Why does the interference patterns in delayed choice quantum eraser cancel out? Why/how does it have a phase shift? Talking about this experiment https://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser#The_experiment_of_Kim_et_al._.282000.29
I am assuming that anyone able to answer my question is already somewhat familiar with the experiment and the wiki page explains it better than I can. But here is the gist of it according to my understanding: you send photons through a double slit then split them into two entangled photons. One goes to D0 and the other goes to a setup of half mirrors and detectors where there is a 50/50 change of erasing or keeping information relating to the path or "which slit" the photon passed through.

While the collective pattern of all photons hitting D0 is just a blurred line you can pick out subsets R1 R2 R3 and R4 using the coincidence counter. That is R1 fx shows only photons hitting D0 which also had a "sister" particle hitting D1. Now R1 and R2 shows an interference pattern, phase shifted in relation to each other such that they cancel out in the collective image of D0.


Now here is what I don't understand: why is there a difference between D1 and D2? On the graphs R1 has a peak in the middle while R2 has a valley, why not reversed? What makes D1 and D2 different? What decides which one gets peaks at certain points and the other gets the opposite? 
Also does D1 and D2 always have a peak or valley in the middle? or are they simply always phase shifted pi in relation to each other but not in relation to the middle? Either way, what I really want to know is why/how does R1 and R2 turn out phase shifted?
 A: 
Delayed_choice_quantum_eraser#The_experiment_of_Kim_et_al. [...]
  Now R1 and R2 shows an interference pattern

These two patterns of coincidence counts both arise as a function of "x" (see the labelled arrow next to detector D0 in the schematic); i.e. as detector D0 is put in different places of the plane of convergence where the "Lens" produces a suitably sharp image of the BBO crystal with the two slits.
Different "image places x" correspond to (ever so slightly) different ray trajectories from the BBO crystal to the lens; i.e. the upper red or blue traces differing (ever so slightly) depending on (the value of) "x".

What makes D1 and D2 different? 

Importantly, due to the properties of the BBO crystal, photon by photon, there is a very precise relation between the exact ray trajectories from the BBO crystal to the lens and the exact ray trajectories from the BBO crystal to the prism "PS". As the former change depending on (the value of) "x", the latter do as well. Therefore the exact light path lengths from from either slit to deterctors D1 or D2 may change (ever so slightly) depending on (the value of) "x". Consequently, separately for detectors D1 or D2, the difference of pathlengths for the two slits may vary, leading to interference changing between constructive and destructive, as (the value of) "x" is being changed in the course of taking data.
Of course, the exact arrangement of experimental components had been optimized (and kept stable enough) for the interference effect to appear prominently.
Also: If it is required (for the setup to be said having "functioned properly and as specified") that the combined counting rate of D1 and D2 (in coincidence with D0) remained constant and independent of (the value of) "x" then the interference patters of D1 and of D2 necessarily appear complementary.
A: If we think the phenomenon in reverse an advance wave leaves either d1 or d2. The wave leaving from d1 strikes BSc and splits into blue and red, but the blue wave is phase shifted wrt to red due to reflection at BSc. similarly for wave leaving from d2,in this case red beam is phase shifted ..
