Spherical lens anisotropic V z

The LFB microscope gives good azimuthal resolution in 0, but is not suitable for imaging. The imaging microscope gives good spatial resolution, but the spherical lens averages over all 0. Therefore, the contrast for an anisotropic specimen becomes 

The integration could be performed by calculating V(z) for each 0, corresponding to V(z) curves such as the measured one in Fig. 11.7(a), and then integrating over 0. Alternatively, a complex mean reflectance function (denoted by prime) may be calculated as 

By swapping the order of integration in (11.13), and assuming axial symmetry of the lens, the contrast may now be written 

This is identical in form to the equation for V (z) in an isotropic material. But of course R hkl (8) is quite different from any isotropic reflectance function. For a cubic material an anisotropy factor can be defined as 

Complex mean reflectance functions for aluminium, nickel, and copper are presented in Fig. 11.10. These represent a series of increasingly anisotropic 

---