Fellgett's advantage or the multiplex advantage is an improvement in
signal-to-noise ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to noise power, often expressed in deci ...
(SNR) that is gained when taking
multiplexed
In telecommunications and computer networking, multiplexing (sometimes contracted to muxing) is a method by which multiple analog or digital signals are combined into one signal over a shared medium. The aim is to share a scarce resource— ...
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
A monochromator is an optics, optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input. The name is .
Uses
A device that can ...
, 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 ''dis''advantage, 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
Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process.
In electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in photon counting in optical devices, where s ...
dominated (which is typically the case for a
photomultiplier tube
Photomultiplier tubes (photomultipliers or PMTs for short) are extremely sensitive detectors of light in the ultraviolet, visible light, visible, and near-infrared ranges of the electromagnetic spectrum. They are members of the class of vacuum t ...
), 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
Fourier-transform spectroscopy (FTS) is a measurement technique whereby Spectrum (physics), spectra are collected based on measurements of the coherence (physics), coherence of a Radiation, radiative source, using time-domain or space-domain meas ...
has never been popular for UV and visible light spectrometry.
See also
*
Fourier transform infrared spectroscopy
Fourier transform infrared spectroscopy (FTIR) is a technique used to obtain an infrared Electromagnetic spectrum, spectrum of Absorption (electromagnetic radiation), absorption or Emission (electromagnetic radiation), emission of a solid, liquid, ...
*
Raman spectroscopy
Raman spectroscopy () (named after physicist C. V. Raman) is a Spectroscopy, spectroscopic technique typically used to determine vibrational modes of molecules, although rotational and other low-frequency modes of systems may also be observed. Ra ...
References
*{{cite book , last = Pelletier , first = Michael , title = Analytical applications of Raman spectroscopy , publisher =
Blackwell publishing
Wiley-Blackwell is an international scientific, technical, medical, and scholarly publishing business of John Wiley & Sons. It was formed by the merger of John Wiley & Sons Global Scientific, Technical, and Medical business with Blackwell Publis ...
, date= 1999 , page = 83 , isbn = 0-632-05305-4
Spectroscopy
Analytical chemistry