## Abstract

We discuss the refractive-index measurement of biological tissues by total internal reflection. The methodology of the measurement is illuminated comprehensively, and an experimental setup, combined with a data processing program, is developed correspondingly. Refractive indices of typical tissue samples are measured by use of the developed methodology. The agreement of our measurements with the reported results shows the validity of our scheme, which has the potential for being a simple, quick, and low-cost practical means for determining the refractive index of a turbid medium. Moreover, an empirical formula for evaluating the refractive index of Intralipid suspensions with different concentrations is also presented according to experimental measurements.

© 2005 Optical Society of America

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### Equations (11)

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(1)
$${R}_{AC}(r)=\frac{I(i)}{{I}_{0}[1-{R}_{AB}(i)][1-{R}_{BC}(i)]},$$
(2)
$$r={\text{sin}}^{-1}\left(\frac{1}{{n}_{0}}\text{sin}(i)\right)+45\xb0,$$
(3)
$${\int}_{0\xb0}^{90\xb0}[R(r)-{R}_{t}(\overline{n},r)]\text{d}r,$$
(4)
$${R}_{t}(\overline{n},r)=\frac{{\text{sin}}^{2}(r-{r}^{\prime})}{{\text{sin}}^{2}(r+{r}^{\prime})},$$
(5)
$${r}^{\prime}=\text{arcsin}\left(\frac{{n}_{0}\hspace{0.17em}\text{sin}\hspace{0.17em}r}{\overline{n}}\right),$$
(6)
$$\underset{{\overline{r}}_{c}}{\text{min}}{\int}_{\overline{r}-5\xb0}^{{\overline{r}}_{c}+5\xb0}[{R}_{AC}(r)-{R}_{t}({\overline{r}}_{c},\mathrm{\hspace{0.17em}\u200a\u200a}r)]\text{d}r,$$
(7)
$$\overline{n}={n}_{0}\hspace{0.17em}\text{sin}\hspace{0.17em}{\overline{r}}_{c},$$
(8)
$$n=a{n}_{1}+b{n}_{2},$$
(9)
$$\mathrm{\Delta}\overline{n}={n}_{0}\hspace{0.17em}\text{cos}({\overline{r}}_{c})\mathrm{\Delta}{\overline{r}}_{c},$$
(10)
$$\mathrm{\Delta}r=\frac{\text{cos}\hspace{0.17em}\hspace{0.17em}i}{{n}_{0}{[1-{(\text{sin}\hspace{0.17em}i/{n}_{0})}^{2}]}^{1/2}}\mathrm{\Delta}i,$$
(11)
$$i={\text{sin}}^{-1}[{n}_{0}\hspace{0.17em}\text{sin}(r-45\xb0)],$$