On the far-field approximation for scattering from randomly rough surfaces

Various authors have justified the far-fields approximation for rough surface scattering using one of the classical approximations for the scattered fields, usually considering either the coherent scattered field or the incoherent scattered intensity. An exact expression for the field scattered from a perfectly conducting rough surface is considered. The expression for the incoherent scattered intensity is formally derived, and a condition under which the far-field approximation is valid is found, independent of specific approximations for the surface or scattered fields or for the surface height statistics. The condition so derived is, under many circumstances, substantially less restrictive than that derived before in the general case. Furthermore, the previous results may be easily recovered by further specialization of our result.     

Maximum likelihood estimation of K distribution parameters for SARdata

The K distribution has proven to be a promising and useful model for backscattering statistics in synthetic aperture radar (SAR) imagery. However, most studies to date have relied on a method of moments technique involving second and fourth moments to estimate the parameters of the K distribution. The variance of these parameter estimates is large in cases where the sample size is small and/or the true distribution of backscattered amplitude is highly non-Rayleigh. The present authors apply a maximum likelihood estimation method directly to the K distribution. They consider the situation for single-look SAR data as well as a simplified model for multilook data. They investigate the accuracy and uncertainties in maximum likelihood parameter estimates as functions of sample size and the parameters themselves. They also compare their results with those from a new method given by Raghavan (1991) and from a nonstandard method of moments technique; maximum likelihood parameter estimates prove to be at least as accurate as those from the other estimators in all cases tested, and are more accurate in most cases. Finally, they compare the simplified multilook model with nominally four-look SAR data acquired by the Jet Propulsion Laboratory AIRSAR over sea ice in the Beaufort Sea during March 1988. They find that the model fits data from both first-year and multiyear ice well and that backscattering statistics from each ice type are moderately non-Rayleigh. They note that the distributions for the data set differ too little between ice types to allow discrimination based on differing distribution parameters     

Dense medium radiative transfer theory for two scattering layerswith a Rayleigh distribution of particle sizes

Dense medium radiative transfer theory is applied to a three-layer model consisting of two scattering layers overlying a homogeneous half space with a size distribution of particles in each layer. A model with a distribution of sizes gives quite different results than those obtained from a model with a single size. The size distribution is especially important in the low frequency limit when scattering is strongly dependent on particle size. The size distribution and absorption characteristics also affect the extinction behavior as a function of fractional volume. Theoretical results are also compared with experimental data. The sizes, permittivities, and densities used in the numerical illustrations are typical values for snow     

Probability density functions for multilook polarimetric signatures

Derives closed-form expressions for the probability density functions (PDF's) for copolar and cross-polar ratios and for the copolar phase difference for multilook polarimetric SAR data, in terms of elements of the covariance matrix for the backscattering process. The authors begin with the case in which scattering-matrix data are jointly Gaussian-distributed. The resulting copolar-phase PDF is formally identical to the phase PDF arising in the study of SAR interferometry, so the authors' results also apply in that setting. By direct simulation, they verify the closed-form PDF's. They show that estimation of signatures from averaged covariance matrices results in smaller biases and variances than averaging single-look signature estimates. They then generalize their derivation to certain cases in which backscattered intensities and amplitudes are K-distributed. They find in a range of circumstances that the PDF's of polarimetric signatures are unchanged from those derived in the Gaussian case. They verify this by direct simulation, and also examine a case that fails to satisfy an important assumption in their derivation. The forms of the signature distributions continue to describe data well in the latter case, but parameters in distributions fitted to (simulated) data differ from those used to generate the data. Finally, the authors examine samples of K-distributed polarimetric SAR data from Arctic sea ice and find that their theoretical distributions describe the data well with a plausible choice of parameters. This allows the authors to estimate the precision of polarimetric-signature estimates as a function of the number of SAR looks and other system parameters     

Dense medium radiative transfer theory: comparison with experimentand application to microwave remote sensing and polarimetry

The dense medium radiative transfer theory is used to study the multiple scattering of electromagnetic waves in a slab containing densely distributed spherical particles overlying a homogeneous half-space. This theory is used to explain phenomena observed in a controlled laboratory experiment. The experimental data indicate that, in a dense medium with small particles, both the coherent attenuation rate and bistatic intensities first increase with the volume fraction of the particles until a maximum is reached, and then decrease when the volume fraction further increases. Thus, attenuation rates and bistatic scattering exhibit a peak as a function of the concentration of particles. The magnitudes of both are also less than those predicted by the independent scattering assumption and the conventional radiative transfer theory. These phenomena cannot be explained by the conventional radiative transfer theory. It is shown that the dense medium radiative transfer theory is in agreement with these experimental features