Is the Maxwell–Shafer fish eye lens able to form super-resolved images?

The imaging capabilities of a modification of the Maxwell fish eye lens proposed by Shafer in the early 1990s are studied theoretically. A wave propagator for this system is derived for a two-dimensional version of this system. This propagator is given in simple analytic terms, and its form suggests that the system has the ability to produce super-resolved images. However, a modal analysis of the system shows that this apparent behavior is an artifact resulting from the fact that the system's input and output are collinear (or coplanar, in the three-dimensional case), and that a realistic implementation of this system would form images that obey the diffraction limit. (paper)