Decorrelation-induced phase errors in phase-shifting speckle interferometry.

The purpose of this research is the quantitative investigation of decorrelation-induced phase errors in speckle interferometry. Measurements in speckle interferometry are inherently affected by decorrelation, i.e., by alterations of the speckle fields during measurement. Likewise, the random phases carrying the interferometric information change during decorrelation. Image plane and pupil plane decorrelation are considered for both smooth and speckle reference wave interferometers. Since the decorrelation effect depends on the aperture and the pixel size, the calculations include not only the case of speckles being well resolved by the camera but also the case of unresolved speckles. Different standard deviations of the phase error are obtained from the probability density of the pixel modulation and the phase before and after decorrelation. Most cases (apart from pupil plane decorrelation in speckle reference wave setups) appear to obey exactly the same phase error statistics. In particular, the number of speckles per pixel does not affect the phase error distribution over the whole image. The only important parameters determining the decorrelation-induced phase errors are the amount of decorrelation and the pixel modulation.