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Comment by throwaway2568 | Hacker News Reader

This article is not that clear (there is no frequency shift occuring). As others say, the authors are using speckle imagery, which relies on the wavevector of the illuminating beam (rather than the frequency). By adding the hyperbolic metamaterial the authors can access wavevectors beyond the diffraction limit, so that once they do the appropriate prost processing achieve super resolution imagery.

It's not directly related but reciprocal space and Fourier imaging is quite interesting for those that are not aware of it (such as estimating the size of a crystal lattice by looking at the diffraction pattern)

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Yes - the technique is called ptychography [0] and there have been several recent electron microscopy papers too demonstrating how this technique (image reconstruction from Fourier space patterns) can reach beyond instrumental resolution limits [1, 2].

References:

[0] https://en.wikipedia.org/wiki/Ptychography

[1] 2018 Nature Paper: https://www.nature.com/articles/s41586-018-0298-5 arXiv version: https://arxiv.org/abs/1801.04630

[2] 2021 Science Paper: https://science.sciencemag.org/content/372/6544/826 arXiv version: https://arxiv.org/abs/2101.00465

Most computer folks are actually unaware that physicists were doing fourier transforms using optics long before the FFT existed. You can do physical convolutions using lenses.

Fascinating! Can you explain this a bit more and share some examples?

As it happens, I did this in a physics lab just a couple of weeks ago. The basic setup is that if you pass a collimated beam of light through a mask and then focus it with a lens, the focus will contain the 2D Fourier transform of the pattern on the mask. Adding another lens does another Fourier transform getting the original image back (but flipped). By masking appropriate sections of the Fourier transform, you can physically implement various filters — e.g. a low-pass filter becomes a mask letting through only the central portion of the Fourier transform. One I remember trying is that if you take a periodic pattern like a rectangular grid, and then pass the Fourier transform through a thin slit, you can filter out only the horizontal or only the vertical component of the grid. Pretty cool stuff.

Lenses bend EM waves proportionately to their frequency, so it naturally separates the different frequencies. Bam, you've described your EM source in the frequency domain.

> Lenses bend EM waves proportionately to their frequency

Is this exact? I was under the impression that it's a linear approximation that's generally good enough for optical component glasses over the range of visual wavelengths.

(I always found it a bit frustrating that in my Mechanical Engineering undergraduate classes, they almost always introduced linear approximations without any discussion about the conditions under which the approximations held. Sometimes, they didn't even mention that the linearization was an approximation.)

It depends on the faculty. Postgraduates knows better.

...Am I having a stroke? Aren't you just talking about a prism? It converts time domain to frequency/space domain, just like the cochlea in the ear does with mechanical time-series.

No.

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