When you use a microscope to magnify something, the objective (magnifying lens) is literally taking the Fourier transform of the image. The optical system recovers up to a limiting frequency, determining the spatial resolution of the image.

Gotta say, I assumed this is some sort of virtual/imaginary thing, but it seems like there's a point in the optical system where if we placed a screen, we'd see the FT of the image coming in! And before we had digital image processing people used to place masks there to filter out low frequency or high frequency details in the image. Which is absolutely insane and I have no comprehension of how the physics works out!