Now showing 1 - 5 of 5
  • Publication
    Controlling speckle using lenses and free space
    The correlation properties of speckle fields are studied for general paraxial systems. The previous studies on lateral and longitudinal speckle size for the case of free-space propagation (Fresnel transform) are generalized to the case of the linear canonical transform. These results have implications for the control of speckle size, through appropriate design of optical systems, with particular relevance for speckle interferometry.
      394Scopus© Citations 17
  • Publication
    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.
      466Scopus© Citations 15
  • Publication
    Lucky imaging and aperture synthesis with low-redundancy apertures
    (Optical Society of America, 2009-01-01) ; ;
    Lucky imaging, used with some success in astronomical and even horizontal-path imaging, relies on fleeting conditions of the atmosphere that allow momentary improvements in image quality, at least in portions of an image. Aperture synthesis allows a larger aperture and, thus, a higher-resolution imaging system to be synthesized through the superposition of image spatial-frequency components gathered by cooperative combinations of smaller subapertures. Acombination of lucky imaging and aperture synthesis strengthens both methods for obtaining improved images through the turbulent atmosphere.We realize the lucky imaging condition appropriate for aperture synthesis imaging for a pair of rectangular subapertures and demonstrate that this condition occurs when the signal energy associated with bandpass spatial-frequency components achieves its maximum value.
      441Scopus© Citations 8
  • Publication
    Three-dimensional speckle size in generalized optical systems with limiting apertures
    (Optical Society of America, 2009-08-01) ; ;
    Correlation properties of speckle fields at the output of quadratic phase systems with hard square and circular apertures are examined. Using the linear canonical transform and ABCD ray matrix techniques to describe these general optical systems, we first derive analytical formulas for determining axial and lateral speckle sizes. Then using a numerical technique, we extend the analysis so that the correlation properties of nonaxial speckles can also be considered. Using some simple optical systems as examples, we demonstrate how this approach may be conveniently applied. The results of this analysis apply broadly both to the design of metrology systems and to speckle control schemes
      628Scopus© Citations 11
  • Publication
    Paraxial speckle-based metrology systems with an aperture
    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.
      460Scopus© Citations 23