The invention relates to methods and systems for measuring and/or monitoring the chemical composition of a sample (e.g., a process stream), and/or detecting specific substances or compounds in a sample, using light spectroscopy such as absorption, emission and fluorescence spectroscopy. In certain embodiments, the invention relates to spectrometers with rotating narrow-band interference optical filter(s) to measure light intensity as a function of wavelength. More specifically, in certain embodiments, the invention relates to a spectrometer system with a rotatable filter assembly with a position detector rigidly attached thereto, and, in certain embodiments, the further use of various oversampling methods and techniques described herein, made particularly useful in conjunction with the rotatable filter assembly. In preferred embodiments, the rotatable filter is tilted with respect to the rotation axis, thereby providing surprisingly improved measurement stability and significantly improved control of the wavelength coverage of the filter spectrometer.