This question is about the intuition on one end of the Fraunhofer double-slit diffraction pattern. It is not about the Fourier transform that connects a pair of rectangles to their sinc function transform, which is clear.
The square of a carefully chosen sinc function appears to model the intensity that appears when the light passes through two slits and reaches a wall or plate. The pair of square waves at the slits are what bother me.
I guess that as the wave front hits the double slit all but two "rectangular" bits are stopped. That is, the light passing through the grating is (?) instantaneously rectangular. But this raises two related questions.
(1) Without knowing in advance that the Fourier transform is an obvious candidate (because of the diffraction pattern), could we have guessed this somehow by assessing the situation at the slits? As in, "Oh, we have two rectangles here, and they are going to form a sinc pattern on yonder wall." Why? "Because that's the FT." But you can't just apply the FT to any pair of rectangles to solve any problem involving rectangles. There has to be some underlying justification.
(2) As the light enters/leaves the slits, at what point do we declare "rectangles?" The light begins to spread immediately.
So the question is about the intuition behind the rectangle end of the situation. I suppose there is a careful derivation of that end, but mostly what I find is like the linked page, a finished analysis with no insight into formulation of the problem at the slits, as in, "this is a good case for application of the FT and here is why."
A bit of intuition would help, or perhaps a reference.