Fourier Optics used for Optical Pattern Recognition

IDK, the more I learn the more it seems to me that Fourier transform is reality's cheat code. It keeps showing up everywhere. Like, the other day I learned[0] that if you shine a light through a small opening, the diffraction pattern you get on the other side is basically the Fourier transform of the aperture outline. (Yes, this also implies that if you take a Fourier transform of an image and make a diffraction grating off the resulting pattern, projecting light through it should paint you the original image.) -- [0] - ▶ this video

Huygens Optics has a great video "Fourier Optics used for Optical Pattern Recognition". He starts with explaining the Fourier Transform wrt audio, then demonstrates a physical filter that screens the resulting convolution pattern to identify matches. Very cool: ▶ this video

You could think of a lens as a "Fourier transformer," not in the LLM sense directly but in the sense of something that executes a Fourier transform. See the excellent videos by Huygens Optics including this one: ▶ this video entitled "Fourier optics used for optical pattern recognition." Having established that, well, it's not hard to imagine that something that's good at running Fourier transforms is probably good for other situations where you need to run a lot of dot products in parallel. That, in turn, should sound like an awfully familiar problem...

Upping a cousin comment. ▶ this video Adding that, again, optics is a difficult and frustrating field. Don't worry that you're struggling to connect it. It took me a few years in an optics lab working hands on with light every day to really come around.

Optical pattern recognition is an established field. Here's a simple version via Fresnel zone plates: ▶ this video

Reminds me of this really cool video about using Fourier Optics for optical pattern recognition.[1] The video happens to have one of the best explanations of Fourier transforms I've yet encountered. 1: ▶ this video

For a somewhat related topic (analog image recognition), for those interested, I can highly recommend this video: ▶ this video

An even better one - holding an image at the focal point of a lens produces its Fourier transform at the focal point on the other side of the lens[0]. It is used for "analog" pattern matching[1]. There is an interesting video explaining this on the Huygen Optics Youtube channel[2]. [0] - link [1] - link [2] - ▶ this video

I was introduced to this idea in a really cool video about using Fourier Optics for optical pattern recognition.[0] The video happens to have one of the best explanations of Fourier transforms I've yet encountered. [0] ▶ this video