Mirror tilt angle

The deflection angle 6q of a single-axis torsional mirror as a function of applied voltage V has been solved analytically by Senturia [7] in cylindrical coordinates, which we follow here. The mirror is grounded and a voltage V is applied to the counter-electrode. The mirror tilt angle 6 is positive in the clockwise direction (Figure 4.5). 

This equation can be solved for the electrostatic torque t, by differentiating the capacitance with respect to the mirror tilt angle. The mechanical... 

Chiral supramolecular architectures are sometimes formed by molecules that stay achiral as a single entity. Hence, chirality arises just because of close-packed self-assembly on the surface. The single pentane molecule in its linear configuration remains achiral. For the close-packed monolayer, a rectangular unit cell has been identified by neutron diffraction. In addition, a tilt of the molecular axis with respect to the adlattice vectors would make the whole layer chiral [33]. For a particular mirror domain, the tilt angle i// can be either turned clockwise or counterclockwise (Fig. 12). 

Fig. 12 Pentane on hopg forms at 11 K a rectangular unit cell. A small tilt angle of the molecular axis with respect to the adsorbate lattice vectors a and b would break the mirror symmetry of the layer. Reproduced with permission of the authors [33]...

Therefore, adjustment of a proper angle of incidence requires not only selection of a proper tilt angle for the mirrors but also adjustment of distances h and H. Figure 9.18 plots values of distances h and H as a function of the angle of incidence for the beam wavenumber 1600 cm . These cahbration curves are essentially independent of the photon frequency within the region where ZnSe is transparent. 

Liquid crystalline phases formed by chiral molecules (i.e. molecules differing from their mirror image) show unique macroscopic properties. The best-known example is the cholesteric phase which is termodynamically equivalent to the nematic phase. In the later phase the free-energy of the system corresponds to a uniform director distribution in the whole sample. On the other hand in cholesterics the molecules tend to form a helical structure the helical axis being perpendicular to the director. A similar helical structure develops in the smectic C phase when the molecules are chiral. In this case the helical axis is parallel to the layer normal the tilt angle is constant while the azimuthal angle is rotating in space. The pitch of the helix in these systems is typically in the order of a micron. 

Figure 2.16. Effect of changing the plane of the moving mirror of an interferometer during a scan. Rays A and B represent the extreme rays of the collimated beam passing through the interferometer, and p is the angle by which the plane of the moving mirror tilts.

Since the mirror is supported by two torsion rods, the total mechanical restoring torque x would be x = 2x. The tilt angle 0q as a function of voltage can be found from equating the electrostatic torque to the total mechanical restoring torque x. The pull-in voltage can be found from setting the torques and the slopes of the torques equal, as was done for the parallel plate actuator ... 

A two-axis tip-tilt mirror was designed and fabricated in the PolyMUMPS process as a student design project [12]. Here the mirror was not lifted out of plane as in the lambda router switch, so the maximum tilt angle was determined by the radius of the mirror, 100 pm, set by the dimensions of the optical fiber core that the switch was designed for, and the maximum sacrificial gap of 2.75 pm obtained... 

We have developed another bench for the measurement of the contrast value. Contrast measurement have been carried out on the MMA fabricated by Texas Instrument, in order to establish the test procedure (Zamkotsian et al., 2002a Zamkotsian et al., 2003). We can address several parameters in our experiment, as the size of the source, its location with respect to the micro-elements, the wavelength, and the input and output pupil size. In order to measure the contrast, the micro-mirrors are tilted between the ON position (towards the spectrograph) or the OFF position (towards a light trap). Contrast exceeding 400 has been measured for a 10° ON/OFF angle. Effects of object position on the micro-mirrors and contrast reduction when the exit pupil size is increasing have also been revealed. 

Figure 2. Optical schematic of the chamber for grazing angle measurements. Heaters and one thermocouple are located directly behind the sample (A). Gas inlet and outlet are near the IR transmitting windows (B). The mirrors (C) can be rotated and tilted to maximize signal and eliminate stray light. The entire cell (D) can be translated to change the angle of incidence.

Chirality (or a lack of mirror symmetry) plays an important role in the LC field. Molecular chirality, due to one or more chiral carbon site(s), can lead to a reduction in the phase symmetry, and yield a large variety of novel mesophases that possess unique structures and optical properties. One important consequence of chirality is polar order when molecules contain lateral electric dipoles. Electric polarization is obtained in tilted smectic phases. The reduced symmetry in the phase yields an in-layer polarization and the tilt sense of each layer can change synclinically (chiral SmC ) or anticlinically (SmC)) to form a helical superstructure perpendicular to the layer planes. Hence helical distributions of the molecules in the superstructure can result in a ferro- (SmC ), antiferro- (SmC)), and ferri-electric phases. Other chiral subphases (e.g., Q) can also exist. In the SmC) phase, the directions of the tilt alternate from one layer to the next, and the in-plane spontaneous polarization reverses by 180° between two neighbouring layers. The structures of the C a and C phases are less certain. The ferrielectric C shows two interdigitated helices as in the SmC) phase, but here the molecules are rotated by an angle different from 180° w.r.t. the helix axis between two neighbouring layers. 

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