Empirical model of total internal reflection from highly turbid media

Abstract

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.

Refractive index measurement of turbid media by transmission of backscattered light near the critical angle

“…When absorption by the material is small, most of the energy flux is carried by the diffuse component. The effective RI assigned to the coherent component of light has been investigated in recent years [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], and its nonlocal nature has been established [19,25]. However, as already said the effective RI seen by diffuse light has been barely investigated, and the only reference reporting efforts in the past that helps address this question is that of Meeten and North [6].…”

Direct detection of aggregates in highly turbid colloidal suspensions of polystyrene nanoparticles

“…Our experimental setup has been described in detail earlier [17,[19][20][21]24]. A turbid sample of refractive index n s n r in i is placed on a glass prism of known refractive index n p .…”

“…In order to determine whether aggregation has occurred or not in a highly turbid medium it is, therefore, natural to turn toward total internal reflection (TIR) based imaging methods where the sample penetration lengths are small, on the order of an optical wavelength, so that the single-scattering assumption is satisfied (i.e., αz ≪ 1 so that no multiple scattering occurs) despite the high attenuation encountered in dense colloids [17].…”

“…Recently one of us proposed an alternative sensing technique based on a new empirical model for total internal reflection (TIR) in highly turbid media which does not use SPR-instead the sample is placed directly on the glass surface [19,20]. Using this new model, accurate measurement of the attenuation coefficient, refractive index, and particle size has been demonstrated in highly turbid, though unaggregated, monodisperse aqueous suspensions of polystyrene nanospheres [17] and intralipid emulsions [21].…”

Real part of refractive index measurement approach for absorbing liquid

“…Recently, supported by theoretical analysis and experiments, many researchers have proposed revised Fresnel models to describe the reflectance of coherent beam for turbid liquids. For instance, Goyal et al have derived an empirical model of TIR from turbid liquids [25]. Gutiérrez-Reyes and co-workers have provided extension of Fresnel formulas by rigorous derivation from Maxwell equations [24,26].…”