Young's Double Slit Experiment with Single Photon Counters and Offset Mask

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I was thinking about this. Setup a Young's double slit experiment as follows.

Single Photon Source /Pulsed Photon source -> Single Slit-> Mask with two Slits (Slit 1 and Slit 2 )-> Detection plane consisting of many single photon counters.

I am assuming it's possible to detect the correlation between emitting of the photon/electron and arrival at the detector. So essentially knowing the time of flight as well the position where the photon/electron hits the screen. Not being a particle physicist maybe this all would be easier with a particle beam ?

I turn the experiment on and I would expect to build up the usual Youngs intereference pattern on my detector along with time of flight data for each event. If i then be able to rotate the mask of the two slits so that Slit 1 is closer to my detector, would i not be able to determine which slit the particle passed through? Since particles that are deflected further away from the axis of the experiment are more likely to have gone through Slit 1 and not Slit 2?
 

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