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Analytical solution of the vector radiative transfer equation for single scattered radiance: erratum

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Abstract

We have discovered a small error in our recently published work [J. Opt. Soc. Am. A 39, 2045 (2022) [CrossRef]  ], which we correct in this erratum. The error is located in Section 2.D and affects the solution for polydisperse distributions.

© 2022 Optica Publishing Group

In Section 2.D of [1], which discusses polydisperse distributions, we made a mistake. We state after Eq. (25) that the probability

$$\frac{{{\sigma _t}({r_j})n({r_j})}}{{{\mu _t}}} \epsilon$$
to interact with a particle of radius ${r_j}$ is equal to the weight in Eq. (23) by which the radiance must be weighted to obtain it for polydisperse distributions. This statement is not correct. The correct weight for the radiance in Eq. (23) is
$$p({r_j}) \approx \frac{{{\sigma _s}({r_j})n({r_j})}}{{{\mu _s}}} \epsilon .$$

This has no effect on the verification in Section 3.B, since we have assumed in these calculations that no absorption can take place on the scattering particles.

Data availability

No data were generated or analyzed in the presented research.

REFERENCE

1. P. Hank, A. Liemert, and A. Kienle, “Analytical solution of the vector radiative transfer equation for single scattered radiance,” J. Opt. Soc. Am. A 39, 2045–2053 (2022). [CrossRef]  

Data availability

No data were generated or analyzed in the presented research.

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Equations (2)

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σ t ( r j ) n ( r j ) μ t ϵ
p ( r j ) σ s ( r j ) n ( r j ) μ s ϵ .
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