Quantitative diffuse reflectance spectroscopy of large powders: the Melamed model revisited

Abstract

The popular statistical theory of absolute diffuse reflectance of powders put forth by Melamed [J. Appl. Phys. 34, 560-570 (1963)] a quarter century ago has been re-examined thoroughly. Substantial errors in the physical formulation of the theory have been found and a corrected version is being presented. Some of Melamed's data fits to the theory are also re-examined in the light of the corrected theoretical model.

Limitations and Improvements of the Leaf Optical Properties Model Leaf Incorporating Biochemistry Exhibiting Reflectance and Transmittance Yields (LIBERTY)

“…Their equations can be found in Nomenclature. However, typographical and other errors in the original physical formulation of the theory have been found and a corrected version given by Mandelis, et al [7] is:…”

“…Mandelis, Boroumand and Bergh [7] physically corrected Melamed theory and gave a different equation for R ∞…”

“…After taking , , and into Equation (8), we cannot get the form like Equation (2) either. Mandelis, Boroumand and Bergh [7] physically corrected Melamed theory and gave a different equation for…”

“…The determination of the x u range is more difficult. According to the study of Mandelis, Boroumand and Bergh [7], the value of x u would lie in [0.1, 0.4]. Simonot, et al [13] also calculated the particle backscattering ratio using ray tracing technique and found the value is in the range 0.25-0.35.…”

Predicting changes in the color of powders: Does Melamed's model fit to real industrial powders?

“…2,3 This study has been carried out using Melamed's model, once the typographical errors corrected. The first attempt of Mandelis and all 2 to improve Melamed's model did not let us describe strongly absorbing materials and the second 3 has not been studied yet.…”