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At least 55 records · Page 3

An Improved Far-Field Small Unmanned Aerial System Optical Detection Algorithm

Onboard far-field aircraft detection is needed for safe non-cooperative traffic mitigation for autonomous small Unmanned Aerial System (sUAS) operations. This work presents an aircraft detect and track pipeline that fuses image differencing and morphological filtering detections for inputs to a Kalman-based object tracking pipeline. The pipeline is evaluated using two types of flight encounters: 1) motorcopter sUAS vs. fixed-wing sUAS 2) motorcopter sUAS vs general aviation plane.

Chester Dolph↗

BioLEAD: BioLogical Exploration via Autonomous Detection – Using Dielectric Spectroscopy to Monitor Biological Changes in Response to Deep Space Radiation

Leveraging the bio-fluidic hardware developed for BioSentinel, we propose a new payload for autonomous missions: BioLEAD – BioLogical Exploration via Autonomous Detection. With NASA's renewed focus to continue human exploration of the Moon (Artemis Program), the BioLEAD payload aims to investigate the effects of the lunar environment on biology, whether onboard a lunar lander, the Lunar Gateway, or as a free-flying CubeSat orbiting the Moon. In place of an optical detection system, BioLEAD will employ a miniaturized, non-invasive dielectric spectroscopy sensor to enable real-time monitoring of biological activity. The sensor operates by relating capacitance measurements to the dielectric properties of the cell, such as cell morphology, doubling time, and cell cycle stage. The implementation of this new sensor technology will address limitations of the optical measurement system used on BioSentinel. It will also advance the use of autonomous bioanalytical microsystems and reveal new information regarding biological responses to the Moon’s radiation environment. Most importantly, BioLEAD’s technology will be adaptable for a wide array of future missions.

Biosensor↗

Hypervelocity impact facility for simulating materials exposure to impact by space debris

The Space Power Institute at Auburn University has constructed an electromagnetically driven particle accelerator for simulating the effects of space debris on the materials for use in advanced spacecraft. The facility consists of a capacitively driven accelerator section, a drift tube and a specimen impact chamber. The drift tube is sufficiently long that all electrical activity has ceased prior to impact in the specimen chamber. The impact chamber is large enough to allow a wide range of specimen geometries, ranging from small coupons to active portions of advanced spacecraft. The electric drive for the accelerator consists of a 67 kJ, 50 k capacitor bank arranged in a low inductance configuration. The bank is discharged through an aluminum armature/plastic ablator plate/projectile load in roughly 1.2 microsec. The evaporation of the ablaitor plate produces an expanding gas slug, mostly H2, traveling at a velocity of some 60 km/sec. Because of the pressure and local density, the expanding gas cloud accelerates projectiles due to plasma drag. To date, we have utilized projectiles consisting of 100 micron SiC, 100 and 400 micron Al2O3, 100 and 145 micron olivines. Since many particles are accelerated in a given experiment, there is a range of velocities for each shot as well as some particle breakup. Advanced diagnostics techniques allow determination of impact coordinates, velocity, and approximate size for as many as 50 individual impacts in a given experiment. We routinely measure velocities in the range 1-15 km/sec. We have used this facility to study a variety of impact generated phenomena on coated surfaces, both paint and plastic, thermal blanket material, solar cell arrays, and optical materials such as glass and quartz lenses. The operating characteristics of the gun, the advanced diagnostic scheme, and the results of studies of crater morphology are described in detail. Projectile residue analysis, as a function of impact velocity for the materials listed above, is also discussed. Wherever possible, these results are compared to those obtained by LDEF investigators and future experiments suggested which could help to explain unique features associated with LDEF impacts.

Rose, M. Frank↗

Study of the effects of gaseous environments on sulfidation attack of superalloys

Studies were conducted to examine the effect of the gaseous corrodents NaCl, HCl, and NaOH on the high temperature oxidation and Na2SO4-induced corrosion behavior of the alumina former NiAl, the chromia former Ni-25 wt.% Cr, elemental Cr, and the superalloy B-1900. Experiments were conducted at 900 and 1050 C in air in the presence and absence of the gaseous corrodents. Effects involving both reaction rates and microstructural changes in oxide morphology were observed due to the presence of these corrodents at levels anticipated to be present in operating industrial and marine gas turbines. The effect of gaseous NaCl, HCl, and possibly NaOH on NiAl in simple oxidation was to remove aluminum from below the protective alumina layer and to simultaneously weaken the adherence of the protective alumina oxide scale to the substrate. The aluminum removed from below the oxide scale was redeposited on its surface as alpha-Al2O3 whiskers. With respect to the chromia formers, gaseous NaCl and HCl promoted breakaway oxidation kinetics and changes in the microstructures of the oxide scales.

Smeggil, J. G.↗

Shear coaxial injector instability mechanisms

There is no definitive knowledge of which of several concurrent processes ultimately results in unstable combustion within liquid rocket chambers employing shear coaxial injectors. Possible explanations are a detrimental change in the atomization characteristics due to a decrease in the gas-to-liquid velocity ratio, a change in the gas side injector pressure drop allowing acoustic coupling to the propellant feed system or the disappearance of a stabilizing recirculation region at the base of the LOX post. The aim of this research effort is to investigate these proposed mechanisms under conditions comparable to actual engine operation. Spray characterization was accomplished with flash photography and planar laser imaging to examine the overall spray morphology and liquid jet breakup processes and with a PDPA to quantify the spatial distribution of droplet size and mean axial velocity. A simplified stability model based on the Rayleigh criterion was constructed for the flow dynamics occurring within the chamber and injector to evaluate the potential coupling between the chamber and injector acoustic modes and was supported by high frequency measurements of chamber and injector pressure oscillations. To examine recirculation within the LOX post recess, velocity measurements were performed in the recess region by means of LDV. Present experiments were performed under noncombusting conditions using LOX/GH2 stimulants at pressures up to 4 MPa.

Puissant, C.↗

Impact Craters on Mars: Natural 3D Exploration Probes of Geological Evolution

Introduction: The population of impact craters preserved on the surface of Mars offers fundamental constraints on the three- dimensional mechanical characteristics of the martian crust, its volatile abundance, and on the styles of erosion that have operated during essentially all epochs of martian geological history. On the basis of the present- day wealth of morphologic and geometric observations of impact landforms on Mars [ 1-31, an emerging understanding of the three-dimensional physical properties of the martian uppermost crust in space and time is at hand. In this summary, the current basis of understanding of the relatively non- degraded population of impact landforms on Mars is reviewed, and new Mars Global Surveyor (MGS)-based (MOLA) measurements of global geometric properties are summarized in the context of upcoming observations by Mars Reconnaissance Orbiter (MRO).

Garvin, James B.↗

The Vestal Cataclysm

The currently operating Dawn mission shows asteroid 4 Vesta to be an extensively cratered body, with craters in a variety of morphologies and preservation states The crater size-frequency distribution for Vesta, modeled using the lunar chronology and scaled to impact frequencies modeled for Vesta, shows that both the north and south pole areas are ancient in age [1]. We have in our meteorite collection products from 4 Vesta in the form of the HED (howardite, eucrite, diogenite) meteorites. The HED parent body globally differentiated and fully crystallized by approx.4.56 Ga; subsequently, the eucrites were brecciated and heated by large impacts into the parent body surface, reflected in their disturbance ages [2, 3]. Dawn images have also shown that Vesta is covered with a well-developed regolith that is spectrally similar to howardite meteorites [4, 5]. Howardites are polymict regolith breccias made up mostly of clasts of eucrites and diogenites, but which also contain clasts formed by impact into the regolith. Impact-melt clast ages from howardites extend our knowledge of the impact history of Vesta, expanding on eucrite disturbance ages and helping give absolute age context to the observed crater-counts on Vesta.

Cohen, Barbara A.↗

The Athena Mars Rover Science Payload

The Mars Surveyor missions that will be launched in April of 2001 will include a highly capable rover that is a successor to the Mars Pathfinder mission's Sojourner rover. The design goals for this rover are a total traverse distance of at least 10 km and a total lifetime of at least one Earth year. The rover's job will be to explore a site in Mars' ancient terrain, searching for materials likely to preserve a record of ancient martian water, climate, and possibly biology. The rover will collect rock and soil samples, and will store them for return to Earth by a subsequent Mars Surveyor mission in 2005. The Athena Mars rover science payload is the suite of scientific instruments and sample collection tools that will be used to perform this job. The specific science objectives that NASA has identified for the '01 rover payload are to: (1) Provide color stereo imaging of martian surface environments, and remotely-sensed point discrimination of mineralogical composition. (2) Determine the elemental and mineralogical composition of martian surface materials. (3) Determine the fine-scale textural properties of these materials. (4) Collect and store samples. The Athena payload has been designed to meet these objectives. The focus of the design is on field operations: making sure the rover can locate, characterize, and collect scientifically important samples in a dusty, dirty, real-world environment. The topography, morphology, and mineralogy of the scene around the rover will be revealed by Pancam/Mini-TES, an integrated imager and IR spectrometer. Pancam views the surface around the rover in stereo and color. It uses two high-resolution cameras that are identical in most respects to the rover's navigation cameras. The detectors are low-power, low-mass active pixel sensors with on-chip 12-bit analog-to-digital conversion. Filters provide 8-12 color spectral bandpasses over the spectral region from 0.4 to 1.1 micron Narrow-angle optics provide an angular resolution of 0.28 mrad/pixel, nearly a factor of four higher than that of the Mars Pathfinder and Mars Surveyor '98 cameras. Image compression will be performed using a wavelet compression algorithm. The Mini-Thermal Emission Spectrometer (Mini-TES) is a point spectrometer operating in -the thermal IR. It produces high spectral resolution (5 /cm) image cubes with a wavelength range of 5-40 gm, a nominal signal/noise ratio of 500:1, and a maximum angular resolution of 7 mrad (7 cm at a distance of 10 in). The wavelength region over which it operates samples the diagnostic fundamental absorption features of rockforming minerals, and also provides some capability to see through dust coatings that could tend to obscure spectral features. The mineralogical information that Mini-TES provides will be used to select from a distance the rocks and soils that will be investigated in more detail and ultimately sampled. Mini-TES is derived from the MO/MGS TES instrument, but is significantly smaller and simpler. The instrument uses an 8-cm Cassegrain telescope, a Michelson interferometer, and uncooled pyroelectric detectors. Along with its mineralogical capabilities, Mini-TES can provide information on the thermophysical properties of rocks and soils. Viewing upward, it can also provide temperature profiles through the martian atmospheric boundary layer. Elemental and Mineralogical Composition: Once promising samples have been identified from a distance using Pancam/Mini-TES, they will be studied in detail using up to three compositional sensors that can be placed directly against them by an Instrument Arm. The two compositional sensors, presently on the payload are an Alpha-Proton-X-Ray Spectrometer (APXS), and a Mossbauer Spectrometer. The APXS is derived closely from the instrument that flew on Mars Pathfinder. Radioactive alpha sources and three detection modes (alpha, proton, and x-ray) provide elemental abundances of rocks and soils to complement and constrain mineralogical data. The Athena APXS will have a revised mechanical design that will cut down significantly on backscattering of alpha particles from martian atmospheric carbon. It will also include a target of known elemental composition that will be used for calibration purposes. The Athena Mossbauer Spectrometer is a diagnostic instrument for the mineralogy and oxidation state of Fe-bearing phases, which are particularly important on Mars. The instrument measures the resonant absorption of gamma rays produced by a Co-57 source to determine splitting of nuclear energy levels in Fe atoms that is related to the electronic environment surrounding them. It has been under development for space flight for many years at the Technical University of Darmstadt. The Mossbauer Spectrometer (and the other arm instruments) will be able to view a small permanent magnet array that will attract magnetic particles in the martian soil. The payload may also include a Raman Spectrometer. If included, the Raman Spectrometer will provide precise identification of major and minor mineral phases. It requires no sample preparation, and is also sensitive to organics. Fine-Scale Texture: The Instrument Arm a also carries a Microscopic Imager that will obtain high-resolution monochromatic images of the same materials for which compositional data will be obtained. Its spatial resolution is 20 micron/pixel over a 1 cm depth of field, and 40 micron/pixel over a 1-cm depth of field. Like Pancam, it uses the same active pixel sensor detectors and electronics as the rover's navigation cameras. The Instrument Arm is a three degree-of-freedom arm that uses designs and components from the Mars Pathfinder and Mars Surveyor '98 projects. Its primary function is instrument positioning. Along with the instruments noted above, it also carries a brush that can be used to remove dust and other loose coatings from rocks. Sample Collection and Storage: Martian rock and soil samples will be collected using a low-power rotary coring drill called the Mini-Corer. An important characteristic of this device is that it can obtain intact samples of rock from up to 5 cm within strong boulders and bedrock, Nominal core dimensions are 8xl7 mm. The Mini-Corer drills a core to the commanded depth in a rock, shears it off, retains it, and extracts it. It can also acquire samples of loose soil, using soil sample cups that are pressed downward into loose material. The Mini-Corer can drill at angles from vertical to 45' off vertical. It has six interchangeable bits for long life. Mechanical damage to the sample during drilling is minimal, and heating is negligible. After acquisition, the sample may be viewed by the arm instruments, and/or placed in one of 104 compartments in the Sample Container. A subset of the acquired samples may be replaced with other samples obtained later if desired. The Sample Container has no moving parts, and is mounted external to the rover for easy removal by the Mars Surveyor 2005 flight system. Operation of the rover will make extensive use of automated onboard navigation and hazard avoidance capabilities. Otherwise, use of onboard autonomy is minimal. Data downlink capability is about 40 Mbit/sol, and the use of the Mars Surveyor '01 orbiter for data relay imposes a limit of at most two command cycles per sol. Because of the significant amount of time available between command cycles, all payload elements will be operated sequentially, rather than in parallel.; this approach also significantly simplifies operations and minimizes peak power usage. The landing site for the '01 rover has not been selected yet. Site selection will make as full use as possible of Mars Global Surveyor data, and will involve substantial input from the broad Mars science community. Summary: The following table describes the mass, power, providers, and key scientific objectives of all the major elements of the Athena payload. Additional Athena payload information may be found at: http://astrosun.tn.cornell.edu/athena/index.html. Additional information contained in the original.

Squyes, S. W.↗

Cloud cover typing from environmental satellite imagery. Discriminating cloud structure with Fast Fourier Transforms (FFT)

The use of two dimensional Fast Fourier Transforms (FFTs) subjected to pattern recognition technology for the identification and classification of low altitude stratus cloud structure from Geostationary Operational Environmental Satellite (GOES) imagery was examined. The development of a scene independent pattern recognition methodology, unconstrained by conventional cloud morphological classifications was emphasized. A technique for extracting cloud shape, direction, and size attributes from GOES visual imagery was developed. These attributes were combined with two statistical attributes (cloud mean brightness, cloud standard deviation), and interrogated using unsupervised clustering amd maximum likelihood classification techniques. Results indicate that: (1) the key cloud discrimination attributes are mean brightness, direction, shape, and minimum size; (2) cloud structure can be differentiated at given pixel scales; (3) cloud type may be identifiable at coarser scales; (4) there are positive indications of scene independence which would permit development of a cloud signature bank; (5) edge enhancement of GOES imagery does not appreciably improve cloud classification over the use of raw data; and (6) the GOES imagery must be apodized before generation of FFTs.

Logan, T. L.↗

Lifetime studies of high power rhodium/tungsten and molybdenum electrodes for application to AMTEC (alkali metal thermal-to-electric converter)

A detailed and fundamental model for the electrochemical behavior of AMTEC electrodes is developed which can aid in interpreting the processes which occur during prolonged operation of these electrodes. Because the sintering and grain growth of metal particles is also a well-understood phenomenon, the changes in electrode performance which accompany its morphological evolution may be anticipated and modeled. The grain growth rate observed for porous Mo AMTEC electrodes is significantly higher than that predicted from surface diffusion data obtained at higher temperatures and incorporated into the grain growth model. The grain growth observed under AMTEC conditions is also somewhat higher than that measured for Mo films on BASE (beta-alumina solid electrolyte) substrates in vacuum or at similar temperatures. Results of modeling indicate that thin Mo electrodes may show significant performance degradation for extended operation (greater than 10,000 h) at higher operating temperatures (greater than 1150 K), whereas W/Rh and W/Pt electrodes are expected to show adequate performance at 1200 K for lifetimes greater than 10,000 h. It is pointed out that current collection grids and leads must consist of refractory metals such as Mo and W which do not accelerate sintering or metal migration.

Williams, R. M.↗

The characterization of widespread fatigue damage in fuselage structure

The characteristics of widespread fatigue damage (WSFD) in fuselage riveted structure were established by detailed nondestructive and destructive examinations of fatigue damage contained in a full size fuselage test article. The objectives of this were to establish an experimental data base for validating emerging WSFD analytical prediction methodology and to identify first order effects that contribute to fatigue crack initiation and growth. Detailed examinations were performed on a test panel containing four bays of a riveted lap splice joint. The panel was removed from a full scale fuselage test article after receiving 60,000 full pressurization cycles. The results of in situ examinations document the progression of fuselage skin fatigue crack growth through crack linkup. Detailed tear down examinations and fractography of the lap splice joint region revealed fatigue crack initiation sites, crack morphology, and crack linkup geometry. From this large data base, distributions of crack size and locations are presented and discussions of operative damage mechanisms are offered.

Piascik, Robert S.↗

The characterization of widespread fatigue damage in fuselage structure

The characteristics of widespread fatigue damage (WSFD) in fuselage riveted structure were established by detailed nondestructive and destructive examinations of fatigue damage contained in a full size fuselage test article. The objectives of this work were to establish an experimental data base for validating emerging WSFD analytical prediction methodology and to identify first order effects that contribute to fatigue crack initiation and growth. Detailed examinations were performed on a test panel containing four bays of a riveted lap splice joint. The panel was removed from a full scale fuselage test article after receiving 60,000 full pressurization cycles. The results of in situ examinations document the progression of fuselage skin fatigue crack growth through crack linkup. Detailed tear down examinations and fractography of the lap splice joint region revealed fatigue crack initiation sites, crack morphology and crack linkup geometry. From this large data base, distributions of crack size and locations are presented and discussions of operative damage mechanisms are offered.

Piascik, Robert S.↗

Workshop on Science and the Human Exploration of Mars

The exploration of Mars will be a multi-decadal activity. Currently, a scientific program is underway, sponsored by NASA's Office of Space Science in the United States, in collaboration with international partners France, Italy, and the European Space Agency. Plans exist for the continuation of this robotic program through the first automated return of Martian samples in 2014. Mars is also a prime long-term objective for human exploration, and within NASA, efforts are being made to provide the best integration of the robotic program and future human exploration missions. From the perspective of human exploration missions, it is important to understand the scientific objectives of human missions, in order to design the appropriate systems, tools, and operational capabilities to maximize science on those missions. In addition, data from the robotic missions can provide critical environmental data - surface morphology, materials composition, evaluations of potential toxicity of surface materials, radiation, electrical and other physical properties of the Martian environment, and assessments of the probability that humans would encounter Martian life forms. Understanding of the data needs can lead to the definition of experiments that can be done in the near-term that will make the design of human missions more effective. This workshop was convened to begin a dialog between the scientific community that is central to the robotic exploration mission program and a set of experts in systems and technologies that are critical to human exploration missions. The charge to the workshop was to develop an understanding of the types of scientific exploration that would be best suited to the human exploration missions and the capabilities and limitations of human explorers in undertaking science on those missions.

Duke, M. B.↗

Dendritic Alloy Solidification Experiment (DASE)

A space experiment, and supporting ground-based research, is proposed to study the microstructural evolution in free dendritic growth from a supercooled melt of the transparent model alloy succinonitrile-acetone (SCN-ACE). The research is relevant to equiaxed solidification of metal alloy castings. The microgravity experiment will establish a benchmark for testing of equiaxed dendritic growth theories, scaling laws, and models in the presence of purely diffusive, coupled heat and solute transport, without the complicating influences of melt convection. The specific objectives are to: determine the selection of the dendrite tip operating state, i.e. the growth velocity and tip radius, for free dendritic growth of succinonitrile-acetone alloys; determine the growth morphology and sidebranching behavior for freely grown alloy dendrites; determine the effects of the thermal/solutal interactions in the growth of an assemblage of equiaxed alloy crystals; determine the effects of melt convection on the free growth of alloy dendrites; measure the surface tension anisotropy strength of succinon itrile -acetone alloys establish a theoretical and modeling framework for the experiments. Microgravity experiments on equiaxed dendritic growth of alloy dendrites have not been performed in the past. The proposed experiment builds on the Isothermal Dendritic Growth Experiment (IDGE) of Glicksman and coworkers, which focused on the steady growth of a single crystal from pure supercooled melts (succinonitrile and pivalic acid). It also extends the Equiaxed Dendritic Solidification Experiment (EDSE) of the present investigators, which is concerned with the interactions and transients arising in the growth of an assemblage of equiaxed crystals (succinonitrile). However, these experiments with pure substances are not able to address the issues related to coupled heat and solute transport in growth of alloy dendrites.

Beckermann, C.↗

Effects of Aircraft On Aerosol Abundance in the Upper Troposphere

A significant increase in sulfuric acid aerosol concentration was detected above 10 km pressure altitude during a cross-corridor flight out of Shannon on October 23, 1997. The source of this aerosol is ascribed to commercial aircraft operations in flight corridors above 10 km, because (1) a stable atmosphere prevented vertical air mass exchanges and thus eliminated surface sources, (2) air mass back trajectories documented the absence of remote continental sources, and (3) temperature profiler data showed the tropopause at least one kilometers above flight altitude throughout the flight. Particle volatility identified 70% H2SO4, 20% (NH4)2SO4 and 10% nonvolatile aerosol in the proximity of flight corridors, and (10-30)% H2SO4, up to 50% (NH4)2SO4, and (40-60)% nonvolatile aerosols in air that was not affected by aircraft operations below 10 km. Only a very small fraction of the nonvolatile particles (determined with a condensation nucleus counter) could be morphologically identified as soot aerosol (validated by scanning electron microscopy of wire impactor samples). The newly formed H2SO4 particles did not measurably affect surface area and volume of the background aerosol due to their small size, hence did not affect radiative transfer directly.

Ferry, G. V.↗

Investigations of Martian Impact Crater Morphologies and Morphometries

We have made substantial progress towards completion of the original objectives and are continuing to include new data from the Mars Global Surveyor MOC and TES instruments as they become available (the MOLA instrument has ceased operation as of 2002). The project funding has been used to provide salary support to the PI and several undergraduate students, cover publication charges for two papers, reimburse travel expenses to conferences and workshops incurred by the PI and students, and cover a number of other expenses such as software upgrades and production costs of slides and color prints. This study is revising the PI's Catalog of Large Martian Impact Craters with information obtained from MGS and is utilizing data in the revised Catalog to investigate which planetary factors (such as location, elevation, terrain type, etc.) primarily affect the formation of specific ejecta morphologies and morphometries.

Barlow, Nadine G.↗

An eastward propagating compressional Pc 5 wave observed by AMPTE/CCE in the postmidnight sector

This paper presents a detailed analysis of a compressional Pc 5 wave observed in the postmidnight sector on July 21, 1986, using data from the magnetometer, the charge-energy-mass spectrometer, and the medium-energy particle analyzer aboard the AMPTE/Charge Composition Explorer (CCE) spacecraft. The Pc 5 wave exhibited harmonically related transverse and compressional magnetic oscillations, modulation of the flux of medium energy protons, and a large azimuthal wave number, i.e., properties that are similar to those of compressional Pc5 waves observed previously at geostationary orbit. The unique observations recorded by the AMPTE/CCE included the occurrence of the wave in the postmidnight sector, its sunward propagation with respect to the spacecraft, and the left-handed polarization of the perturbed magnetic field. In spite of the morphological uniqueness observed, the excitation of the July 21 event is considered to be due to the same type of instability as operates at geostationary orbit.

Takahashi, K.↗

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↗