In the previous lecture we examined plane wave solutions to the wave equation and discussed how an arbitrary field distribution in a given plane could be broken up into a superposition of plane waves. We could then propagate the fields by allowing each of those plane waves to propagate separately, then add everything up after some distance. Earlier this term we discussed the Heisenberg uncertainty principle that told us that it is not possible to know both the position and wavenumber of an electromagnetic wave infinitely precisely. In Lecture 15, we used a basis set that had zero uncertainty in wavenumber, i.e. we knew exactly the direction in which the wave was propagating. However, the plane wave has infinite extent, so the individual basis functions have no localization at all in position. For the rest of the course, we will use the dual representation of the fields. That is, we will choose a basis set that is precisely located in space, but provides no localization in wavenumber. That basis set is the spherical wave: we know exactly the location of the source, but the light propagates away in all directions. For the purposes of this discussion, we will assume that the fields are monochromatic and linearly polarized. This will allow us to use scalar diffraction theory, which ignores polarization in the computation.