Random phase measurement errors in digital speckle pattern interferometry

Phase measurements using digital speckle pattern interferometry are subject to random errors due to speckle decorrelation and electronic noise. A phasor description of speckle decorrelation is introduced from which the r.m.s. phase error is calculated. Phase noise due to additive Gaussian errors on the phase-stepped images is shown to be statistically equivalent to that from decorrelation, allowing the r.m.s. phase error from electronic noise to be obtained analytically. The currently used noise reduction strategy of speckle averaging is shown to be optimal in that it provides the maximum likelihood estimate of speckle phase change. Finally, the effect of speckle integration implicit in digitization by pixels of finite size is considered using computer-generated speckle patterns. It is shown that the phase errors decrease monotonically with decreasing speckle diameter.