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The predictions of the theory of light propagation in weakly absorbing anisotropic minerals are tested against systematic measurements of the infrared absorbance spectra ofcalcite, olivine, and topaz oriented in both principal and random sections, using both polarized and unpolarized light. We show that if the linear polarized maximum absorbance is smaller than -0.3, or if the ratio of maximum and minimum absorbance is close to unity, then (1) the polarized maximum and minimum absorbances as well as the unpolarized absorbance are, to a good approximation, linearly proportional to thickness, regardless of the direction of the incident light; (2) the angular variation of polarized light absorption is indistinguishable from the theoretical predictions within the uncertainty of the measurements; (3) for any section the unpolarized absorbance is the mean of the polarized maximum and minimum absorbance; and (4) the average unpolarized absorbance of randomly oriented grains is one third of the Total Absorbance (defined as the sure of the three principal absorbances). Therefore, calibrations relating Total Absorbance to absorber concentration in minerals that have been developed from measurements with polarized light parallel to the principal axes may be applied to measurements with unpolarized light on a population of randomly oriented sections. We show that 10 such measurements are sufficient to achieve a petrologically useful accuracy. The method enables water concentrations in nominally anhydrous minerals to be determined from samples where the preparation of oriented specimens is not feasible, such as high-pressure experimental runs and fine-grained mantle xenoliths. The method may also be used for obtaining quantitative measurements on low-symmetry minerals. Keywords: Infrared spectroscopy, absorbance spectroscopy, unpolarized light, olivine, calcite, topaz, nominally anhydrous minerals

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.sub.unpol]([PHI], [PSI]), and the principal polarized absorbances, [A.sub.a], [A.sub.b], [A.sub.c] in an anisotropic crystal [A.sub.unpol]([PHI],[PSI]) = 1/2[[A.sub.a]([cos.sup.2][PHI][cos.sup.2][PSI} + [sin.sup.2][PSI]) + [A.sub.b]([cos.sup.2][PHI][sin.sup.2][PSI] + [cos.sup.2][PSI]) + [A.sub.c][sin.sup.2][PHI]]. 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.sub.a] + [A.sub.b] + [A.sub.c]) and principal absorbances from spectroscopic measurements of absorbance using unpolarized light on a set of randomly oriented crystals. Keywords: Absorption index theory, anisotropic media, unpolarized light, spectroscopy

We address the problem of unpolarized light spectroscopy of geological materials. Using infrared radiation, the aim of this technique is to learn about the absorbing species, such as hydroxyl. The use of unoriented samples leads to the need to perform a rigorous statistical analysis, so that the three principal absorbances of the crystal can be retrieved. We present here such an analysis based on a derivation of the probability density function for a single random measurement. Previous methods for retrieval of the absorbances are shown to be suboptimal, producing biased results that are sometimes even unphysical (e.g., negative estimates for an inherently positive quantity). The mathematical structure of the problem is developed to use the maximum likelihood estimation method, and we show how to optimize for the three absorbance parameters. This leads to good parameter retrieval on both synthetic and real data sets. [ABSTRACT FROM AUTHOR]