Speckle Images Using Gaussian and Graded Index Apertures

Recently, speckle formation was investigated using diffusers modulated by linear, conical, quadratic, obstructed circular, deformed kidney, or elliptical modulated apertures (Hamed in J Mod Opt 56:1174–1181, 2009; J Mod Opt 56:1633–1642, 2009; Opt Eng 50:1–7, 2011; Opt Photon J 1:41–52, 2011). Using Fourier optics analysis, we showed that the speckle features for the above-mentioned apertures are dependent upon the aperture distribution. Others proposed a multiple exposure speckle-gram by using an optical system whose multiple aperture pupil changes between exposures (Tebaldi and Toro in Opt Commun 182:95–105, 2000). The characteristics of speckle patterns generated through multi-aperture pupils were also theoretically analyzed based on Fourier techniques (Toro and Tebaldi in Opt Commun 192:37–47, 2001). In another recent work, they analyzed speckle images generated when a diffuser was illuminated by coherent light and imaged by a lens with a pupil mask and multiple apertures forming a closed curve to obtain a clustered speckle structure (Mosso et al. in Opt Commun 283:1285–1290, 2009). The cluster structure results from the complex modulation produced inside each speckle, which is generated by multiple interferences of light through the apertures. When the apertures are uniformly distributed along a closed curve, the resulting image speckle cluster replicates the pupil aperture distribution. The authors in (Mosso et al. in Opt Commun 283:1285–1290, 2009) showed from experimental and theoretical simulations that the cluster features are dependent on the aperture distribution and the size of the closed curve. In the present chapter, modulated graded indices and truncated apertures are considered. The speckle images of diffusers using these modulated apertures were examined. Hence, the autocorrelation function of the modulated speckle images is computed and plotted. The average speckle size of these modulated speckle images is computed from the autocorrelation of the speckle images.