Mirror motion

Advantages of Fourier transform infrared spectrometers are so great that it is nearly impossible to purchase a dispersive infrared spectrometer. Fourier transform visible and ultraviolet spectrometers are not commercially available, because of the requirement to sample the interferometer at intervals of S = l/(2Av). For visible spectroscopy, Av could be 25 000 cm 1 (corresponding to 400 nm), giving S = 0.2 im and a mirror movement of 0.1 xm between data points. Such fine control over significant ranges of mirror motion is not feasible. 

Schematic diagram of a Michelson interferometer. The detector signal variation as a result of mirror motion is displayed for the cases of monochromatic and polychromatic sources.

For many applications, there may be some advantage in employing phase modulation 54,85) instead of the usual amphtude modulation. In the latter technique the path of the radiation from the source to the detector is blocked and opened periodically by a chopper (cf. Fig. 20 and Section 4.3). For phase modulation, the chopper is removed from the spectrometer and the fixed mirror of the Michelson interferometer is moved back and forth about its mean position with a certain frequency. In contrast to the interference modulation (see Section 4.2), the amplitude of the mirror motion is small, being a quarter of the wavelength of the light. For the analogue Fourier transform or interference modulation, the amplitude of the mirror has to have many wavelengths in order to achieve a reasonable resolution... 

The instrument is capable of a 100 cm optical retardation. However, the method by which this path difference is achieved is different from the method of single-mirror motion employed by the previous two instruments. The Kitt Peak interferometer has two cat s-eye reflectors which move in a continuous-scan, reciprocating fashion. One reflector approaches the beam splitter while the other reflector retreats from it. Figure 10 shows the details of this interferometer. Both reflectors move on oil bearings. If the beam splitter is positioned so that the zero path difference occurs when one reflector is near the front of its track while the other... 

The laser power cannot be arbitrarily high because the laser light induces mirror motion because of radiation pressure. The linear spectral density of the radiation pressure noise is... 

The BBM gas consists of an arbitrary number of hard spheres (or balls) of finite diameter that collide elastically both among themselves and with any solid walls (or mirrors) that they may encounter during their motion. Starting out on some site of a two-dimensional Euclidean lattice, each ball is allowed to move only in one of four directions (see figure 6.10). The lattice spacing, d = l/ /2 (in arbitrary units), is chosen so that balls collide while occupying adjacent sites. Unit time is... 

Fig. 6.17 Two-mirror configuration that acts as a 2-block delay to an incoming ball ball s motion follows sequence of arrows.

In Fig. 18 the transition coordinates (Section 6.6.) of the three calculated transition states are shown for illustration of the above discussion. These eigenvectors give a quantitative picture of the atomic motions (towards the minima linked by the transition states) when crossing the respective barriers along the minimum energy path. As expected the transition coordinates of the Cs- and C2 -conformations are symmetric with respect to the mirror plane and the twofold axis, respectively, indicating the conservation of these symmetry elements during the associated transitions. (The transition coordinate of the Cj-form... 

The composite vector is seen to spiral around the z-axis and in projection moves anti-clockwise in a circle around the z-axis. The other component which is the mirror image of the first, performs a clockwise circular motion in projection along z. The decomposition into circularly polarized components can also be formulated in complex notation, Er = E0e t6. 

No beam chopping device is shown in Figure 5. Motion of the moving mirror in the Michel son interferometer is equivalent to beam chopping and the frequency f is given by... 

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