However, theory and experiment do not show quantitative agreement: theoretical lines lie eitherhigher (blue and red lines in the left panel of Fig. 7) or lower (all other lines in Fig. 7) than thedata. The reasons behind this disagreement are the same as in the case of intensity correlationcoefficient c(τ) in Sec. 3.1.

4. Conclusions

In the present paper we presented a study of noise in modern speckle correlation and imagingtechniques. The noise originates from replacing the ensemble averaging (assumed in theoret-ical models) by averaging over a finite number N of pixels of a digital camera. In particular,we studied the noise of the speckle intensity variance c, and of the intensity correlation andstructure coefficients c(τ) and s(τ), respectively. The variances of all these quantities decreaseas 1/N when the number of pixels is increased and depend in complex ways on the spatial (dueto the finite pixel size) and temporal (due to the finite integration time) correlations of inten-sity in the speckle pattern. For stationary speckle patterns, we obtained quantitative agreementbetween measurements and the theoretical model that we developed in this paper. For dynamicspeckle patterns, theoretical predictions reproduce general trends of our data but fail to providea fully quantitative description. We believe that this is due to the approximate character of ourtheoretical model (neglecting correlations between distant pixels, gamma distribution of inten-sity at a single pixel) as well as to imperfections of our experiment (impossibility to achieve aperfectly uniform illumination of the sample, necessity to work with weak signals, etc.). De-spite the absence of quantitative agreement between theory and experiment in the latter case,the results presented in the paper provide an important starting point for estimation of the noiselevel in such applications as the multi-speckle dynamic light scattering, time-resolved correla-tion spectroscopy, speckle visibility spectroscopy, near-field scattering, laser speckle imagingand echo speckle imaging.

Acknowledgements

This work has been supported by the Swiss-French Germaine de Stael collaboration projectNo. 19126RL and the Swiss National Science Foundation projects 200020–126772 and 117762.RC acknowledges financial support from the European Union (Marie Curie Intra-EuropeanFellowship, Contract No. EIF–038772)

#128482 - $15.00 USD Received 17 May 2010; revised 15 Jun 2010; accepted 20 Jun 2010; published 22 Jun 2010

(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14534