Emergent Radiation Research Articles

Intensity and Polarization of the Radiation Emerging from a Plane-Parallel Atmosphere Containing Monodispersed Aerosols

A method for evaluating the intensity, degree of polarization, direction of polarization, and ellipticity of the scattered radiation emerging from a plane-parallel atmosphere containing large spherical particles is described. In this method, all the elements of the normalized phase matrix are represented by fourier series whose maximum required number of terms depend upon the zenith angles of the directions of the incident and scattered radiation. Some results are presented for an atmospheric model containing water spheres with size parameter 10.0 to show that this method can be used to evaluate reliably all the characteristics of the emergent radiation in a reasonable amount of computer time.

An Interferometric Approach to the Measurement of Optical Polarization

After discussing the desirability of determining the variation of polarization with frequency in planetary spectra, the possibility of measuring the intensity and state of polarization of optical radiation by means of the high resolution Fourier spectroscopic method is discussed. In the proposed experimental arrangement a two-beam interferometer is used with a polarizer in each beam. After recombination the emergent radiation is analyzed with a linear polarizer. It is shown that the interferograms obtained in this way contain information about the four Stokes parameters of the incident radiation. The polarizers introduce an asymmetry in the interferograms requiring full (exponential) transforms for retrieval of the desired data. The effects of the finite range of path difference and the variation of its zero point with frequency are considered, and evaluation of the corresponding phase error with a proper choice of the polarizer settings is discussed. The formalism also takes into account the residual polarization introduced by the beam splitter, and the differential transmission of the two beams. Generally, three independent interferograms are needed for determining the phase error and the four Stokes parameters. Some simple arrangements are described in which the two beams are either both linearly or both circularly polarized. It is hoped that instruments based on the principle described here will be built by workers in the field.

Quantitative chemical analysis with X-ray fluorescence spectrometry—an accurate and general mathematical correction method for the interelement effects

It is stated that, for a given element A to be determined, fluorescent intensity I A is dependent as much on the concentration of A as on the absorption characteristics of the unknown sample in regard to both the emergent fluorescent radiation and the generally complex incident exciting radiation. It is also shown that if the primary radiation can be assumed to be equivalent to a constant monochromatic radiation a number of methods, especially dilution or multidilution procedures, can be devised for eliminating the influence of absorption differences between unknown and standard specimens. The theory of “corrected” fluorescent intensities free from matrix effects is put forward. The influence of the usually polychromatic or composite structure of the incident beam is thoroughly investigated, both theoretically and experimentally, and it is demonstrated that matrix effects are completely compensated in all cases, using the dilution methods, whatever the particular structure of the incident beam. So, for the purpose of quantitative analysis, the concentrations calculated from the corrected intensities are in principle exact values, within a 0.1–0.2% relative accuracy. Practical consequences are considerable. Using homogeneous specimens, the method compensates exactly for absorption and enhancement effects and its practical accuracy ranges from a few tenths of one percent to a few percent, relative, according to the more or less favourable measurement conditions encountered. High sensitivity can be retained if necessary. The method is quasi absolute, as only a few standard specimens are used, made up either of pure compounds or of a well known reference sample. No calibration curves are needed and calculations are remarkably simple. All elements relevant to X-ray fluorescence can be determined in every kind of material (ores, rocks, chemicals, metals and alloys, ⋯) using either ordinary solutions or solid solutions as obtained by fusion techniques.

Effect of a Concentrated Turbid Layer on the Polarization of Skylight*†

The effect of a concentrated turbid layer on the polarization of skylight is discussed in this paper. Two idealized models of the turbid atmosphere are employed. In one an aerosol layer is situated below a molecular layer and, in the other, above it. The size distribution of the aerosols of refractive index 1.33 is assumed to follow a power law. Inside the aerosol layer, only primary scattering of light is taken into account and polarization effects are neglected. The importance of the interaction between the aerosol and molecular layers is recognized. The resulting computations show broad agreement with available observations. The importance of the location of the turbid layer in characterizing the emergent radiation is revealed. In particular, the computations have shown that the Babinet and Brewster neutral (zero polarization) points can shift towards the sun from their normal positions in a molecular atmosphere when there is low-level turbidity. Such a shift is indicated by observations.

Kinetic Theory for the Interpretation of Measurements on Fluctuations in Radiation Distributions in Finite, Inhomogeneous Systems

A kinetic (transport) theory is presented for the first- and second-order (and, if necessary, higher) statistical moments of the number densities of the various particles and/or photons that describe the observable fluctuations in the radiation distribution from an emitting system. This treatment is particularly suitable for the analysis of finite, inhomogeneous systems that may be composed of detectors located outside of a radiating source. Because we are largely concerned with the utility of kinetic theory as a physical theory, considerable emphasis is placed upon an appropriate theoretical description of the actual observables of given experimental situations. The quantum Liouville equation is used to generate the coupled set of transport equations, and basic criteria for the applicability of transport and wave theories are discussed. Quantum-statistical effects are also quite naturally accounted for in cases where they are relevant. It is seen that fluctuation measurements are useful for inferring information relevant to the dynamic interactions within a given system. Such measurements often enjoy the feature of being passive with respect to the interacting system of interest. To illustrate the use of this spatially dependent form of kinetic theory on a system emitting optical radiation, we consider an example that interprets a fluctuation measurement on the radiation emergent from a finite nondispersive blackbody. We conclude by discussing the problems of statistical coupling between the radiation field and detector atom distributions.

Numerical results for the estimation of source distributions from external radiation-field measurements

The authors consider a transport process in a slab bounded by two parallel planes. Radiation is both absorbed and scattered isotropically. The radiation is due to continuously distributed internal isotropic sources. The aim is to estimate the distribution of the internal sources based on experimental measurements of the angular dependence of the emergent radiation. First, a system of differential-integral equations for the emergent radiation is deduced. These are approximated by a system of ordinary differential equations, and some numerical results are given. Quasi-linearization is then used to solve the inverse problem numerically. The results of some computational experiments are given which indicate the sensitivity of the estimates of the source distribution to the observational errors in the emergent-radiation measurements. The methods can be generalized to the cases of anisotropic scattering and shell geometry.

Induced and Spontaneous Emission

The problem of induced and spontaneous emission is investigated for an atomic two-level system with incident beams of radiation which are either in a coherent state or in a stationary state (contain a definite number of photons). The treatment is fully quantum-mechanical, and is confined to the case where the frequency spectrum of the incident beam is narrow compared to the natural linewidth of the system. It is shown that, under such conditions, the spontaneous emission for frequencies within the narrow band of the incident radiation is sharply reduced compared to the prediction of the natural lineshape. It is shown that a hole is burned in the natural lineshape within the narrow frequency band, thus effectively quenching the spontaneous emission at some frequency within the band. This effect is shown to occur both for the coherent and stationary beams. Quantities proportional to the induced and spontaneous probability amplitudes and the lifetimes are computed for times comparable to and long compared to the free lifetime of the state. An expression is found for the spectrum of the emergent radiation in terms of these quantities. Its physical meaning is briefly discussed. The density operator of the field for all times is given.

Light Scattering by Cloud Layers

Abstract Results of calculations of diffuse reflection and transmission of cloud-model layers are presented. These calculations which are based on matrix methods developed by the authors and discussed in a previous paper include the effects of cloud thickness, absorption, drop-size distribution, liquid water content, and directions of the incident and emergent radiation.

Estimation of internal source distributions using external field measurements in radiative transfer

A finite homogeneous slab which absorbs radiation and scatters it isotropically possesses internal isotropic sources of radiation. The authors first show how to determine the intensity of the emergent radiation, making use of invariant imbedding techniques, and then show how to determine the distribution of the internal sources that best accounts for an observed emergent radiation pattern. This inverse problem is viewed as a nonlinear two-point boundary value problem which can be resolved numerically using quasilinearization.

Numerical Inversion of Laplace Transforms and Some Inverse Problems in Radiative Transfer

Abstract Consider a semi-infinite homogeneous slab atmosphere which absorbs radiation and scatters it isotropically. A basic inverse problem is the determination of the source function, given the angular dependence of the emergent radiation. We show how to solve this problem, making use of our previous work on the numerical inversion of Laplace transforms.

The Effect of Absorption on a Rayleigh Atmosphere

Abstract Calculations are presented for the reflected and transmitted intensifies and polarizations for the C wavelength pair used for Umkehr measurements. The present calculations utilize a numerical integration of the transfer equation which includes an orders of scattering as well as absorption. These results are compared with solutions which include only scattering, and solutions which include absorption but only single scattering. The importance of higher order scattering for intensity calculations even at higher absorbing wavelengths is demonstrated, as well as the effects of absorption on the polarization of the emergent radiation.

Radiation from explosive-driven shocks in the noble gases

Shock temperatures were calculated for xenon, krypton, and argon using the strong-shock approximation and Composition B explosive as the driver. Temperatures of 38,000 31,000 and 23,000°K were obtained for Xe, Kr and A, respectively. Further calculations were made on the emergent radiation flux from the cold preshocked gas by taking into account radiation absorption in the shocked gas itself, the radiation-heated shock precursor, and the cold gas ahead of the precursor. The frequency integrated power fluxes on a target 100 cm ahead of the shock are 4·1(10) 13, 3·5(10) 13, and 1·4(10) 13 ergs per cm 2 per sec for Xe, Kr and A, respectively.

Tables of Functions of Selected Models of the So@ Atmosphere.

view Abstract Citations (1) References (7) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Tables of Functions of Selected Models of the So@ Atmosphere. Andrews, M. ; Mugglestone, D. Abstract Four solar atmospheric models have been selected (those of Aller and Pierce, de Jager, Swihart, and Vitense), and tables of functions, which are dependent only upon wavelength and the model considered, have been in the wavelength range 3647 <x < 14588 A. At each selected wavelength the functions tabulated are the optical depth in the continuum r,; e the ratio of continuous mass absorption coefficients k /k'; the Planck function B and its derivative with respect to optical depth dBv/dr'. Ml these parameters are tabulated, at each wavelength, as functions of the optical depth in the continuum r' specified by the model. In addition, derived functions, I (0, 0) (the intensity in the continuum), (dB /dr')e (r'), and the "weighting function" g (r') have been tabulated. Various combinations of the tabulated functions, depending on the mathematical formulation of the equations describing the phenomena being considered, are useful in numerical calculations on the emergent solar radiation. Publication: The Astrophysical Journal Supplement Series Pub Date: May 1962 DOI: 10.1086/190071 Bibcode: 1962ApJS....6..481A full text sources ADS |

Experimental Study of the Flow Conditions and Pressure Drop of Steam-Water Mixtures at High Pressures in Heated and Unheated Tubes

The work described in the three parts of this paper was sponsored by the Water-Tube Boilermakers' Association and carried out in the Engineering Department of Cambridge University. In Part I are described the high-pressure experimental plant and its associated instrumentation. A description of the test circuit is followed by a detailed description of the construction and performance of the electrical low-frequency induction heaters specially developed to supply the power input to the test section. Auxiliary electrical resistance heaters are also described. The work required the development of special differential manometers and differential thermocouples suitable for the accurate measurement of small differences in pressure and temperature at high fluid pressures. Gamma-ray absorption equipment was used to make measurements of the apparent density of the two-phase mixture within a cross-section of the tube at the test-section outlet, from which estimates could be obtained of the relative or ‘slip’ velocity between the two phases. Part I of the paper ends with a description of the mode of operation of the plant and the range of variables covered during the tests. Part II deals with the analysis of the experimental results obtained from measurements of the absorption of gamma-rays in their passage through the two-phase mixture at outlet from the test section. The results of tests on the -in. bore pipe are examined first, although they were the last to be carried out. In these tests the tube cross-section was scanned by a narrow pencil of rays from a collimated beam, and scintillation-counter equipment was used to measure the intensity of the emergent radiation. Preliminary tests involving scans along a number of chords of the tube cross-section gave information on the density distribution of the fluid within the cross-section; this was different for the vertical and horizontal pipes. Data from these readings enabled the main series of tests, during which pressure-drop readings were also taken, to be carried out with a single scan along the tube centre-line only. From the readings taken during the latter tests the area dryness-fraction (void fraction) and slip velocity ratio were calculated and correlated as functions of the mass dryness-fraction. The paper then gives a brief presentation of the less satisfactory results obtained on the 1-in. bore pipe with full-area scanning by an uncollimated beam using an ionization chamber as detector. The foregoing correlations are finally used to calculate slip correction factors by means of which the acceleration and gravitational pressure-drops calculated according to homogeneous theory may be corrected for the effects of slip. The application of these factors to the analysis of the experimental pressure-drops is studied in Part III. Part III presents an analysis of the pressure-drop measurements made on the . bore pipes in both the horizontal and vertical positions, giving particular attention to comparisons between the experimental results and values predicted by homogeneous theory. These comparisons are made in terms of dimensionless pressure-drop coefficients which enable the respective contributions of friction, acceleration and gravitation to the total pressure drop to be readily displayed. Use is made of the correction curves derived in Part II to apply a correction for the effects of slip to the acceleration and gravitational pressure-drops predicted by homogeneous theory, and thence to compare the corrected predictions of pressure drop with the experimental values. In an analysis of the results for the horizontal pipes, the frictional pressure-drop under two-phase conditions is evaluated, for the heated pipes, by subtracting from the measured total pressure-drop an estimated acceleration pressure-drop allowing for the effects of slip. Correlation of the frictional pressure-drops in both the heated and unheated pipes enables these to be related to the corresponding homogeneous values through a suitable correction factor. The pipes were fortuitously of different roughness, and the relation of the effective two-phase friction factors to the respective single-phase factors is studied. In the vertical pipes, the gravitational contribution to the total pressure-drop being dominant, the experimental results are compared favourably with predictions in which the gravitational term is computed by correcting the homogeneous value for the effects of slip, while the frictional and acceleration terms are taken to be the same as the homogeneous values. Additional correction of the frictional term in the unheated pipes is seen to give a small improvement in accuracy of prediction. In a concluding section, values of the slip ratio are deduced from pressure-drop measurements on the vertical, unheated pipes, so carrying through the reverse procedure of Part II, and these values are compared with the values deduced from the gamma-ray measurements in Part II.

The Shielding of Helical Ducts

The problem of radiation penetration through a shield containing a helical duct is considered by representing the duct by successive straight ducts joined at a fixed angle. Expressions for the emergent radiation flux are derived and illustrated for a typical case. It is shown that, in a representative example, the contribution from radiation scattered along the duct is a small fraction of the general increase in radiation level due to the reduced effective density of the bulk shield in the vicinity of the helix. (auth)

The calculation of line profiles in a stratified atmosphere.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The calculation of line profiles in a stratified atmosphere. Doherty, L. R. ; Hazen, M. L. ; Menzel, D. H. Abstract The acceptability of a model solar atmosphere depends upon the agreement of the observed and predicted line profiles or curves of growth, at different angles of the emergent beam. One calculates the specific intensity from Milne's familiar integral, in terms of a known source function. The dependence of the result upon changes of model may be difficult to determine and interpret physically when many variables are present and when each integration is a relatively laborious process. We have adopted a simplified model which allows for stratification of the absorbing material and for a wide variety of source functions. The final result appears in algebraic form, so that one can readily examine how the emergent radiation varies with alteration of the parameters of the model. The approximations that we have made are the following. I. We have reproduced the effect of stratification by taking the ratio of line-to-continuous absorption (Eddington's ~) as constant in a layer between two arbitrarily chosen values of the optical depth r. We can also obtain a simple result by taking ~ proportional to r/ (a + r) or 2. We have assumed a constant Doppler temperature throughout the absorbing layer. 3. We have represented the source function as a linear combination of exponential and power terms in the optical depth. Intensities computed under the assumptions ~tated in (I) show that the results for variable 71 may essentially be duplicated by a layer with 71 constant between selected optical depths. In other words, the results are not very sensitive to the detailed form of the stratification. From this fact we conclude that the layer model adequately represents the effects of stratification on profiles of absorption lines. We have also computed curves of growth and find that a layer extending from the surface to an optical depth about 0.5 provides the best fit to the empirical curves for Fei (Bell 1951) and Tii (Claas 1951). As might be expected, this curve also corresponds with the theoretical Schuster-Schwarzschild curve. We anticipate that this method will be particularly useful for source functions that depend on depth in a complicated manner, as in the chromosphere, or that vary over the disk, granulation and spots. This work has been supported by the Geophysics Research Directorate, Air Force Cambridge Research Center, under a contract with Harvard University. Bell, B. 1951, Harvard thesis. Claas, W. 1951, Rech. Astr. Obs. Utrecht 12, Part I. Harvard College Observatory, Cambridge, Mass. Publication: The Astronomical Journal Pub Date: September 1958 DOI: 10.1086/107752 Bibcode: 1958AJ.....63..305D full text sources ADS |

Paschen and Balmer Series in Spectra of Chi Ophiuchi and P Cygni.

view Abstract Citations (21) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Paschen and Balmer Series in Spectra of Chi Ophiuchi and P Cygni. Burbidge, E. Margaret ; Burbidge, G. R. Abstract The intensities of the Paschen and Balmer emission lines of hydrogen in x Oph and P Cyg are given, together with the absorption components in P Cyg The latter star has a Balmer decrement similar to that of a gaseous nebula, while x Oph shows differences, similar to those found in other pole-on stars, which may be due to self-absorption Comparison is made between the populations of the various levels of hydrogen determined from the Paschen and Balmer lines having common upper levels; the results suggest (a) a black-body temperature of 15,000 for the emergent continuous radiation of P Cyg and (b) support for the self-absorption hypothesis for x Oph. Estimates of the extents of the emitting regions are given. Publication: The Astrophysical Journal Pub Date: July 1955 DOI: 10.1086/146057 Bibcode: 1955ApJ...122...89B full text sources ADS | data products SIMBAD (3)

The Variational Method for Problems of Radiative Transfer. III. Reflection Effect.

view Abstract Citations (5) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Variational Method for Problems of Radiative Transfer. III. Reflection Effect. Huang, Su-Shu Abstract The variational method has been applied to the problem of diffuse reflection by a plane-parallel atmosphere scattering radiation isotropically. Approximate expressions with five parameters have been derived both for the source function and for the emergent radiation. The numerical resuits are in good agreement with those computed by other methods. Publication: The Astrophysical Journal Pub Date: January 1953 DOI: 10.1086/145679 Bibcode: 1953ApJ...117..221H full text sources ADS | Related Materials (2) Part 1: 1953ApJ...117..211H Part 2: 1953ApJ...117..215H

The Effect of Electron Scattering on the Line Spectrum of High-Temperature Stars.

view Abstract Citations (46) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Effect of Electron Scattering on the Line Spectrum of High-Temperature Stars. Münch, Guido Abstract In this paper the problem of the transfer of radiation in an atmosphere of free electrons in thermal motion is considered. Proper allowance is made for the noncoherency of the scattered radiation, but the Compton shifts in frequency of the scattered quanta are ignored. By using a Fourier integral transforma- tion over the frequency, the equation of transfer and the relevant boundary conditions are reduced to sub- sidiary forms. It is shown, further, that the transformed equation of transfer can be solved, in the space of the auxiliary variable, by the standard methods of transfer theory. The explicit solution found in a first approximation is inverted, and the dependence on frequency of the emergent radiation is studied. The final solution to the problem is written down as the sum of two terms: one representing the frac- tion of the incident radiation which emerges without having suffered any scattering process and the other representing the diffuse radiation which has arisen after one or more scattering processes. This diffuse radiation for incident monochromatic light has been evaluated numerically and its values tabulated for four optical thicknesses of the electron atmosphere. The numerical examples studied for hypothetical absorption lines reveal that the main effect of the noncoherency of the electron scattering is to fill the center of the lines with radiation from the neighboring continuum and to produce very extended and shallow wings. Finally, some general remarks are made concerning the relationship between the properties of the solu- tions found and certain characteristics of the line spectrum of high-temperature stars Publication: The Astrophysical Journal Pub Date: July 1948 DOI: 10.1086/145048 Bibcode: 1948ApJ...108..116M full text sources ADS |

The Double Current Sheet in Diffraction

The electromagnetic radiation from an aperture in a plane-conducting screen is identical with that which would exist if screen and aperture were replaced by a double current sheet fitting the aperture. The current density $i$ is equal and opposite in the two layers of the sheet and is determined by the original tangential electric field $E$ over the opening so that $E$ is $\ensuremath{-}\frac{1}{2}j\ensuremath{\omega}\ensuremath{\mu}\ensuremath{\delta}i$. The distance $\ensuremath{\delta}$ between layers is infinitesimal. A rigorous expression for the vector potential of the emergent radiation in terms of $E$ is given. This is the expression used by Bethe in finding the diffraction from small holes. It is shown to provide a simpler method of getting the results of Stratton and Chu for rectangular openings. It is then applied to the calculation of the excitation of a rectangular wave guide by a coaxial line termination in one side. An expression for the output resistance is given.