The image you show is misleading or rather wrong, even. In the case where it is detected wether a photon goes left or right (usually done by putting a vertical polarizer in front of one slit and a horizontal polarizer in front of the other), the pattern at the wall behind does not indicate particles. The pattern will consist of two overlapping single slit interference patterns. These are usually much wider than the distance between the two slots, so it will appear as if there was just one single slit pattern. Here is a video showing the pattern (in this experiment, there are polarizers in front of the slits and then there is a third, movable polarizer which can "repair" the double slit pattern by forcing parallel polarization - you can see the single slit pattern when there are no fringes visible or when the third polarizer is not present).
Interference experiments with normal laser light are usually not a good way to demonstrate particle properties of light, since most - if not all - the phenomena visible in such experiments are fully explainable in the wave model of light. To exhibit true quantum mechanical phenomena, one would need a very low intensity light source that is able to deposit an energy of no more than about $10^{-26} \mathrm J$ of energy into our slits, because that energy corresponds to about 20000 photons of red light, not too many to distinguish them on the screen. Particle properties would then be visible on the detector screen: The pattern is not visible at first, only single points where photons were measured. After enough photons have been observed, the pattern will emerge in a granular way like here, though this is a pattern of electrons, but the idea is the same:
If the experiment were done with the polarizers, the single slit pattern would emerge in the same granular way.