Birefringence retarders

Applications of visible light such as the use of polarized light, birefringence, retardation, angles of extinction, dispersion staining, and phase contrast will be explained, discussed and related primarily to asbestos with some discussion of quartz. 

Michel-Levy color charts (28, 29) relate birefringence, retardation color and particle thickness in graphical form. 

The second case refers to generating circularly polarized light by means of birefringent retarders. If the azimuth a of the electric vector is set at 45° and 6 at kKll (vdAn = kl4) respectively, the emerging radiation turns out to be circularly polarized. Such an optical element is often called quarter wave plate since 6 = kitl2 means a quarter wave displacement between the ordinary and extraordinary wave. The necessity of setting the azimuth at -i-45° arises from the requirement for circular polarization of an electromagnetic wave, its electric vector needs two equal components E and on exit of the retarder. 

Birefringent retarders are made of anisotropic uniaxial crystals such as calcite, a-quartz, sapphire, zinc sulphide, cadmium selenide and others. As Eq. (3.2-14) shows, the produced retardation is exact for a definite wavenumber or for its multiples. Between them all remaining possible polarization states are passed through. 

McBride, D.J., Hahn, R.A. and Silver, F.H. (1985) Morphological characterization of tendon development during chick embrvogenesis Measurement of birefringence retardation. Int. J. Biol. MacromoL, 7, 71-76. 

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. 

EO effects can be linear or quadratic, depending on whether the degree of phase retardation varies with either the first or second power of apphed voltage. The variation of birefringence with potential takes the form... 

With polarizers fidly crossed and the specimen rotated to maximum brightness, the sample thickness is determined with the aid of a calibrated eyepiece micrometer, and the polarization (retardation) color is noted. From these the birefringence may be determined mathematically or graphically with the aid of a Michel-L vy chart. 

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 ... 

An interstellar dust cloud containing aligned particles may be looked upon as a linearly birefringent (and possibly linearly dichroic) medium (van de Hulst, 1957, p. 58) the cloud acts like a retarder. We showed at the end of Section 2.11 that linearly polarized light becomes circularly polarized upon transmission by a retarder. The first clear evidence for this kind of polarization mechanism was reported by Martin (1972), where light from the Crab Nebula was the source of linearly polarized incident light. 

Retardation matching Control of birefringence Film elongation... 

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]... 

As in the case of low-molecular liquid crystals the majority of information about the structure of LC polymers is obtained from their optical textures and X-ray diffraction data. Because of high viscosity of polymer melts, which results in retardation of all structural and relaxation processes it is quite difficult to obtain characteristic textures for LC polymers. As is noted by the majority of investigators smectic LC polymers form strongly birefringent films as well from solutions, as from melts11 27-... 

Circular birefringence will induce a differential retardation in the phase of the orthogonal states of circularly polarized light. Circular dichroism, on the other hand, results in anisotropic attenuation of left- and right-circularly polarized light. The Jones matrix of circularly dichroic materials is normally written as ... 

Equation (2.52) satisfies the requirement that the ordering of the lamellae will not affect the final result. Furthermore, the differential propagation Jones matrix for a composite material is simply the sum of the matrices, N., for each of the separate optical effects. The N matrices for different optical properties can be derived using equation (2.44). As an example, consider a birefringent material with retardation S = (InAn z) /X. One form of the Jones matrix for this material is... 

Equations (8.5) bring out an additional problem that is inherent in any birefringence experiment, and that is that the measured intensity is a sinusoidal function of the retardance. This means that there can be ambiguity regarding the absolute magnitude of the retardance, since it will not have a unique value for a given measurement of the intensity. The intensity will oscillate and pass through a maximum whenever S = wtc, where n = 1, 3,. .. and will be zero when n = 0, 2, This problem represents a serious lim-... 

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