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Fellgett's advantage

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Fellgett's advantage or the multiplex advantage is an improvement in signal-to-noise ratio (SNR) that is gained when taking multiplexed measurements rather than direct measurements. The name is derived from P. B. Fellgett, who first made the observation as part of his PhD. When measuring a signal whose noise is dominated by detector noise, a multiplexed measurement such as the signal generated by a Fourier transform spectrometer can produce a relative improvement in SNR, compared to an equivalent scanning monochromator, of the order of the square root of m, where m is the number of sample points comprising the spectrum.

Exit slit

Sellar and Boreman have argued that this SNR improvement can be considered as a result of freedom from needing an exit slit inside the spectrometer, since an exit slit reduces the light collected by the detector by the same factor.

Emission

There is an additional multiplex advantage for emission lines of atomic and molecular spectra. At the peak of the emission line, a monochromator measurement will be noisy, since the noise is proportional to the square root of the signal. For the same reason, the measurement will be less noisy at the baseline of the spectrum. In a multiplexed measurement, however, the noise in a given measurement is spread more or less evenly across the spectrum, regardless of the local signal intensity. Thus, multiplexed measurements can achieve higher SNR at the emission line peaks. There is a corresponding multiplex disadvantage, however. When the signals of interest are absorption lines in the spectrum, then the same principle will produce increased noise at the valleys of the absorption lines relative to the noise of a scanning monochromator.

Shot noise

However, if the detector is shot noise dominated (which is typically the case for a photomultiplier tube), noise will be proportional to the square root of the power, so that for a broad flat spectrum the noise will be proportional to the square root of m, where m is the number of sample points comprising the spectrum, thus this disadvantage precisely offsets the Fellgett advantage. Shot noise is the main reason Fourier transform spectroscopy has never been popular for UV and visible light spectrometry.

See also

References

  1. P. B. Fellgett (1949). Theory of Infra-Red Sensitivities and its Application to Investigations of Stellar Radiation in the Near Infra-Red (PhD thesis).
  2. Fellgett, P. B. (1949). "On the Ultimate Sensitivity and Practical Performance of Radiation Detectors". J. Opt. Soc. Am. 39 (11): 970–6. doi:10.1364/JOSA.39.000970. ISSN 0030-3941. PMID 15407059.
  3. R. Glenn Sellar and Glenn D. Boreman (2005). "Comparison of relative signal-to-noise ratios of different classes of imaging spectrometer". Appl. Opt. 44 (9). OSA: 1614–1624. Bibcode:2005ApOpt..44.1614S. doi:10.1364/AO.44.001614. PMID 15813264.
  4. Stephen E. Bialkowski (1998). "Overcoming the multiplex disadvantage by using maximum-likelihood inversion". Applied Spectroscopy. 52 (4): 591–598. Bibcode:1998ApSpe..52..591B. doi:10.1366/0003702981943923. S2CID 54722734.
  5. Griffiths, Peter R.; James A. De Haseth (2007). "7.4.4 Shot noise". Fourier Transform Infrared Spectrometry. Chemical Analysis: A Series of Monographs on Analytical Chemistry and Its Applications. Vol. 171 (2nd ed.). Hoboken, New Jersey: John Wiley & Sons. pp. 170–171. ISBN 978-0-471-19404-0.
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