Spatial coherence from ducks

It is not generally appreciated that radiation from uncorrelated random sources—for example, radiation generated by spontaneous emission of light by atoms—can produce a well-behaved, spatially coherent field over large regions. An illustration of this fact is the diffraction image of a star in the focal plane of a telescope. On a good observing night, the image will consist of a bright central spot surrounded by dark rings that represent regions in the focal plane where destructive interference cancels the light. This is a manifestation of strong correlation—a high degree of spatial coherence—between light fluctuations in the aperture of the telescope. The phenomenon illustrates the so-called van Cittert-Zernike theorem of optical coherence theory. ^{1  ,  2}  

In this letter we provide an example of the generation of spatial coherence. Thirteen Rouen ducks jump into a still one-acre pond, disturbing the surface at randomly distributed positions and times. The water surface exhibits an irregular, rather incoherent spatial pattern, as seen in panel a of the figure. ³ With increasing distance and time, the pattern evolves into a more regular one, as captured in panels b, c, and d, which clearly indicate the generation of spatial coherence in the far field from randomly distributed sources.