Refractive index errors in the critical-angle and the Brewster-angle methods applied to absorbing and heterogeneous materials

Abstract

High-precision critical-angle refractometers, with automatic refractive index computation and readout, are now available from several manufacturers. In such instruments light is incident from within a transparent reference medium, typically an optical prism, onto a sample material in good optical contact with the prism. The critical angle of reflection is measured at the interface between the prism of known refractive index and the sample material of unknown refractive index. Critical-angle refractometers are calibrated for transparent samples but are commonly used for measurements of refractive index in optically absorbing or optically heterogeneous materials. The instrument will then read an apparent refractive index which differs from the true refractive index of the sample. The optics of the critical-angle refractometer are investigated to quantify errors which arise from the neglect of absorption and heterogeneity in the transparent sample interpretation of the critical angle. Refractive index reading errors will be important when they become larger than the refractive index precision of modern instruments, about 10 −5 . In critical-angle refractometry it is shown that this occurs for samples of surprisingly weak absorption. The critical-angle and Brewster-angle methods are compared for optically absorbing and heterogeneous samples. Errors arising from sample absorption in the Brewster-angle method are shown to be much less than in the critical-angle method.

Refractive indices of chitin, chitosan, and uric acid with application to structural color analysis

“…Esta pregunta es particularmente relevante para aquellos datos obtenidos mediante la técnica de refractómetro de ángulo crítico cuyos resultados son interpretados suponiendo que no hay absorción de luz del todo. De acuerdo con Meeten y colaboradores [34][35][36], el error en la determinación del índice de refracción mediante técnicas de ángulo crítico es muy pequeño (del orden de 10 -5 ) cuando el coeficiente de extinción es menor que 10 -3 . Como mostraremos en la siguiente sección, el coeficiente de extinción de la quitina es del orden de 3.0×10 -4 en el rango espectral del visible.…”

Application of the critical angle method to refractive index measurement of human skinin vivounder partial contact

“…An alternative method has been proposed that involves detecting the maximum of the first derivative. 22 Although detection is difficult, this method is worth considering since it seems to be more robust against absorption than our method. 22 There are some other probable causes of errors in the present measurement method.…”

“…22 Although detection is difficult, this method is worth considering since it seems to be more robust against absorption than our method. 22 There are some other probable causes of errors in the present measurement method. First, there may be multiple reflections in the prism and in the skin, which would reduce the angular resolution.…”

Virtual instrumentation in LabVIEW for multiple optical characterizations on the same opto-mechanical system

“…Thus, the refractive index of the film was calculated using the expression n = tan  B . Usually, the Abelès-Brewster is widely used for the determination of refractive index of dielectric thin film; however, some studies on the determination of complex refractive index of thin film are done using prism or flat substrate [9].…”