Venus Mapping White Paper

Open-File Report 95-519

II. Radar Backscatter Cross Section

Radar backscatter cross section is defined as the area (meters squared) of an isotropic scatterer which would be required to return the observed echo power after adjustments for range, antenna gain, and other systematic variables. A more useful quantity is obtained by dividing this value by the area of the observed terrain, which varies somewhat from the true ground area due to the foreshortening effect of side-looking radar systems. The backscatter cross section per unit area is thus a dimensionless quantity which can be treated as an intrinsic property of the surface at a given wavelength, polarization, and incidence angle. The correct term for this value is backscatter coefficient, but several other terms appear in published papers: sigma zero, specific backscatter cross section, absolute backscatter cross section, or simply the radar cross section. Magellan measurements are corrected to the dimensionless quantity during processing, as are the aircraft data used as planetary analogs.

The backscatter values on a Magellan CD-ROM image (or USGS quadrangle) have been scaled using an empirical model for radar echoes from Venus derived by Muhleman [1964]. The Muhleman law is a best-fit approximation to the average backscatter as a function of incidence angle which incorporates both the quasi-specular and diffuse components, treated separately elsewhere [Hagfors, 1967; 1970]. This scaling allows the dynamic range of the data to be compressed into the 8-bit format of the pixels, regardless of the incidence angle of the observations. The normalization also means that the gray-scale brightness of regions widely separated in latitude (assuming the left-looking angle profile) cannot be compared, because the incidence angles of the two observations will be different. In such cases we are looking at changes with respect to the Muhleman function, not variations in the true radar backscatter coefficient. Additional right-looking and stereo images were collected at a smaller range of incidence angles, but the coverage of these images is limited.

The first step in carrying out quantitative comparisons between map units is to find the backscatter coefficient () from the raw image data. Given the DN (digital number) value of a pixel and its incidence angle, , we can use


where the half-degree shift in incidence angle was added inadvertently during data processing [Saunders et al., 1992]. If only the value in decibels relative to the Muhleman law is desired, then the equation is


The incidence angle is dependent upon the latitude of the target and the type of observation (left-looking, right-looking, stereo, or the special Maxwell geometry; fig. 1). Incidence angle values and Muhleman law correction factors for the four incidence angle modes as a function of latitude on Venus are listed in table 1A-D. Backscatter coefficients are often presented in logarithmic form (value in decibels=) due to their wide dynamic range; equation (2) and table 1 provide a means for deriving this coefficient in decibels for any single Magellan image pixel.

Any averaging of pixels within Magellan images must be carried out with values in the "linear" format above (eq 1). This method was used to produce the C-MIDR files from the original full-resolution (F-BIDR) maps. Significant errors may occur if DN values are averaged prior to rescaling. The reason for averaging in power rather than in logarithmic representation is that the radar echo from a low-resolution image cell generally equals the sum of the power from each of the constituent higher resolution pixels (that is, the scattering process is incoherent from one 75-m area to the next). Energy is conserved in this averaging process but not in calculating the mean of the DN distribution. In order to average over extended areas, you will need software that determines the incidence angle of the pixel, calculates from the DN value, and averages the measurements within a sample area. Appendix 1 describes a Fortran program (mgn_data) available over the Internet which will perform this averaging on Magellan image files. Appendix 2 discusses a program (anc_data) that can be used to obtain emissivity, topography, rms slope, and reflectivity averages for any given latitude, longitude box.