Multivariate calibration transfer in spectroscopy is an active area of interest. Many current approaches rely on the measurement of a subset of calibration samples on each instrument produced, an approach that can be impractical in many applications. Furthermore, such methods attempt to model implicitly, rather than explicitly, interinstrument differences. In Part I of this work, a Fourier transform near-infrared spectroscopy (FT-NIR) system designed to perform noninvasive ethanol measurements is discussed. Optical distortions caused by self-apodization, shear, and off-axis detector field of view (FOV) are examined and equations describing their effects are given. The effects of shear and off-axis detector FOV are shown to yield nonlinear distortions of the amplitude and wavenumber axes of measured spectra that cannot be accommodated by typical wavenumber calibration procedures or background correction. The distortions forecast by these equations are verified using laboratory measurements, and an analysis of the spectral complexity caused by the distortions is presented. The theoretical and experimental aspects presented in Part I are incorporated into a new calibration transfer method whose benefits are illustrated in Part II using noninvasive alcohol measurements. Although this work discusses a specific FT-NIR instrument and application, the methods developed form a general framework for modeling the distortions of other types of optical spectrometers to improve instrument standardization and multivariate calibration transfer.

The numerical solution of the Fredholm integral equation of the first kind is formulated so that the source of instability is identified and can be isolated. The problem is regarded as a minimization with no constraints on the solution. It is shown that the introduction of instability depends on the path taken from the initial to the final estimate of the solution. The initial estimate is the given data, and the path which avoids instabilities is that which requires monotonic variation of these data. The method is applied to the deconvolution of noisy spectra and a more objective procedure results than has been previously obtained. Detailed applications and comparisons with previous methods are given.