Profiles of a planetary limb for space navigation.
Horizon profile of Earth calculated from solutions of plane-parallel Rayleigh scattering atmosphere
RAYLEIGH SCATTERING↗
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Interior radiances in optically deep absorbing media. I - Exact solutions for one-dimensional model.
An exact analytic solution to the one-dimensional scattering problem with arbitrary single scattering albedo and arbitrary surface albedo is presented. Expressions are given for the emergent flux from a homogeneous layer, the internal flux within the layer, and the radiative heating. A comparison of these results with the values calculated from the matrix operator theory indicates an exceedingly high accuracy. A detailed study is made of the error in the matrix operator results and its dependence on the accuracy of the starting value.
Kattawar, G. W.↗
Hypercube matrix computation task
A major objective of the Hypercube Matrix Computation effort at the Jet Propulsion Laboratory (JPL) is to investigate the applicability of a parallel computing architecture to the solution of large-scale electromagnetic scattering problems. Three scattering analysis codes are being implemented and assessed on a JPL/California Institute of Technology (Caltech) Mark 3 Hypercube. The codes, which utilize different underlying algorithms, give a means of evaluating the general applicability of this parallel architecture. The three analysis codes being implemented are a frequency domain method of moments code, a time domain finite difference code, and a frequency domain finite elements code. These analysis capabilities are being integrated into an electromagnetics interactive analysis workstation which can serve as a design tool for the construction of antennas and other radiating or scattering structures. The first two years of work on the Hypercube Matrix Computation effort is summarized. It includes both new developments and results as well as work previously reported in the Hypercube Matrix Computation Task: Final Report for 1986 to 1987 (JPL Publication 87-18).
Calalo, Ruel H.↗
A simplified formulation of photon transport in leaf canopies with scatterers of finite dimensions
A formalism for photon transport in leaf canopies with finite-dimensional scattering centers that mutually cross-shade was recently proposed resulting in an equation set which is rather complicated. In this paper, we propose a simplification of the correction factors that describe the correlation in photon fates. These simplified correction factors permit the derivation of a modified integro-differential transfer equation with two additional terms that arise from considerations of finite size scatterers. A numerical procedure for the solution of this transfer equation in the framework of a successive collisions approach is also presented.
Myneni, Ranga B.↗
Dense fog on the highway: Visual range monitoring in cars?
This paper reports on the development of a new sensor. Laser range-finders are currently installed in cars and trucks to measure the distance to a proceeding car (LEICA). A modification of such a sensor to measure visibility was made. The problems that had to be solved were: (1) choice of wavelength with relation to the human eye for visibility measurements; (2) dependency of the wavelength on atmospheric turbidity; (3) laser eye-safety; and (4) influence of multiple scattering at visibilities smaller than 200 m. The wavelength used for lidar sensors in the near infrared presents no real problems because the object to be sensed is fog appearing white which means that scattering from fog is wavelength independent. There are however differences in backscatter-to-extinction ratio for different fog and weather situations. The two solutions to these problems are polarization and multiple scattering. As known from airport operations of a laser ceilometer, one can use this multiple scattering contribution to determine the visibility.
Hahn, W.↗
A scattering model for ocean surface
A surface-scattering model based on an approximate solution of the integral equations for the surface tangential fields is developed for non-Gaussian distributed finitely conducting surfaces. It is a function of both the surface spectrum and the surface bispectrum which are defined to be the Fourier transforms of the surface-correlation function and the surface-skewness function, respectively. By employing a sea-surface spectrum proposed by Pierson (1964) and modified by Lee and Fung (1982) it is shown that good agreement is obtained between model and field measurements in polarization, incidence angle, and azimuth angle without adjusting surface parameters.
Chen, K. S.↗
Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application
This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches
remote sensing↗
A numerical study of the pitch-angle scattering of cosmic rays
The results are presented of a careful study of finite-difference solutions to the problem of cosmic-ray transport, including pitch-angle scattering. In contrast to some recent studies, the diffusion approximation is confirmed in cases where the scattering mean free path is small compared with other length scales. The reasons for the discrepancy with the conclusions of Gombosi and Owens are discussed.
Kota, J.↗
Multi-Frequency NMM3D Simulations of Wave Propagation in Vegetation for Remote Sensing of Soil Moisture
To investigate the feasibility of using multi-frequencies to fur- ther improve the soil moisture retrieval, the recently devel- oped hybrid method is used to perform full-wave scattering simulations of a wheat field at three different frequencies of L-, S- and C- bands. In the hybrid method, the multiple scattering within a single wheat plant is first captured using the T-matrix of vec- tor cylindrical waves calculated from the full-wave solutions of HFSS. In the second step, the scattering among different plants is considered using the Foldy-Lax equations of multiple scattering theory (MST) and the extracted T-matrix. The transmission of microwaves through wheat field at the L-, S- and C-bands are calculated using the hybrid method. Results show that: (1) the transmission obtained from the full-wave simulations is much larger than those computed from the radiative transfer equations (RTE) model, (2) the hybrid method transmission has a weaker frequency dependence than those of the RTE, and (3) the attenuation caused by the vegetation layer would saturate with an increase in frequency.
Yueh, Simon↗
The radiative transfer equation and environmental effects in the upper atmosphere.
A highly effective approach to the solution of the radiative transfer equation, including the effects of emission, absorption, and multiply scattered radiation, is described. The transfer equation is cast in its unsteady hyperbolic form which is amenable to several different numerical methods of solution. Comparisons of solutions with emission, absorption, and scattering of radiation, are presented to demonstrate the validity of the present approach.
Callis, L. B.↗
Lidar measurements of cloud extinction coefficient distribution and its forward scattering phase function according to multiply scattered lidar returns
The study of the inversion algorithm for the single scatter lidar equation, for quantitative determination of cloud (or aerosol) optical properties, has received much attention over the last thirty years. Some of the difficulties associated with the solution of this equation are not yet solved. One problem is that a single scatter lidar equation has two unknowns. Because of this, the determination of the far-end boundary value, in the case of Klett's algorithm, is a problem if the atmosphere is optically inhomogeneous. Another difficulty concerns multiple scattering. There is a large error in the extinction distribution solution, in many cases, if only the single scattering component is considered, while neglecting the multiple scattering component. However, the use of multiple scattering in the remote sensing of aerosol or cloud optical properties is promising. In our early study, an inversion method for simultaneous determination of the cloud (or aerosol) Extinction Coefficient Distribution (ECD) and its Forward Scattering Phase Function (FSPF) was proposed according to multiply scattered lidar returns with two fields of view for the receiver. The method is based on a parameterized multiple scatter lidar equation. This paper is devoted to further numerical tests and an experimental study of lidar measurements of cloud ECD and FSPF using this method.
Qiu, Jinhuan↗
A Least-Squares Finite Element Method for Electromagnetic Scattering Problems
The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems.
Wu, Jie↗
A high frequency analysis of electromagnetic plane wave scattering by perfectly-conducting semi-infinite parallel plate and rectangular waveguides with absorber coated inner walls
An approximate but sufficiently accurate high frequency solution which combines the uniform geometrical theory of diffraction (UTD) and the aperture integration (AI) method is developed for analyzing the problem of electromagnetic (EM) plane wave scattering by an open-ended, perfectly-conducting, semi-infinite hollow rectangular waveguide (or duct) with a thin, uniform layer of lossy or absorbing material on its inner wall, and with a planar termination inside. In addition, a high frequency solution for the EM scattering by a two dimensional (2-D), semi-infinite parallel plate waveguide with a absorber coating on the inner walls is also developed as a first step before analyzing the open-ended semi-infinite three dimensional (3-D) rectangular waveguide geometry. The total field scattered by the semi-infinite waveguide consists firstly of the fields scattered from the edges of the aperture at the open-end, and secondly of the fields which are coupled into the waveguide from the open-end and then reflected back from the interior termination to radiate out of the open-end. The first contribution to the scattered field can be found directly via the UTD ray method. The second contribution is found via the AI method which employs rays to describe the fields in the aperture that arrive there after reflecting from the interior termination. It is assumed that the direction of the incident plane wave and the direction of observation lie well inside the forward half space tht exists outside the half space containing the semi-infinite waveguide geometry. Also, the medium exterior to the waveguide is assumed to be free space.
Noh, H. M.↗
A moment method solution of a volume-surface integral equation using isoparametric elements and point matching
Three integral equations for TE (transverse electric) scattering by dielectric cylinders having large values of permittivity are examined. A moment-method solution of the volume-surface integral equation is developed employing isoparametric elements and point matching. The solution is shown to be more accurate and stable than the traditional solutions using pulse basis, particularly in the case of scatterers having large refractive indices.
Jin, Jian-Ming↗
[?]Nonlinear Issues in the Aerothermochemistry of Gases and Materials and the Associated Physics and Dynamics of Interfaces
Our research and technology are focused on nonlinear issues in the aerothermochemistry of gases and materials and the associated physics and dynamics of interfaces. Our program is now organized to aggressively support the NASA Aeronautics Enterprise so as to: (a) develop a new generation of environmentally compatible, economic subsonic aircraft; (b) develop the technology base for an economically viable and environmentally compatible high-speed civil transport; (c) develop the technology options for new capabilities in high-performance aircraft; (d) develop hypersonic technologies for air-breathing flight; and (e) develop advanced concepts, understanding of physical phenomena, and theoretical, experimental, and computational tools for advanced aerospace systems. The implications from our research for aeronautical and aerospace technology have been both broad and deep. For example, using advanced computational techniques, we have determined exact solutions for the Schrodinger equation in electron-molecule scattering allowing us to evaluate atmospheric models important to reentry physics. We have also found a new class of exact solutions for the Navier Stokes equations. In experimental fluid dynamics, we have found explicit evidence of turbulence modification of droplet sizes in shock tube flow with condensation. We have developed a new diagnostic tool for the direct estimation of flow velocities at MHz sampling rates in quasi-one dimensional turbulent flow. This procedure suggests an unexpected confirmation of the possibility of 'natural' closure in Reynolds stresses with deep implications for the development of turbulent models. A transient increase is observed in both the spectral energy decay rate and the degree of chaotic complexity at the interface of a shock wave and a turbulent ionized gas. Even though the gas is apparently brought to rest by the shock wave, no evidence is found either of the expected relaminarization. A unique diamond-shaped nozzle has been designed for a detailed investigation of the effect of significant streamwise vorticity on the acoustic and IR characteristics of supersonic jets. Our results provide convincing evidence of the significant effect of vorticity on the far-field noise for the diamond jet as compared to the conventional round jets. We have found that the countercurrent shear layer mixes much more efficiently than conventional coflowing shear layers. We also developed the fluid thrust vectoring procedures which use counter flow to vector a jet. Our materials research has shown that the steep stress gradients at the fiber-matrix interface could be the primary cause of interface cracks after the processing of metallic and intermetallic matrix composites. New techniques have been evolved for: the microcharacterization of materials including microplastic strain and, point by point, the misorientation and plasticity for matrix composites; thermally induced stress measurements and load relaxation; the growth and characterization of metallic matrix composite interfaces; and for the growth of ferrite materials by pulsed laser deposition. The FAMU commitment to the HBCU Research Center also continues to be broad and deep.
Johnson, Joseph A., III↗
Acoustic Scattering by Three-Dimensional Stators and Rotors Using the SOURCE3D Code: Analysis and Results - Volume 1
This report provides a study of rotor and stator scattering using the SOURCE3D Rotor Wake/Stator Interaction Code. SOURCE3D is a quasi-three-dimensional computer program that uses three-dimensional acoustics and two-dimensional cascade load response theory to calculate rotor and stator modal reflection and transmission (scattering) coefficients. SOURCE3D is at the core of the TFaNS (Theoretical Fan Noise Design/Prediction System), developed for NASA, which provides complete fully coupled (inlet, rotor, stator, exit) noise solutions for turbofan engines. The reason for studying scattering is that we must first understand the behavior of the individual scattering coefficients provided by SOURCE3D, before eventually understanding the more complicated predictions from TFaNS. To study scattering, we have derived a large number of scattering curves for vane and blade rows. The curves are plots of output wave power divided by input wave power (in dB units) versus vane/blade ratio. Some of these plots are shown in this report. All of the plots are provided in a separate volume. To assist in understanding the plots, formulas have been derived for special vane/blade ratios for which wavefronts are either parallel or normal to rotor or stator chords. From the plots, we have found that, for the most part, there was strong transmission and weak reflection over most of the vane/blade ratio range for the stator. For the rotor, there was little transmission loss.
Meyer, Harold D.↗
Emittance bounds for transient radiative cooling of a scattering rectangular region
Transient cooling was analyzed for a two-dimensional gray rectangular region that emits, absorbs, and isotropically scatters radiation. The region, initially at uniform temperature, is placed in surroundings at a much lower temperature. The cooling analysis yields two simultaneous equations for the transient temperature and scattering source function distributions. The region starts to cool with the medium at uniform temperature. For this condition, the local emittance around the perimeter was obtained by a numerical solution of the radiative equations, and the rate of heat loss from the entire medium was evaluated. As cooling continues, the emissive ability decreases because of the lower temperatures in the outer regions of the rectangle. Based on some previous work, a lower limit for the transient overall emittance was found by obtaining a similarity solution. For some ranges of optical thickness and scattering albedo, the lower limit is only a small amount below the initial emittance. For these conditions, the initial emittance can be used to compute the entire transient resulting in a considerable simplification.
Siegel, Robert↗
Kaon-nucleus scattering
The derivations of the Lippmann-Schwinger equation and Watson multiple scattering are given. A simple optical potential is found to be the first term of that series. The number density distribution models of the nucleus, harmonic well, and Woods-Saxon are used without t-matrix taken from the scattering experiments. The parameterized two-body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to the imaginary part of the forward elastic scattering amplitude, are presented. The eikonal approximation was chosen as our solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.
Hong, Byungsik↗