A Comparative Study of NIR Diffuse Reflectance of Cottons Grouped According to Fiber Cross-Sectional Dimensions. Part I: Fundamentals

Abstract

Reported here is the development of a comparative reflectance model that predicts the relative change in NIR diffuse reflectance of cotton, a hollow fiber, according to the cross-sectional dimensions of perimeter, wall thickness, and wall area. Two cotton groupings are considered: paired cottons and any number of cottons of the same perimeter. The model is based on a single wavelength of NIR light and the critical assumption that the total fiber length in the optical path is constant for cottons of the same perimeter. Combinations of paired dimensional variables are derived and classified by selection rules as “allowed” or “forbidden.” Seven allowed nontrivial combinations of perimeter, wall thickness, and wall area are identified. On the basis of the derived equation that optical density (O.D., log 1/ R units) is a linear function of wall thickness at constant perimeter, comparative reflectances are predicted for all seven nontrivial combinations. The predicted comparative reflectances at a single wavelength range from nonunique (i.e., overlap or equivalent O.D.) to unique; those across many wavelengths are all unique. Also, a mechanism is proposed to explain the interaction of photons with fiber. Finally, the fundamental fiber property sensed is elucidated in three-dimensional (3-D) and 2-D fiber space.