Existing methods for external calibration of polarimetric synthetic aperture radars (SAR) are all based on point targets with known scattering matrices. The quantity of interest in radar measurement of distributed targets is the backscattering coefficient, which is different from the radar cross section (RCS) formulated for point targets. Therefore, in order to infer the backscattering cross section of a distributed target from a point target rigorously, the polarimetric ambiguity function of the SAR (unknown) is needed for the computation of the effective illumination area. In existing methods the illumination area is approximated by the area of a pixel. The second problem is the uncertainty in the RCS of point calibration targets. The large physical size of the point targets and their interaction with the background produce uncertainties in the measurement of the calibration targets. The third problem with existing methods arises from the application of the calibration algorithm to individual pixels. The measured response of a distributed target by a SAR is the convolution of the actual radar reflectivity of the target with the ambiguity function of the SAR. Thus, the statistics derived from individual pixels is influenced by the ambiguity function and the measurement becomes system dependent. In this paper a calibration algorithm is proposed that circumvents all of the mentioned problems. It is shown that the radar distortion parameters and effective illumination area can be obtained from a homogeneous distributed target with a known differential Mueller matrix. The distortion parameters are then used in an algorithm to provide the calibrated differential Mueller matrix for the other homogeneous targets in the image. This algorithm is tested for the JPL L- and C-band SAR using four different distributed targets measured with polarimetric scatterometers.
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