Experimental Methods of Determining the Photoelastic Constants

Abstract

The earliest attempts to study quantitatively the change of the optical properties of solids under the influence of a mechanical stress were made by Neumann [871]. He described the optical changes in amorphous solids by introducing two constants p and q. These constants (which may be called the strain-optical constants due to Neumann) are defined in terms of a linear strain, say ε _zz , thus:

$$\Delta n_z = n_z - n = - n^2 q\varepsilon _{zz} ,\,\Delta n_x = n_x - n = - n^2 p\varepsilon _{zz}$$

Here p and q relate the strain ε _zz to the change produced by it in the index of refraction for light vibrations perpendicular and parallel to the direction of the linear strain; n is the refractive index of the solid in its undeformed state. It is the difference (p − q) that can be determined using a Babinet compensator. Their individual values can be determined by interferometric methods, though not to a high degree of accuracy. The ratio p/q can be determined by ultrasonic methods (Bergmann and Fues [107]; Hiedemann and Hoesch [514–516]), and combining the values of (p − q) and p/q, one can get the individual values of p and q.