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Fourier-transform infrared spectroscopy (FTIR) is a versatile technique forcharacterizing the chemical composition of the various uncertainties, includingbaseline shift and multiplicative error. This study aims at analyzing theeffect of certain treatment on the FTIR responses subject to theseuncertainties. A two-step method is proposed to quantify the treatment effecton the FTIR signals. First, an optimization problem is solved to calculate thetemplate signal by aligning the pre-treatment FTIR signals. Second, the effectof treatment is decomposed as the pattern of modification $\mathbf{g}$ thatdescribes 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 haveexplicit engineering interpretations and provide useful information on how thetreatment effect change the surface chemical components. The effectiveness ofthe 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 heightsaffects the FTIR signal which indicates the change of the chemical compositionon the composite material. The vector of effects indicates the range ofeffective plasma height, and the pattern of modification matches existingengineering knowledge well.

Learning the Treatment Effects on FTIR Signals Subject to Multiple Sources of Uncertainties