The Radiometric Measurement Quantity for SAR Images

Abstract

A Synthetic Aperture Radar (SAR) system measures among other quantities the terrain radar reflectivity. After image calibration, the pixel intensities are commonly expressed in terms of radar cross sections (for point targets) or as backscatter coefficients (for distributed targets), which are directly related. This paper argues that pixel intensities are not generally proportional to radar cross section or derived physical quantities. The paper further proposes to replace the inaccurate term radar cross section by equivalent radar cross section as the radiometric measurement quantity for SAR images. The measurement procedure as such remains unchanged. Two problems are seen with using radar cross section as the radiometric measurement quantity for point targets. First, the radar cross section is frequency and/or angular dependent for many targets, whereas a SAR system operates not at a single set but through a range of frequencies and aspect angles. This begs the question of which radar cross section within this twodimensional range should actually be taken as the measurement result. Second, the pixel intensities seen in SAR images are the output of a filtering process, which is affected by the complex transfer function of the point target. Radar cross section, on the other hand, does not depend on phase. The equivalent radar cross section expresses the reflectivity in terms of the radar cross section of an equivalent conducting sphere which would result in the same pixel intensity as the one observed if the sphere were to replace the actual target in the scene. This distinction is crucial in defining the measurand for radiometric SAR measurements in principal, and hence it is important for radiometric SAR calibration. It is furthermore of particular practical importance for current and emerging wideband, high-resolution, and high-accuracy SAR systems.

The Three-Transponder Method: A Novel Method for Accurate Transponder RCS Calibration

“…The most typical ones depend on (possibly compact) indoor or outdoor measurement ranges [14]. Alternatively, one can also use a SAR instrument to directly measure the transponder's equivalent radar cross section (ERCS) [3], an approach which is described in detail in [5]. The advantages of the approach are the end-to-end nature of the measurement setup.…”

“…Further problems typically found in other outdoor measurement setups like multipath are similar with respect to the substitution method described above. Also, any pulsed method does not yield the transponder RCS at a single frequency, but as a weighted average of the RCS over the pulse bandwidth (see discussion on RCS vs. ERCS in [3,7]), which results in a mismatch between what shall be measured (RCS over frequency) and what is measured (single weighted RCS average).…”

Hierarchical Bayesian Data Analysis in Radiometric SAR System Calibration: A Case Study on Transponder Calibration with RADARSAT-2 Data

“…This paper adopts the reasoning laid out in [15]. According to it, a reference point target's brightness in a SAR image is not generally proportional to its radar cross section (RCS), which is a body property depending on frequency and incidence angle.…”

“…Under this precondition, a corner's ERCS is, with sufficient accuracy, equal to a corner's RCS at the center frequency [15]. The peak RCS of an ideal corner reflector can be estimated with the physical optics approximation…”

A Novel Channel Calibration Method for Bistatic ISAR Imaging System

“…Channel calibration for monostatic radar imaging systems can be realized by calibration tower with a transponder [21][22][23][24][25][26]. The calibration tower is located at a few kilometers away from the radar.…”