Interferometers

The heart of an FT-IR spectrometer is the interferometer. Most FT-IR spectrometers use the Michelson interferometer, invented by Albert A. Michelson (1852-1931) in 1891, and for which he received the 1907 Nobel Prize in physics. 

In this section we discuss some basic properties of interferometers illustrated by some examples [4.12]. The characteristics of the different types of interferometer that are essential for spectroscopic applications are discussed in more detail. Since laser technology is inconceivable without dielectric coatings for mirrors, interferometers, and filters, an extra section deals with such dielectric multilayers. 

Bisecting the fixed mirror and the movable mirror is a beamsplitter, where a collimated beam of radiation from an external source can be partially reflected to the fixed mirror (at point F for the median ray) and partially transmitted to the movable mirror (at point M). When the beams remm to the beamsplitter, they interfere and are again partially reflected and partially transmitted. Because of the effect of interference, the intensity of each beam passing to the detector and returning to the source depends on the difference in path of the beams in the two arms of the interferometer. The variation in the intensity of the beams passing to the detector and returning to the source as a function of the path difference ultimately yields the spectral information in a Fourier transform spectrometer. 

Fourier Transform Infrared Spectrometry, Second Edition, by Peter R. Griffiths and James A. de Haseth Copyright 2007 John Wiley Sons, Inc. 

The beam that returns to the source is rarely of interest for spectrometry, and usually only the output beam traveling in the direction perpendicular to that of the input beam is measured. Nevertheless, it is important to remember that both of the output beams contain equivalent information. The main reason for measuring only one of the output beams is the difficulty of separating the output beam that returns to the source from the input beam. On rare occasions, both output beams are measured with the use of two detectors or by focusing both beams onto the same detector. In other measurements, separate beams can be passed into each arm of the interferometer and the resulting signal measured using one or two detectors. 

The movable mirror can either be moved at a constant velocity (a continuous-scan interferometer) or be held at equally spaced points for fixed short periods and stepped rapidly between these points (a step-scan interferometer). When the mirror of a continuous-scan interferometer is moved at a velocity greater than 0.1 cm s (the usual case for most commercial instmments), the interferometer is often called a rapid-scan interferometer. 

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This is an analysis frequently conducted on oil lubricants. Generally, the additive is known and its concentration can be followed by direct comparison of the oil with additive and the base stock. For example, concentrations of a few ppm of dithiophosphates or phenols are obtained with an interferometer. However, additive oils today contain a large number of products their identification or their analysis by IR spectrometry most often requires preliminary separation, either by dialysis or by liquid phase chromatography. 

A much better way would be to use phase contrast, rather than attenuation contrast, since the phase change, due to changes in index of refraction, can be up to 1000 times larger than the change in amplitude. However, phase contrast techniques require the disposal of monochromatic X-ray sources, such as synchrotrons, combined with special optics, such as double crystal monochromatics and interferometers [2]. Recently [3] it has been shown that one can also obtain phase contrast by using a polychromatic X-ray source provided the source size and detector resolution are small enough to maintain sufficient spatial coherence. 

In this work, a millimeter wave interferometer operating in the frequency band of 26 to 40 GHz and overcoming these difficulties is presented. 

Figure 1. shows the measured phase differenee derived using equation (6). A close match between the three sets of data points can be seen. Small jumps in the phase delay at 5tt, 3tt and most noticeably at tt are the result of the mathematical analysis used. As the cell is rotated such that tlie optical axis of the crystal structure runs parallel to the angle of polarisation, the cell acts as a phase-only modulator, and the voltage induced refractive index change no longer provides rotation of polarisation. This is desirable as ultimately the device is to be introduced to an interferometer, and any differing polarisations induced in the beams of such a device results in lower intensity modulation. 

McBain reports the following microtome data for a phenol solution. A solution of 5 g of phenol in 1000 g of water was skimmed the area skimmed was 310 cm and a 3.2-g sample was obtained. An interferometer measurement showed a difference of 1.2 divisions between the bulk and the scooped-up solution, where one division corresponded to 2.1 X 10 g phenol per gram of water concentration difference. Also, for 0.05, 0.127, and 0.268M solutions of phenol at 20°C, the respective surface tensions were 67.7, 60.1, and 51.6 dyn/cm. Calculate the surface excess Fj from (a) the microtome data, (b) for the same concentration but using the surface tension data, and (c) for a horizontally oriented monolayer of phenol (making a reasonable assumption as to its cross-sectional area). 

Figure Bl.2.6. Schematic representation of a Michelson interferometer. From Griffiths P R and de Flaseth J A 1986 Fourier transfonn infrared spectroscopy Chemical Analysis ed P J Hiving and J D Winefordner (New York Wiley). Reprinted by pemiission of Jolm Wiley and Sons Inc.

A typical noisy light based CRS experiment involves the splitting of a noisy beam (short autocorrelation time, broadband) into identical twin beams, B and B, tlnough the use of a Michelson interferometer. One ami of the interferometer is computer controlled to introduce a relative delay, x, between B and B. The twin beams exit the interferometer and are joined by a narrowband field, M, to produce the CRS-type third order polarization in the sample ([Pg.1209]

Sarid D, Pax P, Yi L, Howells S, Gallagher M, Chen T, Elings V and Booek D 1992 Improved atomio foroe miorosoope using a laser diode interferometer Rev. Sc/. Instrum. 63 3905... 

Nonetheless, the syimnetric interferometer remains very useful, because there, the wavelengdis of fringes with even cliromatic order, N, strongly depend on the refractive index, n, of the central layer, whereas fringes with odd cliromatic order are almost insensitive to This lucky combhiation allows one to measure the thickness as well as the refractive index of a layer between the mica surfaces independently and siniultaneously [49]. 

To simplify FECO evaluation, it is conmion practice to experimentally filter out one of the components by the use of a linear polarizer after the interferometer. Mica bireftingence can, however, be useftil to study thin films of birefringent molecules [49] between the surfaces. Rabinowitz [53] has presented an eigenvalue analysis of birefringence in the multiple beam interferometer. 

Partial reflections at the iimer optical interfaces of the interferometer lead to so-called secondary and tertiary fringe patterns as can be seen from figure B 1.20.4. These additional FECO patterns become clearly visible if the reflectivity of the silver mirrors is reduced. Methods for analysis of such secondary and tertiary FECO patterns were developed to extract infonnation about the topography of non-unifonn substrates [54]. 

Figure Bl.20.4. Cross-sectional sideview of a syimnetric, tliree-layer interferometer illustrating the origin of primary, secondary, tertiary and gap FECOs. (Reproduced with pennission from [54].)...

In the symmetric, three-layer interferometer, only even-order fringes are sensitive to refractive index and it is possible to obtain spectral infonnation of the confined film by comparison of the difierent intensities of odd-and even-order fringes. The absorption spectmm of tliin dye layers between mica was investigated by Muller and Machtle [M, M] using this method. 

Another interesting extension of the FECO teclmique, using a capillary droplet of mercury as the second mirror, was developed by Flom etal [6f]. The light from this special interferometer is analysed in reflection. 

Horn R G and Smith D T 1991 Anaiyticai soiution for the three-iayer muitipie beam interferometer App/. Opt. 30 59-65... 

Machtie P, Muiier C and Heim C A 1994 A thin absorbing iayer at the center of a Fabry-Perot interferometer J. Physique ii 4 481-500... 

Farreii B, Baiiey A i and Chapman D 1995 Experimentai phase changes at the mica-siiver interface iiiustrate the experimentai accuracy of the centrai fiim thickness in a symmetricai three-iayer interferometer App/. Opt. 34 2914-20... 

On metals in particular, the dependence of the radiation absorption by surface species on the orientation of the electrical vector can be fiilly exploited by using one of the several polarization techniques developed over the past few decades [27, 28, 29 and 30], The idea behind all those approaches is to acquire the p-to-s polarized light intensity ratio during each single IR interferometer scan since the adsorbate only absorbs the p-polarized component, that spectral ratio provides absorbance infonnation for the surface species exclusively. Polarization-modulation mediods provide the added advantage of being able to discriminate between the signals due to adsorbates and those from gas or liquid molecules. Thanks to this, RAIRS data on species chemisorbed on metals have been successfidly acquired in situ under catalytic conditions [31], and even in electrochemical cells [32]. 

Ishida FI, Ishino Y, Bui]s FI, Tripp C and Dignam M J 1987 Polarization-modulation FT-IR refleotion speotrosoopy using a polarizing Miohelson interferometer App/. Spectrosc. 1288-94... 

Figure B2.1.2 Modified Michelson interferometer for non-collinear intensity autocorrelation. Symbols used rl, r2, retroreflecting mirror pair mounted on a translation stage bs, beamsplitter x, nonlinear crystal pint, photomultiplier Pibe.

Kuhl J and Heppner J 1986 Compression of femtosecond optical pulses with dielectric multilayer interferometers IEEE J. Quantum. Electron. 22 182-5... 

Diffey W M and Beck W F 1997 Rapid-scanning interferometer for ultrafast pump-probe spectroscopy with phase-sensitive detection Rev. Sci. Instrum. 3296-300... 

Stamm Ch and Lukosz W 1994 Integrated optical difference Interferometer as biochemical sensor Sensors Aotuators B 18-19 183-7... 

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