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Modeling turbulence in underwater wireless optical communications based on Monte Carlo simulation: erratum

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Abstract

Corrections are given for errors in the presentation of equations in J. Opt. Soc. Am. A 34, 1187 (2017) [CrossRef]  .

© 2021 Optical Society of America

The authors would like to make the following corrections of errors in the presentation of Eqs. (15), (16), and (17) of [1]. The correct forms of Eqs. (15), (16), and (17) in [1] are

$${\mu}_{ z}^{ \prime}= \left({\frac{{1}}{{{{ a}_{ r}}}}} \right)\left[{{{ c}_{ r}}{\mu}_{ x}^{ \prime}- \frac{{{{ n}_{ i}}}}{{{{ n}_{{ i + 1}}}}}\left({{{ c}_{ r}}{{{\mu}}_{ x}}{{- { a}}_{ r}}{{{\mu}}_{ z}}} \right)} \right],$$
$${\mu}_{ y}^{ \prime}= \left({\frac{{1}}{{{{ a}_{ r}}}}} \right)\left[{{{ b}_{ r}}{\mu}_{ x}^{ \prime}- \frac{{{{ n}_{ i}}}}{{{{ n}_{{ i + 1}}}}}\left({{{ b}_{ r}}{{\mu}_{ x}}{{- { a}}_{ r}}{{{\mu}}_{ y}}} \right)} \right],$$
$$\begin{split}&{\mu}{_{ x}^{ \prime 2}}+ 2\left(\frac{{{{ n}_{ i}}}}{{{{ n}_{{ i + 1}}}}}\right)\mu_{ x}^{ \prime}\left[{{{{ a}}_{ r}}\left({{{{ \vec {\textbf n}}}_{\textbf r}}{{{ .\vec {\textbf L}}}_{\rm i}}} \right){{{ -\mu}}_{ x}}} \right]+{\left({\frac{{{{ n}_{ i}}}}{{{{ n}_{{ i + 1}}}}}} \right)^{2}}\\&\quad \times\left[{{{- {2\mu}}_{ x}}{{{ a}}_{ r}}\left({{{ \vec{\textbf{n}}}_{\textbf{r}}}{{ .\vec{\textbf{L}}}_{\textbf{i}}}} \right){{{ +\mu}}_{ x}}^{2}} \right]+ \left[{{{\left({\frac{{{{ n}_{ i}}}}{{{{ n}_{{ i + 1}}}}}} \right)}^{2}}- {1}} \right]{ a}_{ r}^{2}= {0}\end{split}.$$

The correct expressions were used in the simulation tool, and these errors in the presentation do not affect the numerical results obtained in the paper.

Acknowledgment

The authors appreciate Min Li, Yueheng Li, Ping Huang and Meiyan Ju from College of Computer and Information, Hohai University, Nanjing, Jiangsu 211100, People’s Republic of China, who spent time and effort to highlight the error in the presentation of the equations in our paper.

REFERENCE

1. Z. Vali, A. Gholami, Z. Ghassemlooy, D. G. Michelson, M. Omoomi, and H. Noori, “Modeling turbulence in underwater wireless optical communications based on Monte Carlo simulation,” J. Opt. Soc. Am. A 34, 1187–1193 (2017). [CrossRef]  

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Equations (3)

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μ z = ( 1 a r ) [ c r μ x n i n i + 1 ( c r μ x a r μ z ) ] ,
μ y = ( 1 a r ) [ b r μ x n i n i + 1 ( b r μ x a r μ y ) ] ,
μ x 2 + 2 ( n i n i + 1 ) μ x [ a r ( n r . L i ) μ x ] + ( n i n i + 1 ) 2 × [ 2 μ x a r ( n r . L i ) + μ x 2 ] + [ ( n i n i + 1 ) 2 1 ] a r 2 = 0 .
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