The latest self interference experiment makes a weak-measurement of a single photon several times. The average trajectory of the photon can be detected. Please read "Observing the Average Trajectories of Single Photons in a Two Slits Interferometer"(http://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-measurement.pdf) Figure 1 shows the average trajectories of Single photons. You can see that in three ocations, two trajectories merge from the slits and get together toward the center of the figure. This produces the central maximum in the pattern. The rest of the trajectories diverge towards other maxima, but they don't merge. This means that there is no interference as described in the previous paragraph.
Figure 1 Average trajectories of a single photon
These results are very similar to Ashfar's experiment (http://en.wikipedia.org/wiki/Afshar_experiment). He puts a grit of wires at the dark fringes, which in Figure 1 are the spots with lower density of trajectories. Ashfar did not find a significant reduction in the interference pattern with or without the grit! This means that there are regions that the photon avoids, i.e. there is no destructive interference.
Back to Figure 1, at the slit position 0 mm, two trajectories merge toward the center of the figure. This occurs several times, at the distances 3500, 5500 and 6000 mm. At each side of the central trajectories, there are no trajectories. These are the places where the dark fringes occur. The rest of the trajectories diverge from the center, move somewhat sinusoidaly and aim toward other maxima.
Every single photon was divided in two at the slits. Thus, every two trajectories belong to a single photon. If there would be constructive and destructive interference, every two trajectories should merge at the detector. This is not happening. Besides the central trajectories, the divided photon continues being divided as it travels toward the detector.
Also, the trajectories deviate from a straight line and correct its optical paths. It looks that the photon is trying to reach a maximum in the interference pattern. Hence, the probability to reach a minima is very low.
Every single photon reaching the detector, is still in two places at the same time. Upon arrival to detection, the photon still has the chance to collapse in one of the two spots. This last process will be stochastic and the photon will leave a mark at either place of landing.
Given that these maxima and minima occur by following an interference law, these results support a model where the components to produce maxima and minima are internal to the particle. Thus, no merge of the trajectories between slits are required.