By W. Fickett, W. Davis

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17] used a stereographic projection of the Poincare sphere and converted all transformations of the sphere into corresponding transformations on a plane. 18]. 15] used the Poincare sphere in their investigations for the design of an achromatic, multilayer retarder. 21,22] used also the Poincare sphere for the study ofthe interference oftwo coherent beams oflight and the resolution of any polarization form into two prescribed polarization forms. 23-39J. 40-43] studied some polarization-optics problems with applications to two- and three-dimensional photoelasticity by using the orthographic projection of the Poincare sphere on its equatorial plane; he was thus able to work with a two-dimensional instead of the threedimensional model that is required by the method of the Poincare sphere.

4 represents the intersection patterns of the normal surface by the three coordinate planes. A perspective view of the normaJ surface is shown in Fig. 5. z c, z c, y 8, x Fig. 4. Intersections of the normal surface by the coordinate planes of abiaxial crystal References z 19 Fig. 5. Perspective view of the normal surface of abiaxial crystal y x In a similar manner, it can be proved that the ray surface has a shape analogous to the normal surface, but with the above-considered ovals replaced by ellipses, arranged relative to the corresponding circles similarly as in the case of the normal surface.

3 The Stokes and Jones Vectors Because both the Stokes and the lones vectors describe polarization forms, a relationship between these vectors must exist. 6]. 6 Discussion of the Methods of Characterization of Polarized Light The effectiveness, powerfulness, and supenonty of the new methods of characterization of polarization forms over the older methods of using the light vector will be shown in the next chapter, where the optical transformations of polarized light when it passes through a train of optical elements will be discussed.