Mathematically, real space and Fourier space are equivalent (via the Fourier transform). The Fourier domain also has some useful properties, such as efficiency in representing large objects and multi-resolution capabilities. I propose the use of Fourier goggles to automatically perform a Fourier transform
on normal visual input. They could be used for... well, I don't know what.

Possibly surprisingly, this is baked. An ordinary lens does a Fourier transform. This is routinely used to do spatial filtering optically -- you transform into Fourier space, use an ordinary neutral density filter to block selected frequencies and transform back. See the link.

At work we have an optical gadget set up to measure the resolution of the images we put on film.

Of course, it wasn't really
specified whether the Fourier
transform was with spatial or
temporal. (Spatial is probably a
better approximation; a temporal
Fourier transform would just be a
spectrogram of some sort, I guess.)

Yes, we learned about optical transforms in image processing class. (You just focus a lens in a certain way, and the 2D transform of the intensity of the image appears.) But goggles! That is genius! I want to try it. Would it give us any information we can't glean with our plain 'ol eyes?

If I remember right, holography works on somewhat related principles, but the interference patterns for different wavelengths of light do not coincide in any useful way.