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 America
[Optical Society of America ]
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
Lawrence A. Sromovsky, "Radiometric Errors in Complex Fourier Transform Spectrometry," Appl. Opt. 42, 1779-1787 (2003)