Now that we know about the Fourier transforming properties of lenses at the back focal plane of the lens, we are prepared to take the next step and consider the performance of the lens more generally and at other surfaces that might be useful. Consider the system shown in Fig. 1. We know at this point that the diffraction problem is linear. Since it’s linear (but not necessarily shift invariant), we can break up the problem into a collection of point sources in the object plane (xo, yo), track the radiation from each of those point sources through the system, and add up the resulting fields at any particular observation position we choose. Let’s assume that a point source at position (xo, yo) produces an image h(xi, yi; xo, yo). This notation means that the image depends on both the location of the observation (xi, yi) and the location of the source (xo, yo). We can now write the fields in the image plane (xi, yi) in terms of the superposition integral.