We begin by considering the wave pattern created on the observation screen in the experiment which Figure 1 shows. There is a source of waves far to the left. This waves then pass through a diffraction grating, which blocks most of the wave and letting only a small part through, in this case that which passes through a single, very narrow slit. What passes through the grating is then collected on the observation screen. Our goal is to understand what is observed on this screen.
Figure 1: Single-slit experiment
This section explains the reasoning behind the basic results upon
which our analyses rest: (a) that the intensity from a single slit
depends only on distance from the slit, (b) the amplitude of the waves
from a single slit is inversely proportional to distance from
the slit, (c) the phase of the waves from a single slit (in the
complex representation) goes like 
where r is distance from
the slit.