I know that the Englert-Greenberger-Yasin Duality Relation states that as the predictability of finding a photon at a slit in a double slit experiment increases, the visibility of the interference patterns decreases. Now, how exactly is the predictability varied in a double slit experiment?
As you change something in the experiment to better predict a photon at one slit, the interference pattern looks more and more like just the sum of the patterns of each slit taken independently. That is, the extreme case pattern would be the sum of the patterns taken with one slit covered and the other slit covered.
Let us look on the double slit from the end of the history. Suppose one would shot photons on a screen with two slits and he want to know, how near he could place this two slits together and "hit" the slits separately. He starts with a big distance and wide slits and directed his photon source or to the first or to the second slit.
As he is an attentive observer he will see on the observer screen a) that every single photon he shot in the middle of the wide slit will arrive the screen and still will be a photon and b) after a while in the area of the geometrical shadow he will see fringes (intensity distributions), the first fringe is going partially behind the border of the geometrical shadow.
Now he wants to direct the photons from the source as precisely as he could to one edge of the slit. In the result he still see fringes. He tries it with monochromatic light, he make the source pointlike putting into the beam path a mask. He get the fringes more or less sharp, but they still exist.
To get the process he put the observer screen closer and closer to the edge. Photons still there are, but the fringes mutate more and more to a chaotic distribution. Doing this with two slits from the classical experiment, the observer gets the same results. He concluded that photons are indivisible and very real particles. And he concludes, if the photons are going behind the geometrical shadow there has to be an influence between the photons and the material of the edges. The final conclusions I leave you.