Zone Plate Reconstruction I am trying to reconstruct the Zone Plate image and am struggling to remove the last remaining aliasing. 

ShaderToy: https://www.shadertoy.com/view/wdGGWK

In the shader above you can see that I am sampling each pixel independently 1000 times with [-3, 3] jitter, and filtering those samples with (currently) Lanczos2. Why is there still aliasing?

My understanding is that the aliasing just at the edge of the visible pattern is from the filter and can't be removed without a different choice of filter, but the subtle aliasing in the middle of the axis seems like an error, and one that I have been unable to remove.

Any ideas?
Lanczos2 has a frequency response peak of about -40 dB or 0.01 at about 0.9 times the sampling frequency, see this question. Your peak aliasing outside the main lobe is just left from where the aliasing goes to zero frequency so I think it is the same peak. The amplitude of the aliasing is also roughly as expected.

So I don't see any error by you.