Statistical estimation of the probability of the correct substance detection in FTIR spectroscopy

In the present paper a problem of substance identification in FTIR (Fourier transform infrared) spectroscopy is considered. The spectral library hitlist search is chosen as the main tactic. In the paper the Pearson correlation coefficient as a similarity criterion between two spectra is suggested. A situation when one of the measured spectra has an additive narrowband white noise component with a Gaussian distribution is considered. In that case the probability density of the correlation coefficient is found. A concept of the probability of correct detection is proposed and a theoretical expression is found. In addition, we consider a boundary correlation coefficient search algorithm, which allows one to find a boundary value providing the required correct detection. Computational experiments have shown the applicability of the method.