On the measurement of the effective refractive index of biological colloids A. García-Valenzuela 1 , C. Sánchez-Pérez 1 , A. Reyes-Coronado 2 and R. G. Barrera 2 1 Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Apartado Postal 70-186, Distrito Federal 04510, México. 2 Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, Distrito Federal 01000, México. Keywords :, refractive index, colloids, biomeasurement. Abstract. We address the problem of measuring the refractive index of biological materials. We limit our analysis to the case of colloids and consider the use of common automatic critical-angle refractometers to measure their effective refractive index. We provide rough guidelines to when these refractometers will incur in large errors and thus alternative techniques should be used. Introduction The refractive index (RI) of materials can be used to obtain information on their chemical composition and microstructure. Many biological materials are optically inhomogeneous on a scale comparable to the wavelength of visible light, and thus they are optically turbid. Two questions arise when dealing with biological media: What does the effective refractive index of a turbid medium means? and how can we measure it? To answer properly these questions we must recall that light propagation in turbid media is divided in two components: the coherent and the diffuse components. The coherent component corresponds to the average field whereas the diffuse component corresponds to the light fluctuations around its average. By average one usually means the configurational average of the system. Diffuse light gives a turbid appearance to the material. It has been shown by many researchers that the coherent wave in a turbid medium propagates with an effective wavevector. From it, one can assign an effective refractive index to the medium. This effective refractive index is in general complex and its imaginary part takes into account attenuation of the coherent wave due to absorption and scattering by the inhomogeneities. The effective refractive index in colloidal media Let us now restrict our discussion to colloidal media. A colloid is defined as a suspension of particles in a homogeneous phase which we call the matrix. Many biological materials are in fact colloids. A clear example of a biological colloid is blood. But, many tissues can be modeled optically to some extent as colloidal media as well. In recent years, we have developed a Coherent-Scattering model for the coherent light propagation and reflection from dilute colloidal media and tested it experimentally [1,2]. We have found that in general we can not use without restrain the effective refractive index of a turbid colloid as we would do in the case of a homogeneous substance. For instance, when the size parameter of the colloidal particles is not small compared to one, the coherent reflection of light from a turbid colloidal medium is not properly described by the usual Fresnel reflection coefficients. This fact indicates that one may incur in sizable errors when measuring the effective refractive index of colloidal media by optical reflectance methods. More recently we have come to realize that the effective medium associated with a turbid colloidal medium has a non-local character, that is, it is spatially dispersive, and this explains why the Fresnel reflection coefficients are not readily applicable [3].