Radar delay-Doppler observations provide images of celestial objects with a resolution as fine as less than 10 meters per pixel. The dual-polarimetric observations can be used for characterizing the near-surfaces of asteroids, planets, and the Moon in terms of structural composition in centimeter-to-meter scale. The radar signal is typically transmitted fully circularly polarized, and the echo power in the opposite-circular (OC) and the same-circular (SC) polarization can be analyzed to evaluate the near-surface composition and surface roughness. Limited analysis can be done based on single values such as the radar albedo or circular polarization ratio (the ratio of echo power in the SC polarization divided by that in the OC polarization) or further analysis based on the disk function, i.e., the backscatter coefficient as a function of the incidence angle (θi), typically modeled using a cosine law: σ0 = R(C+1) cos2Cθi, where R and C are the fitting parameters for the reflectivity and the surface roughness, respectively.
We conducted numerical simulations of radar scattering to characterize near-surfaces of asteroids using the disk function analysis. We modeled the disk functions by integrating the radar reflectivity of the asteroid in a delay-Doppler image over the frequency space, by converting the range into an incidence angle estimate based on an assumption of a spherical object, and by normalizing the function using the radar cross sections. Figure 1 shows an example of a disk function for (371660) 2007 CN26 with a fitted cosine-law model (R=0.08 and C=0.61 for the OC polarization). Only near-Earth asteroids that appear spheroidal in the delay-Doppler images, are greater than 140 meters, and were observed using the Arecibo S-band (2380 MHz, 12.6 cm) radar system were included in this quantitative analysis to constrain the parameter space. We used publicly available software: PyRISM to model the disk functions in the OC polarization and discrete-dipole approximation code ADDA for the SC polarization chosen based on the discovered strengths and weaknesses of each code. We present how well each software could model the disk functions, the general statistics for the fitted R and C values, and what role the asteroid taxonomy plays in the reflectivity and surface roughness based on those statistics.