Leslie Greengard put me onto thinking about diffraction imaging of non-periodic (non-crystal-lattice) objects. I did some reading and slowly started to get some understanding of how people think about this problem, which is (mathematically) that you observe (something like) the squared-modulus of the Fourier transform of the thing you care about. You have to reconstruct all the (missing) phase information. This requires very strong prior information. Late in the day I had a long conversation with Foreman-Mackey about this and many other things.