Error analysis for polychromatic speckle contrast measurements

Abstract

Revival of interest in speckle technologies raises a curial question on the accuracy calculation of speckle measurements. In particular, the accuracy calculation of speckle contrast, an important metrics of a stochastic process, is quite different from the accuracy calculation of a typical intensity measurement. Speckle contrast depends more on stochastic characteristics of a process rather than on hardware characteristics. In this article, we consider errors introduced by the limited number of available speckle and by intensity saturation for monochromatic and polychromatic speckles. Equations for these types of errors were derived. Particularly, we show that the error due to limited number of speckles is inversely proportional to the square root of the speckle number, in the similar way as the average intensity error. For the error due to limited dynamic range of a recording device, the truncation effect increases the error as the mean intensity increased. Monochromatic speckles are more sensitive to such truncation than polychromatic speckles. We report the optimal mean intensity in terms of the pixel depth of a recording device and the total number of speckle recorded. In addition, a recommendation to minimize the saturation error for a typical camera is included.