We demonstrate a first simultaneous measurement of the real and imaginary parts of the refractive index of a highly turbid medium by observing the real-time reflectance profile of a divergent laser beam made incident on the surface of the turbid medium. We find that the reflectance data are well described by Fresnel theory that correctly includes the effect on total internal reflection of angle-dependent penetration into the turbid medium.

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We demonstrate a first simultaneous measurement of both the refractive index and the attenuation coefficient (defined as the sum of the scattering and absorption coefficients) of highly turbid milk and milk-cream mixtures. We achieve this by observing the real-time reflectance profile of a divergent laser beam made incident on the surface of the milk sample. The experiments were carried out on commercial milk samples with fat volume concentrations of 0.5 or less, 1.6, and 3.3%, and on milk-cream mixtures with fat volume concentrations of 10 and 33.3%, without any dilutions of these samples. We find that the reflectance data are well described, for the first time without any empirical fit-parameters, by Fresnel theory that correctly includes the effect of angle-dependent penetration into the turbid medium on the total internally reflected signal. Therefore, our method provides the most accurate determination to date of the refractive index and attenuation coefficient of milk and milk-cream mixtures. Our sensor is compact, portable, and inexpensive.

We demonstrate, to the best of our knowledge, a first accurate empirical model for reflectance measurements from highly turbid media over the full range of incident angles, i.e., for reflectivity values going from unity in the total internal reflection regime to nearly zero when almost all the light is transmitted. Evidence that our model is accurate is provided by extraction of the particle size, followed by independent verification with dynamic light scattering. Our methodology is in direct contrast with the prevalent approach in turbid media of focusing on only the critical angle region, which is just a small subset of the entire reflectance data.

Peiponen et al. [Opt. Lett.35, 4108 (2010)] have expressed concern that a theoretical model we proposed in Calhoun et al. [Opt. Lett.35, 1224 (2010)] for total internal reflection from a turbid medium may be inconsistent with the experimental data, in the sense that the model fails to take into account unexplained oscillations in our data. We show that their concern arises from misinterpretation of our data and theory, and is, therefore, unfounded. NOTE: Optics Letters apologizes to the authors for the delay in the publication of this Reply.

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Abstract. A first accurate measurement of the complex refractive index in an intralipid emulsion is demonstrated, and thereby the average scatterer particle size using standard Mie scattering calculations is extracted. Our method is based on measurement and modeling of the reflectance of a divergent laser beam from the sample surface. In the absence of any definitive reference data for the complex refractive index or particle size in highly turbid intralipid emulsions, we base our claim of accuracy on the fact that our work offers several critically important advantages over previously reported attempts. First, our measurements are in situ in the sense that they do not require any sample dilution, thus eliminating dilution errors. Second, our theoretical model does not employ any fitting parameters other than the two quantities we seek to determine, i.e., the real and imaginary parts of the refractive index, thus eliminating ambiguities arising from multiple extraneous fitting parameters. Third, we fit the entire reflectanceversus-incident-angle data curve instead of focusing on only the critical angle region, which is just a small subset of the data. Finally, despite our use of highly scattering opaque samples, our experiment uniquely satisfies a key assumption behind the Mie scattering formalism, namely, no multiple scattering occurs. Further proof of our method's validity is given by the fact that our measured particle size finds good agreement with the value obtained by dynamic light scattering. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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