x-v phase space. The model is tested first in the absence of an applied signal and then in the presence of a small-amplitude perturbation. The method is also used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories.

Matsuda, Y.↗
DOE OSTI2026

Materializing Inter-Channel Relationships With Multi-Density Woodcock Tracking

Volume rendering techniques for scientific visualization have recently shifted toward Monte Carlo (MC) methods for their flexibility and robustness, but their use in multi-channel visualization remains underexplored. Traditional multi-channel volume rendering often relies on arbitrary, non-physically based color blending functions that hinder interpretation. Here, we introduce multi-density Woodcock tracking, a simple extension of Woodcock tracking that leverages an MC method to produce high-fidelity, physically grounded multi-channel renderings without arbitrary blending. By generalizing Woodcock’s distance tracking, we provide a unified blending modality that also integrates blending functions from prior works. We further implement effects that enhance boundary and feature recognition. By accumulating frames in real-time, our approach delivers high-quality visualizations with perceptual benefits, demonstrated on diverse datasets.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Rotor Broadband Noise Prediction with Comparison to Model Data

This paper reports an analysis and prediction development of rotor broadband noise. The two primary components of this noise are Blade-Wake Interaction (BWI) noise, due to the blades' interaction with the turbulent wakes of the preceding blades, and "Self" noise, due to the development and shedding of turbulence within the blades' boundary layers. Emphasized in this report is the new code development for Self noise. The analysis and validation employs data from the HART program, a model BO-105 rotor wind tunnel test conducted in the German-Dutch Wind Tunnel (DNW). The BWI noise predictions are based on measured pressure response coherence functions using cross-spectral methods. The Self noise predictions are based on previously reported semiempirical modeling of Self noise obtained from isolated airfoil sections and the use of CAMRAD.Modl to define rotor performance and local blade segment flow conditions. Both BWI and Self noise from individual blade segments are Doppler shifted and summed at the observer positions. Prediction comparisons with measurements show good agreement for a range of rotor operating conditions from climb to steep descent. The broadband noise predictions, along with those of harmonic and impulsive Blade-Vortex Interaction (BVI) noise predictions, demonstrate a significant advance in predictive capability for main rotor noise.

Brooks, Thomas F.↗
NASA NTRS1993

Expansion-based passive ranging

A new technique of passive ranging which is based on utilizing the image-plane expansion experienced by every object as its distance from the sensor decreases is described. This technique belongs in the feature/object-based family. The motion and shape of a small window, assumed to be fully contained inside the boundaries of some object, is approximated by an affine transformation. The parameters of the transformation matrix are derived by initially comparing successive images, and progressively increasing the image time separation so as to achieve much larger triangulation baseline than currently possible. Depth is directly derived from the expansion part of the transformation. To a first approximation, image-plane expansion is independent of image-plane location with respect to the focus of expansion (FOE) and of platform maneuvers. Thus, an expansion-based method has the potential of providing a reliable range in the difficult image area around the FOE. In areas far from the FOE the shift parameters of the affine transformation can provide more accurate depth information than the expansion alone, and can thus be used similarly to the way they were used in conjunction with the Inertial Navigation Unit (INU) and Kalman filtering. However, the performance of a shift-based algorithm, when the shifts are derived from the affine transformation, would be much improved compared to current algorithms because the shifts - as well as the other parameters - can be obtained between widely separated images. Thus, the main advantage of this new approach is that, allowing the tracked window to expand and rotate, in addition to moving laterally, enables one to correlate images over a very long time span which, in turn, translates into a large spatial baseline - resulting in a proportionately higher depth accuracy.

Barniv, Yair↗
NASA NTRS1993

Expansion-based passive ranging

This paper describes a new technique of passive ranging which is based on utilizing the image-plane expansion experienced by every object as its distance from the sensor decreases. This technique belongs in the feature/object-based family. The motion and shape of a small window, assumed to be fully contained inside the boundaries of some object, is approximated by an affine transformation. The parameters of the transformation matrix are derived by initially comparing successive images, and progressively increasing the image time separation so as to achieve much larger triangulation baseline than currently possible. Depth is directly derived from the expansion part of the transformation. To a first approximation, image-plane expansion is independent of image-plane location with respect to the focus of expansion (FOE) and of platform maneuvers. Thus, an expansion-based method has the potential of providing a reliable range in the difficult image area around the FOE. In areas far from the FOE the shift parameters of the affine transformation can provide more accurate depth information than the expansion alone, and can thus be used similarly to the way they have been used in conjunction with the Inertial Navigation Unit (INU) and Kalman filtering. However, the performance of a shift-based algorithm, when the shifts are derived from the affine transformation, would be much improved compared to current algorithms because the shifts--as well as the other parameters--can be obtained between widely separated images. Thus, the main advantage of this new approach is that, allowing the tracked window to expand and rotate, in addition to moving laterally, enables one to correlate images over a very long time span which, in turn, translates into a large spatial baseline resulting in a proportionately higher depth accuracy.

Barniv, Yair↗