Responsivity-based criterion for accurate calibration of FTIR emission spectra: theoretical development and bandwidth estimation.

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 (σr). The criterion σr/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.