Optical retardance

In an electrooptic material the phase retardation angle is controlled by altering birefringence, which is in turn controlled by the potential of an apphed electric field. An electrooptic device thus acts as a variable phase optical retardation plate, and can be used to modulate the wavelength or intensity of an incident beam. 

This technique is also based on the phenomenon of optical retardation. The transmission, T, of light transmitted through crossed polarizers depends on the birefringence of the sample as ... 

For a wavelength X, and an optical retardation 5, one expects that the amplitude of the resultant beam after recombination (the interference signal) will be... 

An approximate calculation for the differences in optical retardation for the central and the extreme ray of a beam-path which is diverging as it travels through the FTIR modulator, separated by a half-angle (in radians) of a, shows that the maximum allowable value of a to achieve a required resolution Av at a wavenumber of is ... 

Figure 1. Background (no sample) spectrum at different scale expansions illustrating system wavelength response, absorption attributable to typical amounts of residual water and carbon dioxide, and high signal-to-noise. The spectrum required 12 minutes of data acquisition at 8-cm optical retardation.

As the beam leaves the prism predisperser, it is focused on the entrance slit of the grating monochromator. The slit is curved, has variable width, and opens symmetrically about the chief ray (optical center line of system). The monochromator itself is of the off-axis Littrow variety (James and Sternberg, 1969 Stewart, 1970 Jennings, 1974) and uses a double-pass system described by McCubbin (1961). The double-pass aspect of the system doubles the optical retardation of the incident wave front and theoretically doubles the resolution of the instrument. The principal collimating mirror is a 5-m-focal-length, 102-cm-diam parabola. 

The photoelastic measurements were carried out in simple extension using strip specimens. In addition to the force/ also the optical retardation S (hence also the birefringence An <5) could be determined and the modulus G, the deformational-optical function A and the stress-optical coefficient C = A/G were calculated using the equations [31]... 

Assuming that the rate of change of the optical retardation introduced by the interferometer is the same for all the input radiation frequencies (which is normally the case), each individual value of v in the broadband source output contributes a different value of /m in the a.c. component of the detector output (see Figure 3.20). These contributions are, of course, summed by the detector. The combined detector output (see Figure 3.21) arising from the simultaneous measurement of all modulated input signals, is a sum of cosine functions. Such a sum is a Fourier series, and the amplitudes of the individual... 

There are of course other causes for exit beam misalignment other than simply the process of optical retardation by mirror scanning. The overall alignment integrity of the cube-corner/beamsplitter/cube-corner module as well as its optical relationship to the collimated input beam from the NIR source, and the collinear HeNe laser are all critical. The thermal and mechanical instability of this whole assembly is roughly a function of its volume. Small compact FTIR modulators will perform better in process analytical... 

While an intensity profile at the detector as a function of retardation may be acquired in a step-scan mode, two major drawbacks affect this method of interferogram acquisition. First, the mirror(s) requires stabilization times with mirror inertia and time constants of the control loop determining this parameter in achieving a given optical retardation. Second, additional hardware and control mechanisms need to be incorporated into the spectrometer, thus increasing instrument cost and complexity. In certain cases, however, the utility of a step-scan instrument justifies this additional expense. Historically, the step-scan approach was favored with slow detectors. With the advent of fast detectors and electronics, step-scan interferometry became... 

Figure 4.11 Two optical retarders. F fast axis, S slow axis. In both cases the incident beam is polarized under 45°. Left a quarter wave plate retards the slow component of the polarization by 7t/2 and elliptical polarization is achieved. Right a half-wave plate rotates the plane of polarization from 45° to -45°.

For thin disks, the rise and decay curves of optical retardation d(t) are related to the particle rotational motion by (3)... 

The desired resolution —v2 of the instrument is the reciprocal of the optical retardation S, which is defined as twice the range of motion R of the moving mirror ... 

Interference between the e-ray and the o-ray, which have travelled with different velocity through the nematic medium, gives rise to the coloured appearance of LCDs operating with plane polarised light. For a wave at normal incidence, the phase difference in radians between the o-ray and the e-ray caused by traversing a birefringent film of thickness d and birefringence An, is referred to as the optical retardation, <5 ... 

Figure 2.21 Schematic representation of the linear structure of a stretched polycarbonate and a stretched polystyrene component of an optical retardation sheet.

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