I am quite unsure of how phase coherence is ensured in the double slit experiment. The most typical answer that I have found is that the path length difference between the lights going in either double slit is zero, and so the phase is coherent. However, if we consider Young's experiment he used sunlight as his source which is incoherent. So in his setup, even though the diffracted light from the single slit pass through the same path length to reach the double slit, wouldn't the light still be incoherent?
I have seen explanations to this pointing out that the single slit acts as a point source for light and produces phase coherent light. If this is true, how can this be when the sunlight reaching the single slit is out of phase?