Problems involving the calculation of the passage of a polarized light beam through a succession of polarizing devices are often difficult and tedious. These may be simplified if modern methods of describing polarized light are used, namely the Stokes and Jones vectors, the Mueller and Jones calculi and the coherency matrix formalism. In this paper these concepts are presented and the vectors for various states of polarized light and the matrices of polarizers and retardation plates are given, together with examples of their method of use.

Modern description of polarized light: matrix methods

On the basis of unitarity of the transformation matrix for inhomogeneously birefringent optical media that may also possess optical activity, it is shown that there are always two perpendicular directions of the polarizer by which the light emerging from the medium is also linearly polarized. These polarization directions of the incident and emergent light are called the characteristic directions. The characteristic directions and phase retardation give an invariant characterization of complicated optical media. Their experimental determination provides information about the parameters of the media. A complete theory of characteristic directions is presented, and several important cases are considered.

Characteristic directions in optics of twisted birefringent media

The application of digital techniques for data acquisition in 2-D transmission photoelasticity and reflection photoelasticity is well developed and these were discussed in the earlier chapters. The extension of digital techniques for data acquisition to integrated photoelasticity and scattered light photoelasticity have just made a beginning. In integrated photoelasticity, one has to determine three parameters experimentally and these are known as characteristic parameters. In scattered light photoelasticity, the illumination levels are quite low due to light scattering. This necessitates the use of high-resolution CCD cameras. The ultimate aim of integrated photoelasticity or scattered light photoelasticity is to evaluate the stress field interior to the model. The current developments on tensorial tomography are discussed in this chapter.

Recent Developments and Future Trends

A new experimental method of obtaining orthotropic stress-intensity factor,K

 I
 , is presented. The orthotropic photoelasticity and orthotropic linear-elastic fracture-mechanics laws are combined. The combined set of equations is used along with half-fringe photoelasticity to determineK

 I
 in a compact-tension specimen made of a transparent unidirectional fiberglass-epoxy material. The results are compared with finite-element-method solutions.

Use of photoelasticity to determine orthotropicK I stress-intensity factor

On presente un formalisme de la polarisation de la lumiere dans lequel les etats et les operateurs de polarisation sont representes par des quaternions construits sur le corps des nombres complexes. On exprime ainsi simplement les polariseurs, les birefringents et les dichroiques a partir d'un meme operateur, mettant en evidence l'aspect unitaire de ces operateurs. On applique cette methode de calcul a la birefringence elliptique.

Représentation des états et des Opérateurs de Polarisation de la Lumière Par des Quaternions

Using the theory of the unitary system of retarders, it is shown that two seemingly different theories of photoelasticity (Sampson’s phenomenological theory and Dally and Prabhakaran’s stress-proportioning concept) are identical if the heterogeneous nature of the composites is respected. It is also shown that the optical isoclinic parameter can be accurately predicted even if the initial birefringence is present in the unloaded specimen.

On photoelastic response of composites

A simple geometrical method, which proved to be very useful, is derived for a quick quantitative analysis of the effect on polarization of any system of linear retarders and rotators. The method is based on the properties of quaternions. The use of this method for analysis of characteristic quantities and the relative flux of light from the analyzer is described together with the method for determination of the coefficients of the quaternion from characteristic quantities.

Simple Geometrical Method for Analysis of Elliptical Polarization

A set of two retardation plates is analyzed in order to find the condition for the quarterwave-plate response. A nearly achromatic quarterwave plate is created when a set of two retarders has a matched ratio of the phase retardation equal to 2.

Towards the achromatic quarterwave plate: Paper shows that a nearly achromatic quarterwave retarder can be assembled from a set of commercially available chromatic reterders

Description of properties and the method of processing of the photoelastic model material, which is suitable for casting three-dimensional photoelastic models, is presented. The material exhibits a negligible ‘rind’ effect, very small residual birefringence and an excellent machinability. The important feature of the material is the possibility to control the exothermicity of the polymerization even in very large castings.

Material for casting three-dimensional photoelastic models

The Chebysev polynomial curve-fitting technique is applied to the shear-difference method. The new approach to stress separation in two-dimensional photoelasticity is shown to be highly accurate.

Jan Cernosek

Papers

On photoelastic response of composites

Simple Geometrical Method for Analysis of Elliptical Polarization

Towards the achromatic quarterwave plate: Paper shows that a nearly achromatic quarterwave retarder can be assembled from a set of commercially available chromatic reterders

Material for casting three-dimensional photoelastic models

Shear-difference method with chebysev polynomials