Abstract

The process of optical power measurement with a heterodyne lidar carry an inherent statistic uncertainty because of the presence of refractive turbulence. Although these uncertainties are usually reduced by taking average values of different measurements, our analysis shows that temporal correlation of the laser-beam fluctuations restricts the effectiveness of the signal averaging in practical systems such as a coherent DIAL.

© 2004 Optical Society of America

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References

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  1. A. Belmonte, "Coherent power measurement uncertainty resulting from atmospheric turbulence," Opt. Express 12, 168-175 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-168">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-168</a>
    [CrossRef] [PubMed]
  2. A. Belmonte, "Coherent DIAL profiling in turbulent atmosphere," Opt. Express 12, 1249-1257 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1249">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1249</a>
    [CrossRef] [PubMed]
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  14. A. Belmonte, ???Angular misalignment contribution to practical heterodyne lidars in the turbulent atmosphere,??? Opt. Express 11, 2525-2531 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-20-2525">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-20-2525</a>.
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Appl. Opt. (3)

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, ???Time-dependent propagation of high energy laser beams through the atmosphere,??? Appl. Phys. 10, 129-160 (1976)
[CrossRef]

J. Mod. Opt. (1)

L. C. Andrews, ???An analytical model for the refractive-index power spectrum and its application to optical scintillation in the atmosphere,??? J. Mod. Opt. 39, 1849-1853, 1992
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Journal of Applied Meteorology (1)

B. J. Rye, ???Power ratio estimation in incoherent backscatter lidar: Heterodyne receiver with square law detection,??? Journal of Applied Meteorology 22, 1899-1913 (1983)
[CrossRef]

Opt. Express (3)

Proc. SPIE (1)

K. J. Gamble, A. R. Weeks, H. R. Myler, W. A. Rabadi, ???Results of two-dimensional time-evolved phase screen computer simulations,??? in Atmospheric Propagation and Remote Sensing IV, C. Dainty, ed., Proc. SPIE 2471, 170-180 (1995)

Wave Propagation in Random Media 1993 (1)

J. Martin, ???Simulation of wave propagation in random media: theory and applications,??? in Wave Propagation in Random Media (Scintillation), V. I. Tatarskii, A. Ishimaru, and V. Zavorotny, eds., SPIE, Washington (1993)

Supplementary Material (1)

» Media 1: MOV (1916 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

The movie (1.9 MB) presents a computer simulation of observed intensity (right) and phase (center) in a laser beam after propagating through a finite set of time evolved random phase screens (left) modeling the atmospheric turbulence. A 16-cm aperture lidar system working at 2-µm wavelength on a moderate refractive turbulence Cn2 daytime value is considered. An atmospheric wind of 10 m/s is imposed along the 3-km propagation path considered in the simulation. This computation is done for 64 milliseconds with a temporal resolution of 1 millisecond. In order to estimate the coherent power statistics properly, we may need to run a continuous temporal series during as much as 10 seconds.

Fig. 2.
Fig. 2.

Coherent-power temporal correlation coefficients for a 16-cm aperture, monostatic lidar system working at 2-µm (left) and 10-µm (right) wavelength. Correlation coefficients are shown for different ranges R and moderate (down) to strong (up) refractive turbulence Cn2 daytime values. Temporal correlation lengths, measured at 1/e2, are also indicated in the graphics (dashed red lines).

Fig. 3.
Fig. 3.

Coherent power standard deviation in a DIAL system as a function of averaged pulses for a 16-cm aperture, monostatic lidar system working at 2-µm (left) and 10-µm (right) wavelength. Different moderate (down) to strong (up) refractive turbulence Cn2 daytime values are considered. The power standard deviation is shown for different lidar pulse repetition frequencies. The black line corresponds to the measurement standard deviation associated with speckle effects where, assuming that all the power samples are independent, the uncertainty is expected to decrease as N-1/2.

Fig. 4.
Fig. 4.

Coherent power decorrelation factor in a DIAL system as a function of the frequency separation between on-line and off-line wavelengths for a 16-cm aperture, monostatic lidar system working at 2-µm (left) and 10-µm (right) wavelength. A strong refractive turbulence Cn2 daytime value is considered.

Equations (3)

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C P ( t 1 , t 2 ) = P ( R , t 1 ) P ( R , t 2 ) P ( R ) 2 1
P ( R , t ) = C ( R ) λ 2 j T ( p , R , t ) j BPLO ( p , R ) d p ,
σ N 2 = σ P 2 N [ 1 + 2 n = 1 N 1 ( 1 n N ) ρ ( 0 , t n ) ] .

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