Scattering Media Research Articles

Coupled atmosphere/canopy model for remote sensing of plant reflectance features

Solar radiative transfer through a coupled system of atmosphere and plant canopy is modeled as a multiple-scattering problem through a layered medium of random scatterers. The radiative transfer equation is solved by the discrete-ordinates finite-element method. Analytic expressions are derived that allow the calculation of scattering and absorption cross sections for any plant canopy layer from measurable biophysical parameters such as the leaf area index, leaf angle distribution, and individual leaf reflectance and transmittance data. An expression for a canopy scattering phase function is also given. Computational results are in good agreement with spectral reflectance measurements directly above a soybean canopy, and the concept of greenness- and brightness-transforms of Landsat MSS data is reconfirmed with our computed results. A sensitivity analysis with the coupled atmosphere/canopy model quantifies how satellite-sensed spectral radiances are affected by increased atmospheric aerosols, by varying leaf area index, by anisotropic leaf scattering, and by non-Lambertian soil boundary conditions. Possible extensions to a 2-D model are also discussed.

Quantum corrections to electron conductivity in a disordered medium of anisotropic scatterers

The density dependence of electron mobility in a medium of anisotropic scatterers is calculated by the Green's function method. The results are compared qualitatively with experimental data on electron mobility in polar gases.

A semiempirical method for analysis of the reflectance spectra of binary mineral mixtures

A simple semiempirical method is presented for determination of the spectral reflectance of a powdered binary mineral mixture. This technique uses a two‐stream radiative transfer model (a modified Kubelka‐Munk model) on a particulate medium of isotropic scatterers. The particles are assumed to be much larger than the wavelength of light under consideration. This same method can be used to determine the relative proportion of components in a mixture for which the spectral reflectance is known. Binary mixtures of olivine, two pyroxenes, and magnetite are used to test this model. The theoretical and empirical results agree approximately within experimental errors.

Polynomial Approximation Solution of Heat Transfer by Conduction and Radiation in a One-Dimensional Absorbing, Emitting, and Scattering Medium

Polynomial Approximation Solution of Heat Transfer by Conduction and Radiation in a One-Dimensional Absorbing, Emitting, and Scattering Medium

Effect Of Various Parameters On Field Uniformity Corrections In Scintillation Cameras

Many Anger scintillation cameras are equipped with microprocessors for live correction of field nonuniformities. The purpose of this study was to evaluate the corrected flood field uniformity after varying count rate, analyzer window size, analyzer window position, and scatter. A 2.54 cm thick Tc-99m disk source was used with large and small field Anger cameras under conditions simulating clinical usage. Uniformity was evaluated quantitatively by computing the location and percentage of cells in a 64X64 matrix that were within ±5% of the mean cell count; it was judged qualitatively by examination of the computer thresholded image. The corrected 2.54 cm thick Tc-99m disk flood image showed virtually no change in uniformity as scatter medium was increased from 0 cm to 8.9 cm. When count rate was varied from 5K to 44K cps as much as a 13% decrease in field uniformity was observed. Changing the analyzer window size produced a 5-21% decrease in uniformity while changing the window position resulted in even more significant image degradation. Knowledge of these camera characteristics is important in improving clinical images.

On the theory of pulse wave propagation in media of discrete random scatterers

The pulse wave propagation is theoretically investigated in a particular case of a medium of discrete random scatterers. As the basic equation the ordinary space‐time transport equation is used under the forward scattering approximation and is solved by means of the eigenfunction method developed in a recent paper. One of the major results is that an explicit expression of pulse intensity is analytically obtained for the realistic scattering amplitude, valid when the size of scatterers is sufficiently large in comparison with the wavelength. The dependence of pulse width broadening on the particle characteristic is also clarified for the case of large optical distances and is compared with that of previous literature. By the same techniques the temporal angular broadening of pulse wave is evaluated in order to find the conditions of applicability of the present method.

Contribution to the statistical theory of the transfer of nonsteady radiation in a medium of variable scatterers

Contribution to the statistical theory of the transfer of nonsteady radiation in a medium of variable scatterers

Experimental investigation of the scattering of electromagnetic waves from a model random medium of discrete scatterers

The paper describes a new three‐dimensional physical model of a random discrete‐scatterer medium and presents the results of an experimental investigation to determine the suitability of the model in studies aimed at the evaluation of approximate scattering theory. In contrast to previous models in which the scatterer statistics were indirectly controlled by a physical process, the present model allows the statistics to be directly controlled as in a Monte Carlo computer simulation. It also permits considerable flexibility in the type of scatterers used. The experimental model investigated consisted of a layered slab region of polystyrene foam (142 × 16 × 21 cm) in which polyethylene spheres of 1.27 cm diameter were embedded at random positions. These positions were generated by computer from a uniform distribution. The medium was scanned by a narrow 35‐GHz beam and the randomly varying transmitted field was recorded, sampled, and statistically analyzed. The accuracy of the first and second field moments, determined in experiments on the model with two different average densities of the spherical scatterers, is evaluated.

Quantitative assessment of field uniformity for gamma cameras.

Objective criteria for judging the uniformity of field floods are developed and the effects of the energy window and scatter material on uniformity are examined. There is a highly significant correlation (p = 0.99) between a 14% difference in average count among adjacent photomultiplier tube regions and observer detection of detuned areas. Similarly, a 10% average count difference is not significantly recognized as a nonuniform area. Results indicate that there is a complex interaction between uniformity, energy window (15-30% symmetrical) and 0-7.6 cm of tissue-equivalent scatter medium interposed between the flood source and the collimator. Quantitation of the flood should be performed to indicate which regions need retuning.

Radiative Heat Transfer in Absorbing, Emitting and Scattering Media Using the Monte Carlo Method

The Monte Carlo Method was used to solve for the radiative transfer in two problems involving the one-dimensional infinite parallel planes system. The media between the planes included a suspension of particles which absorb, emit and scatter anisotropically. One example problem showed results agreeing with a solution obtained by the classical series substitution method. A second indicated that for conditions approximating those of an industrial combustion chamber with suspended solids, the radiative heat transfer is influenced primarily by the absorbing properties of the suspension rather than by its scattering properties.

Holography through Scattering Media

Holography through Scattering Media

Dispersion Law in Anisotropic Scattering Media

Dispersion Law in Anisotropic Scattering Media

Dispersion Law in Anisotropic Scattering Media

Dispersion Law in Anisotropic Scattering Media

A transmission line model for the optical transfer of isotropic scattering media.

The optical radiation transfer of plane parallel isotropic scattering media is for many purposes of technical importance adequately described by the Kubelka and Munk equations. By a simple substitution these can be converted to the set of equations describing an electrical transmission line with resistive parameters. Consequently, such a line can be used to simulate the optical transfer of the medium. For practical purposes the continuous line may be replaced by the series connection of lumped parameter sections. Both transmittance and reflectance of the optical medium can be determined from voltage and current measurements on the model. The model can then be used to invert the transfer equations in terms of incremental absorbance as required in photometric or reflectometric analysis of thin-layer chromatograms, electrophoretograms, etc.

Formulation of two-dimensional radiant heat flux for absorbing-emitting plane layer with nonisothermal bounding walls

Journal of Heat and Mass Transfer, Vol. 9, No. 9, Sept. 1966, pp. 987-992. 20 Nonnemacher, T. F., Jacob! Polynomial Solution of the Boltzmann Equation and Some Remarks about the Connection between the Spherical Harmonics and Case Methods, Developments in Transport Theory, edited by E. Inonu and P. F. Zweifel, Academic Press, New York, 1967, pp. 343-356. 21 Giovanelli, R. G., Transfer in Non-Uniform Media, Australian Journal of Physics, Vol. 12, No. 2, June 1959, pp. 164-170. 22 Traugott, S. C., Heat-Flux Potential for a Nongrey Gas, AIAA Journal, Vol. 4, No. 3, March 1966, pp. 541542. 23 Shen, S. F., On the Differential Equation Approximation in Radiative Gas Dynamics, Rept. NOL TR 67-23, May 1967, Naval Ordnance Lab. 24 Heaslet, M. A. and Warming, R. F., Application of Invariance Principles to a Radiative Transfer Problem in a Homogeneous Spherical Medium, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 5, No. 5, Sept.-Oct. 1965, pp. 669-682. 25 Ambarzumian, V. A., A Point-Source of Light within a Scattering Medium, Bulletin 6, 1945, Erevan Astronomical Observatory. 26 Heaslet, M. A. and Warming, R. F., Transport and Wall Temperature Slip in an Absorbing Planar Medium, International Journal of Heat and Mass Transfer, Vol. 8, No. 6, June 1965, pp. 979-994. Viskanta, R. and Crosbie, A. L., Transfer through a Spherical Shell of an Absorbing-Emitting Gray Medium, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 7, No. 6, Nov.-Dec. 1967, pp. 871-889.

Theoretical Analysis of Radiative Heat Transfer in a Scattering Medium

The problem of radiative heat transfer in a nonisothermal medium is considered. The analysis is carried out for plane parallel plates separated by an anisotropically scattering atmosphere. A usable solution is obtained by iteration of the set of equations that result from approximation of the radiative transport equation.

Wave propagation through an assembly of spheres: IV. Relations between different multiple scattering theories

The exact determinantal equation satisfied by the coherent wave vector in a statistically defined medium of spherical scatterers, which was obtained by Lloyd in III of this series of papers, is used to show two things. First, the determinant can be written as an infinite series similar to that obtained by ordinary resummation methods, except that it does not involve elements of the T matrix off the energy shell. Secondly, the first two terms of the series are specialized to the case of point scatterers which are uncorrelated except for an infinitesimal sphere of exclusion about each of them, and the results found to disagree with those of other calculations; this discrepancy is clarified. The formalism is generalized to deal with vector waves, and it is shown that, for electric dipole scattering, the simplest approximations to the functions appearing in the determinant lead to the Lorentz-Lorenz law.

Diffuse Reflection and Transmission by Non-Coherently Scattering Media

It has become recognized that the dominant mechanism in the formation of the cores of resonance lines in the solar spectrum is non-coherent scattering, e.g., Thomas (1957). A study, preliminary to the theoretical investigation of the spectra of chromospheric structures, is the evaluation of the effect of diffuse reflection and transmission by non-coherently scattering media.

Radiation Reciprocity in a Scattering Medium: An Experimental Study

It is pointed out that the reciprocity principle may hold approximately even when Compton effect is the predominant radiation interaction. Rough calculations supporting this view are reported.Experiments in which the integral absorbed dose Σ is determined in slab-like water phantoms exposed to collimated sources are described. The exposure rate E at the positions previously occupied by the sources when the phantoms are filled with radioactive materialis measured in separate experiments, and the ratio Σ/E is shown to be sufficiently independent of the geometry to permit use of the principle in clinical work. The application of this result in rotation therapy and whole-body irradiation is pointed out.

Time-frequency duality

This paper develops a concept of duality, called time-frequency duality, which is applicable to a class of networks called communication-signal-processing networks. Such networks consist of an interconnection of basic elements such as filters, mixers, delay lines, etc. The usefulness of time-frequency duality stems from the fact that two situations which may be quite distinct physically can have identical behavior patterns except for an interchange of the roles played by time and frequency. As a result, the solution to a detection or estimation problem may be found directly from the solution of the dual problem, if known, merely by replacing variables and quantities by their duals. This application of time-frequency duality is illustrated in the paper by the problem of measuring the transfer function of a scatter medium by means of an optimal gating operation prior to spectrum analysis. Another benefit to be obtained from time-frequency duality is the generation of new ideas for communication signal processing techniques. We illustrate this type of benefit by constructing the dual of the Kineplex communication system. A third benefit is the additional insight gained into a communication problem by the ability to look at it in another way. This benefit is illustrated by the characterization of time-variant linear channels. It is demonstrated that such channels may be characterized in an interesting symmetrical manner in time and frequency variables by defining dual system functions.