A new approach to computing theoretical polarization curves along the low latitude regions of a planetary disk observed at small phase angles

Abstract

Linear polarization distributions computed along and around the intensity equator of a planetary disk observed at small phase angles tend to show a very pronounced artificial oscillatory behavior or wiggles. The purpose of this work is twofold: to direct attention to this rather tenacious, but not duly publicized computational problem on one hand, and to exploit some effective procedure to minimize those wiggles on the other. For these purposes, we have made extensive numerical computations of the linear polarization curves with various procedures at wavelength 365 nm employing the Venus cloud model of Hansen and Hovenier as a sample, some of which are presented in this work. Our results indicate that the use of the [0,1] part of the Gauss–Legendre quadrature points for μ, the cosine of the zenith angle of incident or emergent light, and their corresponding weights generated in the interval [−1,1] works extremely well for interpolating reflection matrix elements. Furthermore, it is shown that sufficiently well-behaved polarization distribution curves can be obtained by computing the single scattering contributions to the reflection matrix elements exactly and those due to multiple scattering approximately using a natural bicubic spline interpolation formula where the independent variable is to be switched from μ to 1−μ 2 if μ⩾0.7071 and vice versa.