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Coherent power measurement uncertainty resulting from atmospheric turbulence

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Abstract

The simulation of beam propagation is used to examine the uncertainty inherent to the process of optical power measurement with a practical heterodyne lidar because of the presence of refractive turbulence. The approach has made possible the foremost study of the statistics of the coherent return fluctuations in the turbulent atmosphere for which there is no existing theory to be considered.

©2004 Optical Society of America

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Coherent DIAL profiling in turbulent atmosphere

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Opt. Express 12(7) 1249-1257 (2004)

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Figures (4)

Fig. 1.
Fig. 1. Statistics of the coherent power turbulent fluctuations as a function of range R and different moderate-to-strong refractive turbulence Cn2 daytime values for a 2-µm wavelength, 16-cm aperture, monostatic lidar system. Along with the coherent power variance, the covariance function is shown for different range resolutions ΔR. The dashed line and y-axis labeling on the right corresponds to the mean coherent power.
Fig. 2.
Fig. 2. Similar to Fig. 1 but for a 10-µm monostatic lidar. Again, along with the coherent power variance, the covariance function is shown for different range resolutions ΔR. The dashed line and y-axis labeling on the right corresponds to the mean coherent power.
Fig. 3.
Fig. 3. Variance and covariance for different range resolutions ΔR of the coherent power turbulent fluctuations as a function of range R for a 2-µm bistatic lidar system. The lidar system parameters and levels of refractive turbulence are similar to those in Fig. 1 for the monostatic system. The dashed line and y-axis labeling on the right corresponds to the mean coherent power.
Fig. 4.
Fig. 4. Similar to Fig.3 but for a 10-µm monostatic lidar. The dashed line and y-axis labeling on the right corresponds to the mean coherent power.

Equations (3)

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P ( R , t ) = C exp [ 2 R α ( R ) ] β ( R ) λ 2 j T ( p , R , t ) j BPLO ( p , R ) d p ,
δ P ( R ) = P on ( R Δ R 2 ) P off ( R + Δ R 2 ) P on ( R + Δ R 2 ) P off ( R Δ R 2 )
C P ( R 1 , R 2 ) = [ j T ( p , R 1 , t ) j BPLO ( p , R 1 ) d p ] [ j T ( p , R 2 , t ) j BPLO ( p , R 2 ) d p ] [ j T ( p , R 1 , t ) j BPLO ( p , R 1 ) d p ] [ j T ( p , R 2 , t ) j BPLO ( p , R 2 ) d p ] 1
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