Generalized Rayleigh-Gans Research Articles

Allometric Vegetation Modeling and SAR Image Simulation for Polarimetry and Interferometry

This paper establishes a low degrees-of-freedom allometric vegetation model based on the Biomass and allometry database (BAAD). It consists of a 5-bit species encoding scheme and a 5-parameter relationship derived from the BAAD data records. Combined with opensource fractal tree generation engine, it can produce realistic tree samples of a large variety of species. A coherent electromagnetic scattering calculation method is developed for the vegetation model where the generalized Rayleigh-Gans (GRG) approximation and the infinite cylinder approximation are used to calculate the scattering matrix of leaves and branches/trunk. Four-path multiple scattering mechanisms between vegetation and the ground are considered and attenuations through vegetation canopy are also considered. The scattering model is validated against numerical methods. In addition, an end-to-end simulation tool is developed. Optical image is used to extract individual trees with center positions and crown diameters. The rest parameters are generated using the derived allometry model. Virtual 3D scene with vegetation on digital elevation map (DEM) can be generated and SAR images can be simulated. Several case studies are carried out for both polarimetric synthetic aperture radar (SAR) interferometry (PolInSAR) and multi-temporal interferometric SAR (InSAR). One case of the Mount Fuji area is simulated and validated against ALOS-2 data and demonstrates an average scattering coefficient error of less than 3dB. Additional cases of Southwest China, Hainan Island and the Great Khingan Mountain demonstrate the feasibility of the proposed simulation scheme for various application scenarios.

Modeling Microwave Backscattering From Parabolic Rice Leaves

Scattering from rice leaves contributes substantially to total vegetation canopy backscattering and detailed knowledge about it is necessary for developing a microwave scattering model. A parabolic curve is generally adopted to simulate the leaf shape but this is rarely incorporated into the calculation of the scattering. In this paper, two specific models, one based on physical optics (PO) approximation and the other on the discrete dipole approximation (DDA), are presented to involve the parabolic leaf curvature effects. Three typical leaves were chosen from 1433 parabolic leaves obtained during ground measurements. The PO and DDA models were used to calculate the leaf scattering. The generalized Rayleigh–Gans (GRG) approximation was also included in the simulation. The method of moments, a computational electromagnetic method, was utilized to evaluate the accuracy of each model. Validation of the models was conducted at incidence angles ranging from 10° to 60°, incidence azimuthal angles ranging from 0° to 360°, and incidence frequencies of 1.2 GHz (L-band), 5.4 GHz (C-band), and 9.65 GHz (X-band). Among the GRG approximation, the DDA model and the PO model, the latter gave the best accuracy −>65% in the cases tested, while the GRG model was the least accurate. The high accuracy of the PO model was maintained at both the low and high frequency bands. The PO model, therefore, has great potential for use to interpret radar measurements from rice fields and other types of vegetation canopy.

Electromagnetic Scattering from a Dielectric Sheet Using the Method of Moments with Approximate Boundary Condition

The phenomenon of electromagnetic scattering from a thin dielectric sheet is investigated by combining the impedance sheet approach and the method of moments (MoM). In general, the impedance used in an MoM-approximate boundary condition is the resistive impedance ZL. However, in the literature, four different impedance expressions have been derived and summarized. These include the above resistive impedance ZL, the more general resistive impedance ZO, the surface impedance ZV or ZH, and the connection impedance Zs. It is found that the surface impedance is optimal for computing the reflection and scattering from a thin dielectric sheet. The radar cross section (RCS) is computed and compared between the MoM-approximate boundary condition and the analytical approaches, viz., the generalized Rayleigh-Gans (GRG) and physical optics (PO) methods.

A scattering model for thin dielectric cylinders of arbitrary cross section and electrical length

A scattering solution for long, thin, dielectric cylinders of arbitrary cross section and electrical length is presented. The infinite-cylinder scattering formulation is shown to be an asymptotic solution for the finite-cylinder case, regardless of cylinder electrical length or cross section. The generalized Rayleigh-Gans (GRG) approximation for circular cylinders is shown to be a specific case of this general formulation, and therefore, the assertions of GRG are explicitly proven. A moment-method (MM) solution for thin circular cylinders is likewise presented and is used to examine and quantify the asymptotic errors associated with this solution.

Electromagnetic wave scattering from some vegetation samples

For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite length. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements. >