Array detector-based instruments are now fundamental to measurements of ozone and other atmospheric trace gases from space in the ultraviolet, visible, and infrared. The present generation of such instruments suffers, to a greater or lesser degree, from undersampling of the spectra, leading to difficulties in the analysis of atmospheric radiances. We provide extended analysis of the undersampling suffered by modern satellite spectrometers, which include the Global Ozone Monitoring Experiment, Scanning Imaging Absorption Spectrometer for Atmospheric Chartography, Ozone Monitoring Instrument, and Ozone Mapping and Profiler Suite. The analysis includes basic undersampling, the effects of binning into separate detector pixels, and the application of high-resolution Fraunhofer spectral data to correct for undersampling in many useful cases.