## Analyzing the efficiency of a practical heterodyne lidar in the turbulent atmosphere: telescope parameters

Optics Express, Vol. 11, Issue 17, pp. 2041-2046 (2003)

http://dx.doi.org/10.1364/OE.11.002041

Acrobat PDF (88 KB)

### Abstract

The simulation of beam propagation permits examination of the signal degradation in a heterodyne receiver caused by refractive turbulence under general atmospheric conditions and at arbitrary transmitter and receiver configurations. At shorter wavelengths, an understanding of turbulence effects is essential for deciding the optimal telescope parameters, i.e., focal length and aperture diameter, of a practical heterodyne lidar.

© 2003 Optical Society of America

## 1. Introduction

1. A. Belmonte and B. J. Rye, “Heterodyne lidar returns in turbulent atmosphere: performance evaluation of simulated systems,” Appl. Opt. **39**, 2401–2411 (2000). [CrossRef]

*l*

_{0}of 1 cm and outer scale

*L*

_{0}of the order of 5 m. Outer-scale effects of turbulence are less pronounced than inner scale effects in our analysis because monostatic systems have immunity to beam wander or tilt [2

2. S.F. Clifford and S. Wandzura, “Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,” Appl. Opt. **20**, 514–516 (1981). [CrossRef] [PubMed]

3. A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. **39**, 5426–5445 (2000). [CrossRef]

## 2. Coherent solid angle

*A*

_{R}/

*R*

^{2}presented by a lidar telescope with aperture area

*A*

_{R}at range

*R*:

*C(R)*groups the conversion efficiencies and parameters that describe the various system components and the atmospheric scattering conditions: The SNR is maximized through high pulse energy, narrow receiver bandwidth, high transmission optics, high backscatter coefficient, and low extinction. One’s first thought would be also to make the telescope aperture as large as possible. After propagating back through the system optics, the backscattered energy must mix effectively with the LO beam at the signal detector:

*η*

_{S}

*(R)*is the system-antenna efficiency [4

4. B. J. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. **18**, 1390–1398 (1979). [CrossRef] [PubMed]

*COH*:

*C(R)*in Eq. (1) are irrelevant. The coherent solid angle is expressed in terms of the maximum available value

*A*

_{R}/

*R*

^{2}and the efficiency parameter

*η*

_{S}

*(R)*that describes the extent to which this value is degraded. In the ideal case of deterministic transmitted optical fields, optimal beam truncation, far-field conditions, and absence of turbulence, the system-antenna efficiency can reach a maximum of approximately 0.4 [5

5. B.J. Rye and R.G. Frehlich, “Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,” Appl. Opt. **31**, 2891–2899 (1992). [CrossRef] [PubMed]

2. S.F. Clifford and S. Wandzura, “Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,” Appl. Opt. **20**, 514–516 (1981). [CrossRef] [PubMed]

6. K. Tanaka and N. Ohta, “Effects of tilt and offset of signal field on heterodyne efficiency,” Appl. Opt. **26**, 627–632 (1987). [CrossRef] [PubMed]

7. R.G. Frehlich and M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. **30**, 5325–5352 (1991). [CrossRef] [PubMed]

*COH*(i.e., antenna efficiency) under any realistic conditions. The coherent solid angle is equal in every respect to the so-called coherent responsivity [7

7. R.G. Frehlich and M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. **30**, 5325–5352 (1991). [CrossRef] [PubMed]

8. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta **26**, 627–644 (1979). [CrossRef]

*λ*, and aperture diameter

*D*through the same dimensionless Fresnel number

*N*

_{F}=

*kD*

^{2}/

*4R*that defines the beam’s far-field conditions,

*N*

_{F}<

*1*. Here,

*k*=

*2π*/

*λ*is the beam wave number.

3. A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. **39**, 5426–5445 (2000). [CrossRef]

9. L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. **A 16**, 1417–1429 (1999). [CrossRef]

*N*

_{F}is not enough to describe the heterodyne lidar returns.

*N*

_{T}=

*4R*has been used to describe both the magnitude of the irradiance fluctuations and the beam expansion associated with arbitrary turbulence conditions [10

10. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE **63**, 1669–1692 (1975). [CrossRef]

11. L. C. Andrews, W. B. Miller, and J. C. Ricklin, “Spatial coherence of a Gaussian-beam wave in weak and strong optical turbulence,” J. Opt. Soc. Am. **A 11**, 1653–1660 (1994). [CrossRef]

*k*and level of refractive turbulence

*r*

_{0}=

*(0.42 k*

^{2}

*)*

^{-3/5}is the transverse-field coherence diameter on the receiver plane of a point source located at the target at range

*R*. It is appealing to appreciate the similarity between this parameter

*N*

_{T}, which describes the refractive-turbulence effects on the propagated beam, and the previous Fresnel number

*N*

_{F}, which describes the free-space propagation: Now coherence diameter

*r*

_{0}assumes the role of aperture diameter

*D*.

8. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta **26**, 627–644 (1979). [CrossRef]

*N*

_{T}were used to describe the performance of CLR, the results referred only to a lidar that employed well-separated receiver and transmitting optics, i.e., a bistatic system, under restrictive turbulence conditions. It was shown from simulation of beam propagation [12] that just the combination of both numbers

*N*

_{F}and

*N*

_{T}permits the contribution of refractive turbulence to incoherent backscatter heterodyne lidar returns to be made in a comprehensive way. Any two monostatic lidars with the same

*N*

_{F}and

*N*

_{T}should exhibit the same turbulent effects in their performance. Distinctive interdependencies of the parameters that define the coherent system configuration and the atmospheric condition appear easily from a study of the similarity between parameters

*N*

_{F}and

*N*

_{T}[12]. Those results will help us to understand how the choice of telescope parameter may affect the performance of a practical heterodyne lidar in the presence of atmospheric turbulence.

## 3. Analysis of relevant telescope-related parameters

*F*.

*COH*pattern is altered in several ways. Indeed, a reduction factor

*r*=

*D*

_{2}/

*D*

_{1}of the aperture diameter would degrade Ω

*COH*by 1/

*r*

^{2}(a factor of 2 would translate into a Ω

*COH*loss of 6 dB). With respect only to this mostly obvious consideration, it would erroneously seem necessary to increase the size of the system aperture to improve the lidar performance. Otherwise, reducing the aperture size by a factor of

*r*will yield the far-field condition

*N*

_{F}<

*1*, so the maximum antenna efficiency

*η*

_{S}will be reached for ranges

*r*

^{2}times smaller (for example, reducing

*D*by a factor of 2 will produce the optimum 0.4 described in Section 2 for ranges that are four times closer to the transmitter). That would improve Ω

*COH*in the short ranges.

*COH*is less sensitive to turbulence when lidar aperture decreases. Parameterization of the effects of turbulence on heterodyne systems shows that reducing the aperture diameter by a factor of

*r*is equivalent to attenuating the refractive-turbulence effects to situations in which the turbulence intensity level

*r*

^{11/3}smaller (

*r*=

*2*corresponds to a reduction in turbulence level of more than 1 order of magnitude). It is worth noting that this payoff is useful in the far ranges, where the principal mechanism that describes the effect of atmospheric refractive turbulence is the additional expansion of the beam, which always reduces the overall signal coherence over the receiver plane. Equivalent weak turbulence levels may eventually translate into less-intense beam spreading

*COH*of an operating lidar system with that which results from considering different aperture diameters several times smaller. Transmitted and virtual LO beams were assumed to be matched, collimated, perfectly aligned, Gausssian, and truncated at the telescope aperture. For any aperture diameter shown in Fig. 1, the beam truncation was 1.25 (i.e.,

*D*=

*1.25*×

*2ω*

_{0}, where ω

_{0}is the 1/e

^{2}beam irradiance radius). This truncation maximizes far-field system-antenna efficiency in the ideal case of absence of turbulence [5

5. B.J. Rye and R.G. Frehlich, “Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,” Appl. Opt. **31**, 2891–2899 (1992). [CrossRef] [PubMed]

*D*=16 cm at the shortest range is 0 dB. In most practical situations, a coherent solid angle decay (i.e., a wideband SNR decay) of -15 dB defines the lidar’s maximum range. All the effects described previously that were associated with an aperture reduction are included in the simulations, for which two different realistic turbulent levels

*COH*is improved as a consequence of improved system-antenna efficiency (see above), and, at larger ranges, the effect of the beam size is mostly compensated for by the decrease of the refractive-turbulence effects (see the previous paragraph). Certainly, in many circumstances, smaller initial beams could perform at least as well as their larger counterparts.

2. S.F. Clifford and S. Wandzura, “Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,” Appl. Opt. **20**, 514–516 (1981). [CrossRef] [PubMed]

8. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta **26**, 627–644 (1979). [CrossRef]

*F*

_{T}=

*R*. A more-compact target is illuminated, resulting in an almost backscattering point source. When a focused system is considered, Fresnel number

*N*

_{F}that characterizes the free-space antenna efficiency must be modified as

*N*

_{F}

*(1*-

*R*/

*F*

_{T}

*)*to encompass focal length

*F*

_{T}or the radius of curvature of the transmitted beam. Now the far-field condition-small Fresnel number-occurs at ranges

*R*close to

*F*

_{T}, and the angular size of the illuminated area at this range is the collimated beam divergence once again. Using focusing techniques to improve the performance at ranges of interest was an extensive practice in earlier CO

_{2}lidar systems working at wavelengths in the far infrared (9–11 µm). At these wavelengths, turbulence effects are less remarkable.

*r*is equivalent to increasing the refractive-turbulence effects such that turbulence intensity level

*r*

^{3}larger (for

*r*=

*5*, i.e., when a

*2-µm*system is compared with a

*10-µm*lidar, that means an increase in the turbulence level of more than two 2 orders of magnitude).. Consequently, the same turbulence that reduces the coherence of the received beam may destroy the initial phase curvature introduced by the transmitter, decreasing its ability to focus the transmitting beam’s energy in a small area at the target plane.

*F*

_{T}

*2 km*, under most conditions the beam wave is so distorted by the turbulence that the initial phase that describes the focusing is barely sufficient, and just some weak enhancement can be appreciated. Shorter focal lengths (1 km or less) are only slightly more effective. In any case, for longer ranges the initially focused lidar exhibits a performance similar to that observed in the simpler collimated system. The problem is characterized mainly by the turbulence conditions, independently of the initial beam conditions.

## 4. Conclusions

*N*

_{F}and

*N*

_{T}parameter dependencies.

## References and links

1. | A. Belmonte and B. J. Rye, “Heterodyne lidar returns in turbulent atmosphere: performance evaluation of simulated systems,” Appl. Opt. |

2. | S.F. Clifford and S. Wandzura, “Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,” Appl. Opt. |

3. | A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. |

4. | B. J. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. |

5. | B.J. Rye and R.G. Frehlich, “Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,” Appl. Opt. |

6. | K. Tanaka and N. Ohta, “Effects of tilt and offset of signal field on heterodyne efficiency,” Appl. Opt. |

7. | R.G. Frehlich and M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. |

8. | H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta |

9. | L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. |

10. | R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE |

11. | L. C. Andrews, W. B. Miller, and J. C. Ricklin, “Spatial coherence of a Gaussian-beam wave in weak and strong optical turbulence,” J. Opt. Soc. Am. |

12. | A. Belmonte, B. J. Rye, W. A. Brewer, and R. M. Hardesty, “Coherent lidar returns in turbulent atmosphere from simulation of beam propagation,” presented at the Tenth Biennial Coherent Laser Radar Technology and Applications Conference, Mount Hood, Ore., June28–July 2, 1999. |

13. | See papers on device technology presented at the Twelfth Biennial Coherent Laser Radar Technology and Applications Conference, Bar Harbor, Me., June 15–20, 2003. |

**OCIS Codes**

(010.1290) Atmospheric and oceanic optics : Atmospheric optics

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(030.6600) Coherence and statistical optics : Statistical optics

(280.3640) Remote sensing and sensors : Lidar

**ToC Category:**

Research Papers

**History**

Original Manuscript: July 17, 2003

Revised Manuscript: August 9, 2003

Published: August 25, 2003

**Citation**

Aniceto Belmonte, "Analyzing the efficiency of a practical heterodyne lidar in the turbulent atmosphere: telescope parameters," Opt. Express **11**, 2041-2046 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-17-2041

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### References

- A. Belmonte and B. J. Rye, �??Heterodyne lidar returns in turbulent atmosphere: performance evaluation of simulated systems,�?? Appl. Opt. 39, 2401-2411 (2000). [CrossRef]
- S.F. Clifford and S. Wandzura, �??Monostatic heterodyne lidar performance: the effect of the turbulent atmosphere,�?? Appl. Opt. 20, 514-516 (1981). [CrossRef] [PubMed]
- A. Belmonte, �??Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,�?? Appl. Opt. 39, 5426-5445 (2000). [CrossRef]
- B. J. Rye, �??Antenna parameters for incoherent backscatter heterodyne lidar,�?? Appl. Opt. 18, 1390-1398 (1979). [CrossRef] [PubMed]
- B.J. Rye and R.G. Frehlich, �??Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,�?? Appl. Opt. 31, 2891-2899 (1992). [CrossRef] [PubMed]
- K. Tanaka and N. Ohta, �??Effects of tilt and offset of signal field on heterodyne efficiency,�?? Appl. Opt. 26, 627-632 (1987). [CrossRef] [PubMed]
- R.G. Frehlich and M. J. Kavaya, �??Coherent laser radar performance for general atmospheric refractive turbulence,�?? Appl. Opt. 30, 5325-5352 (1991). [CrossRef] [PubMed]
- H. T. Yura, �??Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,�?? Opt. Acta 26, 627-644 (1979). [CrossRef]
- L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, �??Theory of optical scintillation,�?? J. Opt. Soc. Am. A 16, 1417-1429 (1999). [CrossRef]
- R. L. Fante, �??Electromagnetic beam propagation in turbulent media,�?? Proc. IEEE 63, 1669-1692 (1975). [CrossRef]
- L. C. Andrews, W. B. Miller, and J. C. Ricklin, �??Spatial coherence of a Gaussian-beam wave in weak and strong optical turbulence,�?? J. Opt. Soc. Am. A 11, 1653-1660 (1994). [CrossRef]
- A. Belmonte, B. J. Rye, W. A. Brewer, and R. M. Hardesty, �??Coherent lidar returns in turbulent atmosphere from simulation of beam propagation,�?? presented at the Tenth Biennial Coherent Laser Radar Technology and Applications Conference, Mount Hood, Ore., June28�??July 2, 1999.
- See papers on device technology presented at the Twelfth Biennial Coherent Laser Radar Technology and Applications Conference, Bar Harbor, Me., June 15�??20, 2003.

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