# A 1D Radiative Transfer Benchmark with Polarization via Doubling and Adding

## TL;DR

This paper presents a highly precise numerical solution for the 1D radiative transfer equation with polarization, using a doubling and adding method with convergence acceleration, and updates benchmark results to high precision.

## Contribution

It introduces a novel, highly accurate numerical method for polarized radiative transfer in 1D media, improving benchmark precision and handling complex scattering and heterogeneity.

## Key findings

- Benchmark solutions updated to 7 decimal places for reflectance and transmittance.
- Method achieves high-precision solutions for polarized radiative transfer.
- Successfully applied to heterogeneous media with partial absorption.

## Abstract

Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2- Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to 7 places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

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Source: https://tomesphere.com/paper/1705.08274