Optical parameters estimation in inhomogeneous turbid media using backscattered light: for transcutaneous scattering measurement of intravascular blood: erratum

Shiyang Liang; Takeo Miyake; Koichi Shimizu

doi:10.1364/BOE.517856

Abstract

This erratum corrects several typographical errors in Eqs. (2), (8) and (10) of our paper [Biomed. Opt. Express 15(1), 237 (2024). [CrossRef] ].

Erratum

In this erratum we correct several typographical errors in Eqs. (2), (8) and (10) of our recently published paper [1]. In Eq. (2), l from two locations should be omitted. In Eq. (8), an italic subscript a should be inserted into the right-hand side of the equation. In Eq. (10), the subscript s is changed into an italic subscript a in the nominator of the first equation. The ff1 in the nominator of the first equation is subscripted to make it as μ_eff1². A “=” is inserted at the right of μ_s’ in the second equation. The correct equations are shown as:

(2)$$ln [{{\rho^2}R(\rho )} ]={-} {\mu _{eff}}\rho + ln \left( {{\mu_{eff}} + \frac{1}{\rho }} \right) + ln\frac{{{z_0}{A_d}}}{{2\pi }}$$

(8)$${\mu _a}({\lambda _2})\, = \,{k_a}{\mu _a}({\lambda _1})$$

(10)$$\left\{ \begin{array}{c} {\mu_s}^{\prime} = \frac{{ - 5G({3{\mu_a}^2 - {\mu_{eff1}}^2} )- 3{\mu_a}^2 + \sqrt {{{[{5G({3{\mu_a}^2 - {\mu_{eff1}}^2} )+ 3{\mu_a}^2} ]}^2} - 60G{\mu_a}^2({3{\mu_a}^2 - 5{\mu_{eff1}}^2} )} }}{{30G{\mu_a}}}\\ {\mu_s}^{\prime} = \frac{{ - 5G({3{k_a}^2{\mu_a}^2 - {\mu_{eff2}}^2} )- 3{k_a}^2{\mu_a}^2 + \sqrt {{{[{5G({3{k_a}^2{\mu_a}^2 - {\mu_{eff2}}^2} )+ 3{k_a}^2{\mu_a}^2} ]}^2} - 60G{k_a}^2{\mu_a}^2({3{k_a}^2{\mu_a}^2 - 5{\mu_{eff2}}^2} )} }}{{30G{k_s}{k_a}{\mu_a}}} \end{array} \right.$$

Funding

Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (20K20537).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

1. L. Shiyang, M. Takeo, and S. Koichi, “Optical parameters estimation in inhomogeneous turbid media using backscattered light: for transcutaneous scattering measurement of intravascular blood,” Biomed. Opt. Express 15(1), 237–255 (2024). [CrossRef]

Previous Article Next Article

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

l n [ρ^{2} R (ρ)] = - μ_{e f f} ρ + l n (μ_{e f f} + \frac{1}{ρ}) + l n \frac{z_{0} A_{d}}{2 π}

μ_{a} (λ_{2}) = k_{a} μ_{a} (λ_{1})

{\begin{matrix} {μ_{s}}^{'} = \frac{- 5 G (3 {μ_{a}}^{2} - {μ_{e f f 1}}^{2}) - 3 {μ_{a}}^{2} + \sqrt{{[5 G (3 {μ_{a}}^{2} - {μ_{e f f 1}}^{2}) + 3 {μ_{a}}^{2}]}^{2} - 60 G {μ_{a}}^{2} (3 {μ_{a}}^{2} - 5 {μ_{e f f 1}}^{2})}}{30 G μ_{a}} \\ {μ_{s}}^{'} = \frac{- 5 G (3 {k_{a}}^{2} {μ_{a}}^{2} - {μ_{e f f 2}}^{2}) - 3 {k_{a}}^{2} {μ_{a}}^{2} + \sqrt{{[5 G (3 {k_{a}}^{2} {μ_{a}}^{2} - {μ_{e f f 2}}^{2}) + 3 {k_{a}}^{2} {μ_{a}}^{2}]}^{2} - 60 G {k_{a}}^{2} {μ_{a}}^{2} (3 {k_{a}}^{2} {μ_{a}}^{2} - 5 {μ_{e f f 2}}^{2})}}{30 G k_{s} k_{a} μ_{a}} \end{matrix}