Speckle, averaging

We are interested in < E (0[,(t)i)E3(62,, where <> means the average over the ensemble of surfaces, the subindexes 1 and 2 refer to two different points of observation and the subindexes A and B belong to two different conditions of illumination, which for example arise from two different wavelengths, two different incident angles, etc.. If A = B and 1 = 2, the above expression gives the angular distribution of the mean scattered intensity, otherwise it turns to be the intensity correlation coefficient y from < E Eb >, assuming that we deal with fully developed speckle. 

Since speckle artifacts depend on the direction of the ultrasound beam, frames obtained from different view angles have different speckle patterns, which average out when combined in the compound image. 

However, the advantage is that the statistics of the speckle for backscattered light fram random rough surfaces is known, namely for uncorrelated speckle samples it is Poissonian. Therefore averaging over large number (N) of... 

The contrast C of a speckle pattern is defined as the ratio of the standard deviation (Os) of the intensity variations to the ensemble average of the intensity [12]. 

The speckle pattern is captured by a CCD camera that has a finite integration time and thus some of the fluctuations will be averaged out and the net contrast value of the... 

The contrast of one grid completely illuminated by the laser has been computed using eqn. (1). Three sets of images were taken for each condition with a time gap of 10 seconds and the average speckle contrast of the three images was computed. The results are presented in table 1 and table 2. 

The small relaxations of the pull-out force during interruptions between successive steps of loading were taken into account and considered as the decrement of the slip proportional to the load relaxation. The interruptions were caused by the requirements of the speckle photography method itself and lasted several minutes each. The degree of load relaxation was relatively low (as average 4% of the global pull-out force... 

Figure 3 Principle of echo technique. Echoes at multiples of the rotational period by continuous rotation of the cell exhibit peaks as shown on the right, where one of the echoes of intensity correlation fif ( (=g (0 in Pn [147]) is shown. The echo width is determined by rotation velocity and number of speckles per revolution, while the echo height is associated with the dynamics of the sample. We can usually take ensemble average over 500-800 different speckles in one revolution. Reproduced from illustrations of Medebach, M. Freiberger, N. Glatter, 0. Rev. Sci. Instrum. 2008,79,073907, ° with permission.

Figure 9 A speckle pattern (a) and (1>t/0a vs. <1)t plots (b) based on eqn [166] for a thermoreversible gel of poly(vinyl alcohol) (PVA) with Congo red (CR) In water at 20 °C In the gel region. Concentrations of PVA and CR are 680 and 10 mM, respectively. The horizontal solid and dashed lines in (a) indicate the ensemble average <1)e and the fluctuation component

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