Generalized Yamaguchi correlation factor for coherent quadratic phase speckle metrology systems with an aperture.

In speckle-based metrology systems, a finite range of possible motion or deformation can be measured. When coherent imaging systems with a single limiting aperture are used in speckle metrology, the observed decorrelation effects that ultimately define this range are described by the well-known Yamaguchi correlation factor. We extend this result to all coherent quadratic phase paraxial optical systems with a single aperture and provide experimental results to support our theoretical conclusions.

[1]  P. Rastogi,et al.  Digital Speckle Pattern Interferometry & Related Techniques , 2000 .

[2]  S. A. Collins Lens-System Diffraction Integral Written in Terms of Matrix Optics , 1970 .

[3]  Martin J. Bastiaans,et al.  Fractional Transforms in Optical Information Processing , 2005, EURASIP J. Adv. Signal Process..

[4]  Bryan M Hennelly,et al.  Speckle photography: mixed domain fractional Fourier motion detection. , 2006, Optics letters.

[5]  Soo-Chang Pei,et al.  Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[6]  Unnikrishnan Gopinathan,et al.  Paraxial speckle-based metrology systems with an aperture. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  Thomas Fricke-Begemann Three-dimensional deformation field measurement with digital speckle correlation. , 2003, Applied optics.

[8]  Jose M Diazdelacruz Multiwindowed defocused electronic speckle photographic system for tilt measurement. , 2005, Applied optics.

[9]  T. Fricke-Begemann Optical measurement of deformation fields and surface processes with digital speckle correlation , 2003 .

[10]  J. Walkup,et al.  Statistical optics , 1986, IEEE Journal of Quantum Electronics.

[11]  Hans J. Tiziani,et al.  A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately , 1972 .

[12]  Bryan M Hennelly,et al.  Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform. , 2005, Applied optics.

[13]  John T. Sheridan,et al.  Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation. , 1994, Optics letters.

[14]  J. Goodman Introduction to Fourier optics , 1969 .

[15]  K. Stetson,et al.  Progress in optics , 1980, IEEE Journal of Quantum Electronics.

[16]  C. Sheppard,et al.  Theory and practice of scanning optical microscopy , 1984 .