On Kirchhoff's law and its generalized application to absorption and emission by cavities.
Validity of Kirchhoff law for apparent local spectral emittance and absorptance and total flux calculations for spacecraft cavities
RADIANT ENERGY↗
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Electromagnetic fluctuations for anisotropic media and the generalized Kirchhoff's law
In this paper the polarimetric emission parameters for anisotropic media are derived using the generalized Kirchhoff's law for media with a uniform temperature and the fluctuation-dissipation theory for media with a temperature profile. Both finite-size objects and half-space media are considered. When the object has a uniform temperature across its body, the Kirchhoff's law, based on the condition of energy conservation in thermal equilibrium is generalized to obtain the emission parameters of an anisotropic medium, which can be interpreted as the absorptivity or the absorption cross section of the complementary object with a permittivity that is the transpose of the original object. When the medium has a nonuniform temperature distribution, the fluctuation-dissipation theory is applied for deriving the covariances between vector components of the thermal currents and, consequently, the covariances of the polarizations of electric fields radiated by the thermal currents. To verify the formulas derived from the fluctuation-dissipation theory, we let the temperature of the object be a constant and show that the results reduce to those obtained from the generalized Kirchhoff's law.
Yueh, Simon H.↗
Thermal-infrared remote sensing and Kirchhoff's Law. 1: Laboratory measurements
By the end of this century the Earth Observing System (EOS) will provide worldwide, thermal infrared, multispectral images of the Earth, presenting geologists with a new kind of remote sensing data for interpretation. Thus it has become essential to understand the spectral emittance behavior of terrestrial surface materials. Perhaps the most fundamental question to be answereed is the extent to which such materials follow Kirchhoff's law (epsilon = 1 -R) under laboratory and field conditions, especially when a sample displays a thermal gradient. We present the first rigorous quantitative comparison of directional and hemispherical reflectance and directional emittance of rock and soil samples in the laboratory, with thermal gradients induced by heating them from below and allowing them to radiate to a colder background. The results show that only an extemeley low density sample composed of fine particles sifted into a 'fairy castle' structure displays a thermal gradient steep enough within the infrared skin depth to cause significant (6%) departure from Kirchhoff's law. There is no detectable effect on the more normal terrestrial samples, such as soils and rocks measured in the laboratory, even when semitransparent coatings are involved. Thus both emittance and reflectance measurements can be used to calculate sample emissivity for most terrestrial surface materieals. However, the effect on Kirchhoffian behavior of different field environments, which may induce a steeper thermal gradient in particulate samples, has yet to be determined, and some low-density surface materials like newly fallen snow, frost, and efflorescent salts on playas have yet to be measured in emittance.
Salisbury, John W.↗
On the validity of a generalized Kirchhoff's Law for a nonisothermal scattering and absorptive medium.
The relationship of directional hemispherical reflectivity to emissivity is investigated for a nonisothermal medium with isotropic coherent scattering and absorption. Departures from a generalized Kirchhoff's Law occur due to the long range nature of the scattering process. Such departures occur in lunar thermal emission at microwave but not at infrared frequencies.
Linsky, J. L.↗
Thermal infrared remote sensing and Kirchhoff's law: 1. Laboratory measurements
Kirchoff's Law, as originally conceived, applies only to samples in thermal equilibrium with their surroundings. Most laboratory measurements of emissivity only approach this condition and it never applies in remote sensing applications. In particular, the background is often much cooler than the radiating sample, and this has led to a long controversy about the applicability of Kirchhoff's Law under such conditions. It has also led to field and laboratory measurement techniques that use some form of the 'emissivity box' approach, which surrounds the sample with a background as close as possible to the sample temperature. In our experiments, we have heated soil samples in air on a hot plate in the laboratory to a much higher temperature than the room temperature background. Spectral emissivity was measured, except the known emissivities of both the primary and secondary Christiansen features were used, instead of assuming an emissivity of unity at these wavelengths. The results from this investigation are discussed in brief.
Salisbury, J. W.↗
Kirchhoff's theorem in the acoustics of a moving medium
Generalized Kirchhoff law in acoustic energy calculation for moving point source of sound
SOUND WAVE↗
Thermal Behaviour of Unusual Local-Scale Surface Features on Vesta
On Vesta, the region of the infrared spectrum beyond approximately 3.5 micrometers is dominated by the thermal emission of the asteroid's surface, which can be used to determine surface temperature by means of temperature-retrieval algorithms. The thermal behavior of areas of unusual albedo seen at the local scale can be related to physical properties that can provide information about the origin of those materials. Dawn's Visible and Infrared Mapping Spectrometer (VIR) hyperspectral cubes are used to retrieve surface temperatures, with high accuracy as long as temperatures are greater than 180 K. Data acquired in the Survey phase (23 July through 29 August 2011) show several unusual surface features: 1) high-albedo (bright) and low-albedo (dark) material deposits, 2) spectrally distinct ejecta, 3) regions suggesting finer-grained materials. Some of the unusual dark and bright features were re-observed by VIR in the subsequent High-Altitude Mapping Orbit (HAMO) and Low-Altitude Mapping Orbit (LAMO) phases at increased pixel resolution. To calculate surface temperatures, we applied a Bayesian approach to nonlinear inversion based on the Kirchhoff law and the Planck function. These results were cross-checked through application of alternative methods. Here we present temperature maps of several local-scale features that were observed by Dawn under different illumination conditions and different local solar times. Some bright terrains have an overall albedo in the visible as much as 40% brighter than surrounding areas. Data from the IR channel of VIR show that bright regions generally correspond to regions with lower thermal emission, i.e. lower temperature, while dark regions correspond to areas with higher thermal emission, i.e. higher temperature. This behavior confirms that many of the dark appearances in the VIS mainly reflect albedo variations. In particular, it is shown that during maximum daily insolation, dark features in the equatorial region may rise to temperatures greater than 270 K. However, individual features may show different thermal behaviours, as a result of differences in composition and/or structure (e.g, average grain size of the surface regolith, porosity, etc.). To complement the temperature and near-infrared emissivity derived from the infrared spectra, a separate work is devoted to calculate thermal inertia and other thermal properties using theoretical models which solve the heat equation for airless bodies, and model the distribution of temperatures due to surface roughness variations.
Tosi, F.↗
Thermal Behavior of Unusual Local-Scale Features on Vesta
On Vesta, the thermal behavior of areas of unusual albedo seen at the local scale can be related to physical properties that can provide information about the origin of those materials. Dawn's Visible and Infrared Mapping Spectrometer (VIR) hyperspectral cubes are used to retrieve surface temperatures and emissivities, with high accuracy as long as temperatures are greater than ~180 K. Data acquired in the Survey phase (23 July through 29 August 2011) show several unusual surface features: 1) high-albedo (bright) and low-albedo (dark) material deposits, 2) spectrally distinct ejecta and pitted materials, 3) regions suggesting finer-grained materials. Some of the unusual dark and bright features were re-observed by VIR in the subsequent High-Altitude Mapping Orbit (HAMO) and Low-Altitude Mapping Orbit (LAMO) phases at increased pixel resolution. In particular, bright and dark surface materials on Vesta, and pitted materials, are currently being investigated by the Dawn team. In this work we present temperature maps and emissivities of several local-scale features that were observed by Dawn under different illumination conditions and different local solar times. To calculate surface temperatures, we applied a Bayesian approach to nonlinear inversion based on the Kirchhoff law and the Planck function, and whose results were compared with those provided by the application of alternative methods. Data from the IR channel of VIR show that bright regions generally correspond to regions with lower thermal emission, i.e. lower temperature, while dark regions correspond to areas with higher thermal emission, i.e. higher temperature. This behavior confirms that many of the dark appearances in the VIS mainly reflect albedo variations, and not, for example, shadowing. During maximum daily insolation, dark features in the equatorial region may rise to temperatures greater than 270 K, while brightest features stop at roughly 258 K for similar local solar times. However, pitted materials, showing relatively low reflectance, have significantly lower temperatures, as a result of differences in composition and/or structure (e.g, average grain size of the surface regolith, porosity, etc.). To complement this work, we provide preliminary values of thermal inertia for some bright and dark features.
Tosi, Federico↗
A theoretical and numerical study of polarimetric scattering and emission from random rough surfaces with anisotropic directional spectrum
In this paper, theoretical and numerical results of the polarimetric scattering and emission from random rough surfaces with anisotropic directional spectrum are presented for the remote sensing of ocean and soil surfaces. The polarimetric scattered field for rough dielectric surfaces is derived to the second order by the small perturbation method (SPM). It is found that the second-order scattered field is coherent in nature, and its coefficients for different polarizations present the lowest-order corrections to the Fresnel reflection coefficients of the surfaces. In addition, the cross-polarized (HV and VH) components of the coherent fields are reciprocal and not zero for surfaces with anisotropic directional spectrum when the azimuth angle of the incident direction is not aligned with the symmetry directions of surfaces. In order to verify the energy conservation condition of the theoretical results, which is important if the theory is to be applied to the passive polarimetry of rough surfaces, a Monte Carlo simulation is performed to numerically calculate the polarimetric reflectivities of one-dimensional random rough surfaces which are generated with a prescribed power-law spectrum in the spectral domain and transformed to the spatial domain by the FFT. The surfaces simulated by this approach are periodic with the period corresponding to the low-wavenumber cutoff. To calculate the scattering from periodic dielectric surfaces, the authors present a new numerical technique which applies the Floquet theorem to reduce the problem to one period and does not require the evaluation of one-dimensional periodic Green's function used in the conventional method of moment formulation. Once the scattering coefficients are obtained, the polarimetric Stokes vectors for the emission from the random surfaces are then calculated according to the Kirchhoff's law and are illustrated as functions of relative azimuth observation and row directions. The second-order SPM is also reduced to this one-dimensional case, and theoretical results for all four Stokes parameters are in excellent agreement with the numerical results obtained from the Monte Carlo simulation. Moreover, the second order coherent fields are found to be necessary for the theoretical evaluation of the third and fourth Stokes parameters. Without that, the reflectivities of random rough surfaces are significantly over-estimated, and the signs of the third and the fourth Stokes parameters are found to be incorrect, if calculated by using the first-order incoherent fields alone.
Yueh, S. H.↗
Foundations of linear inelastic shell theory progress report
Foundations of linear inelastic thin shell theory
SHELL THEORY↗
Asymptotic theory of statics and dynamics of elastic circular cylindrical shells and analysis of the accuracy of the different variants of the Kirchhoff-Love theory
Asymptotic formulas for elastic cylindrical shells and analysis of Kirchhoff-Love theory
ELASTIC SHELL↗
Displacement formulations of the thin elastic shell equations.
Displacement formulations of first order linear thin elastic shell equations in terms of stress resultant and middle surface, using modified Kirchhoff hypothesis
FIRST ORDER EQUATION↗
MTRAC - Computer program for transient analysis of circuits including magnetic cores
MTRAC program for transient analysis of circuits with square loop magnetic cores based on linearization of nonlinear circuit elements and Kirchhoff current law
Nitzan, D.↗
Transient solution for megajoule energy release in a lumped-parameter series RLC circuit
A method is developed for optimizing the energy release from a megajoule capacitive discharge in a series RLC circuit with an RL load. Both the resistance and inductance of the load are represented by effective values that characterize their behavior during the discharge. Using Kirchhoff's laws, equations utilizing the load impedance and the external circuit impedance are derived for determining the instantaneous load voltage and energy characteristics. A program (ERES) computes and displays the load characteristics and the circuit current. Use of the ERES program allows a designer to perturbate values of the circuit elements in order to produce the desired time distribution for the load energy input.
Barnes, G.↗
Infrared (2.08-14 micron) spectra of powered stony meteorites
Infrared biconical reflectance spectra of 60 powdered meteorite samples, representing 50 different stony meteorites, were measured as analogues of asteroidal regolith. Representative samples were measured in directional hemispherical reflectance to assure that Kirchhoff's Law can be used to predict relative emissivity from the reflectance spectra. These spectral data confirm that the O-H fundamental absorption band near 2.9 microns is an extremely sensitive indicator of incipient alteration, which often has taken place in powdered meteorite samples exposed only to water vapor in the air. Such non-carbonaceous samples typically contain less than 1 percent water by weight. Likewise, the C-H fundamental absorption bands near 3.4 and 3.5 microns are equally sensitive indicators of contamination with volatile hydrocarbons, which can also be absorbed from the air. The heavy, macromolecular hydrocarbons native to chondrites do not display such heavy bands, making detection of these bands in remote sensing of asteroids unlikely. Despite the spectral artifacts introduced by alteration and hydrocarbon contamination, powdered stony meteorites display a wide variety of real spectral features that can be used for their identification, including residual reststrahlen bands, absorption bands, and the Christiansen feature. Researchers found that the wavelengths of the peaks or troughs of each of these spectral features can be used independently to infer meteorite composition, but the best results are obtained when the entire spectral curve is used, or at least the portion of it encompassed by the 8 to 14 micron atmospheric window, in a digital search library.
Salisbury, J. W.↗
Multiwavelength pyrometry for nongray bodies
A multiwavelength technique was developed and applied to measure the temperatures of nongray surfaces. The instruments required are a spectral radiometer, a dedicated auxiliary radiation source, and a computer. In general, three radiation spectra are recorded: (1) spectrum S sub 0 of the auxiliary radiation source; (2) spectrum S sub 1 of the surface-emitted radiation; and (3) spectrum S sub 2, the sum of the radiation of S sub 1 plus the reflected radiation due to the incidence of the auxiliary radiation source on the surface. Subtracting spectrum S sub 1 from spectrum Sub 2 yields the reflection spectrum resulting from the incidence radiation. From these spectra, a quantity z(lambda) is derived and is related to the reflectivity r(lambda) by r(lambda) = z(lambda)/f, where f is a constant. Spectrum S sub 1 is represented mathematically as the product of a wavelength-dependent emissivity obtained from Kirchhoff's law and a Planck function of temperature T. Application of two-variable (lambda and z), nonlinear, least-squares curve-fitting computer software to fit spectrum S sub 1 to this mathematical expression yielded the surface temperature. This technique also measured the spectral reflectivity and emissivity of the surface. Instrumentation necessary to extend measurement to elevated temperatures and in the presence of reflective interference is discussed.
Ng, Daniel↗
The role of volume scattering in reducing spectral contrast of reststrahlen bands in spectra of powdered minerals
The first high-resolution quantitative directional hemispherical reflectance spectra of minerals were obtained for different particle sizes, and were used to develop an accurate prediction of the particles' spectral emissivity, using Kirchhoff's law (Nicodemus, 1965) and to interpret the nature and causes of changes in the spectral contrast of reststrahlen bands. It was found that the reststrahlen bands change in shape as well as intensity; this is explained by the occurrence of substantial volume scattering at fine particle sizes. The implication of this finding for remote sensing of the earth, moon, Mercury, Mars, and the asteroids is discussed.
Salisbury, John W.↗
Emissivity of terrestrial materials in the 8-14 microns atmospheric window
Remotely sensed infrared radiance emitted by a surface is a function both of its kinetic temperature and its spectral emissivity. Consequently, assumptions are usually made about the emissivity of earth surface materials to allow their temperatures to be determined, or vice versa. To increase the accuracy of these assumptions, the directional hemispherical spectral reflectance of a wide range of natural earth surface materials has been measured and is summarized here. These include igneous, metamorphic, and sedimentary rocks, desert varnish, soils, vegetation, water, and ice. Kirchhoff's Law can be used to predict directional spectral emissivity from these data.
Salisbury, John W.↗