Abstract
Critical angle refractometry is an established technique for determining the refractive index of liquids and solids. For transparent samples, the critical angle refractometry precision is limited by incidence angle resolution. For lossy samples, the precision is also affected by reflectance measurement error. In the present study, it is demonstarted that reflectance error can be practically eliminated, provided that the sample’s extinction coefficient is a priori known with sufficient accuracy (typically, better than 5%) through an independent measurement. Then, critical angle refractometry can be as precise with lossy media as with transparent ones.
Highlights
Critical angle refractometry is the standard for determining the refractive index of transparent media [1,2,3,4,5,6]
The method relies on measurements of the reflectance, R(θ ), of the interface, formed by a transparent front medium of known refractive index, no, and the sample of unknown index, n, for a range of incidence angles, θ, that includes the critical angle, θc, of total internal reflection (TIR) [7,8,9]
The universal attenuated total internal reflection (a-TIR) condition is exploited in order to accurately determine the real part of the refractive index), nr, of lossy media from the critical incidence angle, θc, at s-polarisation given the extinction coefficient, μ
Summary
Critical angle refractometry is the standard for determining the refractive index of transparent media [1,2,3,4,5,6]. The method relies on measurements of the reflectance, R(θ ), of the interface, formed by a transparent front medium (which is commonly a prism) of known refractive index, no , and the sample of unknown index, n, for a range of incidence angles, θ, that includes the critical angle, θc , of total internal reflection (TIR) [7,8,9]. Is still valid (at least approximately) and that it can be used to obtain an estimate of the real index of the lossy sample [11,12] This assumption introduces systematic errors that have been the subject of extensive discussion; see, e.g., [13,14,15] Let us note that fitting the reflectance profile, R(θ ), to Fresnel equations is another way to compute the complex optical constants [16,17,18]. This is a significant advancement in the field of optical characterisation of absorbing and/or scattering media, which include, among others, various forms of biological matter, non-transparent liquids, colloids and food products
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