Optical path difference of the interferometer

An idealized Michelson interferometer is illustrated in Figure 3. The interferometer modulates the incident beam by changing the optical path difference of the interferometer. The optical path difference can be changed continuously or in increments, methods called rapid scanning and step scanning, respectively. 

So far we have said little about how an FTIR measures the optical path difference of the interferometer. Here s how Since the laser hits its detector after passing through the interferometer, the interferogram of the laser is measured as shown in... 

Since the laser measures the optical path difference of the interferometer, an FTIR cannot measure anything without a functional laser. Like other light sources, lasers will wear out, typically lasting for 3-5 years. Laser power supplies also wear out after several years and are frequently replaced at the same time as the laser. The infrared source, laser, and its power supply are the most commonly replaced components on an FTIR. Some FTIRs are designed so that the user can replace the laser. In this case it makes sense to keep a spare laser and spare laser power supply in your lab. Alternatively, if you have a service contract on your instrument, the laser and its power supply are among the things that will be tested and replaced on a regular basis. If you cannot replace the laser, and you do not have a service contract, you may have to pay for a repair person to visit your lab for the repairs, or you may even have to ship the instrument back to the manufacturer to get it fixed. 

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. 

At higher frequencies, FT spectroscopy is generally carried out with a Michelson interferometer rather than by detection of a coherent transient decay. The Michelson interferometer divides the input radiation into two parts with a beamsplitter and then recombines them. As the optical path difference of the two parts is varied, the interference of the recombined beams produces an interferogram. If the optical path difference, x, changes at a constant rate, v, then the interferogram becomes a function of time, f x)=f vt), and the FT yields the desired spectrum, F(v). In general, double-sided interferograms are... 

Since the approximate full-width at half-height (FWHH) of each pulse is 100 fs, the distance occupied by each pulse is about 30 pm. The spectra shown in Figure 12.16 are measured at a resolution of 6 cm , which means that the maximum optical path difference for the interferometer is 0.17 cm or 1700 pm. The water vapor absorption that is evident in Figure 12.14 indicates that the... 

This interferometric dilatometer consists of a rather simple and small Michelson interferometer, in which the two arms are parallel, and of a 4He cryostat, in which the sample to be measured is hold. The sample is cooled to 4 K, and data are taken during the warm up of the cryostat. The optical path difference between the two arms depends on the sample length hence a variation of the sample length determines an interference signal. The Michelson interferometer consists of a He-Ne stabilized laser (A = 0.6328 xm), two cube corner prisms, a beam splitter, three mirrors and a silicon photodiode detector placed in the focal plane of a 25 mm focal length biconvex lens (see Fig. 13.1). 

The total optical path difference between the two arms of the interferometer, for a sample length of about 50 mm, is of the order of 10 mm or less, minimizing the systematic error due to laser frequency fluctuations. To reduce the thermal effects on the interferometer assembly, the interferometer support plate is stabilized to a temperature slightly higher than room temperature and insulated from air currents by a polystyrene foam shield. The temperature variation of the interferometer support is kept below 0.1 K. 

For monochromatic radiation the radiation from both arms of the Michelson interferometer will be in phase at the beamsplitter if the two mirrors are equidistant from the beamsplitter. In practice one mirror is fixed, the other is variable in its distance from the beamsplitter. Using the conventional symbol, 8, for the optical path difference between the two mirrors, constructive interference of the two beams from both arms will occur when they are in phase, or when... 

Figure 2 shows the interference fringes produced by the interferometer as the mirror moves along its track. The independent variable in this plot is optical path difference rather than mirror position. The use of optical path difference simplifies the discussion when more exotic interferometer designs employing multiple moving mirrors, or multipass optics are used. 

Here, 8 is the optical path difference called the optical retardation in the interferometer, Iq is the maximun intensity, and radiation measured in cm"l (measuring optical frequencies with Fourier spectroscopy, because it is the reciprocal of the units for measuring optical retardation. This unit for frequency simplifies the mathematical expressions and will therefore be adopted in this chapter. The increment do- represents a differential bandwidth which encompasses the "monochromatic" radiation. 

The moving mirror produces an optical path difference between the two arms of the interferometer. For path differences of (n + 1 /2)X, the two beams interfere destructively in the case of the transmitted beam and constructively in the case of the reflected beam. The resultant interference pattern is shown in Figure 2.5 for (a) a source of monochromatic radiation and (b) a source of polychromatic radiation (b). The former is a simple cosine function, but the latter is of a more complicated form because it contains all of the spectral information of the radiation falling on the detector. 

The two waves travel along different paths with a path difference = la cos o (Fig. 4.30b). Inserting a transparent object into one arm of the interferometer alters the optical path difference between the two beams. This results in a change of the interference pattern, which allows a very accurate determination of the refractive index of the sample and its local variation. The Mach-Zehnder interferometer may be regarded therefore as a sensitive refractometer. 

The Fourier transform spectrometer (FTS) is a dual-beam interferometer, which is most frequently of the Michelson type, as shown in Fig.6.32. If the arms of the interferometer have equal lengths the path difference between the two interferring beams would be 0. If the mirror is moved A/2 an optical path difference of A is introduced. For the case of monochromatic radiation and equally intense beams the intensity at the detector will be... 

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