Electromagnetic Scattering Modeling of Rough Surfaces and Selection of Chang’e-7 SAR Polarimetric Lunar Calibration Fields

Chang’e-7 will carry a fully polarimetric Synthetic Aperture Radar (SAR) to investigate the topography and material properties of the lunar polar regions, which necessitates reliable polarimetric calibration. However, conventional ground-based calibration strategies are infeasible for lunar missions, underscoring the need for new relative polarimetric calibration methods tailored to the lunar surface. To address this challenge, we adopt a normal-incidence observation geometry and analyze how the co-polarization ratio $ {\sigma _{{\text{HH}}}} $/$ {\sigma _{{\text{VV}}}} $ and the HH–VV phase difference vary with local slope, where $ \sigma $ denotes the backscattering coefficients. H and V represent horizontal and vertical polarizations, respectively. We introduce a parameter v to quantify the uniformity of the polarization orientation angle distribution and use it to identify suitable lunar calibration sites. Simulation results show that, as terrain slopes become more uniform, the copolarization ratio distribution converges toward unity and the phase difference distribution approaches 0°. Combining rough-surface electromagnetic scattering simulations with Chandrayaan-2 polarimetric observations, we further develop a statistically constrained estimator for determining the minimum number of observations required for robust calibration. This work provides both a theoretical basis and a practical pathway for achieving relative calibration of lunar polarimetric SAR systems.