Hybrid 2D Correlation-based Loss Function for the Correction of Systematic Errors

in: Analytical Chemistry (2021)
Mayerhöfer, Thomas G.; Richard-Lacroix, Marie; Pahlow, Susanne; Hübner, Uwe; Heintzmann, Rainer; Popp, Jürgen
We present the derivation of a new kind of loss function from the symmetry rules of synchronous and asynchronous two-dimensional correlation maps. This loss function, which takes into account correlations that are based on causal relations among the members of a series of spectra, can be employed to solve non-linear inverse problems that are plagued by systematic multiplicative errors. This possibility results from the correlationbased loss function being practically insensitive to such systematic errors, which often arise in spectroscopy because sample spectra are usually ratioed against reference spectra. Using dispersion analysis, a sophisticated method of band fitting, of the spectra of poly(methyl methacrylate) films deposited on gold, we demonstrate the applicability and validity of the new loss function. If gold is used as a substrate, experimental spectra are often unphysical, that is, they display reflectance values larger than unity. In such cases, our correlation-based loss function not only helps to achieve accurate fits but also provides corrections to obtain physically meaningful spectra, which leads to results that are superior to conventional correction methods. The validity of the results is checked and proved with help of the results of dispersion analysis of spectra of films of poly(methyl methacrylate) on calcium fluoride (CaF2) and silicon (Si), which do not suffer from the systematic errors.

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