Algorithms

This method subtracts two files using the following equation:

Result file = Sample file - (Subtrahend file x Subtraction factor)

By interactively varying the Subtraction Factor and looking at the results, the user can determine when the Subtrahend has been adequately "removed" from the Sample data. This is a commonly used function throughout all spectroscopy software packages. However, they all deal with the problem of differences in data point spacing differently. Clearly, to properly subtract one spectrum from another, the data points must line up (i.e. fall on the same X values). However, what do you do when they don’t?

Thermo Galactic’s answer to the data point spacing problem is to automatically interpolate or deresolve the Subtrahend file to match the Sample file during the subtraction operation. This simply uses a linear interpolation function to create data points in the Subtrahend file at the same X values as the Sample.

One problem with spectral subtraction is that it tends to be very subjective. Give the same two spectra to 5 different people and ask them to perform a spectral subtraction and you will get back 5 different results. In addition, try using a manual subtraction method to remove interferences from a large set of spectra (such as from hyphenated chromatography-spectroscopy techniques). Therefore, more automated methods are required to remove the subjectivity and tedium of the human part of the operation. One of the most useful methods for this is to use the "Dewiggle" Auto Subtraction algorithm (see References). This is basically an iterative algorithm which calculates the subtraction factor by minimizing the complexity of the residual spectrum. While it is very well described in the literature, the basic steps are as follows:

1. Estimate a Starting Value for subtraction factor and 2 additional values that are (Starting Value +/- Constant).
2. Calculate the spectral subtraction at each of the 3 factor values.
3. Calculate absolute area of the 1st derivative of the resulting spectra for all 3 subtraction factors
4. Fit a second order polynomial to the 3 points and calculate the subtraction factor at the minimum (apex).
5. Use new subtraction factor from step 4 as the new Starting Value and 2 other values that are Starting Value +/- 20% of previous range; repeat from Step 2.
6. Iterate until the change in the subtraction factor values is less than a preset tolerance or range is too small.

NOTE: If no minimum is found, then this indicates that the reference spectrum is not a significant component of the sample spectrum.

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