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N-fold joint photocounting distribution for modulated laser radiation: Transmission through the turbulent atmosphere

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Abstract

In this paper a generalised result for theN-fold joint photoelectron counting distribution for independently modulated radiation is given. We extend the recent results of Diament and Teich, for the one-fold photoelectron counting distribution for light propagated through an atmosphere characterised by log-normal irradiance fluctuations, to theN-fold joint photoelectron counting distribution. An approximate solution for thisN-fold distribution is obtained, for detection intervals {Ti} «τ a whereτ a is the characteristic time of the atmospheric turbulence. We present specifically the two-fold joint photocounting distribution for amplitude-stabilised laser radiation passing through such an atmosphere for several levels of turbulence and degrees of correlation. Cases including additive, independent, non-interfering Poisson noise are considered. Computer generated plots of the photocounting distribution are presented. For noise-free detection, the otherwise narrow-peaked photocounting distribution is seen to broaden markedly and shift its peak to lower counts as the turbulence level increases. Furthermore, a non-singular counting distribution is obtained for fully correlated detection. In the presence of additive noise and varying only the signal-to-noise ratioγ, the probability surface is intermediate between that of the Poisson and that of the noise-free log-normal fading counting distribution. The peak, however, is observed to decrease and then again increase in magnitude asγ → ∞, for correlated detection only. These results are expected to be of use in the study of atmospheric turbulence, as well as in the evaluation of certain stochastic functionals that occur in optical communication theory for the turbulent atmospheric channel.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Columbia University, 10027, New York, New York, USA

    M. C. Teich & S. Rosenberg

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  1. M. C. Teich
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  2. S. Rosenberg
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Additional information

This work was supported in part by the US National Science Foundation under Grant Number NSF-GK-16649.

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Teich, M.C., Rosenberg, S. N-fold joint photocounting distribution for modulated laser radiation: Transmission through the turbulent atmosphere. Opto-electronics 3, 63–76 (1971). https://doi.org/10.1007/BF01424084

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  • DOI: https://doi.org/10.1007/BF01424084

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