Comment by sillysaurusx
5 years ago
The diffraction bands are approximately the Fourier transform of the slit function.
Is this correct from a physics standpoint? Feynman had a lot to say about light in his book (QED https://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/06...) and never framed it this way. At one point he remarked that the explanations in the book were related to diffraction, and the explanation there was very different from the Fourier transform.
In short, yes. An ideal image source incident on a positive optical lens produces its spatial Fourier transform at the lense's focal point. This is easiest to see with a lasersl backlighting a transparency, since the light is collimated and monochromatic. The transparency produces diffraction at its edges, which causes the effect. Actually, you'd also see the spatial Fourier transform at infinity if you took away the lens. The result of this is that you can do cool spatial frequency filtering effects at the focal point, then convert it back into an image with another lens. Laser systems that require high precision will use such a setup to remove high-frequency components and pass just the collimated light.