Passive remote sensing of pollutant clouds by Fourier-transform infrared spectrometry: signal-to-noise ratio as a function of spectral resolution

In a passive infrared remote sensing measurement, the spectral radiance difference caused by the presence of a pollutant cloud is proportional to the difference between the temperature of the cloud and the brightness temperature of the background (first-order approximation). In many cases, this difference is of the order of a few kelvins. Thus the measured signals are small, and the signal-to-noise ratio (SNR) is one of the most important quantities to be optimized in passive remote sensing. A model for the SNR resulting from passive remote sensing measurements with a Fourier-transform infrared spectrometer is presented. Analytical expressions for the SNR of a single Lorentzian line for the limiting cases of high and low spectral resolutions are derived. For constant measurement time the SNR increases with decreasing spectral resolution, i.e., low spectral resolutions yield the highest SNRs. For a single scan of the interferometer, a spectral resolution that maximizes the SNR exists. The calculated SNRs are in good agreement with the measured SNRs.