To add to your comment: This is how Electron Crystallograpy works. You can choose to get half the Fourier transform (aka the diffraction pattern) with phase in

To add to your comment: This is how Electron Crystallograpy works. You can choose to get half the Fourier transform (aka the diffraction pattern) with phase information lost, or use a secondary lens to get the full picture back after correction. It's quite magical. Then you can do FT on that final image on a computer and then modify that pattern in reciprocal space to fix flaws with the image like astigmatism and noise. http://www.calidris-em.com http://www.calidris-em.com is the software for this.