## Radiometric Errors in Complex Fourier Transform Spectrometry

Applied Optics, Vol. 42, Issue 10, pp. 1779-1787 (2003)

http://dx.doi.org/10.1364/AO.42.001779

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### 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 ς_{R} = 2*X* ×NEP/(η*A*Ω√τ*N*), 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 *A*Ω 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.

© 2003 Optical Society of America

**OCIS Codes**

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation

**Citation**

Lawrence A. Sromovsky, "Radiometric Errors in Complex Fourier Transform Spectrometry," Appl. Opt. **42**, 1779-1787 (2003)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-42-10-1779

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