posted on 2021-12-20, 05:45authored byThomas G. Mayerhöfer, Marie Richard-Lacroix, Susanne Pahlow, Uwe Hübner, Rainer Heintzmann, Jürgen Popp
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 correlation-based 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.