Error in FTIR spectrometer radiances due to noise at high levels

A significant contribution to error in calibrated spectra measured by Fourier transform IR spectrometers is random noise in uncalibrated spectra of the scene and hot and cold calibration sources (with standard deviations σ_s, σ_h and σ_c). For low noise, the well-known equation for the variance in the calibrated radiance (σ_L²) is related simply to σ_s, σ_h, σ_c and the instrument responsivity (r). An estimate of σ_L² is needed at higher noise levels for setting a practical limit for the low noise threshold and for measurements that exceed it. Additionally, a criterion is needed for rejection of spectral data points having unacceptably large errors. Such errors can occur at wavenumbers where the absorption coefficient is so strong that trace gases between source and detector absorb and re-emit all source radiation. The expression for the error in the calibrated spectrum is found to have a singularity for a particular pair of uncalibrated source-spectrum errors, making σ_L² infinite; the median error is suggested as an alternative. Errors and biases in calibrated radiances at high noise levels are shown for two FTIR instruments used for atmospheric radiation measurements: the Atmospheric Emitted Radiance Interferometer (AERI) and the Interferometric Monitor for Greenhouse Gases (IMG). A criterion (σ_r/r < 0.3) is suggested for identification of spectral data points having unacceptably large errors and is applied to AERI data.