An analytical expression for the variance of the radiance measured by Fourier-transform infrared (FTIR) emission spectrometers exists only in the limit of low noise. Outside this limit, the variance needs to be calculated numerically. In addition, a criterion for low noise is needed to identify properly calibrated radiances and optimize the instrument bandwidth. In this work, the variance and the magnitude of a noise-dependent spectral bias are calculated as a function of the system responsivity (r) and the noise level in its estimate (sigma(r)). The criterion sigma(r)/r < 0.3, applied to downwelling and upwelling FTIR emission spectra, shows that the instrument bandwidth is specified properly for one instrument but needs to be restricted for another.
Rowe, Penny M., Steven P. Neshyba, and Von P. Walden. 2011. "Responsivity-based criterion for accurate calibration of FTIR emission spectra: theoretical development and bandwidth estimation." Optics Express 19(6): 5451-5463.