Fractional differentiation is introduced as a mathematical tool for analysis of diffuse-reflectance spectra. The quantity -log10e/R dqR/ d lambda q, where R is the measured reflectance and q is a real number greater than zero, is defined and shown to have properties analogous to those of the integer-order derivatives of log10 (1/ R) that are commonly employed in near-infrared spectroscopy. Like conventional derivative spectroscopy, fractional derivative spectroscopy (FDS) is effective for reducing baseline variations and separating overlapping peaks. FDS has the additional benefit that it enables the user to control the weight given to the slope and curvature of spectral features and, therefore, provides greater flexibility in the choice of wavelengths for regression. FDS also enables the user to adjust the relative sensitivities of the regressions to constant offsets and high-frequency noise. An example is given in which FDS is used to estimate the concentration of hemoglobin in a scattering liquid containing a large background concentration of water.
Joseph M. Schmitt, "Fractional Derivative Analysis of Diffuse Reflectance Spectra," Appl. Spectrosc. 52, 840-846 (1998)