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Corrigendum: The Green's function for the radiative transport equation in the slab geometry

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2012 J. Phys. A: Math. Theor. 45 459501(http://iopscience.iop.org/1751-8121/45/45/459501)
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IOP PUBLISHING

JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL

doi:10.1088/1751-8113/45/45/459501

J. Phys. A: Math. Theor. 45 (2012) 459501 (2pp)

Corrigendum: The Green’s function for the radiativetransport equation in the slab geometry
2010 J. Phys. A: Math. Theor. 43 065402
Manabu Machida 1 , George Y Panasyuk 2 , John C Schotland 1and Vadim A Markel 3
1 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
2 Aerospace Systems Directorate, Air Force Research Laboratory, Wright-Patterson Air ForceBase, OH 45433, USA
3 Departments of Radiology and Bioengineering and the Graduate Group in Applied Mathematics
and Computational Science, University of Pennsylvania, Philadelphia, PA 19104, USA

E-mail: mmachida@umich.edu, George.Panasyuk.ctr@wpafb.af.mil, schotland@umich.edu andvmarkel@mail.med.upenn.edu

Received 1 October 2012
Published 23 October 2012
Online at stacks.iop.org/JPhysA/45/459501

In the previously published paper [1], we have computed the energy density of electromagnetic
radiation u(r) by the analytical method developed in the paper (the method of rotated reference
frames (MRRF)) and by the Monte Carlo method. The results were compared in figure 9 of[1]. The figure displays a discrepancy between the two curves that we attributed to unknown
imprecisions inherent in both methods. However, we have discovered an error in the computercode which was used to produce the MRRF curve. When this error was corrected, much better
agreement was obtained. The corrected figure is presented below. We thus conclude that,

100u/Z

10−1MRRF
MC10−210−3
10−40 1 2 3 4 5 6 7 8 9 10∗

Figure 9. Density u(z, ρ) computed by the MRRF and by Monte Carlo simulations for a slabwith L = 10∗ . From top to bottom, the curves correspond to ρ = 4∗ , ρ = 7∗ and ρ = 10∗ .
Normalization factor Z = I0 /(∗ )2 .

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J. Phys. A: Math. Theor. 45 (2012) 459501

Corrigendum

for the parameters considered, the MRRF agrees with Monte Carlo simulations with goodprecision. This finding is consistent with the recent paper of Liemert and Kienle [2].
We note that the other figures or simulation data in [1] have not been affected by the error
mentioned above.
Acknowledgments
This research was supported by the NSF under grants EEC-0615857 and DMS-0554100.
References[1] Machida M, Panasyuk G Y, Schotland J C and Markel V A 2010 The Green’s function for the radiative transport
equation in the slab geometry J. Phys. A: Math. Theor. 43 065402[2] Liemert A and Kienle A 2012 Light transport in three-dimensional semi-infinite scattering media J. Opt. Soc.
Am. A 29 1475–81

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