In the far field with a narrow bandwidth coherent light source (i.e., a laser), the projected image should be the FT of the aperture. That limiting condition is sometimes known as Fraunhofer diffraction, and generalizes to arbitrary apertures (not just a single hole).
Consider a narrow-band laser incident upon a diffraction grating for example. It produces a single point (well, two or three points, mirrored across the grating), not the uniform smudge that you'd expect by naively adding up the diffraction patterns of a bunch of slits. You should actually try this experiment for yourself!
The only trick is that you need a collimated laser and you need it to illuminate the entire inverse-FT-chip-grating aperture at once.
In the far field with a narrow bandwidth coherent light source (i.e., a laser), the projected image should be the FT of the aperture. That limiting condition is sometimes known as Fraunhofer diffraction, and generalizes to arbitrary apertures (not just a single hole).
Consider a narrow-band laser incident upon a diffraction grating for example. It produces a single point (well, two or three points, mirrored across the grating), not the uniform smudge that you'd expect by naively adding up the diffraction patterns of a bunch of slits. You should actually try this experiment for yourself!
The only trick is that you need a collimated laser and you need it to illuminate the entire inverse-FT-chip-grating aperture at once.
This deck has some nice examples of multi-hole apertures on slides 20 and 22: https://www.brown.edu/research/labs/mittleman/sites/brown.ed...