Relationship Between And Measurement Of Differential Scattering Coefficient (σ°) And Bidirectional Reflectance Distribution Function (Brdf)

ABSTRACT The physical mechanism of scattering of electromagnetic beams from a surface can be quantified by either differential scattering coefficient ( cr ) or bidirectional reflectance distribution function (BRDF). The differential scattering coefficient is an extension of radar scattering cross section of targets, and the geometrical constraints inferred in its measurement at microwave frequencies are relatively easily satisfied. These same con­ straints must also be met in the measurement of BRDF using coherent optical frequency beams and these may influence the geometrical configuration to obtain range-independent values. For a diffuse surface, cr° = 47T BRDF cos G. cos O where O. and G are the incidence and reflected angles, respectively, from surface normal. Considerably more care in the design of the configuration is required for the measurement of surfaces entailing specular com­ ponents than for diffuse surfaces. 1. INTRODUCTION Scattering of optical wavelengths from a surface as a part of the total visual process has been known for many years, however the analyses of this phenomenon had not been under­ taken until recent times. The analysis of scattering of electromagnetic radiation has taken on a significantly different aspect since the advent of "monochromatic" microwave beams and coherent laser beams. The underlying scattering mechanism for microwave and optical beams is exactly the same. It is the purpose of this paper to review the microwave and optical scattering formulations, to present the relationship between them at the same wavelength, and to discuss the measurement conditions for obtaining range-independent values. The scattering coefficients of surfaces are of considerable importance to remote sensing applications.In this paper the early concepts and development will be reviewed of both the radar scattering cross section and the bidirectional reflectance distribution function (BRDF) . There are some geometrical constraints implied in their measurement and these are discussed. Two special aspects mentioned the paper are source brightness and specular component of the scattering surface. In remote sensing applications, the scattering of microwave and opti­ cal radiation ' has been used for surface classification and to infer surface parameters.The scattering of microwave beams from targets and the measurement of the propagation time led to the invention of radar many years ago. The radiation is essentially monochro­ matic, and the radiated beam is polarized due to the antenna. In 1951, Kerr introduced the concept of radar cross section of small targets. The formulation assumed a monostatic geometry and a target size small compared to the transverse dimension of the antenna beam.In most optical scattering problems, bistatic geometries are encountered. For these, Nicodemus in 1964 introduced the bidirectional reflectance distribution function (BRDF). The concept was developed for incoherent incident radiation, unpolarized beams and diffuse surfaces. In the laboratory bright sources of light are used to measure the BRDF of sample surfaces, and laser beams have, been used recently as sources because of their brightness, convenience and availability. However, since laser radiation is coherent, the same type of constraints must be invoked as for the measurement of microwave radar scattering in order to obtain range-independent values. These are the issues addressed in this paper.