Stationary Interferometers

There are many other types of two-beam interferometers besides the one originally described by Michelson (see Chapter 5). Many of these interferometers do not vary the path difference between two beams by a single mirror moving at constant velocity. Except for stationary interferometers used for Fourier transform spectroscopy (Section 5.6), an optical element or combination of optical elements is moved so that the optical path difference is changed at a certain rate, known as the optical velocity or OPD velocity, V. For the Michelson interferometer, V = 2V. In general, the Fourier frequency for radiation of wavenumber v is given by... 

Some interferometers have been designed where the beam is dispersed across a linear array detector so that the interferogram is measured simply by reading the signal at each detector element without scanning any type of optical element. Such stationary interferometers are very attractive, as there are no moving parts and hence they are not susceptible to velocity errors. 

Stationary interferometers that are used for two-dimensional imaging have the added criterion that the detector array must be aligned exactly with the entrance slit to the interferometer. An imaging stationary interferometer has a slit instead of a circular aperture. If the slit and the array are not aligned exactly, the interfer-ograms are spread across more than one row or column of the array detector and serious data loss occurs. 

Mach-Zehnder interferometers allow the monitoring of gas concentrations and even the determination of analytes in liquids. Normally one of the measurement arms is covered with a thin polymer film into which the analyte can sorp. According to Nemst s distribution law, we have an equilibrium between the mobile and the stationary phase if a gas or a liquid pass the measurement window . Figure 12 shows a variety of results. 

FT-IR utilizes the Michelson interferometer rather than the grating or prism of the dispersive system. The Michelson interferometer has two mutually perpendicular arms. One arm of the interferometer contains a stationary, plane mirror the other arm contains a moveable mirror. Bisecting the two arms is a beamsplitter which splits the source beam into two equal beams. These two light beams travel their respective paths in the arms of the interferometer and are reflected back to the beam splitter and on to the detector. The two reunited beams will interfere constructively or destructively, depending on their path differences and the wavelengths of the light. When the path lengths in the two arms are the same, all of the frequencies... 

The heart of a Fourier transform infrared spectrophotometer is the interferometer in Figure 20-26. Radiation from the source at the left strikes a beamsplitter, which transmits some light and reflects some light. For the sake of this discussion, consider a beam of monochromatic radiation. (In fact, the Fourier transform spectrophotometer uses a continuum source of infrared radiation, not a monochromatic source.) For simplicity, suppose that the beamsplitter reflects half of the light and transmits half. When light strikes the beamsplitter at point O, some is reflected to a stationary mirror at a distance OS and some is transmitted to a movable mirror at a distance OM. The rays reflected by the mirrors travel back to the beamsplitter, where half of each ray is transmitted and half is reflected. One recombined ray travels in the direction of the detector, and another heads back to the source. 

Now, let me, the author, and you, the reader, be stationary in the stationary space and study the moving interferometer from there. The velocity of the interferometer from left to right is (v) while the speed of light is (c). The time... 

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. 

Smaller values of are obtained for interferometers operated in a double-beam mode, since the moveable mirror must be left stationary for a fraction of the cycle time to allow the detector to stabilize each time the beam is switched from the sample to the reference position. With an optical null grating spectrometer the chopper is used not only to modulate the beam but also to alternate the beam between sample and reference channels. Thus, it takes approximately the same time to measure a transmittance spectrum using a double beam optical null spectrometer as it takes to measure a single-beam spectrum with the same S/R. Hence, for this type of spectrometer may be assigned a value of 2. 

Time-resolved spectra can also be obtained for processes characterized by time constants which are smaller than the time to acquire an interferogram. To make this possible the experiment must be repeated many times in a reproducible fashion. The data for an interferogram are acquired in the following manner. The moveable mirror of the interferometer is advanced stepwise through M position increments. At each retardation, s, the mirror is held stationary for one cycle of the experiment and N+l measurements of the interferometric signal are made. These measurements are represented by I(tQ,sj) through I(tjj,Sj). 

A few years ago I proposed a method (the "atomic interferometer" method) which allows one to observe a stationary interference pattern for a long time while being able to arbitrarily change the phase shift, thus noticeably improving the accuracy of measurement. The interference of atomic states can be observed, in principle, with the aid of a device similar in main details to a standard two beam optical interferometer (e.g. Michelson s interferometer). 

Fig. 7.1. Layout of the infrared spectrometer showing the Michelson Interferometer Optical System. An FTIR spectrometer s optical system requires two mirrors, an infrared light source, an infrared detector and a beamsplitter. The beamsplitter reflects about 50% of an incident light beam and transmits the remaining 50%. One part of this split light beam travels to a moving interferometer mirror, while the other part travels to the interferometer s stationary mirror. Both beams are reflected back to the beamsplitter where they recombine. Half of the recombined light is transmitted to the detector and half is reflected to the infrared source.

The Michelson interferometer is shown schematically in Figure 1. It consists of two mutually perpendicular plane mirrors, one of which can move at a constant rate along the axis and one of which is stationary. Between the fixed mirror and the movable mirror is a beam splitter where a beam of radiation from an external source can be partially... 

Figure 1. Diagram of a Michelson interferometer. Key l, unmodulated incident beam A, moving mirror B, stationary mirror E, modulated exit beam D, detector MD, mirror drive.

The depolarized low-frequency LS measurement is performed under stationary excitation by means of a double monochromator for a wide frequency range and a Sandercock-type tandem Fabry-Perot interferometer for a high-resolution study. The same samples as above are measured using 1 cm glass cell. The LS is measured under a depolarized condition in a right-angled configuration. 

According to their calculations the Michelson interferometer should have registered a fringe shift of about four-tenths (0.4) of a fringe. Instead, no fringe shift was observed. They were forced to conclude that their experiment had shown that the hypothesis of a stationary, luminiferous ether was not correct. 

The interferometer used in a non-dispersive instrument is a device that divides the beam of radiation into two paths and recombines the two beams after a path difference has or has not been introduced. The basic concept of the interferometer was introduced by Michelson almost a century ago (Fig. 2). It consists of a stationary mirror, a moving mirror, and a beam splitter. The radiation from the infrared source is divided at the beam splitter half the beam is passed to a fixed mirror and the other half is reflected to the moving mirror. The two beams are later recombined at the beam splitter and passed through the sample to the detector. For any particular wavelength, the... 

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