The Arago/Poisson spot is an excellent example of a constructive interference of diffracted light. In the traditional experimental layout, you observe projected light on the screen. The theory in this case is completely straight-forward, just add together phase-delayed contributions (Fresnel integral).
However, I'm not sure what would happen, if instead of a screen, you put an optical apparatus (eye, pinhole camera, lensed camera) on the symmetry axis? What confuses me is that all these optical imaging systems form an image by angle, not by absolute spatial position! Adjacent pixels focus light from slightly different angles. Because the spot actually collects light coming around the circular obstacle, you shouldn't see a bright spot in the middle. I'm almost certain that you wouldn't see anything special at all (nothing different from what you see if you are looking from an off-center position - you're in the geometric shadow after all). My reasoning is that because the eye projects light from different directions to different pixels, the contributions can't constructively interfere.
I'm worried about the following things:
- The angular imaging description is ray-optics... the phenomenon requires wave-optics. Is the reasoning still valid if you pretend wavefront normals are rays?
- Constructive interference should form a head-on wavefront even before it gets to your eye. This indicates that you would indeed see a spot. If the front is wide enough to be considered a geometric ray and not get refracted by the lens.
- Would the optical apparatus just introduce slight variations in phase and ruing the phenomenon? Would you see "speckle" pattern?
- In a pinhole camera, the screen around the pinhole blocks precisely the path from the parts that contribute to the interference. If the wavefront forms in front of the screen, does it diverge back into a wide disperse wave after "cutting off" the income of new waves?
Short of doing full wave optical calculation of a camera, can we reconstruct what would happen? Would a pinhole camera give a fundamentally different image from a lensed camera? Please elaborate. We can treat this as a discussion-type question.