Simple empirical master-slave dual-source configuration within the diffusion approximation enhances modeling of spatially resolved diffuse reflectance at short-path and with low-scattering from a semi-infinite homogeneous medium: erratum

Daqing Piao; Sanjay Patel

doi:10.1364/AO.57.007942

On page 1449 of the original paper [1], the Eqs. (10)–(12) were given with a typographical error. The fraction between the only or second “=” sign and the square bracket shall not have “ $D$ ” at the denominator. The Eqs. (10)–(12) with the typographical error corrected are presented in the following:

\vec{J} (ρ) = - D \frac{\partial Ψ}{\partial r} \vec{r} = \frac{S}{4 π} [\frac{(μ_{eff} l_{real} + 1) \exp (- μ_{eff} l_{real})}{{(l_{real})}^{2}} {\hat{l}}_{real} - \frac{(μ_{eff} l_{imag} + 1) \exp (- μ_{eff} l_{imag})}{{(l_{imag})}^{2}} {\hat{l}}_{imag}],

J |_{({\hat{z}}^{-})} (ρ) = \frac{S}{4 π} [\frac{z_{a} (μ_{eff} l_{real} + 1) \exp (- μ_{eff} l_{real})}{{(l_{real})}^{3}} + \frac{(z_{a} + 2 z_{b}) (μ_{eff} l_{imag} + 1) \exp (- μ_{eff} l_{imag})}{{(l_{imag})}^{3}}],

J^{*} |_{({\hat{z}}^{-})} (ρ) = \frac{S^{*}}{4 π} [\frac{z_{a}^{*} (μ_{eff} l_{real}^{*} + 1) \exp (- μ_{eff} l_{real}^{*})}{{(l_{real}^{*})}^{3}} + \frac{(z_{a}^{*} + 2 z_{b}) (μ_{eff} l_{imag}^{*} + 1) \exp (- μ_{eff} l_{imag}^{*})}{{(l_{imag}^{*})}^{3}}] .

The results are unaffected by the change, as the numerical implementations of the Eqs. (11) and (12) were coded using the correct forms as shown above and the Eq. (10) was not involved in numerical implementation.

REFERENCE

1. D. Piao and S. Patel, “Simple empirical master-slave dual-source configuration within the diffusion approximation enhances modeling of spatially resolved diffuse reflectance at short-path and with low scattering from a semi-infinite homogeneous medium,” Appl. Opt. 56, 1447–1452 (2017). [CrossRef]

Simple empirical master-slave dual-source configuration within the diffusion approximation enhances modeling of spatially resolved diffuse reflectance at short-path and with low-scattering from a semi-infinite homogeneous medium: erratum

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Applied Optics