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This Article Figures Only Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Google Scholar Articles by Sambridge, M. Articles by Hermann, J.

Quantitative absorbance spectroscopy with unpolarized light: Part I. Physical and mathematical development

Research School of Earth Sciences, Australian National University, ACT 0200, Australia

Correspondence: ^* E-mail: malcolm{at}rses.anu.edu.au

A new approach to the use of spectroscopic absorbance measurements for anisotropic crystals allows results to be extracted using unpolarized light incident on random crystal orientations. The theory of light propagation in anisotropic absorbing crystals is developed from Maxwell’s equations to devise an expression for the transmittance of linearly polarized light traveling in an arbitrary direction in weakly absorbing media. This theory predicts the distribution of transmittance and absorbance as a function of direction and polarization angle of incident light. It is shown how a previously deduced empirical expression, commonly used in infrared spectroscopy, is a good approximation to the full theory under a wide range of conditions. The new theory shows that principal polarized absorbances correspond to the eigenvalues of an absorbance ellipsoid. An expression is derived for the unpolarized absorbance as a function of the angles describing incident light direction, A_unpol(, ), and the principal polarized absorbances, A_a, A_b, A_c in an anisotropic crystal

Integration of this expression over all incident angles leads to a simple relationship between total measured unpolarized absorbance and the three principal polarized absorbances. Using this theory, a procedure is proposed for estimating both total (A_a + A_b + A_c) and principal absorbances from spectroscopic measurements of absorbance using unpolarized light on a set of randomly oriented crystals.

Key Words: Absorption index theory • anisotropic media • unpolarized light • spectroscopy

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