Stationary plane mirrors

FT-IR utilizes the Michelson interferometer rather than the grating or prism of the dispersive system. The Michelson interferometer has two mutually perpendicular arms. One arm of the interferometer contains a stationary, plane mirror the other arm contains a moveable mirror. Bisecting the two arms is a beamsplitter which splits the source beam into two equal beams. These two light beams travel their respective paths in the arms of the interferometer and are reflected back to the beam splitter and on to the detector. The two reunited beams will interfere constructively or destructively, depending on their path differences and the wavelengths of the light. When the path lengths in the two arms are the same, all of the frequencies... 

Even though cube comers largely eliminate the effect of tilt, lateral displacements produce a shear that has a similar effect on the interferogram. In practice, it is easier to meet the tolerance on lateral displacements than on tilts, so that retroreflectors have a definite experimental advantage over plane mirrors for a given drive. Steel [3] has suggested a combination of a movable cube comer and stationary plane mirrors that introduces neither shear nor tilt. An interferometer based on this principle, shown... 

The Michelson interferometer is shown schematically in Figure 1. It consists of two mutually perpendicular plane mirrors, one of which can move at a constant rate along the axis and one of which is stationary. Between the fixed mirror and the movable mirror is a beam splitter where a beam of radiation from an external source can be partially... 

The interferometer was developed by Michelson in 1887 and used by him to measure the wavelength of light. Figure 3-13 shows the essential features of an interferometer. It consists of two plane mirrors and a beam splitter. The beam splitter transmits approximately half of all incident radiation to a movable mirror and reflects half to a stationary mirror. Each component reflected by the two mirrors returns to the beam splitter, where the waves are combined. 

Because the arrangement of successive apertures is equivalent to the plane-mirror resonator, the solutions of this integral equation also represent the stationary modes of the open resonator. The diffraction-dependent phase shifts 0 for the modes are determined by the condition of resonance, which requires that the mirror separation d equals an integer multiple of A/2. 

The general integral equation (5.28) cannot be solved analytically, therefore one has to look for approximate methods. For two identical plane mirrors of quadratic shape (2a), (5.28) can be solved numerically by splitting it into two one-dimensional equations, one for each coordinate x and y, if the Fresnel number N = a l(dX) is small compared with dld), which means if a < id X) . Such numerical iterations for the infinite strip resonator have been performed by Fox and Li [5.19]. They showed that stationary field configurations do exist and computed the field distributions of these modes, their phase shifts, and their diffraction losses. 

Fig. 2 Schemes of the optical part in the LICRM system. 1, Laser light source 2, movable plane mirror or corner reflector 3, polarizer 4 and 5, photocells 6 and 7, semi-transparent (half-sUvered) mirrors 8 and 9, stationary mirrors 10, the directions for the reflector 2 displacement...

Biopolymers in Chiral Chromatography. Biopolymers have had a tremendous impact on the separation of nonsupernnposable. mirror-image isomers known as enantiomers. Enantiomers have identical physical and chemical properties in an achiral environment except that they rotate the plane of polarized light in opposite directions. Thus separation of enantiomers by chromatographic techniques presents special problems. Direct chiral resolution by liquid chromatography (lc) involves diastereomenc interactions between the chiral solute and the chiral stationary phase. Because biopolymers are chiral molecules and can form diastereomeric... 

The mode configurations of open resonators can be obtained by an iterative procedure using the Kirchhoff-Fresnel diffraction theory [5.17]. Concerning the diffraction losses, the resonator with two plane square mirrors can be replaced by the equivalent arrangement of apertures with size 2a) and a distance d between successive apertures (Fig. 5.7). When an incident plane wave is traveling into the -direction, its amplitude distribution is successively altered by diffraction, from a constant amplitude to the final stationary distribution An(x,y). The spatial distribution An(x,y) in the plane of the nth aperture is determined by the distribution An- (x, y) across the previous aperture. 

Only atoms that remain in place contribute. Every such atom contributes 3 to since all three coordinates are retained. It contributes 1 to any reflection because the coordinate system can be rotated until the atom lies in a mirror plane, say xy, so that cr(xy) retains the sign of two coordinates and reverses the sign of one. Inversion changes the sign of all three coordinates, so each atom at the inversion center provides — 3. C2 reverses the sign of two of the atom s coordinates and retains one, so it contributes —1. Cn z) retains the sign of 2 for any n and Sn z) reverses it, but when n > 2 both sym-ops mix x and y or -at best - interconvert them. It can be shown by elementary trigonometry that each unshifted atom contributes 1+2 cos and —1+2 cos respectively to the character of Cn and since cos 90° = 0, the respective contributions of C4 and 4 per stationary atom are 1 and —1. 

In Sect. 2.1 we have seen that any stationary field configuration in a closed cavity (called a mode) can be composed of plane waves. Because of diffraction, plane waves cannot give stationary fields in open resonators, since the diffraction losses depend on the coordinates (x, y) and increase from the z-axis of the resonator towards its edges. This imphes that the distribution A x,y), which is independent of X and y for a plane wave, will be altered with each round-trip for a wave traveling back and forth between the mirrors of an open resonator until it approaches... 

FIG. 8. Profiles of the density of dissociated atoms, p/Po ( ) of Fig-7, vs lattice plane number at different times. Data have been smoothed by averaging over 2 neighboring planes ahead of the reaction front, and 6 behind the reaction front, and over 15 time steps. Solid lines are the steady-state trajectories of the head and foot of the reaction front. Dashed lines are the corresponding trajectories of the shock front obtained from a similar plot of the stress profiles vs time and distance. Dotted line marks the trajectories of some local reaction sites initiated by shock compression. Velocities refer to the stationary mirror plane. From reference [38b]. 

---