Speckle Pattern Errors in Self-Mixing Interferometry

Abstract— We analyze the random errors occurring in interferometric measurements because of the speckle pattern regime, when the remote target is a diffusing surface. First, we review the statistical properties of speckle and discuss amplitude fading affecting the self-mixing interferometer (SMI) signal and methods to alleviate it. Second, we derive intra-speckle phase errors using the bivariate conditional probability, and find that the noise-equivalent-displacement (NED) for small displacement \delta is proportional to the ratio of \delta to speckle longitudinal size sl. Last, we extend the analysis to inter-speckle displacements (\delta >sl) and, after deriving speckle systematic and random errors, show that operation up to meters on a diffusing surface target is possible with a small (≈\lambda error. Results are mainly focussed on SMI, yet they have general validity for any configuration of interferometry.