Extinction, optical crossed

Figure 4. A practical distinction between optically uniaxial and optically biaxial drawn (or extruded) material. For optically uniaxial material, the area fraction exhibiting extinction between crossed circular polars is greatest when the normal to the plane of the thin section is parallel to the draw axis. For optically biaxial material, the greatest area fraction is observed in a section cut so that the angle between its normal and the draw axis is equal to half the optic axial angle of a monodomain.

These different contrast mechanisms can all be used to reveal the scale of liquid crystalline polymer microstructures. In specimens that exhibit a mosaic texture, and in those that contain predominantly planar defects, domain size is easily defined in terms of areas that uniformly show extinction between crossed polars. However, if the defects are predominantly linear, as in specimens that exhibit schlieren textures, such simple characterization of microstructural scale is no longer possible. Here it is more convenient to look at the length of disclination line per unit volume, which is equivalent to the number of lines intersecting unit area, and analogous to the dislocation density as defined for crystalline solids. Good contrast is essential in order to obtain an accurate count. Technologically, microstructural scale is of growing interest because of its relevance to processability, mechanical properties and optical transparency. 

Acrilan (Figure 12.5) had a thin skin of crystallites with the c axes aligned radially and Orion (Figure 12.6) had the whole cross-section optically inactive with complete extinction under crossed Nicols. 

Our presentation is focused on the analysis of the scattered field in the far-held region. We begin with a basic representation theorem for electromagnetic scattering and then introduce the primary quantities which dehne the single-scattering law the far-held patterns and the amplitude matrix. Because the measurement of the ampUtude matrix is a comphcated experimental problem, we characterize the scattering process by other measurable quantities as for instance the optical cross-sections and the phase and extinction matrices. 

Essentially, Cgcat and Cabs represent the electromagnetic powers removed from the incident wave as a result of scattering and absorption of the incident radiation, while Cext gives the total electromagnetic power removed from the incident wave by the combined effect of scattering and absorption. The optical cross-sections have the dimension of area and depend on the direction and polarization state of the incident wave as well on the size, optical properties and orientation of the particle. The efficiencies (or efficiency factors) for extinction, scattering and absorption are defined as... 

The cross sections for extinction and scattering by an optically active particle are different for incident left-circularly and right-circularly polarized light. For an optically active sphere, the cross sections can be obtained in a manner similar to that for a nonactive sphere (Section 4.4). Therefore, we give only the results and omit the details ... 

In previous chapters we have always taken particles to be in a nonabsorbing medium. We now briefly remove this restriction. The notion of extinction by particles in an absorbing medium is not devoid of controversy more than one interpretation is possible. But Bohren and Gilra (1979) showed that if the extinction cross section is interpreted as the reduction in area of a detector because of the presence of a particle [see Section 3.4, particularly the development leading up to (3.34)], then the optical theorem for a spherical particle in an absorbing medium is formally similar to that for a nonabsorbing medium ... 

Measurements of extinction by small particles are easier to interpret and to compare with theory if the particles are segregated somehow into a population with sufficiently small sizes. The reason for this will become clear, we hope, from inspection of Fig. 12.12, where normalized cross sections using Mie theory and bulk optical constants of MgO, Si02, and SiC are shown as functions of radius the normahzation factor is the cross section in the Rayleigh limit. It is the maximum infrared cross section, the position of which can shift appreciably with radius, that is shown. The most important conclusion to be drawn from these curves is that the mass attenuation coefficient (cross section per unit particle mass) is independent of size below a radius that depends on the material (between about 0.5 and 1.0 fim for the materials considered here). This provides a strong incentive for deahng only with small particles provided that the total particle mass is accurately measured, comparison between theory and experiment can be made without worrying about size distributions or arbitrary normalization. 

To introduce phase-differences, small mica plates have been used. Buerger (1951) cut small plates from the same uniform cleavage sheet, and placed one over each hole, suitably tilted to give the appropriate increase in optical path-length. Hanson, Taylor, and Lipson (1951) used mica plates to control both amplitude and phase the reciprocal lattice was represented by an array of equal holes, and placed between crossed polarizers a mica plate over each hole was rotated to some position between the two extinction positions to give the correct amplitude different signs were obtained by rotating the plate either clockwise or anti-clockwise. 

---