In Chapter 11 we discussed why diffraction occurs; in this chapter we give a more detailed mathematical treatment. It may be more detailed than you need at this stage. Diffraction is one of those phenomena that lends itself directly to a detailed mathematical modeling, but there is a danger:
don’t become so engrossed in the math that you miss the principles involved; conversely, don’t ignore the subject because it is mathematically daunting!
The topic of this chapter is one which causes major problems for many microscopists. The treatment we will follow is known as the ‘dynamical theory.’ Later we will make some gross simplifications, partly because this is instructive and partly because these simplifications do apply to some important special cases; the kinematical approximation is one such simplification. Many other texts begin with the so-called ‘kinematical’ treatment and then advance to the more realistic, more general dynamical case. We will not do this but we will introduce the words and assumptions in Chapter 27.