Optimization of Gap Derivatives for Measuring Blood Concentration of Fabric Using Vibrational Spectroscopy

Derivatives are common preprocessing tools, typically implemented as Savitzky–Golay (SG) smoothing derivatives. This work discusses the implementation and optimization of fourth-order gap derivatives (GDs) as an alternative to SG derivatives for processing infrared spectra before multivariate calibration. Gap derivatives approximate the analytical derivative by calculating finite differences of spectra without curve fitting. Gap derivatives offer an advantage of tunability for spectral data as the distance (gap) over which this finite difference is calculated can be varied. Gap selection is a compromise between signal attenuation, noise amplification, and spectral resolution. A method and discussion of the importance of fourth derivative gap selections are presented as well as a comparison to SG preprocessing and lower-order GDs in the context of multivariate calibration. In most cases, we found that optimized GDs led to calibration models performing comparably to or better than SG derivatives, and that optimized fourth-order GDs behaved similarly to matched filters.