  High-order coherence effects between two first-order incoherent sources with
fully independent phases have been well studied in the literature, which shows
interference fringes with respect to the position separations among different
space points. Here we show that this is not the whole story, and find that the
high-order coherence effects depend on the mode of the phase random walk of the
first-order incoherent sources, which can be controlled artificially and
represented geometrically by vectorial polygons. Interestingly, by scanning the
detectors along the same direction with the position separations between them
kept constant, a set of high-order coherence fringes, which fingerprint the
phase random walk of the first-order incoherent sources, can be observed. Our
results show that it is possible to control the high-order coherence of two
first-order incoherent sources, which could have important practical
applications such as superhigh resolution optical lithography.
