Correlation of Spatially Filtered Dynamic Speckles in Distance Measurement Application

In this paper statistical properties of spatially filtered dynamic speckles are considered. This phenomenon was not sufficiently studied yet while spatial filtering is an important instrument for speckles velocity measurements. In case of spatial filtering speckle velocity information is derived from the modulation frequency of filtered light power which is measured by photodetector. Typical photodetector output is represented by a narrow-band random noise signal which includes non-informative intervals. Therefore more or less precious frequency measurement requires averaging. In its turn averaging implies uncorrelated samples. However, conducting research we found that correlation is typical property not only of dynamic speckle patterns but also of spatially filtered speckles. Using spatial filtering the correlation is observed as a response of measurements provided to the same part of the object surface or in case of simultaneously using several adjacent photodetectors. Found correlations can not be explained using just properties of unfiltered dynamic speckles. As we demonstrate the subject of this paper is important not only from pure theoretical point but also from the point of applied speckle metrology. E.g. using single spatial filter and an array of photodetector can greatly improve accuracy of speckle velocity measurements.