Angular correlation function of speckle patterns scattered from a one-dimensional rough dielectric film on a glass substrate

Abstract

We present the experimental results of the angular correlation function of far-field speckle patterns scattered by a one-dimensionally random rough surface of a thin dielectric film on a glass substrate when a polarized beam of light is incident upon the rough surface from vacuum. This surface, which separates the vacuum and the dielectric, is rough enough that only diffused speckles are observed. The experiment for the correlation measurement was set up to make use of a CCD camera to obtain the image of the speckle pattern in the specular direction for each given angle of incidence; the cross-correlation function is then calculated from the digitized images. It is found that the intensity correlation functions exhibit two distinct maxima: one arises from the autocorrelation and the other from the reciprocity condition. It is also found that different scattering processes give rise to quite different correlation functions: multiple-scattering processes produce narrow peaks with secondary maxima and single-scattering processes produce relatively broad peaks.

<title>Dynamic behavior of speckles from rough surface scattering</title>

“…If we have one scattered speckle intensity 1(8 ,O Si) observed at the scattering angle e sl generated by an incident light at angle of incidence of 0 and another scattered speckle intensity 1(0 j2 s2 ) observed at the scattering angle 0 s2 generated by an incident light at angle of incidence of 0 j2 the normalized angular correlation between them is defined by: (1) [(< I(O,O)2 > < I(O,e) >2)(< I(0j2,052)2 > < I(0i2,0S2) >2)]2 the <.. .> denotes ensemble averaging among the speckles of the speckle distribution. It has been shown that a strong correlation can be observed if the following conditions are satisfied: (8) sin 0 -sinO = sinO i2 sinO s2 .…”

Angular correlation properties of 2D‐nano‐roughness‐induced speckle patterns for silica‐on‐silicon wafers

“…The speckle pattern is obtained by direct illumination of the CCD camera, without the use of an optical objective. This approach experimentally differs from previous similar experiments [9,10]. As summarized in [14], every pixel composing the speckle pattern in our case is an average of scattering contributions from all the surface elements illuminated by the laser.…”

“…3 Results and discussion When a first speckle pattern I(θ i1 ,θ s1 ) is recorded using illumination and observation angles θ i1 and θ s1 respectively, its correlation coefficient with a second image I(θ i2 ,θ s2 ) obtained for angles θ i2 and θ s2 is given by [9]: …”

“…Experimental observation of C (1) [9] with mono-dimensional roughness and C (10) [10] with 2D-roughness were reported for the case of a dielectric layer over a glass substrate, with the sample being wedgeshaped to avoid reflection from the substrate to lie in the plane of incidence.…”

Experimental study of the angular correlation function in the double passage of waves through a one-dimensional random phase screen

“…These phenomena have now been confirmed theoretically and experimentally for volume scattering [2-81. Correlation in light scattering from random rough surfaces has also been studied [9-141. Taking into account multiple scattering, the intensity correlation function for light elastically scattered from a randomly rough metallic grating was calculated [9] and the angular correlation function of speckle patterns scattered from a one-dimensional (ID) rough dielectric film on a glass substrate was investigated [14]. Recent theoretical analysis of the angular intensity correlation function in the double passage of waves through a random phase screen has been carried out by Escamilla er a1 [ 151.…”