What are "spectrum" and "zone plate" here?
@ak-47: I think Kayvon may have mentioned this example in lecture; in this context, you can think of a zone plate as just a difficult test pattern that has features at every scale. These patterns are notoriously hard to sample, and typically lead to all sorts of nasty aliasing artifacts. An ideal sampling (under certain assumptions about what "ideal" means...) should become uniformly gray after some point.
The spectrum is the 2D FFT of the sample pattern itself. Or, since the pattern consists of infinitely small dots, it is typically the 2D FFT of the pattern rendered as finite-sized disks. The FFT is used to get some sense of how good a given sampling is. For instance, it should be radially symmetric (no preferred directions) and smoothly varying in amplitude (no special frequencies). Of course, there are some features that are unavoidable: below some wavelength, there will be no signal because there will always be some nonzero minimum distance between samples (indicated by the black spot at the center). There will typically be a strong peak corresponding to the spacing between samples (indicated by the bright ring around the black spot). And there will typically be "overtones" of this peak, corresponding to integer multiples of the spacing (indicated by the successively darker concentric rings).