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The fractions of light absorbed by and remitted from samples consisting of different numbers of plane parallel layers can be related with the use of statistical equations. The fractions of incident light absorbed (A), remitted (R), and transmitted (T) by a sample of any thickness can be related by an absorption/remission function, A(R,T): A(R,T) = [(1 - R)2 - T2]/R = (2 - A - 2R)A/R = 2A0/R0. Being independent of sample thickness, this function is a material property in the same sense as is the linear absorption coefficient in transmission spectroscopy. The absorption and remission coefficients for the samples are obtained by extrapolating the measured absorption and remission fractions for real layers to the fraction absorbed (A0) and remitted (R0) by a hypothetical layer of infinitesimal thickness. A sample of particulate solids can be modeled as a series of layers, each of which is representative of the sample as a whole. In order for the layer to be representative of the properties of the individual particles of which it is comprised, it should nowhere be more than a single particle thick, and should have the same void fraction as the sample; further, the volume fraction and cross-sectional surface area fraction of each particle type in the layer should be identical to its volume fraction and surface area fraction in the sample as a whole. At lower absorption levels, the contribution of a particle of a particular type to the absorption of a sample is approximately weighted in proportion to its volume fraction, while its contribution to remission is approximately weighted in proportion to the fraction of cross-sectional surface area that the particle type makes up in the representative layer.

A system of equations described by Benford relate the absorption and remission properties of a layer of a material to the properties of any other thickness of the material. R, the fraction of light remitted from an infinitely thick sample, may be calculated from Benford's equations by increasing the sample thickness until the total remission converges to its upper limit. The fractions of light absorbed (a 0) and remitted (r 0) by a very thin layer may be similarly calculated. The relationship A(r,t) = [(1-r) 2-t 2 ] / r = (2-a-2r) a / r = 2 a 0 / r 0 = (1-R) 2 / R describes an Absorption/Remission Function for the material as a function of a, r and t, the fractions of light absorbed, remitted and transmitted by a specified layer. This is a more general expression than the widely used Kubelka-Munk equation, but gives results equivalent to it for the case of infinitesimal particles.

Since the commercial development of modern near-infrared spectroscopy in the 1970s, analysts have almost invariably used units of weight percent as the measure of analyte concentration, due largely to the historical precedent from other analytical methods, including other spectroscopic techniques. The application of the CLS algorithm to a set of binary and ternary liquid mixtures reveals that the spectroscopic measurement sees the sample differently; that the measured absorbance spectrum is in fact sensitive to the volume fraction of the various components of the mixture. Because there is not a one-to-one relationship between volume fraction and other measures of analyte concentration, nor is the relationship linear, this has important implications for the application of both the CLS algorithm and the various other, more conventional, calibration algorithms that are commonly used.

Equations of Benford used in the Representative Layer Theory are able to describe spectroscopic remission from layered plane parallel samples (plastic sheets) quite effectively. Losses due to reflection directly back in the direction of the incident beam are a major cause of discrepancies. Non-compositional variation and experimental errors tended to produce linear changes in the absorption coefficient, with the remission coefficient being more drastically affected. The remission coefficients obtained experimentally, in general, vary inversely to the absorption coefficient, although, as predicted by theory, front surface reflectance causes a direct variation. In transflectance, the log(1/R) spectrum of the thinnest samples is the one that is most like the absorption coefficient curve, but the shape of the Kubelka-Munk (absorption/remission) spectra are less affected by sample thickness, especially in the absence of surface reflection.

This paper describes the development of rubrics that help evaluate student performance and relate that performance directly to the educational objectives of the program. Issues in accounting for different constituencies, selecting items for evaluation, and minimizing time required for data analysis are discussed. Aspects of testing the rubrics for consistency between different faculty raters are presented, as well as a specific example of how inconsistencies were addressed. Finally, a considerat ion of the difference between course and programmatic assessment and the applicability of rubric development to each type is discussed.

The physical interpretation of the absorbance observed in a non-scattering sample is straightforward; it is a simple function of the concentration of the analyte(s) and its (their) ability to absorb light. In a scattering sample, the phenomena of absorption and scattering affect each other. Consequently, the measured "absorbance" is more difficult to interpret and is not suitable for direct comparison to an "absorbance" obtained from a non-scattering sample. This paper describes a strategy for separating the effects of scatter and absorption. The amount of light absorbed by a sample can be determined by measuring both the amount of light remitted and the amount transmitted by the sample. Using the mathematics of plane parallel layers, it is possible to model the sample as a series of "layers" of any thickness and calculate the absorption, remission and transmission for each of these hypothetical layers. The absorption computed for a layer having a thickness of one particle, which we term the "representative layer", can be used to benchmark the absorbance that would be observed from the sample in the absence of scatter.

is a professor of chemical engineering at Bucknell University. She earned her B.S. in chemical engineering from Cornell University, and her M.S. and Ph.D., also in chemical engineering, from the University of Virginia. Her primary research focus is on engineering pedagogy at the undergraduate level. She is particularly interested in the teaching and learning of concepts related to thermodynamics. She is also interested in active, collaborative, and problem-based learning, and in the ways hands-on activities such as making, technology, and games can be used to improve student engagement.