Would it than be possible to change the position of this beam systematically?
Would the position of the detection depend on the position of the beam left from the double slit plane?
Would the sum of all measurements result in the same known pattern of a double slit if all positions had been used for the same period of time?
I have added a file with an image to illustrate what I mean.
The answer could be very helpful in figuring out the path of photons near the slit. I have done some investigations, documented in
Preprint Is this the path of the photons in a double slit experiment?
But the central question has not yet been answered: Is there a random effect in the double-slit experiment or not?