Three-dimensional static speckle fields Part II Experimental investigation

Abstract

When monochromatic light is scattered from an optically rough surface a complicated three-dimensional (3D) field is generated. These fields are often described by reference to the 3D volume (extent) of their speckles, leading to the definition of lateral ðx; yÞ and longitudinal speckle sizes (z). For reasons of mathematical simplicity the longitu- dinal speckle size is often derived by examining the decorrelation of the speckle field for a single point lying on axis, i.e., x 1⁄4 y 1⁄4 0, and this size is generally assumed to be representative for other speckles that lie further off- axis. Some recent theoretical results, however, indicate that in fact longitudinal speckle size gets smaller as the observation position moves to off-axis spatial locations. In this paper (Part I), we review the physical argument leading to this conclusion and support this analysis with a series of robust numerical simulations. We discuss, in some detail, computational issues that arise when simulating the propagation of speckle fields numerically, show- ing that the spectral method is not a suitable propagation algorithm when the autocorrelation of the scattering surface is assumed to be delta correlated. In Part II [J. Opt. Soc. Am. A 28, 1904 (2011)] of this paper, experimental results are provided that exhibit the predicted variation of longitudinal speckle size as a function of position in x and y. The results are not only of theoretical interest but have practical implications, and in Part II a method for locating the optical system axis is proposed and experimentally demonstrated.