Particle image fields and partial coherence

The accuracy of Young's fringe method for reducing velocity field data is compromized 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.