TWO-BEAM INTERFEROMETERS

Therefore for fixed v and a linearly changing 5, the output of the ideal two-beam interferometer is a cosine function. In other words it is a cosine modulator of the original DC light source. The modulation frequency observed in the AC output of the FTIR spectrometer detector is dependent on the rate at which 5 is increased or decreased, and is given by... 

In operation, the apparatus functions as a two-beam interferometer, utilizing a gaseous laser as the source and a photomultiplier tube as a detector. The 155-mcps-beat note is demodulated by a standard communications receiver. 

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. 

With the method of Fourier transform spectroscopy, the hght is not separated into spectral elements. The scientist uses a two-beam interferometer and studies the interference or correlation properties of the light as a function of path difference the results of this study are then converted mathematically to the spectrum on a computer. This conversion is a Fourier transform, which is why the method is called Fourier transform spectroscopy. All this is explained in much more detail below. The point being made here is that this method employs mathematics, computers, and electronic data processing, all perhaps strange, new tools for the... 

In practical applications of Fourier transform spectroscopy, such an interferogram [Eq. (3.2) and Fig. 10] is recorded by means of a two-beam interferometer. As in the case of a discrete spectrum with narrow hues, the spectrum I (v) is calculated from I ) by executing the Fourier transform. For this purpose, again only the oscillatory part of I (s) is needed... 

Fig. 18. Two-beam interferometer efficiencies of a Michelson interferometer with a thin-film mylar beam splitter —), witli a metal screen as beam splitter (- -), and with a lamellar grating (----). These data were taken from Ref.

Summarizing the results of our discussion of the practice of Fourier transform spectroscopy, we start with the presumption that the equipment for most routine spectroscopic investigations consists of a Fourier spectrometer with a Michelson interferometer and a digital computer. In other words, the advantages of the lamellar grating used as a two-beam interferometer, and of phase modulation, for example, have been utilized only for certain special applications in the extreme far-infrared. All commercial Fourier spectrometers are available with a computer attached, which in most cases not only performs the Fourier transform but is also programmed to control the instrument. Commercial instruments have a remote switch for the selection of the different spectral ranges, and the filters and beams... 

Two-beam interference microscopes operating according to the principle of the Michelson interferometer and accessory devices converting an ordinary microscope into a two-beam interferometer are commercially available. In such microscopes, collimated monochromatic light is half reflected onto the sample surface and half transmitted to an adjustable flat reference mirror by a beam splitter. The two reflected beams recombine in the microscope and the resulting variation in the optical path difference of the beams produces parallel interference lines of equal thickness which are also displaced at the position of the film step. The lines obtained are, however, relatively broad limiting the resolution and the accuracy of such measurements by the uncertainty in selecting the line centre. 

Coherent light shows phase-independent noise. This can be demonstrated by a two-beam interferometer, such as the Mach-Zehnder interferometer shown in Fig. 9.96. The monochromatic laser beam with the mean intensity /q is split by the beam splitter BSi into two partial beams bi and b2 with amplitudes E and E2, which are superimposed again by BS2. The beam b2 passes a movable optical wedge, causing a variable phase shift 0 between the two partial beams. The detectors PDl and PD2 receive the intensities... 

Taking into account absorption and reflection losses, the maximum transmission Ij/Io = To < 1 becomes less than 100%. Within a small wavelength interval, the difference An = no — n can be regarded as constant. Therefore (4.92) gives the wavelength-dependent transmission function, cos cp, typical of a two-beam interferometer (Fig. 4.26). For extended spectral ranges the different dispersion of no(k) and e( ) has to be considered, which causes a wavelength dependence, An(k). 

The basis of Fourier transform infrared (FT-IR) spectroscopy is the two-beam interferometer, designed by Michelson in 1891 [28]. and shown... 

A further method of monitoring Doppler-free signals using transmitted beams is also possible. In this technique (saturated interference spectroscopy) [9.175,176], the change in refractive index for the atoms at the "hole" position is used to influence the light interference condition in a two-beam interferometer. If the set-up is initially adjusted for destructive interference an increase in light intensity will be observed at the line centre. 

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... 

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