Analysis and design of an anamorphic optical processor for speckle metrology and velocimetry

Two-dimensional velocity or displacement fields that are recorded as double-exposure speckle patterns may be measured with an anamorphic optical processor. The anamorphic optical processor measures one component of the velocity or displacement throughout a linear region of the double-exposure speckle pattern. The signal in the output plane of such a processor is a fringe pattern. An analysis to predict fringe modulation based on Fourier optics and the statistics of speckle patterns is developed. The analysis specifies the effects of both the speckle-recording optics and the anamorphic optical processor on the fringe modulation. The observed loss of modulation when the velocity or displacement component perpendicular to the measured component is increased is also described. Measurements of fringe modulations that are produced by anamorphic optical processors with and without increased tolerance to the perpendicular velocity component are compared to results of the analysis. Fringe modulation versus relative exposure in the double-exposure speckle pattern are also measured and compared to the results of this analysis. An anamorphic processor that reduces the time for digital processing of the fringe patterns by a factor of N (typically 128, 256, or 512) relative to the two-dimensional Fourier transform optical processor (with identical spatial resolution) is demonstrated.