Optical model enabling the use of Abbe-type refractometers on turbid suspensions

Abstract

We derive a simple model for the angular-intensity profiles of diffuse light transmitted from a turbid colloid into a transparent medium of higher refractive index (RI) near the critical angle. Adjusting this model to experimental profiles obtained with an Abbe-type refractometer offers a sensitive and robust way of measuring the complex effective RI of highly scattering media.

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

“…Nevertheless, from an experimental point of view, the possibility of measuring the real part of the effective RI of turbid colloids was clearly demonstrated. Recently we derived a theoretical model predicting the shape of the angular-intensity profiles of light transmitted from turbid suspensions of particles to a transparent prism near the critical angle [27] and found it reproduced well a few experimental angular-intensity profiles around the critical angle. With this new model at hand, our aim is to resume the pioneering work by Meeten and North and establish in substantiated grounds the measurement of the effective RI of turbid colloidal suspensions using Abbe-type refractometers.…”

“…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].…”

“…It also predicts that the intensity profile extends beyond the angle one would calculate as the critical, considering only the real part of the effective RI of the turbid medium. The model we developed in [27] yields the following expression for the angular-intensity profile of diffusely scattered light reflected back into the prism:…”

Real part of refractive index measurement approach for absorbing liquid

“…However, turbid liquid is inhomogeneous with suspended scattering particles. The turbid liquid has a complex effective RI, even in the absence of absorption, due to scattering [3]. In reflected refractometers, the reflected beam includes a coherent field and a diffuse field when the sample is turbid [23].…”

“…Reflected refractometers are widely used in the science and engineering fields, as they offer the advantages of high accuracy, high stabilization, low cost, and insusceptibility to external perturbation [3]. Commonly, reflected refractometers are only calibrated at one wavelength (e.g., sodium D-line 589 nm).…”