Interference resulting from the measurement of four-time fourth-order correlation functions of a wave field is discussed. The fringes that are observed are peculiar because they have a statistical origin, and show the greatest contrast when the coherence time of the field is finite. This is demonstrated with a simple acoustic experiment. Random telegraph phase noise is used in this experiment to vary the field coherence in order to highlight the problem of interpreting this interference; for this noise the Gaussian moment theorem may not be invoked to reduce the description of the interference to one in terms of first order interference. A second example using the pseudorandom phase fluctuations that are encoded on GPS satellite transmissions is also presented.
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