Photodetection of Low-Level Radiation through the Turbulent Atmosphere*

Abstract

Photoelectron-counting distributions are obtained for stochastic light that is caused to scintillate by passage through a random medium. The result is applied specifically to transmission of amplitude-stabilized radiation, with and without independent additive background, and of chaotic radiation, through the turbulent atmosphere. The counting distribution is found to broaden markedly and its peak occurs at decreasing count numbers for increasing turbulence. The cases studied here are of particular interest for low-level direct optical communications and radar using single-mode lasers, multimode lasers, thermal sources, and scattering targets. The results are obtained by extending the usual formulation of photoelectron counting; a product of two random variables, the source intensity and the effect of the turbulent medium, rather than the usual single stochastic irradiance, is considered. Plots of the counting distributions for various degrees of turbulence and for several signal-to-noise ratios are presented. A possible explanation is given for the observed decrease of the log-amplitude variance to values below the saturation value in long path length and high turbulence experiments.

Effects of propagation in air on photon statistics

“…The results (5) and (6) are valid in the weak-perturbation limit of small D . Experiments by Gracheva and Gurvich4 indicated that the log-normal distribution is reasonably accurate for u2 < 0.3.5 Using (6) with X = 772 nm and L = 10 km, their results would imply that the log-normal distribution should be accurate for C i < 9.8 x mm2l3.…”

Performance of photon-pair quantum key distribution systems

“…More accurate estimates of the dependence of freespace qkd performance on source characteristics and on the communication distance d can be obtained by applying existing analyses of atmospheric effects on optical signals [14][15][16].…”

Improved cumulative probabilities and range accuracy of a pulsed Geiger-mode avalanche photodiode laser ranging system with turbulence effects

“…29 / October 10 2017 / Applied Opticsprocess in the Gm-APD. Therefore, when the turbulence effects are added, the probability with m primary electrons fired in the Gm-APD during the integration times t 1 and t 2 is [7,9] PmjK…”

“…When the turbulence effects are added, a reducing detection performance will be produced, the influence of the turbulence effects on the photon flux can be modeled as a modulation of the mean irradiance, the statistics of the modulated echo photons is assumed to obey the lognormal distribution and be statistically independent of the echo photon detection, and the detection probability of the echo photons with turbulence effects is considered to obey the modulated Poisson distribution [7][8][9]. Cumulative pulse detection has the ability to improve the target detection probability and restrain the false alarm probability effectively [1,2,10,11].…”