2020
OPTICS LETTERS / Vol. 40, No. 9 / May 1, 2015
Forward-peaked scattering of polarized light: erratum Julia P. Clark1,* and Arnold D. Kim1,2 1
Applied Mathematics Unit, School of Natural Sciences, University of California, 5200 North Lake Road, Merced, California 95343, USA 2 e-mail: [email protected] *Corresponding author: [email protected] Received March 26, 2015; posted March 31, 2015 (Doc. ID 236713); published April 24, 2015
We intend to correct the typographical errors that occurred in our recent Letter [Opt. Lett. 39, 6422 (2014)]. © 2015 Optical Society of America OCIS codes: (030.5620) Radiative transfer; (290.4210) Multiple scattering; (290.5855) Scattering, polarization. http://dx.doi.org/10.1364/OL.40.002020
2
In what follows, we correct the errors that appeared in [1]. The integrals in Eqs. (6) and (20) are each missing a normalization factor of 1∕2. Equation (6) should read
1 2
Z
π 0
a1 Θ sin ΘdΘ 1;
1−g
0
0
0
3
6 7 0 7 c¯ 2 0 1 6 6 0 7 L2 ΔΩˆ 6 7 7 2 6 0 ¯ 2 0 0 c 4 5 2 0 0 0 a¯ 4 2 0 0 0 6 cos θ 6 0 1 − cot2 θ ∂ 6 sin2 θ φ 2¯c2 6 cos θ 6 − sin2 θ ∂φ 1 − cot2 θ 4 0 0 0
(6)
0
3
7 07 7 7: 07 5 0
(18)
and Eq. (20) should read
αj2k
1 2
Z
π 0
1 − cos Θk aj Θ sin ΘdΘ:
(20)
As a consequence of the errata in Eq. (18), which are addressed above, Eqs. (23) and (24) have errors. The corrected equations are ˆ · ∇Q μa Q μs 1 − γ 0 Q − 1 μs γ 2 Δ ˆ Q Ω Ω 2 cos θ −2γ 2 1 − cot2 θQ − 2γ 2 2 ∂φ U 0; sin θ
The second and third diagonal entries of the 4 × 4 matrix L0 given in Eq. (16) are incorrect. The correct result for L0 is
(23)
and 2
0 6 60 6 L0 −6 60 4 0
0
1−
0 0
a¯ 0 a¯ 0 2 3 2
0 0
1−
a¯ 0 a¯ 0 2 3
0
2
0 0
3
7 7 7 7: 0 7 5 1 − a¯ 0 4
(16)
The second term in the definition of L2 given in Eq. (18) contains several errors: there is a missing scalar factor of 2, and the (2, 2), (2, 3), and (3, 2) entries are incorrect. The correct definition of L2 is
0146-9592/15/092020-01$15.00/0
ˆ · ∇U μa U μs 1 − α0 U − 1 μs c¯ 2 Δ ˆ U Ω Ω 3 2 cos θ 2γ 2 1 − cot2 θU − 2γ 2 2 θ∂φ Q 0: sin θ
(24)
In these corrected equations, we have introduced k γ k αk 2 α3 ∕2 for k 0, 2. Reference 1. J. Clark and A. D. Kim, Opt. Lett. 39, 6422 (2014).
© 2015 Optical Society of America
OPTICS LETTERS / Vol. 40, No. 9 / May 1, 2015
Forward-peaked scattering of polarized light: erratum Julia P. Clark1,* and Arnold D. Kim1,2 1
Applied Mathematics Unit, School of Natural Sciences, University of California, 5200 North Lake Road, Merced, California 95343, USA 2 e-mail: [email protected] *Corresponding author: [email protected] Received March 26, 2015; posted March 31, 2015 (Doc. ID 236713); published April 24, 2015
We intend to correct the typographical errors that occurred in our recent Letter [Opt. Lett. 39, 6422 (2014)]. © 2015 Optical Society of America OCIS codes: (030.5620) Radiative transfer; (290.4210) Multiple scattering; (290.5855) Scattering, polarization. http://dx.doi.org/10.1364/OL.40.002020
2
In what follows, we correct the errors that appeared in [1]. The integrals in Eqs. (6) and (20) are each missing a normalization factor of 1∕2. Equation (6) should read
1 2
Z
π 0
a1 Θ sin ΘdΘ 1;
1−g
0
0
0
3
6 7 0 7 c¯ 2 0 1 6 6 0 7 L2 ΔΩˆ 6 7 7 2 6 0 ¯ 2 0 0 c 4 5 2 0 0 0 a¯ 4 2 0 0 0 6 cos θ 6 0 1 − cot2 θ ∂ 6 sin2 θ φ 2¯c2 6 cos θ 6 − sin2 θ ∂φ 1 − cot2 θ 4 0 0 0
(6)
0
3
7 07 7 7: 07 5 0
(18)
and Eq. (20) should read
αj2k
1 2
Z
π 0
1 − cos Θk aj Θ sin ΘdΘ:
(20)
As a consequence of the errata in Eq. (18), which are addressed above, Eqs. (23) and (24) have errors. The corrected equations are ˆ · ∇Q μa Q μs 1 − γ 0 Q − 1 μs γ 2 Δ ˆ Q Ω Ω 2 cos θ −2γ 2 1 − cot2 θQ − 2γ 2 2 ∂φ U 0; sin θ
The second and third diagonal entries of the 4 × 4 matrix L0 given in Eq. (16) are incorrect. The correct result for L0 is
(23)
and 2
0 6 60 6 L0 −6 60 4 0
0
1−
0 0
a¯ 0 a¯ 0 2 3 2
0 0
1−
a¯ 0 a¯ 0 2 3
0
2
0 0
3
7 7 7 7: 0 7 5 1 − a¯ 0 4
(16)
The second term in the definition of L2 given in Eq. (18) contains several errors: there is a missing scalar factor of 2, and the (2, 2), (2, 3), and (3, 2) entries are incorrect. The correct definition of L2 is
0146-9592/15/092020-01$15.00/0
ˆ · ∇U μa U μs 1 − α0 U − 1 μs c¯ 2 Δ ˆ U Ω Ω 3 2 cos θ 2γ 2 1 − cot2 θU − 2γ 2 2 θ∂φ Q 0: sin θ
(24)
In these corrected equations, we have introduced k γ k αk 2 α3 ∕2 for k 0, 2. Reference 1. J. Clark and A. D. Kim, Opt. Lett. 39, 6422 (2014).
© 2015 Optical Society of America
