Application of Linear Additive Conditions for Near-Infrared Diffuse Reflectance Absorption Spectroscopy

Determining the homogeneity of material mixing in real time during product processing is critical for quality control. According to the Kubelka–Munk (K-M) function of diffuse reflectance absorption spectrum, absorbance (A) is approximately linear with the content of the components when the sample scattering coefficient (S) is in a certain range. The S is determined by the particle size of powder samples. Therefore, this study determined particle size ranges that satisfy linear additivity in near-infrared diffuse reflectance spectroscopy (NIRDRS). Thus, the proposed NIRDRS analysis technique can be used to determine the homogeneity of material mixes or analyze the percentages of the components in the mixture. In this study, vitamin B3 and vitamin C were used for preparing mixed samples with varying percentages. The experimental results revealed that linear additivity is satisfied when the powder particle size is in the range of less than 280, 280–450, and 450–900 μm. When the confidence level is 0.01, the actual mixed spectra are not significantly different from the “simulated mixed spectra” constructed by linear addition, with their relative deviations less than 1.08%. The absolute errors of the actual and analytic percentages were within 2.98% for each component in the mixtures. The above conclusions also hold for sorghum, which has a complex material composition. Statistical models cannot analyze the percentages of components in the mixture. In contrast, linear addition and direct calibration approach avoids the use of a large number of samples for statistical modeling and analyze the percentages of mixed samples. Meanwhile, it can be used to discriminate and analyze the material mixing uniformity by building a mechanistic model.