Fourier-transform infrared spectroscopy

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Fourier-transform_infrared_spectroscopy

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.

The term Fourier transform infrared spectroscopy originates from the fact that a Fourier transform (a mathematical process) is required to convert the raw data into the actual spectrum.

An example of an FTIR spectrometer with an attenuated total reflectance (ATR) attachment

Conceptual introduction

An FTIR interferogram. The central peak is at the ZPD position ("zero path difference" or zero retardation), where the maximal amount of light passes through the interferometer to the detector.

The goal of absorption spectroscopy techniques (FTIR, ultraviolet-visible ("UV-vis") spectroscopy, etc.) is to measure how much light a sample absorbs at each wavelength. The most straightforward way to do this, the "dispersive spectroscopy" technique, is to shine a monochromatic light beam at a sample, measure how much of the light is absorbed, and repeat for each different wavelength. (This is how some UV–vis spectrometers work, for example.)

Fourier transform spectroscopy is a less intuitive way to obtain the same information. Rather than shining a monochromatic beam of light (a beam composed of only a single wavelength) at the sample, this technique shines a beam containing many frequencies of light at once and measures how much of that beam is absorbed by the sample. Next, the beam is modified to contain a different combination of frequencies, giving a second data point. This process is rapidly repeated many times over a short time span. Afterwards, a computer takes all this data and works backward to infer what the absorption is at each wavelength.

The beam described above is generated by starting with a broadband light source—one containing the full spectrum of wavelengths to be measured. The light shines into a Michelson interferometer—a certain configuration of mirrors, one of which is moved by a motor. As this mirror moves, each wavelength of light in the beam is periodically blocked, transmitted, blocked, transmitted, by the interferometer, due to wave interference. Different wavelengths are modulated at different rates, so that at each moment or mirror position the beam coming out of the interferometer has a different spectrum.

As mentioned, computer processing is required to turn the raw data (light absorption for each mirror position) into the desired result (light absorption for each wavelength). The processing required turns out to be a common algorithm called the Fourier transform. The Fourier transform converts one domain (in this case displacement of the mirror in cm) into its inverse domain (wavenumbers in cm⁻¹). The raw data is called an "interferogram".

History

The first low-cost spectrophotometer capable of recording an infrared spectrum was the Perkin-Elmer Infracord produced in 1957. This instrument covered the wavelength range from 2.5 μm to 15 μm (wavenumber range 4,000 cm⁻¹ to 660 cm⁻¹). The lower wavelength limit was chosen to encompass the highest known vibration frequency due to a fundamental molecular vibration. The upper limit was imposed by the fact that the dispersing element was a prism made from a single crystal of rock-salt (sodium chloride), which becomes opaque at wavelengths longer than about 15 μm; this spectral region became known as the rock-salt region. Later instruments used potassium bromide prisms to extend the range to 25 μm (400 cm⁻¹) and caesium iodide 50 μm (200 cm⁻¹). The region beyond 50 μm (200 cm⁻¹) became known as the far-infrared region; at very long wavelengths it merges into the microwave region. Measurements in the far infrared needed the development of accurately ruled diffraction gratings to replace the prisms as dispersing elements, since salt crystals are opaque in this region. More sensitive detectors than the bolometer were required because of the low energy of the radiation. One such was the Golay detector. An additional issue is the need to exclude atmospheric water vapour because water vapour has an intense pure rotational spectrum in this region. Far-infrared spectrophotometers were cumbersome, slow and expensive. The advantages of the Michelson interferometer were well-known, but considerable technical difficulties had to be overcome before a commercial instrument could be built. Also an electronic computer was needed to perform the required Fourier transform, and this only became practicable with the advent of minicomputers, such as the PDP-8, which became available in 1965. Digilab pioneered the world's first commercial FTIR spectrometer (Model FTS-14) in 1969. Digilab FTIRs are now a part of Agilent Technologies's molecular product line after Agilent acquired spectroscopy business from Varian.

Michelson interferometer

Main article: Michelson interferometer

Schematic diagram of a Michelson interferometer, configured for FTIR

In a Michelson interferometer adapted for FTIR, light from the polychromatic infrared source, approximately a black-body radiator, is collimated and directed to a beam splitter. Ideally 50% of the light is refracted towards the fixed mirror and 50% is transmitted towards the moving mirror. Light is reflected from the two mirrors back to the beam splitter and some fraction of the original light passes into the sample compartment. There, the light is focused on the sample. On leaving the sample compartment the light is refocused on to the detector. The difference in optical path length between the two arms to the interferometer is known as the retardation or optical path difference (OPD). An interferogram is obtained by varying the retardation and recording the signal from the detector for various values of the retardation. The form of the interferogram when no sample is present depends on factors such as the variation of source intensity and splitter efficiency with wavelength. This results in a maximum at zero retardation, when there is constructive interference at all wavelengths, followed by series of "wiggles". The position of zero retardation is determined accurately by finding the point of maximum intensity in the interferogram. When a sample is present the background interferogram is modulated by the presence of absorption bands in the sample.

Commercial spectrometers use Michelson interferometers with a variety of scanning mechanisms to generate the path difference. Common to all these arrangements is the need to ensure that the two beams recombine exactly as the system scans. The simplest systems have a plane mirror that moves linearly to vary the path of one beam. In this arrangement the moving mirror must not tilt or wobble as this would affect how the beams overlap as they recombine. Some systems incorporate a compensating mechanism that automatically adjusts the orientation of one mirror to maintain the alignment. Arrangements that avoid this problem include using cube corner reflectors instead of plane mirrors as these have the property of returning any incident beam in a parallel direction regardless of orientation.

Interferometer schematics where the path difference is generated by a rotary motion.

Systems where the path difference is generated by a rotary movement have proved very successful. One common system incorporates a pair of parallel mirrors in one beam that can be rotated to vary the path without displacing the returning beam. Another is the double pendulum design where the path in one arm of the interferometer increases as the path in the other decreases.

A quite different approach involves moving a wedge of an IR-transparent material such as KBr into one of the beams. Increasing the thickness of KBr in the beam increases the optical path because the refractive index is higher than that of air. One limitation of this approach is that the variation of refractive index over the wavelength range limits the accuracy of the wavelength calibration.

Measuring and processing the interferogram

The interferogram has to be measured from zero path difference to a maximum length that depends on the resolution required. In practice the scan can be on either side of zero resulting in a double-sided interferogram. Mechanical design limitations may mean that for the highest resolution the scan runs to the maximum OPD on one side of zero only.

The interferogram is converted to a spectrum by Fourier transformation. This requires it to be stored in digital form as a series of values at equal intervals of the path difference between the two beams. To measure the path difference a laser beam is sent through the interferometer, generating a sinusoidal signal where the separation between successive maxima is equal to the wavelength of the laser (typically a 633 nm HeNe laser is used). This can trigger an analog-to-digital converter to measure the IR signal each time the laser signal passes through zero. Alternatively, the laser and IR signals can be measured synchronously at smaller intervals with the IR signal at points corresponding to the laser signal zero crossing being determined by interpolation. This approach allows the use of analog-to-digital converters that are more accurate and precise than converters that can be triggered, resulting in lower noise.

Values of the interferogram at times corresponding to zero crossings of the laser signal are found by interpolation.

The result of Fourier transformation is a spectrum of the signal at a series of discrete wavelengths. The range of wavelengths that can be used in the calculation is limited by the separation of the data points in the interferogram. The shortest wavelength that can be recognized is twice the separation between these data points. For example, with one point per wavelength of a HeNe reference laser at 0.633 μm (15800 cm⁻¹) the shortest wavelength would be 1.266 μm (7900 cm⁻¹). Because of aliasing, any energy at shorter wavelengths would be interpreted as coming from longer wavelengths and so has to be minimized optically or electronically. The spectral resolution, i.e. the separation between wavelengths that can be distinguished, is determined by the maximum OPD. The wavelengths used in calculating the Fourier transform are such that an exact number of wavelengths fit into the length of the interferogram from zero to the maximum OPD as this makes their contributions orthogonal. This results in a spectrum with points separated by equal frequency intervals.

For a maximum path difference d adjacent wavelengths λ₁ and λ₂ will have n and (n+1) cycles, respectively, in the interferogram. The corresponding frequencies are ν₁ and ν₂:

d = nλ1	and d = (n+1)λ2
λ1 = d/n	and λ2 =d/(n+1)
ν1 = 1/λ1	and ν2 = 1/λ2
ν1 = n/d	and ν2 = (n+1)/d
ν2 − ν1 = 1/d

The separation is the inverse of the maximum OPD. For example, a maximum OPD of 2 cm results in a separation of 0.5 cm⁻¹. This is the spectral resolution in the sense that the value at one point is independent of the values at adjacent points. Most instruments can be operated at different resolutions by choosing different OPD's. Instruments for routine analyses typically have a best resolution of around 0.5 cm⁻¹, while spectrometers have been built with resolutions as high as 0.001 cm⁻¹, corresponding to a maximum OPD of 10 m. The point in the interferogram corresponding to zero path difference has to be identified, commonly by assuming it is where the maximum signal occurs. This so-called centerburst is not always symmetrical in real world spectrometers so a phase correction may have to be calculated. The interferogram signal decays as the path difference increases, the rate of decay being inversely related to the width of features in the spectrum. If the OPD is not large enough to allow the interferogram signal to decay to a negligible level there will be unwanted oscillations or sidelobes associated with the features in the resulting spectrum. To reduce these sidelobes the interferogram is usually multiplied by a function that approaches zero at the maximum OPD. This so-called apodization reduces the amplitude of any sidelobes and also the noise level at the expense of some reduction in resolution.

For rapid calculation the number of points in the interferogram has to equal a power of two. A string of zeroes may be added to the measured interferogram to achieve this. More zeroes may be added in a process called zero filling to improve the appearance of the final spectrum although there is no improvement in resolution. Alternatively, interpolation after the Fourier transform gives a similar result.

Advantages

There are three principal advantages for an FT spectrometer compared to a scanning (dispersive) spectrometer.^[1]

1. The multiplex or Fellgett's advantage (named after Peter Fellgett). This arises from the fact that information from all wavelengths is collected simultaneously. It results in a higher signal-to-noise ratio for a given scan-time for observations limited by a fixed detector noise contribution (typically in the thermal infrared spectral region where a photodetector is limited by generation-recombination noise). For a spectrum with m resolution elements, this increase is equal to the square root of m. Alternatively, it allows a shorter scan-time for a given resolution. In practice multiple scans are often averaged, increasing the signal-to-noise ratio by the square root of the number of scans.
2. The throughput or Jacquinot's advantage (named after Pierre Jacquinot). This results from the fact that in a dispersive instrument, the monochromator has entrance and exit slits which restrict the amount of light that passes through it. The interferometer throughput is determined only by the diameter of the collimated beam coming from the source. Although no slits are needed, FTIR spectrometers do require an aperture to restrict the convergence of the collimated beam in the interferometer. This is because convergent rays are modulated at different frequencies as the path difference is varied. Such an aperture is called a Jacquinot stop. For a given resolution and wavelength this circular aperture allows more light through than a slit, resulting in a higher signal-to-noise ratio.
3. The wavelength accuracy or Connes' advantage (named after Janine Connes). The wavelength scale is calibrated by a laser beam of known wavelength that passes through the interferometer. This is much more stable and accurate than in dispersive instruments where the scale depends on the mechanical movement of diffraction gratings. In practice, the accuracy is limited by the divergence of the beam in the interferometer which depends on the resolution.

Another minor advantage is less sensitivity to stray light, that is radiation of one wavelength appearing at another wavelength in the spectrum. In dispersive instruments, this is the result of imperfections in the diffraction gratings and accidental reflections. In FT instruments there is no direct equivalent as the apparent wavelength is determined by the modulation frequency in the interferometer.

Resolution

The interferogram belongs in the length dimension. Fourier transform (FT) inverts the dimension, so the FT of the interferogram belongs in the reciprocal length dimension([L⁻¹]), that is the dimension of wavenumber. The spectral resolution in cm⁻¹ is equal to the reciprocal of the maximal retardation in cm. Thus a 4 cm⁻¹ resolution will be obtained if the maximal retardation is 0.25 cm; this is typical of the cheaper FTIR instruments. Much higher resolution can be obtained by increasing the maximal retardation. This is not easy, as the moving mirror must travel in a near-perfect straight line. The use of corner-cube mirrors in place of the flat mirrors is helpful, as an outgoing ray from a corner-cube mirror is parallel to the incoming ray, regardless of the orientation of the mirror about axes perpendicular to the axis of the light beam.

A spectrometer with 0.001 cm⁻¹ resolution is now available commercially. The throughput advantage is important for high-resolution FTIR, as the monochromator in a dispersive instrument with the same resolution would have very narrow entrance and exit slits.

In 1966 Janine Connes measured the temperature of the atmosphere of Venus by recording the vibration-rotation spectrum of Venusian CO₂ at 0.1 cm⁻¹ resolution. Michelson himself attempted to resolve the hydrogen H_α emission band in the spectrum of a hydrogen atom into its two components by using his interferometer.

Motivation

FTIR is a method of measuring infrared absorption and emission spectra. For a discussion of why people measure infrared absorption and emission spectra, i.e. why and how substances absorb and emit infrared light, see the article: Infrared spectroscopy.

Components

FTIR setup. The sample is placed right before the detector.

IR sources

FTIR spectrometers are mostly used for measurements in the mid and near IR regions. For the mid-IR region, 2−25 μm (5,000–400 cm⁻¹), the most common source is a silicon carbide (SiC) element heated to about 1,200 K (930 °C; 1,700 °F) (Globar). The output is similar to a blackbody. Shorter wavelengths of the near-IR, 1−2.5 μm (10,000–4,000 cm⁻¹), require a higher temperature source, typically a tungsten-halogen lamp. The long wavelength output of these is limited to about 5 μm (2,000 cm⁻¹) by the absorption of the quartz envelope. For the far-IR, especially at wavelengths beyond 50 μm (200 cm⁻¹) a mercury discharge lamp gives higher output than a thermal source.

Detectors

Far-IR spectrometers commonly use pyroelectric detectors that respond to changes in temperature as the intensity of IR radiation falling on them varies. The sensitive elements in these detectors are either deuterated triglycine sulfate (DTGS) or lithium tantalate (LiTaO₃). These detectors operate at ambient temperatures and provide adequate sensitivity for most routine applications. To achieve the best sensitivity the time for a scan is typically a few seconds. Cooled photoelectric detectors are employed for situations requiring higher sensitivity or faster response. Liquid nitrogen cooled mercury cadmium telluride (MCT) detectors are the most widely used in the mid-IR. With these detectors an interferogram can be measured in as little as 10 milliseconds. Uncooled indium gallium arsenide photodiodes or DTGS are the usual choices in near-IR systems. Very sensitive liquid-helium-cooled silicon or germanium bolometers are used in the far-IR where both sources and beamsplitters are inefficient.

Beam splitter

Simple interferometer with a beam-splitter and compensator plate

An ideal beam-splitter transmits and reflects 50% of the incident radiation. However, as any material has a limited range of optical transmittance, several beam-splitters may be used interchangeably to cover a wide spectral range.

In a simple Michelson interferometer, one beam passes twice through the beamsplitter but the other passes through only once. To correct for this, an additional compensator plate of equal thickness is incorporated.

For the mid-IR region, the beamsplitter is usually made of KBr with a germanium-based coating that makes it semi-reflective. KBr absorbs strongly at wavelengths beyond 25 μm (400 cm⁻¹), so CsI or KRS-5 are sometimes used to extend the range to about 50 μm (200 cm⁻¹). ZnSe is an alternative where moisture vapour can be a problem, but is limited to about 20 μm (500 cm⁻¹).

CaF₂ is the usual material for the near-IR, being both harder and less sensitive to moisture than KBr, but cannot be used beyond about 8 μm (1,200 cm⁻¹).

Far-IR beamsplitters are mostly based on polymer films, and cover a limited wavelength range.

Attenuated total reflectance

Main article: Attenuated total reflectance

Attenuated total reflectance (ATR) is one accessory of FTIR spectrophotometer to measure surface properties of solid or thin film samples rather than their bulk properties. Generally, ATR has a penetration depth of around 1 or 2 micrometers depending on sample conditions.

Fourier transform

The interferogram in practice consists of a set of intensities measured for discrete values of retardation. The difference between successive retardation values is constant. Thus, a discrete Fourier transform is needed. The fast Fourier transform (FFT) algorithm is used.

Spectral range

Far-infrared

The first FTIR spectrometers were developed for far-infrared range. The reason for this has to do with the mechanical tolerance needed for good optical performance, which is related to the wavelength of the light being used. For the relatively long wavelengths of the far infrared, ~10 μm tolerances are adequate, whereas for the rock-salt region tolerances have to be better than 1 μm. A typical instrument was the cube interferometer developed at the NPL and marketed by Grubb Parsons. It used a stepper motor to drive the moving mirror, recording the detector response after each step was completed.

Mid-infrared

With the advent of cheap microcomputers it became possible to have a computer dedicated to controlling the spectrometer, collecting the data, doing the Fourier transform and presenting the spectrum. This provided the impetus for the development of FTIR spectrometers for the rock-salt region. The problems of manufacturing ultra-high precision optical and mechanical components had to be solved. A wide range of instruments are now available commercially. Although instrument design has become more sophisticated, the basic principles remain the same. Nowadays, the moving mirror of the interferometer moves at a constant velocity, and sampling of the interferogram is triggered by finding zero-crossings in the fringes of a secondary interferometer lit by a helium–neon laser. In modern FTIR systems the constant mirror velocity is not strictly required, as long as the laser fringes and the original interferogram are recorded simultaneously with higher sampling rate and then re-interpolated on a constant grid, as pioneered by James W. Brault. This confers very high wavenumber accuracy on the resulting infrared spectrum and avoids wavenumber calibration errors.

Near-infrared

Main article: Near-infrared spectroscopy

The near-infrared region spans the wavelength range between the rock-salt region and the start of the visible region at about 750 nm. Overtones of fundamental vibrations can be observed in this region. It is used mainly in industrial applications such as process control and chemical imaging.

Applications

FTIR can be used in all applications where a dispersive spectrometer was used in the past (see external links). In addition, the improved sensitivity and speed have opened up new areas of application. Spectra can be measured in situations where very little energy reaches the detector. Fourier transform infrared spectroscopy is used in geology, chemistry, materials, botany and biology research fields.

Nano and biological materials

FTIR is also used to investigate various nanomaterials and proteins in hydrophobic membrane environments. Studies show the ability of FTIR to directly determine the polarity at a given site along the backbone of a transmembrane protein. The bond features involved with various organic and inorganic nanomaterials and their quantitative analysis can be done with the help of FTIR.

Microscopy and imaging

An infrared microscope allows samples to be observed and spectra measured from regions as small as 5 microns across. Images can be generated by combining a microscope with linear or 2-D array detectors. The spatial resolution can approach 5 microns with tens of thousands of pixels. The images contain a spectrum for each pixel and can be viewed as maps showing the intensity at any wavelength or combination of wavelengths. This allows the distribution of different chemical species within the sample to be seen. This technique has been applied in various biological applications including the analysis of tissue sections as an alternative to conventional histopathology, examining the homogeneity of pharmaceutical tablets, and for differentiating morphologically-similar pollen grains.

Nanoscale and spectroscopy below the diffraction limit

The spatial resolution of FTIR can be further improved below the micrometer scale by integrating it into scanning near-field optical microscopy platform. The corresponding technique is called nano-FTIR and allows for performing broadband spectroscopy on materials in ultra-small quantities (single viruses and protein complexes) and with 10 to 20 nm spatial resolution.

FTIR as detector in chromatography

The speed of FTIR allows spectra to be obtained from compounds as they are separated by a gas chromatograph. However this technique is little used compared to GC-MS (gas chromatography-mass spectrometry) which is more sensitive. The GC-IR method is particularly useful for identifying isomers, which by their nature have identical masses. Liquid chromatography fractions are more difficult because of the solvent present. One notable exception is to measure chain branching as a function of molecular size in polyethylene using gel permeation chromatography, which is possible using chlorinated solvents that have no absorption in the area in question.

TG-IR (thermogravimetric analysis-infrared spectrometry)

Measuring the gas evolved as a material is heated allows qualitative identification of the species to complement the purely quantitative information provided by measuring the weight loss.

Water content determination in plastics and composites

FTIR analysis is used to determine water content in fairly thin plastic and composite parts, more commonly in the laboratory setting. Such FTIR methods have long been used for plastics, and became extended for composite materials in 2018, when the method was introduced by Krauklis, Gagani and Echtermeyer. FTIR method uses the maxima of the absorbance band at about 5,200 cm−1 which correlates with the true water content in the material.

Near-infrared spectroscopy

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Near-infrared_spectroscopy 

Near-IR absorption spectrum of dichloromethane showing complicated overlapping overtones of mid IR absorption features.

Near-infrared spectroscopy (NIRS) is a spectroscopic method that uses the near-infrared region of the electromagnetic spectrum (from 780 nm to 2500 nm). Typical applications include medical and physiological diagnostics and research including blood sugar, pulse oximetry, functional neuroimaging, sports medicine, elite sports training, ergonomics, rehabilitation, neonatal research, brain computer interface, urology (bladder contraction), and neurology (neurovascular coupling). There are also applications in other areas as well such as pharmaceutical, food and agrochemical quality control, atmospheric chemistry, combustion propagation.

Theory

Near-infrared spectroscopy is based on molecular overtone and combination vibrations. Overtones and combinations exhibit lower intensity compared to the fundamental, as a result, the molar absorptivity in the near-IR region is typically quite small. (NIR absorption bands are typically 10–100 times weaker than the corresponding fundamental mid-IR absorption band.) The lower absorption allows NIR radiation to penetrate much further into a sample than mid infrared radiation. Near-infrared spectroscopy is, therefore, not a particularly sensitive technique, but it can be very useful in probing bulk material with little to no sample preparation.

The molecular overtone and combination bands seen in the near-IR are typically very broad, leading to complex spectra; it can be difficult to assign specific features to specific chemical components. Multivariate (multiple variables) calibration techniques (e.g., principal components analysis, partial least squares, or artificial neural networks) are often employed to extract the desired chemical information. Careful development of a set of calibration samples and application of multivariate calibration techniques is essential for near-infrared analytical methods.

History

Near-infrared spectrum of liquid ethanol.

The discovery of near-infrared energy is ascribed to William Herschel in the 19th century, but the first industrial application began in the 1950s. In the first applications, NIRS was used only as an add-on unit to other optical devices that used other wavelengths such as ultraviolet (UV), visible (Vis), or mid-infrared (MIR) spectrometers. In the 1980s, a single-unit, stand-alone NIRS system was made available.

In the 1980s, Karl Norris (while working at the USDA Instrumentation Research Laboratory, Beltsville, USA) pioneered the use NIR spectroscopy for quality assessments of agricultural products. Since then, use has expanded from food and agricultural to chemical, polymer, and petroleum industries; pharmaceutical industry; biomedical sciences; and environmental analysis.

With the introduction of light-fiber optics in the mid-1980s and the monochromator-detector developments in the early 1990s, NIRS became a more powerful tool for scientific research. The method has been used in a number of fields of science including physics, physiology, or medicine. It is only in the last few decades that NIRS began to be used as a medical tool for monitoring patients, with the first clinical application of so-called fNIRS in 1994.

Instrumentation

Instrumentation for near-IR (NIR) spectroscopy is similar to instruments for the UV-visible and mid-IR ranges. There is a source, a detector, and a dispersive element (such as a prism, or, more commonly, a diffraction grating) to allow the intensity at different wavelengths to be recorded. Fourier transform NIR instruments using an interferometer are also common, especially for wavelengths above ~1000 nm. Depending on the sample, the spectrum can be measured in either reflection or transmission.

Common incandescent or quartz halogen light bulbs are most often used as broadband sources of near-infrared radiation for analytical applications. Light-emitting diodes (LEDs) can also be used. For high precision spectroscopy, wavelength-scanned lasers and frequency combs have recently become powerful sources, albeit with sometimes longer acquisition timescales. When lasers are used, a single detector without any dispersive elements might be sufficient.

The type of detector used depends primarily on the range of wavelengths to be measured. Silicon-based CCDs are suitable for the shorter end of the NIR range, but are not sufficiently sensitive over most of the range (over 1000 nm). InGaAs and PbS devices are more suitable and have higher quantum efficiency for wavelengths above 1100 nm. It is possible to combine silicon-based and InGaAs detectors in the same instrument. Such instruments can record both UV-visible and NIR spectra 'simultaneously'.

Instruments intended for chemical imaging in the NIR may use a 2D array detector with an acousto-optic tunable filter. Multiple images may be recorded sequentially at different narrow wavelength bands.

Many commercial instruments for UV/vis spectroscopy are capable of recording spectra in the NIR range (to perhaps ~900 nm). In the same way, the range of some mid-IR instruments may extend into the NIR. In these instruments, the detector used for the NIR wavelengths is often the same detector used for the instrument's "main" range of interest.

NIRS as an analytical technique

The use of NIR as an analytical technique did not come from extending the use of mid-IR into the near-IR range, but developed independently. A striking way this was exhibited is that, while mid-IR spectroscopists use wavenumbers (cm⁻¹) when displaying spectra, NIR spectroscopists used wavelength (nm), as is used in ultraviolet–visible spectroscopy. Early practitioners of IR spectroscopy, who depended on assignment of absorption bands to specific bond types, were frustrated by the complexity of the bonding regions being measured. However, as a quantitative tool, the lower molar absorption levels in the bonding region tended to keep absorption maxima "on-scale", enabling quantitative work with little sample preparation. Techniques applied to extract the quantitative information from these complex spectra were unfamiliar to analytical chemists, and the technique was viewed with suspicion in academia.

Generally, quantitative NIR analysis is accomplished by selecting a group of calibration samples, for which the concentration of the analyte of interest has been determined by a reference method, and finding a correlation between various spectral features and those concentrations using a chemometric tool. The calibration is then validated by using it to predict the analyte values for samples in a validation set, whose values have been determined by the reference method but have not been included in the calibration. A validated calibration is then used to predict the values of samples. The complexity of the spectra are overcome by the use of multivariate calibration. The two tools most often used a multi-wavelength linear regression and partial least squares.

Applications

Typical applications of NIR spectroscopy include the analysis of food products, pharmaceuticals, combustion products, and a major branch of astronomical spectroscopy.

Astronomical spectroscopy

Near-infrared spectroscopy is used in astronomy for studying the atmospheres of cool stars where molecules can form. The vibrational and rotational signatures of molecules such as titanium oxide, cyanide, and carbon monoxide can be seen in this wavelength range and can give a clue towards the star's spectral type. It is also used for studying molecules in other astronomical contexts, such as in molecular clouds where new stars are formed. The astronomical phenomenon known as reddening means that near-infrared wavelengths are less affected by dust in the interstellar medium, such that regions inaccessible by optical spectroscopy can be studied in the near-infrared. Since dust and gas are strongly associated, these dusty regions are exactly those where infrared spectroscopy is most useful. The near-infrared spectra of very young stars provide important information about their ages and masses, which is important for understanding star formation in general. Astronomical spectrographs have also been developed for the detection of exoplanets using the Doppler shift of the parent star due to the radial velocity of the planet around the star.

Agriculture

Near-infrared spectroscopy is widely applied in agriculture for determining the quality of forages, grains, and grain products, oilseeds, coffee, tea, spices, fruits, vegetables, sugarcane, beverages, fats, and oils, dairy products, eggs, meat, and other agricultural products. It is widely used to quantify the composition of agricultural products because it meets the criteria of being accurate, reliable, rapid, non-destructive, and inexpensive. Abeni and Bergoglio 2001 apply NIRS to chicken breeding as the assay method for characteristics of fat composition.

Remote monitoring

Techniques have been developed for NIR spectroscopic imaging. Hyperspectral imaging has been applied for a wide range of uses, including the remote investigation of plants and soils. Data can be collected from instruments on airplanes, satellites or unmanned aerial systems to assess ground cover and soil chemistry.

Remote monitoring or remote sensing from the NIR spectroscopic region can also be used to study the atmosphere. For example, measurements of atmospheric gases are made from NIR spectra measured by the OCO-2, GOSAT, and the TCCON.

Materials science

Techniques have been developed for NIR spectroscopy of microscopic sample areas for film thickness measurements, research into the optical characteristics of nanoparticles and optical coatings for the telecommunications industry.

Medical uses

The application of NIRS in medicine centres on its ability to provide information about the oxygen saturation of haemoglobin within the microcirculation. Broadly speaking, it can be used to assess oxygenation and microvascular function in the brain (cerebral NIRS) or in the peripheral tissues (peripheral NIRS).

Cerebral NIRS

When a specific area of the brain is activated, the localized blood volume in that area changes quickly. Optical imaging can measure the location and activity of specific regions of the brain by continuously monitoring blood hemoglobin levels through the determination of optical absorption coefficients.

Infrascanner 1000, a NIRS scanner used to detect intracranial bleeding.

NIRS can be used as a quick screening tool for possible intracranial bleeding cases by placing the scanner on four locations on the head. In non-injured patients the brain absorbs the NIR light evenly. When there is an internal bleeding from an injury, the blood may be concentrated in one location causing the NIR light to be absorbed more than other locations, which the scanner detects.

So-called functional NIRS can be used for non-invasive assessment of brain function through the intact skull in human subjects by detecting changes in blood hemoglobin concentrations associated with neural activity, e.g., in branches of cognitive psychology as a partial replacement for fMRI techniques. NIRS can be used on infants, and NIRS is much more portable than fMRI machines, even wireless instrumentation is available, which enables investigations in freely moving subjects. However, NIRS cannot fully replace fMRI because it can only be used to scan cortical tissue, whereas fMRI can be used to measure activation throughout the brain. Special public domain statistical toolboxes for analysis of stand alone and combined NIRS/MRI measurement have been developed.

Example of data acquisition using fNIRS (Hitachi ETG-4000)

The application in functional mapping of the human cortex is called functional NIRS (fNIRS) or diffuse optical tomography (DOT). The term diffuse optical tomography is used for three-dimensional NIRS. The terms NIRS, NIRI, and DOT are often used interchangeably, but they have some distinctions. The most important difference between NIRS and DOT/NIRI is that DOT/NIRI is used mainly to detect changes in optical properties of tissue simultaneously from multiple measurement points and display the results in the form of a map or image over a specific area, whereas NIRS provides quantitative data in absolute terms on up to a few specific points. The latter is also used to investigate other tissues such as, e.g., muscle, breast and tumors. NIRS can be used to quantify blood flow, blood volume, oxygen consumption, reoxygenation rates and muscle recovery time in muscle.

By employing several wavelengths and time resolved (frequency or time domain) and/or spatially resolved methods blood flow, volume and absolute tissue saturation (${\displaystyle St{O}_2}$ or Tissue Saturation Index (TSI)) can be quantified. Applications of oximetry by NIRS methods include neuroscience, ergonomics, rehabilitation, brain-computer interface, urology, the detection of illnesses that affect the blood circulation (e.g., peripheral vascular disease), the detection and assessment of breast tumors, and the optimization of training in sports medicine.

The use of NIRS in conjunction with a bolus injection of indocyanine green (ICG) has been used to measure cerebral blood flow and cerebral metabolic rate of oxygen consumption (CMRO2). It has also been shown that CMRO2 can be calculated with combined NIRS/MRI measurements. Additionally metabolism can be interrogated by resolving an additional mitochondrial chromophore, cytochrome-c-oxidase, using broadband NIRS.

NIRS is starting to be used in pediatric critical care, to help manage patients following cardiac surgery. Indeed, NIRS is able to measure venous oxygen saturation (SVO2), which is determined by the cardiac output, as well as other parameters (FiO2, hemoglobin, oxygen uptake). Therefore, examining the NIRS provides critical care physicians with an estimate of the cardiac output. NIRS is favoured by patients, because it is non-invasive, painless, and does not require ionizing radiation.

Optical coherence tomography (OCT) is another NIR medical imaging technique capable of 3D imaging with high resolution on par with low-power microscopy. Using optical coherence to measure photon pathlength allows OCT to build images of live tissue and clear examinations of tissue morphology. Due to technique differences OCT is limited to imaging 1–2 mm below tissue surfaces, but despite this limitation OCT has become an established medical imaging technique especially for imaging of the retina and anterior segments of the eye, as well as coronaries.

A type of neurofeedback, hemoencephalography or HEG, uses NIR technology to measure brain activation, primarily of the frontal lobes, for the purpose of training cerebral activation of that region.

The instrumental development of NIRS/NIRI/DOT/OCT has proceeded tremendously during the last years and, in particular, in terms of quantification, imaging and miniaturization.

Peripheral NIRS

Peripheral microvascular function can be assessed using NIRS. The oxygen saturation of haemoglobin in the tissue (StO2) can provide information about tissue perfusion. A vascular occlusion test (VOT) can be employed to assess microvascular function. Common sites for peripheral NIRS monitoring include the thenar eminence, forearm and calf muscles.

Particle measurement

NIR is often used in particle sizing in a range of different fields, including studying pharmaceutical and agricultural powders.

Industrial uses

As opposed to NIRS used in optical topography, general NIRS used in chemical assays does not provide imaging by mapping. For example, a clinical carbon dioxide analyzer requires reference techniques and calibration routines to be able to get accurate CO₂ content change. In this case, calibration is performed by adjusting the zero control of the sample being tested after purposefully supplying 0% CO₂ or another known amount of CO₂ in the sample. Normal compressed gas from distributors contains about 95% O₂ and 5% CO₂, which can also be used to adjust %CO₂ meter reading to be exactly 5% at initial calibration.

Louis de Broglie

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Louis_de_Broglie

 

De Broglie in 1929

Louis Victor Pierre Raymond, 7th Duc de Broglie (/də ˈbroʊɡli/, also US: /də broʊˈɡliː, də ˈbrɔɪ/;French: [də bʁɔj]^[ or [də bʁœj] ^ⓘ; 15 August 1892 – 19 March 1987) was a French physicist and aristocrat known for his contributions to quantum theory. In his 1924 PhD thesis, he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave-particle duality, and forms a central part of the theory of quantum mechanics.

De Broglie won the Nobel Prize in Physics in 1929, after the wave-like behaviour of matter was first experimentally demonstrated in 1927.

The wave-like behaviour of particles discovered by de Broglie was used by Erwin Schrödinger in his formulation of wave mechanics. De Broglie's pilot-wave concept, was presented at the 1927 Solvay Conferences then abandoned, in favor of the quantum mechanics, until 1952 when it was rediscovered and enhanced by David Bohm.

Louis de Broglie was the sixteenth member elected to occupy seat 1 of the Académie française in 1944, and served as Perpetual Secretary of the French Academy of Sciences. De Broglie became the first high-level scientist to call for establishment of a multi-national laboratory, a proposal that led to the establishment of the European Organization for Nuclear Research (CERN).

Biography

Family and education

François-Marie, 1st duc de Broglie (1671–1745) ancestor of Louis de Broglie and Marshal of France under Louis XV of France

Louis de Broglie belonged to the famous aristocratic family of Broglie, whose representatives for several centuries occupied important military and political posts in France. The father of the future physicist, Louis-Alphonse-Victor, 5th duc de Broglie, was married to Pauline d’Armaille, the granddaughter of the Napoleonic General Philippe Paul, comte de Ségur and his wife, the biographer, Marie Célestine Amélie d'Armaillé. They had five children; in addition to Louis, these were: Albertina (1872–1946), subsequently the Marquise de Luppé; Maurice (1875–1960), subsequently a famous experimental physicist; Philip (1881–1890), who died two years before the birth of Louis, and Pauline, Comtesse de Pange (1888–1972), subsequently a famous writer.

Louis was born in Dieppe, Seine-Maritime. As the youngest child in the family, Louis grew up in relative loneliness, read a lot, and was fond of history, especially political. From early childhood, he had a good memory and could accurately read an excerpt from a theatrical production or give a complete list of ministers of the Third Republic of France. For this, he was predicted to become a great statesman in the future.

De Broglie had intended a career in humanities, and received his first degree (licence ès lettres) in history. Afterwards he turned his attention toward mathematics and physics and received a degree (licence ès sciences) in physics. With the outbreak of the First World War in 1914, he offered his services to the army in the development of radio communications.

Military service

After graduation, Louis de Broglie joined the engineering forces to undergo compulsory service. It began at Fort Mont Valérien, but soon, on the initiative of his brother, he was seconded to the Wireless Communications Service and worked on the Eiffel Tower, where the radio transmitter was located. Louis de Broglie remained in military service throughout the First World War, dealing with purely technical issues. In particular, together with Léon Brillouin and brother Maurice, he participated in establishing wireless communications with submarines. Louis de Broglie was demobilized in August 1919 with the rank of adjudant. Later, the scientist regretted that he had to spend about six years away from the fundamental problems of science that interested him.

Scientific and pedagogical career

His 1924 thesis Recherches sur la théorie des quanta (Research on the Theory of the Quanta) introduced his theory of electron waves. This included the wave–particle duality theory of matter, based on the work of Max Planck and Albert Einstein on light. This research culminated in the de Broglie hypothesis stating that any moving particle or object had an associated wave. De Broglie thus created a new field in physics, the mécanique ondulatoire, or wave mechanics, uniting the physics of energy (wave) and matter (particle). He won the Nobel Prize in Physics in 1929 "for his discovery of the wave nature of electrons".

In his later career, de Broglie worked to develop a causal explanation of wave mechanics, in opposition to the wholly probabilistic models which dominate quantum mechanical theory; it was refined by David Bohm in the 1950s. The theory has since been known as the De Broglie–Bohm theory.

In addition to strictly scientific work, de Broglie thought and wrote about the philosophy of science, including the value of modern scientific discoveries. In 1930 he founded the book series Actualités scientifiques et industrielles published by Éditions Hermann.

De Broglie became a member of the Académie des sciences in 1933, and was the academy's perpetual secretary from 1942. He was asked to join Le Conseil de l'Union Catholique des Scientifiques Francais, but declined because he was non-religious. In 1941, he was made a member of the National Council of Vichy France. On 12 October 1944, he was elected to the Académie Française, replacing mathematician Émile Picard. Because of the deaths and imprisonments of Académie members during the occupation and other effects of the war, the Académie was unable to meet the quorum of twenty members for his election; due to the exceptional circumstances, however, his unanimous election by the seventeen members present was accepted. In an event unique in the history of the Académie, he was received as a member by his own brother Maurice, who had been elected in 1934. UNESCO awarded him the first Kalinga Prize in 1952 for his work in popularizing scientific knowledge, and he was elected a Foreign Member of the Royal Society on 23 April 1953.

Louis became the 7th duc de Broglie in 1960 upon the death without heir of his elder brother, Maurice, 6th duc de Broglie, also a physicist.

In 1961, he received the title of Knight of the Grand Cross in the Légion d'honneur. De Broglie was awarded a post as counselor to the French High Commission of Atomic Energy in 1945 for his efforts to bring industry and science closer together. He established a center for applied mechanics at the Henri Poincaré Institute, where research into optics, cybernetics, and atomic energy were carried out. He inspired the formation of the International Academy of Quantum Molecular Science and was an early member.

Louis never married. When he died on 19 March 1987 in Louveciennes at the age of 94, he was succeeded as duke by a distant cousin, Victor-François, 8th duc de Broglie. His funeral was held 23 March 1987 at the Church of Saint-Pierre-de-Neuilly.

Scientific activity

Physics of X-ray and photoelectric effect

The first works of Louis de Broglie (early 1920s) were performed in the laboratory of his older brother Maurice and dealt with the features of the photoelectric effect and the properties of x-rays. These publications examined the absorption of X-rays and described this phenomenon using the Bohr theory, applied quantum principles to the interpretation of photoelectron spectra, and gave a systematic classification of X-ray spectra. The studies of X-ray spectra were important for elucidating the structure of the internal electron shells of atoms (optical spectra are determined by the outer shells). Thus, the results of experiments conducted together with Alexandre Dauvillier, revealed the shortcomings of the existing schemes for the distribution of electrons in atoms; these difficulties were eliminated by Edmund Stoner. Another result was the elucidation of the insufficiency of the Sommerfeld formula for determining the position of lines in X-ray spectra; this discrepancy was eliminated after the discovery of the electron spin. In 1925 and 1926, Leningrad physicist Orest Khvolson nominated the de Broglie brothers for the Nobel Prize for their work in the field of X-rays.

Matter and wave–particle duality

Main article: De Broglie hypothesis

Studying the nature of X-ray radiation and discussing its properties with his brother Maurice, who considered these rays to be some kind of combination of waves and particles, contributed to Louis de Broglie's awareness of the need to build a theory linking particle and wave representations. In addition, he was familiar with the works (1919–1922) of Marcel Brillouin, which proposed a hydrodynamic model of an atom and attempted to relate it to the results of Bohr's theory. The starting point in the work of Louis de Broglie was the idea of Einstein about the quanta of light. In his first article on this subject, published in 1922, the French scientist considered blackbody radiation as a gas of light quanta and, using classical statistical mechanics, derived the Wien radiation law in the framework of such a representation. In his next publication, he tried to reconcile the concept of light quanta with the phenomena of interference and diffraction and came to the conclusion that it was necessary to associate a certain periodicity with quanta. In this case, light quanta were interpreted by him as relativistic particles of very small mass.

It remained to extend the wave considerations to any massive particles, and in the summer of 1923 a decisive breakthrough occurred. De Broglie outlined his ideas in a short note "Waves and quanta" (French: Ondes et quanta, presented at a meeting of the Paris Academy of Sciences on September 10, 1923), which marked the beginning of the creation of wave mechanics. In this paper and his subsequent PhD thesis, the scientist suggested that a moving particle with energy E and velocity v is characterized by some internal periodic process with a frequency ${\displaystyle E/h}$ (later known as Compton frequency), where ${\displaystyle h}$ is the Planck constant. To reconcile these considerations, based on the quantum principle, with the ideas of special relativity, de Broglie associated wave he called a "phase wave" with a moving body, which propagates with the phase velocity ${\displaystyle c^2/v}$. Such a wave, which later received the name matter wave, or de Broglie wave, in the process of body movement remains in phase with the internal periodic process. Having then examined the motion of an electron in a closed orbit, the scientist showed that the requirement for phase matching directly leads to the quantum Bohr-Sommerfeld condition, that is, to quantize the angular momentum. In the next two notes (reported at the meetings on September 24 and October 8, respectively), de Broglie came to the conclusion that the particle velocity is equal to the group velocity of phase waves, and the particle moves along the normal to surfaces of equal phase. In the general case, the trajectory of a particle can be determined using Fermat's principle (for waves) or the principle of least action (for particles), which indicates a connection between geometric optics and classical mechanics.

This theory set the basis of wave mechanics. It was supported by Einstein, confirmed by the electron diffraction experiments of G P Thomson and Davisson and Germer, and generalized by the work of Erwin Schrödinger.

From a philosophical viewpoint, this theory of matter-waves has contributed greatly to the ruin of the atomism of the past. Originally, de Broglie thought that real wave (i.e., having a direct physical interpretation) was associated with particles. In fact, the wave aspect of matter was formalized by a wavefunction defined by the Schrödinger equation, which is a pure mathematical entity having a probabilistic interpretation, without the support of real physical elements. This wavefunction gives an appearance of wave behavior to matter, without making real physical waves appear. However, until the end of his life de Broglie returned to a direct and real physical interpretation of matter-waves, following the work of David Bohm.

Conjecture of an internal clock of the electron

de Broglie presented at the Solvay conference 1927 (third from right in middle row)

In his 1924 thesis, de Broglie conjectured that the electron has an internal clock that constitutes part of the mechanism by which a pilot wave guides a particle. Subsequently, David Hestenes has proposed a link to the zitterbewegung that was suggested by Schrödinger.

While attempts at verifying the internal clock hypothesis and measuring clock frequency are so far not conclusive, recent experimental data is at least compatible with de Broglie's conjecture.

Non-nullity and variability of mass

According to de Broglie, the neutrino and the photon have rest masses that are non-zero, though very low. That a photon is not quite massless is imposed by the coherence of his theory. Incidentally, this rejection of the hypothesis of a massless photon enabled him to doubt the hypothesis of the expansion of the universe.

In addition, he believed that the true mass of particles is not constant, but variable, and that each particle can be represented as a thermodynamic machine equivalent to a cyclic integral of action.

Generalization of the principle of least action

See also: Hamilton's optico-mechanical analogy

In the second part of his 1924 thesis, de Broglie used the equivalence of the mechanical principle of least action with Fermat's optical principle: "Fermat's principle applied to phase waves is identical to Maupertuis' principle applied to the moving body; the possible dynamic trajectories of the moving body are identical to the possible rays of the wave." This latter equivalence had been pointed out by William Rowan Hamilton a century earlier, and published by him around 1830, for the case of light.

Duality of the laws of nature

Far from claiming to make "the contradiction disappear" which Max Born thought could be achieved with a statistical approach, de Broglie extended wave–particle duality to all particles (and to crystals which revealed the effects of diffraction) and extended the principle of duality to the laws of nature.

His last work made a single system of laws from the two large systems of thermodynamics and of mechanics:

When Boltzmann and his continuators developed their statistical interpretation of Thermodynamics, one could have considered Thermodynamics to be a complicated branch of Dynamics. But, with my actual ideas, it's Dynamics that appear to be a simplified branch of Thermodynamics. I think that, of all the ideas that I've introduced in quantum theory in these past years, it's that idea that is, by far, the most important and the most profound.

That idea seems to match the continuous–discontinuous duality, since its dynamics could be the limit of its thermodynamics when transitions to continuous limits are postulated. It is also close to that of Gottfried Wilhelm Leibniz, who posited the necessity of "architectonic principles" to complete the system of mechanical laws.

However, according to him, there is less duality, in the sense of opposition, than synthesis (one is the limit of the other) and the effort of synthesis is constant according to him, like in his first formula, in which the first member pertains to mechanics and the second to optics:

${\displaystyle m{c}^2=h\nu }$

Neutrino theory of light

Main article: Neutrino theory of light

This theory, which dates from 1934, introduces the idea that the photon is equivalent to the fusion of two Dirac neutrinos. In 1938, the concept was challenged as not rotationally invariant and work on the concept was largedly discontinued.

Hidden thermodynamics

De Broglie's final idea was the hidden thermodynamics of isolated particles. It is an attempt to bring together the three furthest principles of physics: the principles of Fermat, Maupertuis, and Carnot.

In this work, action becomes a sort of opposite to entropy, through an equation that relates the only two universal dimensions of the form:

${\displaystyle \frac{\text{action}}{h}=-\frac{\text{entropy}}{k}}$

As a consequence of its great impact, this theory brings back the uncertainty principle to distances around extrema of action, distances corresponding to reductions in entropy.