Windowed defocused photographic speckle vibration measurement

Abstract: The out-of-plane vibration of a rough surface causes an in-plane vibration of its speckle pattern when observed with a defocused optical photographic system. If the frequency of the oscillations is high enough, a time-averaged specklegram is recorded from which the amplitude of the vibration can be estimated. The statistical character of speckle distributions along with the pixel sampling and intensity analog-to-digital conversion inherent to electronic cameras degrade the accuracy of the amplitude measurement to an extent that is analyzed and experimentally tested in this paper. The relations limiting the mutually competing metrological features of a defocused speckle system are also deduced mathematically.