  Fourier-transform infrared spectroscopy (FTIR) is a versatile technique for
characterizing the chemical composition of the various uncertainties, including
baseline shift and multiplicative error. This study aims at analyzing the
effect of certain treatment on the FTIR responses subject to these
uncertainties. A two-step method is proposed to quantify the treatment effect
on the FTIR signals. First, an optimization problem is solved to calculate the
template signal by aligning the pre-treatment FTIR signals. Second, the effect
of treatment is decomposed as the pattern of modification $\mathbf{g}$ that
describes the overall treatment effect on the spectra and a vector of effect
$\boldsymbol{\delta}$ that describes the degree of modification. $\mathbf g$
and $\boldsymbol{\delta}$ are solved by another optimization problem. They have
explicit engineering interpretations and provide useful information on how the
treatment effect change the surface chemical components. The effectiveness of
the proposed method is first validated in a simulation. In a real case study,
it's used to investigate how the plasma exposure applied at various heights
affects the FTIR signal which indicates the change of the chemical composition
on the composite material. The vector of effects indicates the range of
effective plasma height, and the pattern of modification matches existing
engineering knowledge well.
