Radiometric Errors in Complex Fourier Transform Spectrometry

A complex spectrum arises from the Fourier transform of an asymmetric interferogram. A rigorous derivation shows that the rms noise in the real part of that spectrum is indeed given by the commonly used relation (sigma) R = 2X xNEP /((eta) A (radikal) (omega) (radikal)TN ), where NEP is the delay-independent and uncorrelated detector noise-equivalent power per unit bandwidth, +/-X is the delay range measured with N samples averaging for a time (T) per sample, (eta) is the system optical efficiency, and A (omega) is the system throughput. A real spectrum produced by complex calibration with two complex reference spectra [Appl. Opt. 27, 3210 (1988) has a variance (sigma)L^2 = (sigma)R^2 + (sigma)c^2 (Lh - Ls )^2 /(Lh - Lc ) ^2 +(sigma)h^2 (Ls - Lc )^2 /(Lh - Lc )^2 , valid for(sigma)R ,(sigma)c , and (sigma)h small compared with Lh - Lc , where Ls , Lh , and Lc are scene, hot reference, and cold reference spectra, respectively, and (sgma)c and (sigma)h are the respective combined uncertainties in knowledge and measurement of the hot and cold reference spectra.