In the arrangement shown L1, L2 are slits and S1, S2 two independent sources on the screen, interference fringes

On the screen, we have four amplitudes pair wise coherent.  A1+A2+A3+A4≡A12+A34  However, if A12 and A34 have equal magnitude because of random   phase of A12 and A34, no fringes will be seen.