A Review of Some Recent Work in the Area of Imaging and Optical Signal Processing <s> IWA1.pdf <s> 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. <s> BIB001 </s> A Review of Some Recent Work in the Area of Imaging and Optical Signal Processing <s> IWA1.pdf <s> 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 de correlation 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. <s> BIB002 </s> A Review of Some Recent Work in the Area of Imaging and Optical Signal Processing <s> IWA1.pdf <s> 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. <s> BIB003 </s> A Review of Some Recent Work in the Area of Imaging and Optical Signal Processing <s> IWA1.pdf <s> 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. © 2009 Optical Society of America OCIS codes: 070.2580, 030.6140, 110.6150. <s> BIB004
It was found necessary, when using such a speckle based metrology systems, in order to avoid ambiguity in relation to the direction of motion, to use correlation techniques. The measurement process, including the resolution and dynamic range of the system, thus depended critically on the speckle correlation properties. In order to design and interpret the results from such systems it was necessary to determine how the speckle evolved as it passed through apertures and through QPSs BIB001 BIB002 BIB003  . In our most recent work in this area we have shown how longitudinal and lateral speckle size depends on the aperture (shape, size) and varies on-and off-axis BIB004  .