Intelligent information extraction from reflectance spectra: Absorption band positions

A multiple high‐order derivative analysis algorithm has been developed that automatically extracts absorption band positions from reflectance spectra. Absorption band positions occur where the fifth derivative of the spectrum equals zero, the fourth derivative has positive sign, and the second derivative is negative. The algorithm assumes that bands are approximately symmetric about the band center. Continuum contributions, phase angle effects, and broad low‐frequency calibration errors are suppressed. Overlapping bands with centers as close as 0.3–0.5 W (full band width at half maximum intensity) can be resolved, as long as bands have comparable widths and intensities. If overlapping bands are dissimilar, band center separations of 0.6–1.0 W are safer limits of resolution. Results are relatively insensitive to whether constituent bands convolve additively or multiplicatively. Spectral resolution can be moderately low, requiring only four to eight data points per W . Errors of derived band centers are <3% W for separations greater than 0.6–1.0 W . For overlapping bands with widths of a few thousand cm −1 errors would be typically less than 150 cm −1 from actual band positions. The band detection algorithm is sensitive to noise, and data smoothing is required. The segment length for smoothing (number of points averaged) needs to be continually adjusted to ∼0.5 W to minimize signal distortion. A spectral pattern recognition algorithm, which statistically characterizes the frequency distribution of intensity variations in a sliding segment across the spectrum, can be used to predetect the signal spectrum (low‐frequency components of the sliding intensity distributions) and to calculate approximate W (predetected W ) across the spectrum using its second derivative. An intelligent control algorithm can then continuously locally adjust the segment lengths for smoothing to 0.5 W (predetected W ). Smooths are repeated (typically, 20–30 times) until the high‐frequency components of the sliding intensity variation distributions across the spectrum are suppressed. A single‐pass cubic spline is applied to the smoothed data. The intelligent control algorithm then applies the multiple high‐order derivative algorithm. A sliding segment sixth‐order polynomial is fit to the spectrum, with the length of the segment being continuously locally adjusted to 1.0 W (predetected W ) across the spectrum. Adjustment of the segment length to ∼1.0 W insures that the signal spectrum is minimally distorted and that weak features are not suppressed. Derivatives are calculated for the center point of the sliding segment using the coefficients of the sixth‐order polynomial. The system has successfully extracted band positions from low‐quality (6% peak‐to‐peak noise) synthetic spectra with relatively little degradation of accuracy. Application to natural laboratory and earth‐based telescope spectra displayed good reliability and consistency. Processing is fully automated, and the same standardized procedure is followed for all spectra. No continuum removal or band modeling is needed. The automation of analysis could potentially significantly increase the efficiency and yield of information extraction, particularly for high‐rate repetitive scan laboratory and synoptic remote sensing spectroscopy applications.