Second-order Statistics of Integrated Intensities and of Detected Photoelectrons

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Abstract
The second-order statistics associated with the time-integrated intensity in photoelectron counting and with the aperture-integrated intensity in laser speckle are investigated with special emphasis placed upon the long-measurement-time (large-aperture) regime. Both the joint probability density function and the conditional probability density function of the integrated intensities are obtained as a power series in the integrated intensity correlation function with coefficients given by associated Laguerre polynomials in the two integrated intensities. The conditional variance is evaluated and discussed. The corresponding problem of the second-order statistics of detected photoelectrons is also solved.

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