Microwave scattering model for grass blade structures

The EM scattering solution for a grass blade with complex cross-section geometry is considered. It was previously shown that the scattering solution for such problems, in the form of a polarizability tensor, can be obtained using the low-frequency approximation in conjunction with the method of moments. In addition, that study showed that the relationship between the polarizability tensor of a dielectric cylinder and its dielectric constant can be approximated by a simple algebraic expression. The results of that study are used to show that this algebraic approximation is valid also for cylinders with cross sections the shape of grass blades, providing that proper values are selected for each of three constants appearing in the expression. These constants are dependent on cylinder shape, and if the relationship between the constants and the three parameters describing a grass blade shape can be determined, an algebraic approximation relating polarizability tensor to blade shape, as well as dielectric constant, can be formed. This algebraic approximation can replace the cumbersome method of moments model. The moment method model is therefore used to generate a small but representative set of polarizability tensor data over the range of values commonly observed in nature. A conjugate gradient method is then implemented to correctly determine the three constants of the algebraic approximation for each blade shape. A third-order polynomial fit to the data is then determined for each constant, thus providing a complete analytic replacement to the numerical (moment method) scattering model     

A backscattering model for ocean surface

A surface scattering model based on an approximate solution of the integral equations for the surface tangential fields has been developed for non-Gaussian distributed, finitely conducting surfaces. It consists of two parts. One part is proportional to the surface roughness spectrum, and the other to the surface bispectrum. The bispectrum part comes into the model when the third-order surface statistics are included. While the second-order statistics account for the wind directional dependence, the third-order statistics account for the dependence on the sense of direction of the wind. Thus, it is the critical part for explaining the difference between upwind and downwind observations. In general, the bispectrum is a complex quantity and the asymmetric effect of the sea surface is represented by its imaginary part. The model characteristics, such as polarization and azimuthal dependence, are illustrated through numerical calculations. The predictions of the model are compared with field measurements, and excellent agreement is obtained     

Radar backscattering model for multilayer mixed-species forests

A multilayer canopy scattering model is developed for mixed-species forests. The multilayer model provides a significantly enhanced representation of actual complex forest structures compared to the conventional canopy-trunk layer models. Multilayer Michigan Microwave Canopy Scattering model (Multi-MIMICS) allows overlapping layer configuration and a tapered trunk model applicable to forests of mixed species and/or mixed growth stages. The model is the first-order solution to a set of radiative transfer equations and includes layer interactions between overlapping layers. It simulates SAR backscattering coefficients based on input dimensional, geometrical, and dielectric variables of forest canopies. The Multi-MIMICS is an efficient realization of actual forest structures and can be shaped for specific interest of forest parameters. We present the model's application and validation in the paper. The model is parameterized using data collected from a 220,000-ha area of forests in central Queensland, Australia. Fifteen 50/spl times/50 m test sites representing the general forest diversity and growth stages are chosen as ground truth. Polarimetric backscattering airborne SAR (AIRSAR) data of the same area are acquired to validate the model simulations. The model predicts SAR backscattering coefficients of the test areas. Simulation results show a good agreement with AIRSAR data at most frequencies and polarizations. The simulated backscattering coefficient from the multilayer model and the standard MIMICS are also compared and significant improvements are observed.     

Amplified spontaneous emission and Rayleigh backscattering instrongly pumped fiber amplifiers

Amplified spontaneous emission (ASE) and Rayleigh backscattering (RBS) in strongly pumped fiber amplifiers are studied, employing a rate equation model. Approximate expressions for the ASE and RES, as well as for the amplifier noise figure are derived, based on approximate analytical expressions for the amplified signal, which are valid for both three-level and four-level systems. Numerical examples for rare-earth-doped fibers, show good agreement between these approximate expressions and the exact numerical solutions for strong pumping and for injected signals which are not too weak     

Radiative transfer model for microwave bistatic scattering from forest canopies

A bistatic forest scattering model is developed to simulate scattering coefficients from forest canopies. The model is based on the Michigan Microwave Canopy Scattering (MIMICS) model (hence called Bi-MIMICS) and uses radiative transfer theory, where the first-order fully polarimetric transformation matrix is used. Bistatic radar systems offer advantages over monostatic radar systems because of the additional information provided by the diversity of the geometry. By simulating the forest canopy scattering from multiple viewpoints, we can better understand how the forest scatterers' shape, orientation, density, and permittivity affect the canopy scattering. Bi-MIMICS is parametrized using selected forest stands with different canopy compositions and structure. The simulation results show that bistatic scattering is more sensitive to forest biomass changes than backscattering. Analyzing scattering contributions from different parts of the canopy gives us a better understanding of the microwave's interaction with the tree components. The ground effects can also be studied. Knowledge of the canopy's bistatic scattering behavior combined with additional synthetic aperture radar measurements can be used to improve forest parameter retrievals. The simulation results of the model provide the required information for the design of future bistatic radar systems for forest sensing applications.     

Microwave thermal emission of rain

The effective medium temperature necessary for the conversion of microwave thermal emission to slant-path attenuation has been calculated for 11.8 GHz for a homogeneous slab of rain. The first results from calculations on a cylindrical model of rain at 11.8 GHz are also presented. The influence of ground reflectivity coefficient is investigated.     

A three-dimensional radar backscatter model of forest canopies

A three-dimensional forest backscatter model, which takes full account of spatial position of trees in a forest stand is described. A forest stand was divided into cells according to arbitrary spatial resolution. The cells may include “crown”, “trunk”, and “gap” components, determined by the shape, size and position of the trees. The forest floor is represented by a layer of “ground” cells. A ray tracing method was used to calculate backscattering components of 1) direct crown backscatter, 2) direct backscattering from ground, 3) direct backscattering from trunk, 4) crown-ground scattering, and 5) trunk-ground scattering. Both the attenuation and time-delay of microwave signals within cells other than “gap” were also calculated from ray tracing. The backscattering Mueller matrices of these components within the same range intervals were incoherently added to yield the total backscattering of an image pixel. By assuming a zero-mean, multiplicative Gaussian noise for image speckle, the high-resolution images were aggregated to simulate a SAR image with a given spatial resolution and number of independent samples (looks). A well-characterized 150 m×200 m forest stand in Maine, USA, was used to parameterize the model. The simulated radar backscatter coefficients were compared with actual JPL SAR data. The model gives reasonable prediction of backscattering coefficients averaged over the entire stand with agreement between model and data within 1.35 dB for all channels. The correlations between simulated images and SAR data (10 by 15 pixels) were positive and significant at the 0.001 level for all frequencies (P, L, and C bands) and polarizations (HH, HV, and VV)     

Microwave L-band emission of freezing soil

We report on field-measured microwave emission in a period of frost penetration into a grassland soil. The measurements were recorded with a high temporal resolution using an L-band radiometer mounted on a 7-m high tower. The observation period (December 2002 to March 2003) included two cycles of soil freezing and thawing with maximum frost depth of 25 cm. In situ soil temperature and liquid water content were measured at five depths down to 45 cm. Soil moisture profiles were calculated using the COUP numerical soil water and heat model in combination with measured soil properties and meteorological data monitored at the site. The L-band radiation data clearly showed the penetration and thawing of seasonal soil frost. We calculated soil reflectivities based on in situ measured and modeled soil moisture profiles by applying a coherent radiative transfer model. The calculated reflectivities were compared with the radiometrically determined soil reflectivities. It was demonstrated that the quantitative consistency between these reflectivities was significantly improved by applying an impedance matching approach accounting for surface effects. In this particular case, the dielectric structure of the uppermost soil horizon was largely influenced by soil roughness, vegetation, and snow cover. The radiometrically measured soil reflectivities were fitted using a radiative transfer model in combination with a roughness model assuming a soil surface roughness of 25 mm. The analysis during a period of frost penetration shows coherent behavior of the soil reflectivity. Temporal oscillation of the measured L-band radiation appears to be a coherent effect. This effect has the potential to be used for estimating the frost penetration velocity.     

Microwave emission and acoustoelectric excitation in differently orientated nInSb

Xband microwave emission was observed from defined small areas of [110] and [100] crystallographically orientated nInSb rods in a static magnetic field and a low electric field at 77° K, with close relations to acoustoelectric current oscillations and/or saturation. For the acoustical explanation of the emission, off-axis gain and nonlinear effects in the acoustoelectric excitation seem to be important.     

Microwave emission of vegetation: sensitivity to leafcharacteristics

The effects of leaf characteristics on the microwave emission of land surfaces are analyzed. In order to simulate these effects, a radiative transfer model is presented. The medium consists of a vegetated layer containing randomly oriented leaves, modeled as elliptic-shaped scatterers, over the ground surface. Radiative transfer equations are solved with a discrete-ordinate-eigenanalysis method. The calculation of the phase matrix of the elliptic scatterers is based on the generalized Rayleigh-Gans approximation, which increases the frequency range of the modeling. The sensitivity of brightness temperature and polarization ratio to leaf characteristics, volume fraction, gravimetric moisture, size, shape, and inclination distribution is investigated at C-, and X-band. The behavior of the simulated emission of a soybean canopy versus frequency and incidence angle is studied for different soil moisture levels. Up to 10 GHz the microwave emission appears to contain significant information on underlying soil moisture     

A microwave backscattering model for deformed first-year sea iceand comparisons with SAR data

Like-polarized backscattering from randomly tilted ice blocks in deformed first-year sea ice is modeled. An approximation for the coherent and incoherent scattering cross section of a single ice block is formulated and validated by comparison with moment method computations. It is found that the model is accurate for lossy ice blocks but underestimates the scattering when the loss is low, which is attributed to multiple scattering within the blocks. The backscattering coefficient is evaluated by averaging over an ensemble of blocks with a distribution of slopes and effects of shadowing are estimated. In situ measurements of ice ridge properties in the Baltic Sea are used as input when comparing the model results with coincident ERS-1 SAR data. The model is found to agree with the data to within 1.5 dB, where the discrepancies are mainly due to the uncertainty of the dielectric loss factor in the ice blocks. The model also shows good agreement with airborne 5.3 GHz SAR data of a first-year shear ridge in the Beaufort Sea for incidence angles between 25-50     

A semi-empirical backscattering model at L-band and C-band for asoybean canopy with soil moisture inversion

Radar backscatter measurements of a pair of adjacent soybean fields at L-band and C-band are reported. These measurements, which are fully polarimetric, took place over the entire growing season of 1996. To reduce the data acquisition burden, these measurements were restricted to 45° in elevation and to 45° in azimuth with respect to the row direction. Using the first order radiative transfer solution as a form for the model of the data, four parameters were extracted from the data for each frequency/polarization channel to provide a least squares fit to the model. For inversion, particular channel combinations were regressed against the soil moisture and area density of vegetation water mass. Using L-band cross-polarization and VV-polarization, the vegetation water mass can be regressed with an R ²=0.867 and a root mean square error (RMSE) of 0.0678 kg/m ². Similarly, while a number of channels, or combinations of channels, can be used to invert for soil moisture, the best combination observed, namely, L-band VV-polarization, C-band HV- and VV-polarizations, can achieve a regression coefficient of R²=0.898 and volumetric soil moisture RMSE of 1.75%     

微波/光学植被散射模型及其在热带森林中的应用

建立了一个微波/光学合成散射模型来模拟森林植被层各组分的后向散射,模拟的后向散射系数与JERS-1 SAR和VNIR遥感测量数据的相关系数(R2)为0.81,均方根误差为0.96dB,大部分余差都分布在士ldB之间.结果表明,微波与光学遥感数据结合可以提高热带森林生物量估测的准确度.     

High-resolution InSAR image simulation for forest canopies

High-resolution interferometric airborne synthetic aperture radar (SAR) images of Indonesian tropical rain forests have been acquired during the European Space Agency (ESA) Indonesian Radar Experiment (INDREX) 1996 campaign. Research efforts are directed toward development of automated canopy reconstruction algorithms. In this paper, interferometric synthetic aperture radar (InSAR) image simulation is discussed as one of the tools to support development of such inversion algorithms. First, the relevant physics, observation geometry, and radar characteristics are described. It is assumed that a forest can be modeled as a cloud of uniformly distributed isotropically scattering elements located within crown volumes. These volumes were measured during a field experiment for a 7.2 ha plot. Simulated data comprise intensity, phase, as well as coherence images. These are compared, in a statistical sense, with real data acquired in C- and X-bands. The canopy attenuation was simulated over a range of values. The normalized second intensity moment, the mean coherence magnitude, the coherence histogram, and the autocorrelation function of coherence were taken as measures for comparison. It can be concluded that simulated and real C-band images compare well for an extinction coefficient in the range of 0.15-0.3 m/sup -1/. For X-band, the selected measures of agreement lead to contradictions, indicating that the physical assumptions made may be less valid than for C-band.     

Investigating of snow wetness parameter using a two-phase backscattering model

A two-phase backscattering model with nonsymmetrical inclusions is applied to calculate radar backscatter from a half-space of wet snow using strong fluctuation theory. Wet snow is assumed to consist of dry snow (host) and liquid water (inclusions). The shape and size of water inclusions are considered using an anisotropic and azimuth symmetric correlation function. The relationship between correlation lengths and snow wetness is presented by comparing strong fluctuation theory with the experimental data at 1.2, 8.6, 17, and 35.6 GHz. In the comparisons, correlation lengths are used as free fitting parameters. The effect of snow wetness on the backscattering coefficient is investigated. Numerical results of comparison between the two-phase backscattering model with nonsymmetrical inclusions and the experimental data are illustrated at 1.2, 8.6, 17, and 35.6 GHz. The effect of size and shape of water inclusions at different snow wetness values to backscatter level is shown. The comparison of angular response of backscattering coefficient (decibels) to wet snow between the model and the experimental data is presented at 2.6, 8.6, 17, and 35.6 GHz.     

A coherent scattering model to determine forest backscattering inthe VHF-band

A coherent scattering model to determine the forest radar backscattering at VHF frequencies (20-90 MHz) has been developed. The motivation for studying this frequency band is the recent development of the CARABAS Synthetic Aperture Radar (SAR). In order to model the scattering from branches and trunks, homogeneous dielectric cylinders placed above a semi-infinite di-electric ground have been analyzed. An analytical approach, where the theoretically exact currents induced in an infinite cylinder are truncated, has been compared to a numerical solution using the finite difference time domain (FDTD) method. If the first-order coherent ray tracing is included in the analytical approach, the results match well with the numerically exact FDTD solution. The results show that, in order to determine the VHF-backscattering from a forest stand, the coherent ground interaction is an important part and has to be considered. In this paper, modeling results are in good agreement with CARABAS measurements     

A reappraisal of the validity of the IEM model for backscattering from rough surfaces

An integral equation method (IEM) surface scattering model was examined in terms of its applicability to laboratory measurement and numerical simulations. New expressions for both single scattering and multiple scattering were obtained by rederiving the scattering coefficient to keep all the phase terms in the spectral representation of the Green's function. After quite intricate mathematical manipulations, a fairly compact form is obtained for the scattering coefficients. In addition, the Fresnel reflection coefficients used in the model were replaced by a transition function that takes surface roughness and permittivity into account. The results of comparisons with both the numerical simulations and measurements for the backscattering case indicate that the IEM is improved, becoming more accurate and practical to use.     

A physical simulation model for field emission triode

A simple but accurate physical model, which can be incorporated into circuit simulation programs such as SPICE for the field emission triode (FET), is developed. The model is based on the Fowler-Nordheim (F-N) current density-electric field (J-E) relationship. An electric field form is adopted to calculate the current density distribution along the surface of the sphere-shape tip. The cathode current is obtained by integration of the current density over the emission surface. The gate current is derived by the same integration, but over part of the emission area. A procedure to extract the values for the parameters of the model is also given. The model and the procedure has been applied to experimental devices to demonstrate its accuracy     

Microwave emission from plasmas in InSb with and without magnetic fields

A theory of wave propagation through semiconductors, assuming general orientations of the carrier drift velocities, the propagation vector, and the RF electric field relative to an applied steady magnetic field, is derived. This is specialized to obtain a theory of pseudolongitudinal wave interactions in electron and hole streams in InSb in a transverse and in a parallel (or zero) magnetic field. The theory explains the various features of high electric-field microwave emission and RF oscillations observed by experimenters over several years in a wide variety of material conditions and field configurations. Explained in particular are the facts that: 1) starting n- or p-type materials with initial density ≲ 10¹⁴cm^-3have to be impact ionized to achieve electron or hole number densities adequate for microwave emission; 2) for impact-ionized plasmas, it takes a minimum transverse magnetic field (Bperp) on the order of 1.5-2.5 kG for the onset of microwave emission and the threshold current thereafter diminishes monotonically with increasingBperp; 3) p-type material with high enough initial density (nh≳ 1 - 3 × 10¹⁵cm^-3) is unstable with electron injecting contacts in the presence of 15-20 percent (or more) electron injection; and 4) in the absence ofBperp, a longitudinal magnetic field is necessary mainly to prevent pinching of the plasma at the high current densities needed for microwave emission, etc. RF oscillations observed in n- and p-type InSb with or withoutBperpare also explained. The dependence of the oscillation frequency on the magnitude ofBperpshows a remarkable correlation with experimental observations.     

Microwave sintering process model.

In order to simulate and optimize the microwave sintering of a silicon nitride and tungsten carbide/cobalt toolbits process, a microwave sintering process model has been built. A cylindrical sintering furnace was used containing a heat insulating layer, a susceptor layer, and an alumina tube containing the green toolbit parts between parallel, electrically conductive, graphite plates. Dielectric and absorption properties of the silicon nitride green parts, the tungsten carbide/cobalt green parts, and an oxidizable susceptor material were measured using perturbation and waveguide transmission methods. Microwave absorption data were measured over a temperature range from 20 degrees C to 800 degrees C. These data were then used in the microwave process model which assumed plane wave propagation along the radial direction and included the microwave reflection at each interface between the materials and the microwave absorption in the bulk materials. Heat transfer between the components inside the cylindrical sintering furnace was also included in the model. The simulated heating process data for both silicon nitride and tungsten carbide/cobalt samples closely follow the experimental data. By varying the physical parameters of the sintering furnace model, such as the thickness of the susceptor layer, the thickness of the allumina tube wall, the sample load volume and the graphite plate mass, the model data predicts their effects which are helpful in optimizing those parameters in the industrial sintering process.