Radiometric errors in complex Fourier transform spectrometry

摘要

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 σ_(R)=2X×NEP/(ηAΩ(τN)~(1/2)), 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 σ_(L)~(2)=σ_(R)~(2)+σ_(c)~(2)(L_(h)-L_(s))~(2)/(L_(h)-L_(c))~(2)+σ_(h)~(2)(L_(s)-L_(c))~(2)/(L_(h)-L_(c))~(2), valid for σ_(R), σ_(c), and σ_(h) 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 σ_(c) and σ_(h) are the respective combined uncertainties in knowledge and measurement of the hot and cold reference spectra.