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

Abstract

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.

Reversible Gap Derivatives and Their Integration

“…Two overlapping traces are shown in Figure 2a. The first trace is the difference spectrum of the original, unmodified data (black; this is the same curve that appears in Figure 2 of DeJong et al 5 ). The second trace is the difference spectrum, modified to facilitate integration (red).…”

“…[1][2][3][4][5] can be repeated n times to form the nth-order RGD, and a different gap size may be selected for each iteration. The order in which the different gaps are applied does not influence the central portion of the RGD.…”

“…directly influence the efficacy of subsequent multivariate calibration, a topic discussed in DeJong et al 5 …”

“…[1][2][3][4] The simplest gap derivative (GD) transform approximates the analytical derivative by determining the difference between two spectral points separated by a given distance (the gap, g). The difference is then divided by the gap, and this calculation is repeated n times to determine the GD of order n. 5 The combination of gap sizes used for differentiation can be chosen to discriminate for spectral features of interest. Small gap sizes better approximate the analytical derivative, but they often result in a noisy derivative spectrum.…”

“…We compare the calibration performance of conventional GDs and reversible gap derivatives (RGDs) as applied to the infrared diffuse reflection spectra of blood on the surface of cotton fabric, one of the data sets discussed in the earlier publication. 5 The integration routine is then applied to both the derivative spectra and the corresponding latent variables and RVs. The usefulness of integrated PLSR vectors to discuss model performance is discussed using these examples.…”