As the song would have it - we are going to 'start from the very beginning'...
First we need to understand the basics of scattering of waves from an object.
Consider the general object shown below (Fig. 1.1). Let us assume that it receives a parallel beam of radiation of unit amplitude and every point within it re-emits radiation in all directions. Consider the radiation coming off in a direction at an arbitrary angle 2θ to the incident beam direction.
Figure 1.1: Diffraction from a General Object
Figure 1.2: Adding the components
Figure 1.3: Definition of the Scattering Vector S
Scattering from the whole Object