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NASA NTRS1992

Variance of phase fluctuations of waves propagating through a random medium

As an electromagnetic wave propagates through a random scattering medium, such as a forest, its energy is attenuated and random phase fluctuations are induced. The magnitude of the random phase fluctuations induced is important in estimating how well a Synthetic Aperture Radar (SAR) can image objects within the scattering medium. The two-layer random medium model, consisting of a scattering layer between free space and ground, is used to calculate the variance of the phase fluctuations induced between a transmitter located above the random medium and a receiver located below the random medium. The scattering properties of the random medium are characterized by a correlation function of the random permittivity fluctuations. The effective permittivity of the random medium is first calculated using the strong fluctuation theory, which accounts for large permittivity fluctuations of the scatterers. The distorted Born approximation is used to calculate the first-order scattered field. A perturbation series for the phase of the received field in the Rytov approximation is then introduced and the variance of the phase fluctuations is also calculated assuming that the transmitter and receiver are in the paraxial limit of the random medium, which allows an analytic solution to be obtained. Results are compared using the paraxial approximation, scalar Green's function formulation, and dyadic Green's function formulation. The effects studied are the dependence of the variance of the phase fluctuations on receiver location in lossy and lossless regions, medium thickness, correlation length and fractional volume of scatterers, depolarization of the incident wave, ground layer permittivity, angle of incidence, and polarization.

Chu, Nelson C.↗

NASA NTRS1991

Remote sensing of earth terrain

In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.

Yueh, Herng-Aung↗

NASA NTRS1993

Radiation and scattering by cavity-backed antennas on a circular cylinder

Conformal arrays are popular antennas for aircraft and missile platforms due to their inherent low weight and drag properties. However, to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer. In fact, it has been common practice to use limited measurements and planar approximations in designing such non-planar antennas. The finite element-boundary integral method is extended to scattering and radiation by cavity-backed structures in an infinite, metallic cylinder. In particular, the formulation specifics such as weight functions, dyadic Green's function, implementation details, and particular difficulties inherent to cylindrical structures are discussed. Special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements. Both scattering and radiation parameters are computed and validated as much as possible.

Kempel, Leo C.↗

NASA NTRS1994

Scattering by cavity-backed antennas on a circular cylinder

Conformal arrays are popular antennas for aircraft, spacecraft, and land vehicle platforms due to their inherent low weight and drag properties. However, to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer. In fact, it has been common practice to use limited measurements and planar approximations in designing such non-planar antennas. The finite element-boundary integral method is extended to scattering by cavity-backed structures in an infinite, metallic cylinder. In particular, the formulation specifics such as weight functions, dyadic Green's function, implementation details and particular difficulties inherent to cylindrical structures are discussed. Special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements. Scattering results are presented and validated as much as possible.

Kempel, Leo C.↗

NASA NTRS1993

LRAT: Lightning Radiative Transfer

In this report, we extend to cloud physics the work done for single and multiple scattering of electromagnetic waves. We consider the scattering of light, visible or infrared, by a spherical cloud represented by a statistically homogeneous ensemble of configurations of N identical spherical water droplets whose centers are uniformly distributed in its volume V. The ensemble is specified by the average number rho of scatterers in unit volume and by rho f(R) with f(R) as the distribution function for separations R of pairs. The incident light, vector-phi(sub 0) a plane electromagnetic wave with harmonic time dependence, is from outside the cloud. The propagation parameter kappa(sub 0) and the index of refraction eta(sub 0) determine physically the medium outside the distribution of scatterers. We solve the interior problem separately to obtain the bulk parameters for the scatterer equivalent to the ensemble of spherical droplets. With the interior solution or the equivalent medium approach, the multiple scattering problem is reduced to that of an equivalent single scatterer excited from outside illumination. A dispersion relation which determines the bulk propagation parameter K and the bulk index of refraction eta of the cloud is given in terms of the vector equivalent scattering amplitude vector-G and the dyadic scattering amplitude tilde-g of the single object in isolation. Based on this transfer model we will have the ability to consider clouds composed of inhomogeneous distribution of water and/or ice particles and we will be able to take into account particle size distributions within the cloud. We will also be able to study the effects of cloud composition (i.e., particle shape, size, composition, orientation, location) on the polarization of the single or the multiple scattered waves. Finally, this study will provide a new starting point for studying the problem of lightning radiative transfer.

Phanord, Dieudonne D.↗

NASA NTRS1994

Two space scatterer formalism calculation of bulk parameters of thunderclouds

In a previous study, we used a modified two-space scatterer formalism of Twersky to establish for a cloud modeled as a statistically homogeneous distribution of spherical water droplets, the dispersion relations that determine its bulk propagation numbers and bulk indexes of refraction in terms of the vector equivalent scattering amplitude and the dyadic scattering amplitude of the single water droplet in isolation. The results were specialized to the forward direction of scattering while demanding that the scatterers preserve the incident polarization. We apply this approach to obtain specific numerical values for the macroscopic parameters of the cloud. We work with a cloud of density rho = 100 cm(exp -3), a wavelength lambda = 0.7774 microns, and with spherical water droplets of common radius alpha = 10 microns. In addition, the scattering medium is divided into three parts, the medium outside the cloud, moist air (the medium inside the cloud but outside the droplets), and the medium inside the spherical water droplets. The results of this report are applicable to a cloud of any geometry since the boundary does not interfere with the calculations. Also, it is important to notice the plane wave nature of the incidence wave in the moist atmosphere.

Phanord, Dieudonne D.↗

NASA NTRS1993

A Model with Ellipsoidal Scatterers for Polarimetric Remote Sensing of Anisotropic Layered Media

This paper presents a model with ellipsoidal scatterers for applications to polarimetric remote sensing of anisotropic layered media at microwave frequencies. The physical configuration includes an isotropic layer covering an anisotropic layer above a homogeneous half space. The isotropic layer consists of randomly oriented spheroids. The anisotropic layer contains ellipsoidal scatterers with a preferential vertical alignment and random azimuthal orientations. Effective permittivities of the scattering media are calculated with the strong fluctuation theory extended to account for the nonspherical shapes and the scatterer orientation distributions. On the basis of the analytic wave theory, dyadic Green's functions for layered media are used to derive polarimetric backscattering coefficients under the distorted Born approximation. The ellipsoidal shape of the scatterers gives rise to nonzero cross-polarized returns from the untilted anisotropic medium in the first-order approximation. Effects of rough interfaces are estimated by an incoherent addition method. Theoretical results and experimental data are matched at 9 GHz for thick first-year sea ice with a bare surface and with a snow cover at Point Barrow, Alaska. The model is then used to study the sensitivity of polarimetric backscattering coefficients with respect to correlation lengths representing the geometry of brine inclusions. Polarimetric signatures of bare and snow-covered sea ice are also simulated based on the model to investigate effects of different scattering mechanisms.

Nghiem, S. V.↗

NASA NTRS2003

Integrated Power and Attitude Control for a Spacecraft with Flywheels and Control Moment Gyroscopes

A law is designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as all integrated set of actuators for attitude control. General. nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as it means of compensating for damping exerted by rotor bearings. Two flywheel 'steering laws' are developed such that torque commanded by all attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude and illustrate the benefits of kinetic energy error feedback.

Roithmayr, Carlos M.↗

NASA NTRS2003

Dynamics and Control of Attitude, Power, and Momentum for a Spacecraft Using Flywheels and Control Moment Gyroscopes

Several laws are designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as an integrated set of actuators for attitude control. General, nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as a means of compensating for damping exerted by rotor bearings. Two flywheel steering laws are developed such that torque commanded by an attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude, and illustrate the benefits of kinetic energy error feedback. Control laws for attitude hold are also developed, and used to show the amount of propellant that can be saved when flywheels assist the CMGs. Nonlinear control laws for large-angle slew maneuvers perform well, but excessive momentum is required to reorient a vehicle like the International Space Station.

Roithmayr, Carlos M.↗

NASA NTRS2013

A T Matrix Method Based upon Scalar Basis Functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

wave functions↗

NASA NTRS2017

Electromagnetic Scattering and Emission by a Fixed Multi-Particle Object in Local Thermal Equilibrium: General Formalism

The majority of previous studies of the interaction of individual particles and multi-particle groups with electromagnetic field have focused on either elastic scattering in the presence of an external field or self-emission of electromagnetic radiation. In this paper we apply semi-classical fluctuational electrodynamics to address the ubiquitous scenario wherein a fixed particle or a fixed multi-particle group is exposed to an external quasi-polychromatic electromagnetic field as well as thermally emits its own electromagnetic radiation. We summarize the main relevant axioms of fluctuational electrodynamics, formulate in maximally rigorous mathematical terms the general scattering emission problem for a fixed object, and derive such fundamental corollaries as the scattering emission volume integral equation, the Lippmann Schwinger equation for the dyadic transition operator, the multi-particle scattering emission equations, and the far-field limit. We show that in the framework of fluctuational electrodynamics, the computation of the self-emitted component of the total field is completely separated from that of the elastically scattered field. The same is true of the computation of the emitted and elastically scattered components of quadratic linear forms in the total electromagnetic field. These results pave the way to the practical computation of relevant optical observables.

Electromagnetic scattering; Thermal emission; Fluc↗

NASA NTRS2018

An Overview of Methods for Deriving the Radiative Transfer Theory from the Maxwell Equations. II: Approach Based on the Dyson and Bethe-Salpeter Equations

In this paper, the vector radiative transfer equation is derived by means of the vector integral Foldy equations describing the electromagnetic scattering by a group of particles. By assuming that in a discrete random medium the positions of the particles are statistically independent and by applying the Twersky approximation to the order-of-scattering expansion of the total field, we derive the Dyson equation for the coherent field and the ladder approximated Bethe–Salpeter equation for the dyadic correlation function. Then, under the far-field assumption for sparsely distributed particles, the Dyson equation is reduced to the Foldy integral equation for the coherent field, while the iterated solution of the Bethe–Salpeter equation ultimately yields the vector radiative transfer equation.

Electromagnetic scattering↗

NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. III: The Vector Radiative Transfer Equation

A vector radiative transfer equation with an additional source term typical of dense media is obtained. The analysis includes (i) the derivation of an integral equation for the correlation matrix of the exciting field coefficients accounting for the correlation between the particles, (ii) the derivation of an integral representation for the specific coherency dyadicin terms of this matrix, and (iii) the simplification of the integral equation for the correlation matrix and of the integral representation for the specific coherency dyadic by employing a series of approximations which are characteristic of sparse media.

Adrian Doicu↗

NASA NTRSDate not supplied

Perceived Similarity Predicts Viable Relationships and Team Performance

Conditions expected for future space exploration require an expanded understanding of interpersonal compatibility. Limited research has examined interpersonal perception at the dyadic level and how these perceptions shape relationships and team performance over time. We investigated the extent to which a novel approach for assessing interpersonal compatibility - focused on interpersonal perception and perceived similarity between dyads - predicts the viability of relationships and team performance over time in simulated space crews.

Jessica Chackoria↗

NASA NTRSDate not supplied

Teams in Space: Knowledge Gained, but More to Explore

NASA’s Human Research Program oversees the Team Risk (i.e., Risk of Performance and Behavioral Health Decrements due to Inadequate Cooperation, Coordination, Communication and Psychosocial Adaptation within a Team). Research in this area informs all aspects of an astronaut’s career, from hiring to training to mission support, and works to address new challenges related to lunar and Mars missions. NASA’s astronaut selection process creates an astronaut corps of highly qualified, team-oriented individuals, which allows mission planners much flexibility in composing small crews for specific missions. These crews are further developed and supported through extensive training, including team skills training, and countermeasures available to the crew throughout the mission. However, in the high consequence environment of long-duration missions, team composition is complex and is not a one-time concern to be addressed pre-mission. Team factors such as team cohesion, dyadic relationships, and shared team cognition are likely to change dynamically in response to each interaction and event experienced by the individuals and the team as a whole. Thus, monitoring and optimizing team composition at a more micro level (e.g., per task) is one way to support team functioning and performance. Spaceflight teams research also includes the multi-team system of Mission Control and coordination between space-to-ground, adding another avenue in which risk might be introduced, particularly under exploration missions that experience significant communication delays. Spaceflight teams research has recently experienced a concentrated flurry of analog research over the past decade, shedding light on the many unique challenges and potential solutions to mitigate the team risk in long-duration exploration missions. However, questions still remain about how to, for example, create unobtrusive operational measures and how to advance interdisciplinary teams research and countermeasure development. We present an overview of the challenges facing teams in space, our current knowledge, and the next steps for research and spaceflight operations.

Lauren Blackwell Landon↗

NASA NTRS2025

Navigating Team Dynamics: Automated Detection of Micro-Behaviors Between Team Members Through Longitudinal Interaction Data

The success in future long term space exploration missions will depend on the cooperation, coordination, and mutual understanding among the crew members. Micro-behaviors are momentary, subtle linguistic and paralinguistic indicators of thinking and feeling toward another member of the team (Cortina et al., 2001; Smith & Griffiths, 2022) that can significantly impact team dynamics and influence the overall team performance (Paromita & Chaspari, 2024). Due to their interactive nature, micro-behaviors have a sender (i.e., the team member expressing the micro-behavior) and a target (the team member impacted by the micro-behavior). Detection of these behaviors can assist in avoiding possible conflict among crew members and promoting the overall team success. Our prior research focused on an initial proof of concept of machine learning (ML) models and natural language processing (NLP) techniques that were used for automatically detect micro-behaviors among crew members of the US National Aeronautics and Space Administration’s (NASA) Human Exploration Research Analog (HERA) Campaigns 4 and 5 missions (Paromita et al., 2023). Results underscored the importance of incorporating contextual information in the ML models in the form of sentiment analysis, type of task, and dyadic interaction among team members. Here, we expand the scope of our prior work in two ways. First, we assess ML/NLP methods on new behavioral annotations coded using an adapted version of Smith & Griffins (2022) theoretical framework in terms of Violation (i.e., presence of valenced behavior, uplifting/positive or discouraging/negative), Intensity (i.e., force of behavior in terms of how uplifting or discouraging is the behavior), and Intent (i.e., motive of the behavior in terms of whether it was deliberate or unintentional). Second, we expand the design of the ML model to preserve information about the role of each team member within the occurrence of the micro-behavior (in contrast to the previous model that only considered the sender and the target without determining the team member role). This allows to consider all team members' contributions in the conversation and model long-term dependencies in the dialogue. Our experiments for this study are conducted on data from 5 teams of the NASA HERA C4 (NASA grant NNX16AQ48G (PI: Bell)). Conversations were extracted from the 1.5 hour Team Interaction Battery (TIB) task that occurred 5 times in-mission per crew. This resulted in a total of 13,058 conversational turns (i.e., 17.8% uplifting, 3.3% discouraging, 75.76% neutral, 3.14% nulls). Our findings with the revised behavioral coding and ML/NLP models indicate a 43.66% macro F1-score (i.e., 38.29% precision (P), 50.8% recall (R)) for a dialog state-tracking model that includes information from the sender only, and a 40.9% F1-score (i.e., 38.7% P, 43.36% R) for the same model that includes information from both the sender and the target of the micro-behavior. These are significantly higher compared to simple random forest models that classify behaviors strictly based on speech content and do not consider iterative team dynamics, achieving a 36.07% F1-score (i.e., 39.04% R, 33.53% P). Our findings demonstrate potential ways to leverage large conversational datasets to better capture complex team dynamics. We will discuss future directions including proposed models that can incorporate additional mission days and tasks beyond the TIB for objectively quantifying team behavior at high temporal resolution in space exploration missions.

Projna Paromita↗

NASA NTRS2018

Impressed Sources and Fields in the Volume-Integral-Equation Formulation of Electromagnetic Scattering by a Finite Object: A Tutorial

Although free space cannot generate electromagnetic waves, the majority of existing accounts of frequency-domain electromagnetic scattering by particles and particle groups are based on the postulate of existence of an impressed incident field, usually in the form of a plane wave. In this tutorial we discuss how to account for the actual existence of impressed source currents rather than impressed incident fields. Specifically, we outline a self-consistent theoretical formalism describing electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents, some of which can be far removed from the object and some can reside in its vicinity, including inside the object. To make the resulting formalism applicable to a wide range of scattering-object morphologies, we use the framework of the volume integral equation formulation of electromagnetic scattering, couple it with the notion of the transition operator, and exploit the fundamental symmetry property of this operator. Among novel results, this tutorial includes a streamlined proof of fundamental symmetry (reciprocity) relations, a simplified derivation of the Foldy equations, and an explicit analytical expression for the transition operator of a multi-component scattering object.

Symmetry relations↗

NASA NTRS2018

Addendum to "Impressed Sources and Fields in the Volume-Integral-Equation Formulation of Electromagnetic Scattering by a Finite Object: A Tutorial"

Our recent tutorial referred to in the title has summarized a general theoretical formalism of electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents. This addendum builds on the tutorial to provide a streamlined discussion of specific far-field limits and the corresponding reciprocity relations by introducing appropriate far-field operators and linear maps and deriving the reciprocity relations through the pseudo adjoint of these maps. We thereby extend the compact operator calculus used previously to consider the fields and sources near or inside the scattering object.

Impressed Sources↗