Thomas Mayerhöfer from the department spectroscopy/imaging at Leibniz-IPHT.Īt the institute in Jena, dispersion analysis is used for the quantitative evaluation of IR spectra.
Residual sum of squares series#
Since we mainly deal with the quantitative analysis of IR spectra, it made sense to use this method to quantitatively compare series of measured and simulated spectra,“ explains Dr. “Our original intention was to use 2D correlation analysis to quantitatively estimate the correlations between two series of spectra. Based on symmetry conditions, the smart residual sum of squares was derived from this comparison. The scientists use 2D correlation analysis to compare series of measured and simulated IR spectra. In this way, for example, overlapping peaks can be identified and coincident processes can be separated. With 2D correlation spectroscopy, linear and non-linear variabilities of spectra based on systematic changes of boundary conditions are represented semi-quantitatively. This so-called 2D correlation analysis has proven itself to be invaluable in the field of spectroscopy and has been used for many years with different spectroscopic methods, such as IR, UV/VIS, and Raman spectroscopy. The researchers use a method that can quantify correlations between different curves. The approach recently developed at Leibniz-IPHT can address this problem. This leads to erroneous results and since the magnitude of the systematic error is usually unknown, a correction cannot be made. However, the result of curve fitting can still look reasonable, even if the spectra contain systematic errors, for example due to thermal fluctuations. In spectroscopy, fitting methods based on the residual sum of squares are applied in order to adapt simulated to the measured spectra and to determine band positions, half-widths and areas (band fitting). Scientists from the Leibniz Institute of Photonic Technology (Leibniz-IPHT) in Jena developed an „intelligent“ residual sum of squares that cannot only be used despite systematic errors but can also correct them.
Residual sum of squares free#
The prerequisite for the application of fitting methods is therefore that the measurements are free of systematic errors. Fitting methods optimize the parameters of a given function in such a way that the deviations between measured and calculated curves are minimized. Otherwise, significant deviations may occur. In the absence of bias, the median or arithmetic mean can be excellent estimates of this true value.
Optical Molecular Diagnostics and System Technology.Photophysics and Photochemistry of Functional Interfaces.
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