Fourier transform Michelson

It is the self-coherence function that is measured in Fourier transform spectroscopy. Writing the measured on-axis intensity at the output of the Michelson interferometer as... 

In the mid-IR, routine infrared spectroscopy nowadays almost exclusively uses Fourier-transform (FT) spectrometers. This principle is a standard method in modem analytical chemistry45. Although some efforts have been made to design ultra-compact FT-IR spectrometers for use under real-world conditions, standard systems are still too bulky for many applications. A new approach is the use of micro-fabrication techniques. As an example for this technology, a miniature single-pass Fourier transform spectrometer integrated on a 10 x 5 cm optical bench has been demonstrated to be feasible. Based upon a classical Michelson interferometer design, all... 

Figure 4.5 Schematic diagram of a Fourier transform infrared (FTIR) spectrometer. Infrared radiation enters from the left and strikes a beam-splitting mirror (BS) angled such that half of the beam is directed towards a fixed mirror (Mi) and half towards a moveable mirror (M2). On reflection the beam is recombined and directed through the sample towards the detector. M2 is moved in and out by fractions of a wavelength creating a phase difference between the two beam paths. This type of device is called a Michelson interferometer.

A Fourier transform infrared spectroscopy spectrometer consists of an infrared source, an interference modulator (usually a scanning Michelson interferometer), a sample chamber and an infrared detector. Interference signals measured at the detector are usually amplified and then digitized. A digital computer initially records and then processes the interferogram and also allows the spectral data that results to be manipulated. Permanent records of spectral data are created using a plotter or other peripheral device. 

Fourier-transform infrared (FTIR) spectrometers encode infrared wavenumbers by moving a mirror in a Michelson interferometer which results in a unique, path-dependent pattern of interference for each light wavelength in the IR beam. FTIRs have come to totally dominate the IR market and are the means by which most of the work described in this review was accomplished. Only for some special applications (modulation spectra and time-dependence studies) are dispersive-based (scanning monochromator or tuned laser) spectrometers still used. The advantages of the FTIR approach are that the entire spectral region of interest can... 

This Fourier transform process was well known to Michelson and his peers but the computational difficulty of making the transformation prevented the application of this powerful interferometric technique to spectroscopy. An important advance was made with the discovery of the fast Fourier transform algorithm by Cooley and Tukey 29) which revived the field of spectroscopy using interferometers by allowing the calculation of the Fourier transform to be carried out rapidly. The fast Fourier transform (FFT) has been discussed in several places 30,31). The essence of the technique is the reduction in the number of computer multiplications and additions. The normal computer evaluation requires n(n — 1) additions and multiplications whereas the FFT method only requires (n logj n) additions and multiplications. If we have a 4096-point array to Fourier transform, it would require (4096) (4095) or 16.7 million multiplications. The FFT allows us to reduce this to... 

Fourier transform infrared spectrometers first appeared in the 1970s. These single beam instruments, which differ from scanning spectrometers, have an interferometer of the Michelson type placed between the source and the sample, replacing the monochromator (Figs 10.9c and 10.11). 

Figure 10.11—Optical arrangement of a Fourier transform IR spectrometer, a) A 90c Michelson interferometer including the details of the beam splitter (expanded view) b) optical diagram of a single beam spectrometer (based on a Nicolet model). A weak intensity HeNe laser (632.8 nm) is used as an internal standard to measure precisely the position of the moving mirror using an interference method (a simple sinusoidal interferogram caused by the laser is produced within the device). According to the Nyquist theorem, at least two points per period are needed to calculate the wavelength within the given spectrum.

In Fourier transform spectrometry, the wavelength components of light are not physically separated. Instead, the light is analyzed in the time frame of reference (the time domain) by passing it through a Michelson interferometer. The Michelson interferometer is so constructed that light is separated into two beams by a beamsplitter. One beam strikes a stationary mirror and is reflected back to the beamsplitter. 

Fourier transform (FT) IR spectroscopy is one of several nondispersive optical spectroscopies based on interferometry. A two-beam interferometer first proposed by Michelson is the basis of most modern FT-IR spectrometers, as exemplified by the schematic of the Bruker Equinox 55 spectrometer (Bruker Optik, Ettlingen, Germany) in Fig. 2. Simply described, the interferometer comprises a beam splitter and two mirrors. A collimated beam of IR energy is split at the beam splitter into equal halves. Half of the energy travels through the beam splitter to one of the mirrors, which is positioned at a fixed distance away from the beam splitter. The reflected beam travels perpendicular to the incident beam to a moving mirror. IR radiation reflects off the fixed and moving mirrors and recombines at the beam splitter. The recombined IR beam projects from the interferometer towards the detector on an optical path perpendicular to the source beam. 

Fourier transform infrared (FTIR) spectroscopy has been extensively developed over the past decade and provides a number of advantages. The main part of FTIR spectrophotometer is the Michelson interferometer. Radiation containing all IR wavelengths (e.g., 4000-400 cm 1) is emitted by source of infrared radiation (Globar) and is split into two beams. One beam is of fixed length, and the other is of variable length (movable mirror). 

A mid-infrared absorption instrument generally consists of a Fourier transform design with the same basic components as noted above for the Fourier transform near-infrared spectrometers (broadband light source, Michelson interferometer, and detector optimized for the mid-infrared spectral region.)... 

A miniaturized Fourier transform spectrometer for near-infrared measurements (FTIR, 2500-8330 nm) was developed at the Forschungszentrum Karlsruhe [120], Near-infrared measurements give information, for example, about the oil, water and protein content of liquids or solids. The dimensions of the detector chip are 11.5 x 9.4 mm, the device is essentially a miniaturized Michelson interferometer and it consists of a micro optical bench with beamsplitter, ball lenses, mirrors and the detector chip. The light beam is coupled in via a glass-fiber and an electromagnetic actuator. The signal is derived from the signal response of the detector by Fourier transformation. 

There are two types of spectrometers that one can use to generate such spectra.12 One uses a monochromator to evaluate each frequency in turn. The second uses a Michelson interferometer to examine all frequencies simultaneously, and then a Fourier transform to display the spectrum. The advantage of the latter approach is its greater sensitivity, and the speed with which it can produce a spectrum. 

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