My mind was blown when I saw the 4F experiment, where a lens transforms an image into the Fourier domain. I'm not sure if it's related to the Fresnel zone (I think it is not or only very vaguely), but it's pretty amazing:
A widened beam of collimated light (i.e. parallel beams) is sent through e.g. a slide with some image printed on it. Using a lens placed one focal length away, it is focused down to a point (one focal length from the lens). One more focal length from that point, the beam will have reached its original width again, and another lens makes it parallel again, projecting it onto a screen placed one focal length from the second lens:
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image lens point lens screen
This will behave exactly as expected at first glance. The image will be visible on the screen (upside down IIRC) and if you hold a piece of paper into the point, you'll just see a single bright dot. However, what's actually present (due to diffraction) is the Fourier transform of the image! If you put an iris around the point, the image on the screen becomes blurry because you just filtered the high frequencies! And what's even more impressive, if you remove the center of the point (e.g. by inserting a glass slide with a small black circle in the middle), you'll get only the high frequencies, and the image on the screen will be the edges of the original image.
A widened beam of collimated light (i.e. parallel beams) is sent through e.g. a slide with some image printed on it. Using a lens placed one focal length away, it is focused down to a point (one focal length from the lens). One more focal length from that point, the beam will have reached its original width again, and another lens makes it parallel again, projecting it onto a screen placed one focal length from the second lens:
This will behave exactly as expected at first glance. The image will be visible on the screen (upside down IIRC) and if you hold a piece of paper into the point, you'll just see a single bright dot. However, what's actually present (due to diffraction) is the Fourier transform of the image! If you put an iris around the point, the image on the screen becomes blurry because you just filtered the high frequencies! And what's even more impressive, if you remove the center of the point (e.g. by inserting a glass slide with a small black circle in the middle), you'll get only the high frequencies, and the image on the screen will be the edges of the original image.