Fellgett's advantage

Last updated

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[ definition needed ] measurements. The name is derived from P. B. Fellgett, who first made the observation as part of his PhD. [1] 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. [2]

Contents

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. [3]

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. [4]

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. [5]

See also

Related Research Articles

Atomic absorption spectroscopy Type of spectroanalytical procedure

Atomic absorption spectroscopy (AAS) and atomic emission spectroscopy (AES) is a spectroanalytical procedure for the quantitative determination of chemical elements using the absorption of optical radiation (light) by free atoms in the gaseous state. Atomic absorption spectroscopy is based on absorption of light by free metallic ions.

Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It can be applied to a variety of types of spectroscopy including optical spectroscopy, infrared spectroscopy, nuclear magnetic resonance (NMR) and magnetic resonance spectroscopic imaging (MRSI), mass spectrometry and electron spin resonance spectroscopy.

Ultraviolet–visible spectroscopy Range of spectroscopic analysis

UV spectroscopy or UV–visible spectrophotometry refers to absorption spectroscopy or reflectance spectroscopy in part of the ultraviolet and the full, adjacent visible regions of the electromagnetic spectrum. Being relatively inexpensive and easily implemented, this methodology is widely used in diverse applied and fundamental applications. The only requirement is that the sample absorb in the UV-vis region, i.e. be a chromophore. Absorption spectroscopy is complementary to fluorescence spectroscopy. Parameters of interest, besides the wavelength of measurement, are absorbance (A) or Transmittance (%T) or Reflectance (%R), and its change with time.

X-ray fluorescence Emission of secondary X-rays from a material excited by high-energy X-rays

X-ray fluorescence (XRF) is the emission of characteristic "secondary" X-rays from a material that has been excited by being bombarded with high-energy X-rays or gamma rays. The phenomenon is widely used for elemental analysis and chemical analysis, particularly in the investigation of metals, glass, ceramics and building materials, and for research in geochemistry, forensic science, archaeology and art objects such as paintings.

Spectrum analyzer Electronic testing device

A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most common spectrum analyzers measure is electrical; however, spectral compositions of other signals, such as acoustic pressure waves and optical light waves, can be considered through the use of an appropriate transducer. Spectrum analyzers for other types of signals also exist, such as optical spectrum analyzers which use direct optical techniques such as a monochromator to make measurements.

Absorption spectroscopy Spectroscopic techniques that measure the absorption of radiation

Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating field. The intensity of the absorption varies as a function of frequency, and this variation is the absorption spectrum. Absorption spectroscopy is performed across the electromagnetic spectrum.

Fluorescence spectroscopy Type of electromagnetic spectroscopy

Fluorescence spectroscopy is a type of electromagnetic spectroscopy that analyzes fluorescence from a sample. It involves using a beam of light, usually ultraviolet light, that excites the electrons in molecules of certain compounds and causes them to emit light; typically, but not necessarily, visible light. A complementary technique is absorption spectroscopy. In the special case of single molecule fluorescence spectroscopy, intensity fluctuations from the emitted light are measured from either single fluorophores, or pairs of fluorophores.

A spectroradiometer is a light measurement tool that is able to measure both the wavelength and amplitude of the light emitted from a light source. Spectrometers discriminate the wavelength based on the position the light hits at the detector array allowing the full spectrum to be obtained with a single acquisition. Most spectrometers have a base measurement of counts which is the un-calibrated reading and is thus impacted by the sensitivity of the detector to each wavelength. By applying a calibration, the spectrometer is then able to provide measurements of spectral irradiance, spectral radiance and/or spectral flux. This data is also then used with built in or PC software and numerous algorithms to provide readings or Irradiance (W/cm2), Illuminance, Radiance (W/sr), Luminance (cd), Flux, Chromaticity, Color Temperature, Peak and Dominant Wavelength. Some more complex spectrometer software packages also allow calculation of PAR μmol/m2/s, Metamerism, and candela calculations based on distance and include features like 2- and 20-degree observer, baseline overlay comparisons, transmission and reflectance.

Gamma-ray spectroscopy is the quantitative study of the energy spectra of gamma-ray sources, such as in the nuclear industry, geochemical investigation, and astrophysics.

A spectrofluorometer is an instrument which takes advantage of fluorescent properties of some compounds in order to provide information regarding their concentration and chemical environment in a sample. A certain excitation wavelength is selected, and the emission is observed either at a single wavelength, or a scan is performed to record the intensity versus wavelength, also called an emission spectrum. The instrument is used in fluorescence spectroscopy.

Graphite furnace atomic absorption spectroscopy (GFAAS) is a type of spectrometry that uses a graphite-coated furnace to vaporize the sample. Briefly, the technique is based on the fact that free atoms will absorb light at frequencies or wavelengths characteristic of the element of interest. Within certain limits, the amount of light absorbed can be linearly correlated to the concentration of analyte present. Free atoms of most elements can be produced from samples by the application of high temperatures. In GFAAS, samples are deposited in a small graphite or pyrolytic carbon coated graphite tube, which can then be heated to vaporize and atomize the analyte. The atoms absorb ultraviolet or visible light and make transitions to higher electronic energy levels. Applying the Beer-Lambert law directly in AA spectroscopy is difficult due to variations in the atomization efficiency from the sample matrix, and nonuniformity of concentration and path length of analyte atoms. Concentration measurements are usually determined from a working curve after calibrating the instrument with standards of known concentration. The main advantages of the graphite furnace comparing to aspiration atomic absorption are the following:

Attenuated total reflectance Infrared spectroscopy sampling technique

Attenuated total reflection (ATR) is a sampling technique used in conjunction with infrared spectroscopy which enables samples to be examined directly in the solid or liquid state without further preparation.

Time-of-flight mass spectrometry Method of mass spectrometry

Time-of-flight mass spectrometry (TOFMS) is a method of mass spectrometry in which an ion's mass-to-charge ratio is determined by a time of flight measurement. Ions are accelerated by an electric field of known strength. This acceleration results in an ion having the same kinetic energy as any other ion that has the same charge. The velocity of the ion depends on the mass-to-charge ratio. The time that it subsequently takes for the ion to reach a detector at a known distance is measured. This time will depend on the velocity of the ion, and therefore is a measure of its mass-to-charge ratio. From this ratio and known experimental parameters, one can identify the ion.

Optical heterodyne detection is a method of extracting information encoded as modulation of the phase, frequency or both of electromagnetic radiation in the wavelength band of visible or infrared light. The light signal is compared with standard or reference light from a "local oscillator" (LO) that would have a fixed offset in frequency and phase from the signal if the latter carried null information. "Heterodyne" signifies more than one frequency, in contrast to the single frequency employed in homodyne detection.

Atomic emission spectroscopy Analytical method using radiation to identify chemical elements in a sample

Atomic emission spectroscopy (AES) is a method of chemical analysis that uses the intensity of light emitted from a flame, plasma, arc, or spark at a particular wavelength to determine the quantity of an element in a sample. The wavelength of the atomic spectral line in the emission spectrum gives the identity of the element while the intensity of the emitted light is proportional to the number of atoms of the element. The sample may be excited by various methods.

Fourier-transform infrared spectroscopy Technique to analyze the infrared spectrum of matter

Fourier-transform infrared spectroscopy (FTIR) is a technique used to obtain an infrared spectrum of absorption or emission of a solid, liquid or gas. An FTIR spectrometer simultaneously collects high-resolution spectral data over a wide spectral range. This confers a significant advantage over a dispersive spectrometer, which measures intensity over a narrow range of wavelengths at a time.

Angle-resolved low-coherence interferometry (a/LCI) is an emerging biomedical imaging technology which uses the properties of scattered light to measure the average size of cell structures, including cell nuclei. The technology shows promise as a clinical tool for in situ detection of dysplastic, or precancerous tissue.

Incoherent broad band cavity enhanced absorption spectroscopy (IBBCEAS), sometimes called broadband cavity enhanced extinction spectroscopy (IBBCEES), measures the transmission of light intensity through a stable optical cavity consisting of high reflectance mirrors. The technique is realized using incoherent sources of radiation e.g. Xenon arc lamps, LEDs or supercontinuum (SC) lasers, hence the name.

Stationary-wave integrated Fourier-transform spectrometry (SWIFTS), or standing-wave integrated Fourier-transform spectrometry, is an analytical technique used for measuring the distribution of light across an optical spectrum. SWIFTS technology is based on a near-field Lippmann architecture. An optical signal is injected into a waveguide and ended by a mirror. The input signal interferes with the reflected signal, creating a standing, or stationary, wave.

Peter Berners Fellgett FRS, FIEE was a British physicist. He was the professor of Cybernetics at the University of Reading.

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. OSA. 44 (9): 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.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.