Abstract
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 ), 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 σL 2 = σR 2 + σc 2(L h - L s)2/(L h - L c)2 + σh 2(L s - L c)2/(L h - L c)2, valid for σR, σc, and σh small compared with L h - L c, where L s, L h, and L c 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 America
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