The accuracy of Young’s fringe method for reducing velocity field data is compromised by a spatially incoherent background field which originates in the random locations of the seeding particles. The probability density function for the spatial frequency cutoff of this background is derived as a function of the particle count, the distribution governing the power in each frequency interval is derived, and conditions are found under which the Van Cittert-Zernike theorem applies. The background field resembles the far field of a partially coherent source in the high particle count limit, but departs significantly at low and moderate counts.
Robert Rubinstein and Paul S. Greenberg, "Particle image fields and partial coherence," Appl. Opt. 29, 5282-5291 (1990)