Speckle spots ride phase saddles sidesaddle

The relationship between bright speckle spots in a random speckle pattern and the structure of the underlying phase field is studied by experiment and by computer simulation. The phase field is found to be dominated by phase saddles strung between phase singularities (vortices). Phase extrema (maxima and minima) are found to be relatively rare, with saddles outnumbering extrema by ∼ 14:1. The major regions of nearly constant phase in a random wave field therefore correspond to phase saddles. Speckle spots are shown to be associated with these saddles, tending to lie on the sides of the saddles rather than directly over the centers. Because of this, there is a significant phase gradient across a speckle spot. The average value of this gradient at the center of the spot (intensity maximum) is ∼ 50° per coherence length, which is somewhat less than 1 3 the average phase gradient for the whole speckle field.