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

Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform

Damien P. Kelly, Bryan M. Hennelly, and John T. Sheridan
Appl. Opt. 44(14) 2720-2727 (2005)

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

Damien P. Kelly, Jennifer E. Ward, Unnikrishnan Gopinathan, Bryan M. Hennelly, Feidhlim T. O'Neill, and John T. Sheridan
Opt. Lett. 31(23) 3444-3446 (2006)

Three-dimensional speckle size in generalized optical systems with limiting apertures

Jennifer E. Ward, Damien P. Kelly, and John T. Sheridan
J. Opt. Soc. Am. A 26(8) 1855-1864 (2009)

Speckle orientation in paraxial optical systems

Dayan Li, Damien P. Kelly, Raoul Kirner, and John T. Sheridan
Appl. Opt. 51(4) A1-A10 (2012)

Three-dimensional speckle dynamics in paraxial optical systems

H. T. Yura, S. G. Hanson, R. S. Hansen, and B. Rose
J. Opt. Soc. Am. A 16(6) 1402-1412 (1999)