Signal-to-noise ratios of multiplexing spectrometers in high backgrounds

Signal-to-noise ratios and the amount of multiplexing gain achieved with a Michelson spectrometer during detector and background noise are studied. Noise caused by the warm background is found in 10 and 20-micron atmospheric windows in high resolution Fourier spectroscopy. An equation is derived for the signal-to-noise ratio based on the number of channels, total time to obtain the complete spectrum, the signal power in one spectral element, and the detector noise equivalent power in the presence of negligible background. Similar expressions are derived for backgrounds yielding a noise equivalent power to a spectral element, and backgrounds having flat spectra in the frequency range under investigation.