22 October 2004 Speckle correlation and the fractional Fourier transform
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The Fractional Fourier Transform (FRT) in combination with speckle photography has previously been used to measure surface tilting and translation. Previous Optical Fractional Fourier Transform (OFRT) based techniques used to determine such motion, have not been able to discern the direction of the tilt/translation. A simple new approach involving the use of correlation is presented to overcome this limitation. This is combined with an OFRT system, and controlled variation of the minimum resolution and dynamical range of measurement is demonstrated. It is then confirmed that if a rigid body’s motion is captured using two separate OFRT systems, the direction of both the tilting and in plane translation motion of the body can be determined without apriori knowledge. Experimental results are presented which confirm the validity of theoretical predictions.
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Damien P. Kelly, Damien P. Kelly, Bryan M. Hennelly, Bryan M. Hennelly, John T. Sheridan, John T. Sheridan, } "Speckle correlation and the fractional Fourier transform", Proc. SPIE 5557, Optical Information Systems II, (22 October 2004); doi: 10.1117/12.560489; https://doi.org/10.1117/12.560489

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