Li, DayanDayanLiKelly, Damien P.Damien P.KellyKirner, RaoulRaoulKirnerSheridan, John T.John T.Sheridan2012-11-082012-11-082012 Optic2012-02Applied Opticshttp://hdl.handle.net/10197/3902The statistical properties of speckles in paraxial optical systems depend on the system parameters. In particular, the speckle orientation and the lateral dependence (x and y) of the longitudinal speckle size can vary significantly. For example, the off-axis longitudinal correlation length remains equal to the on-axis size for speckles in a Fourier transform system, while it decreases dramatically as the observation position moves off axis in a Fresnel system. In this paper, we review the speckle correlation function in general linear canonical transform (LCT) systems, clearly demonstrating that speckle properties can be controlled by introducing different optical components, i.e., lenses and sections of free space. Using a series of numerical simulations, we examine how the correlation function changes for some typical LCT systems. The integrating effect of the camera pixel and the impact this has on the measured first- and second-order statistics of the speckle intensities is also examined theoretically. A series of experimental results are then presented to confirm several of these predictions. First, the effect the pixel size has on the measured first-order speckle statistics is demonstrated, and second, the orientation of speckles in a Fourier transform system is measured, showing that the speckles lie parallel to the optical axis.enThis paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-4-A1. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.Statistical opticsDiffractionSpeckle imagingWave propagationSpeckleDiffractionFourier transform opticsJournal Article514A1A1010.1364/AO.51.0000A12012-10-17https://creativecommons.org/licenses/by-nc-nd/3.0/ie/