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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 11 — Nov. 1, 2006
  • pp: 2861–2870

Paraxial speckle-based metrology systems with an aperture

Damien P. Kelly, Jennifer E. Ward, Bryan M. Hennelly, Unnikrishnan Gopinathan, Feidhlim T. O’Neill, and John T. Sheridan  »View Author Affiliations


JOSA A, Vol. 23, Issue 11, pp. 2861-2870 (2006)
http://dx.doi.org/10.1364/JOSAA.23.002861


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Abstract

Digital speckle photography can be used in the analysis of surface motion in combination with an optical linear canonical transform (LCT). Previously [ D. P. Kelly et al. Appl. Opt. 44, 2720 (2005) ] it has been shown that optical fractional Fourier transforms (OFRTs) can be used to vary the range and sensitivity of speckle-based metrology systems, allowing the measurement of both the magnitude and direction of tilting (rotation) and translation motion simultaneously, provided that the motion is captured in two separate OFRT domains. This requires two bulk optical systems. We extend the OFRT analysis to more general LCT systems with a single limiting aperture. The effect of a limiting aperture in LCT systems is examined in more detail by deriving a generalized Yamaguchi correlation factor. We demonstrate the benefits of using an LCT approach to metrology design. Using this technique, we show that by varying the curvature of the illuminating field, we can effectively change the output domain. From a practical perspective this means that estimation of the motion of a target can be achieved by using one bulk optical system and different illuminating conditions. Experimental results are provided to support our theoretical analysis.

© 2006 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.6150) Instrumentation, measurement, and metrology : Speckle imaging

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: February 10, 2006
Revised Manuscript: May 11, 2006
Manuscript Accepted: May 16, 2006

Citation
Damien P. Kelly, Jennifer E. Ward, Bryan M. Hennelly, Unnikrishnan Gopinathan, Feidhlim T. O'Neill, and John T. Sheridan, "Paraxial speckle-based metrology systems with an aperture," J. Opt. Soc. Am. A 23, 2861-2870 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-11-2861


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