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 σR = 2X ×NEP/(ηAΩ τN), 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 τ per sample, η is the system optical efficiency, and AΩ is the system throughput. A real spectrum produced by complex calibration with two complex reference spectra [Appl. Opt.27, 3210 (1988)] has a variance σL2 = σR2 + σc2(Lh - Ls)2/(Lh - Lc)2 + σh2(Ls - Lc)2/(Lh - Lc)2, valid for σR, σc, and σh small compared with Lh - Lc, where Ls, Lh, and Lc are scene, hot reference, and cold reference spectra, respectively, and σc and σh are the respective combined uncertainties in knowledge and measurement of the hot and cold reference spectra.
© 2003 Optical Society of AmericaPDF Article