Savitzky and Golay differentiation in AES

For the analysis of Auger electron spectra it is popular and very useful to differentiate the acquired direct spectra numerically by Savitzky and Golayʹs method to provide peaks whose peak-to-peak height may be measured. To compare data recorded at different channel separations, ε (number of eV per channel), it is important to be able to assign an energy equivalent, ED, to the differentiating function which is independent of ε. It is shown that the adoption of 2mε for the differential width, where 2m + 1 is the number of points in the Savitzky and Golay function, leads to errors and inconsistencies. It is recommended that (2m + 1)ε be identified with ED. To obtain ED values intermediate between those possible with Savitzky and Golayʹs method, a modified function is developed with added ±(m + 1)th terms. The strength of these terms is between 0 and ±(m + 1)N, where N is the normalisation constant, and the exact value is roughly in proportion to the fractional excess of ED in the interval between the values permitted in Savitzky and Golayʹs original approach. An accurate assessment is made for the value to be used for ED values mid-way between those usually obtained by Savitzky and Golayʹs method.