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Full Spectrum Matching Method
These two Full Spectrum search algorithms are identical to their non-derivative counterparts except that before the Absolute Value or Least Squares HQI is calculated, the derivative of the unknown and library entry are calculated. This derivative is simply the difference between each set of points in the spectrum. For the 1st Derivative Absolute Value
Where Lib is the library entry being searched, Unkn is the unknown spectrum, and n is the number of data points in the library entry and reduced unknown spectrum. The values of Lib0 and Unkn0 are defined to be the same as Lib1 and Unkn1, respectively. Spectral regions are excluded from the calculation by setting the corresponding values in the Lib and Unkn to zero.
The two derivative searches have the advantage of removing most of the error from a slowly varying baseline error in the unknown from the search results. They are especially useful when the baseline error is not linear and therefore cannot be removed by the standard GIFTS algorithm in the baseline correction program of GRAMS/AI. | 
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