## Angular misalignment contribution to practical heterodyne lidars in the turbulent atmosphere

Optics Express, Vol. 11, Issue 20, pp. 2525-2531 (2003)

http://dx.doi.org/10.1364/OE.11.002525

Acrobat PDF (240 KB)

### Abstract

The simulation of beam propagation is used to examine the sensitivity to misalignments of a practical heterodyne lidar because of the presence of refractive turbulence. At shorter wavelengths, and under general atmospheric conditions, the performance of a realistic instrument is never well described by either of the ideal monostatic and bistatic arrangements when misalignment is taken into consideration.

© 2003 Optical Society of America

## 1. Introduction

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

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

3. B. J. Rye, “Refractive-turbulent contribution to incoherent backscatter heterodyne lidar returns,” J. Opt. Soc. Am. **71**, 687–691 (1981). [CrossRef]

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

_{0}of 1 cm and realistic outer scale L

_{0}of the order of 5 m. It will be interesting to consider which setup would be more sensitive to misalignment in turbulent atmosphere, and how misalignments together with refractive turbulence make unnecessary to distinguish monostatic from bistatic arrangements. Their performance can not be described by either of the ideal configurations and they ought to be just considered as limit situations.

6. S. C. Cohen, “Heterodyne detection: phase front alignment, beam spot size, and detector uniformity,” Appl. Opt. **14**, 1953–1959 (1975). [CrossRef] [PubMed]

8. R.G. Frehlich, “Effects of refractive turbulence on coherent laser radar,” Appl. Opt. **32**, 2122–2139 (1993). [CrossRef] [PubMed]

8. R.G. Frehlich, “Effects of refractive turbulence on coherent laser radar,” Appl. Opt. **32**, 2122–2139 (1993). [CrossRef] [PubMed]

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

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

## 2. Two-beam model for the coherent solid angle

*A*

_{R}at range

*R*in terms of an effective coherent solid angle e Ω

*COH*[5

5. A. Belmonte, “Analyzing the efficiency of a practical heterodyne lidar in the turbulent atmosphere: telescope parameters,” Opt. Express **11**, 2041–2046 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-17-2041. [CrossRef] [PubMed]

*A*

_{R}/

*R*

^{2}and the system-antenna efficiency

*η*

_{S}

*(R)*that describes the extent to which this value is degraded [9

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

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

*SNR*)

*C(R)*describing conversion efficiencies, various system components, and atmospheric scattering conditions. As we are mainly concerned with the effects of the refractive turbulence, those parameters are mostly irrelevant here.

**p**[2

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

*λ*is the optical wavelength of the transmitted laser. The irradiances

*jT*and

*j*

_{BPLO}have been normalized to the laser 〈

*P*

_{L}(

*t*)〉 and local oscillator (LO) 〈

*P*

_{LO}〉 average power, respectively. The problem of heterodyne lidar performance in the presence of atmospheric turbulence is reduced to one of computing intensity along the propagation paths. With this formulation, the random nature of the problem arises because of the randomness of the intervening atmospheric medium, which requires averaging (〈〉) over different time scales.

*COH*is easily computed by using simulation techniques: for a given propagation path, we have to estimate the overlap integral of the normalized irradiances in the two beams at the target plane in the presence of turbulence. In the absence of turbulence, the optical fields are deterministic and ensemble averages over the random media and random fields are not required, so the calculation is straightforward and not computer intensive.

*C*is the intensity fluctuations correlation of the transmitter and BPLO beams

_{j}(**p**,R)*C*=

_{j}(**p**,R)*0*. For the bistatic configuration, the principal mechanism that describes the effect of atmospheric refractive turbulence is the additional expansion of both the transmitted and the BPLO beams, which always reduces performance below the free-space results. The statistically independent path result is a lower bound for the coherent solid angle.

*j*=

_{T}(**p**,R)*j*and

_{BPLO}(**p**,R)*C*transforms into the beam scintillation index

_{j}(**p**,R)*. This always positive addition produces the so-called backscattering enhancement effect: Turbulence causes small bright spots on the scattering target, increasing the value of the overlap integral, and so, compared with that of the bistatic calculation, monostatic performance is enhanced. For any specific atmospheric turbulence condition, the perfectly matched beams result is an upper bound for the coherent solid angle. As a consequence of the enhancement effect, and for practical reasons, the configuration of feasible heterodyne lidars is usually monostatic.*σ j 2 (

**p**,R)≥012. W.B. Miller, J.C. Ricklin, and L.C. Andrews, “Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,” J. Opt. Soc. Am. A **10**, 661–672 (1993). [CrossRef]

*k*=

*2π*/

*λ*is the beam wavenumber. However, in most practical lidar systems beam paths of interest are often long enough to cause saturation effects. Notably, when the ground lidar systems working at 1–2 µm wavelengths under development [13] are considered, the effects of refractive turbulence are important for ranges as short as a few hundreds meters for any condition of turbulence. In these situations, the irradiance fluctuations are not properly described by the weak-turbulence analysis.

*C*in Eq. (4) that result from turbulent fluctuations for whatever lidar geometry and alignment condition. Next, simulations of beam propagation will be used to quantify these misalignment effects on the performance of a heterodyne lidar.

_{j}(**p**,R)## 3. Lidar performance degradation due to misalignments

**ϑ**|. Here, Δ

**ϑ**is the misalignment angle and λ/πD is the diffraction limit of the lidar circular aperture. The beam divergence is directly proportional to the ratio between the wavelength λ and the aperture diameter

*D*(i.e., the beam-waist diameter 2ω

_{0}). To obtain a highly directional beam, a short wavelength and a large aperture should be used. For a specific misalignment angle Δ

**ϑ**, if the aperture is reduced, the beam will diverges, πD/λ |Δ

**ϑ**| will gets smaller and the lidar system will become less sensitivity to angular misalignment.

*Δ*between the transmitted irradiance and BPLO irradiance in the target plane. For large wavelengths, or weak-turbulence conditions, it will cause a degeneration of the overlap integral of the transmitter and BPLO beams. However, when the turbulence-induced beam spreading becomes important -shorter wavelengths, higher turbulence levels, or larger ranges—this effect will be negligible. More interesting for shorter wavelengths, the small-scale scintillation structure will produces a decrease in performance with misalignment sharper and more sensitive than those observed in the free-space case: small misalignments will destroy the short-scale correlation of the transmitter irradiance and BPLO irradiance at the target and the overlap integral will become more similar to the result obtained for the bistatic situation. The enhancement in performance produced by large-scale irradiance correlation will be observed even with larger misalignment angles.

**p***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. The initially considered lidar aperture

*D*was 16 cm in diameter (middle figure) and its performance is compared with lidar systems with 32-cm (up) and 8-cm (down) diameter apertures. In any case, the misalignment angle |Δ

**ϑ**| has values of 10 µrad, 20 µrad, 30 µrad, and 40 µrad. Because we are interested primarily in turbulent effects, and in order to simplify the graphs, we have normalized the plots so the coherent solid angle at the shortest range is 0 decibels (dB). In most practical situations, coherent solid angle decay (i.e., a wideband

*SNR*decay) of about -15 dB defines the lidar maximum range. All the previously described effects associated with increasing misalignments are considered by the simulations, where the level of refractive turbulence has the typical daytime value of moderate-to-strong condition,

^{-12}m

^{-2/3}.

*Δ*

**ϑ**will translate into an offset

*Δ*=

**p***RΔ*

**ϑ**between the transmitted irradiance and BPLO irradiance in the target plane at range

*R*, decreasing the value of the intensity fluctuations correlation

*C*in Eq. (5). Small-scale fluctuations in the two beams will make the heterodyne lidar extremely sensible to even relatively small misalignment angles. In many practical situations the two-beam offset |

_{j}(**p**,R)*Δ*| will be larger than the coherence diameter

**p***r*

_{0}characterizing small irradiance fluctuations. When larger apertures are considered (see Fig. 2, upper graph), the effects are pronounced for misalignment angles as short as 10

*µrad*. In this case, when large apertures make the lidar system most sensitive to turbulence effects, coherence diameter is less than 1 cm for ranges as short as 2000 m [17

17. H.T. Yura, “Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium,” Appl. Opt. **11**, 1399–1406 (1972). [CrossRef] [PubMed]

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

16. R.F. Lutomirski and H.T. Yura, “Propagation of a finite optical beam in an inhomogeneous medium,” Appl. Opt. **10**, 1652–1658 (1971). [CrossRef] [PubMed]

**39**, 5426–5445 (2000). [CrossRef]

*µrad*make monostatic behavior almost identical to that expected for bistatic situations (see Fig. 2, middle and down graphs).

*Δ*|

**p***/*

**≥**4R*kr*

_{0}. Although the residual large-scale irradiance correlation still produces an enhancement in performance, for a misalignment of just 40

*µrad*the behavior of the initially monostatic geometry closely approaches that expected for a bistatic system (see Fig. 2, up and middle graphs). Just for the smaller aperture considered in Fig. 2 (lower graph), misalignment is not able to step down the lidar performance to bistatic levels. For ranges longer -or misalignment angles slightly larger—than those shown in the figures, even this small large-scale enhancement term will eventually vanishes. Perfect angular alignment in most practical, operational lidar ground systems can not be pinned down and all the previous considerations become useful in almost any feasible experimental situation.

**ϑ**| even larger than those regarded in our simulations, misalignment will override almost any other consideration about the geometry of our lidar system.

## 4. Conclusions

5. A. Belmonte, “Analyzing the efficiency of a practical heterodyne lidar in the turbulent atmosphere: telescope parameters,” Opt. Express **11**, 2041–2046 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-17-2041. [CrossRef] [PubMed]

## References and links

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

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

3. | B. J. Rye, “Refractive-turbulent contribution to incoherent backscatter heterodyne lidar returns,” J. Opt. Soc. Am. |

4. | J. Martin, “Simulation of wave propagation in random media: theory and applications,” in |

5. | A. Belmonte, “Analyzing the efficiency of a practical heterodyne lidar in the turbulent atmosphere: telescope parameters,” Opt. Express |

6. | S. C. Cohen, “Heterodyne detection: phase front alignment, beam spot size, and detector uniformity,” Appl. Opt. |

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

8. | R.G. Frehlich, “Effects of refractive turbulence on coherent laser radar,” Appl. Opt. |

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

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

11. | A. Ishimaru, |

12. | W.B. Miller, J.C. Ricklin, and L.C. Andrews, “Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,” J. Opt. Soc. Am. A |

13. | See papers presented on the Device Technology’s session in |

14. | A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE |

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

16. | R.F. Lutomirski and H.T. Yura, “Propagation of a finite optical beam in an inhomogeneous medium,” Appl. Opt. |

17. | H.T. Yura, “Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium,” Appl. Opt. |

**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: August 14, 2003

Revised Manuscript: September 17, 2003

Published: October 6, 2003

**Citation**

Aniceto Belmonte, "Angular misalignment contribution to practical heterodyne lidars in the turbulent atmosphere," Opt. Express **11**, 2525-2531 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-20-2525

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### References

- A. Belmonte, �??Feasibility study for the simulation of beam propagation consideration of coherent lidar performance�?? Appl. Opt. 39, 5426-5445 (2000). [CrossRef]
- A. Belmonte and B. J. Rye, �??Heterodyne lidar returns in turbulent atmosphere performance evaluation of simulated systems,�?? Appl. Opt. 39, 2401-2411 (2000). [CrossRef]
- B. J. Rye, �??Refractive-turbulent contribution to incoherent backscatter heterodyne lidar returns,�?? J. Opt. Soc. Am. 71, 687-691 (1981). [CrossRef]
- 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)
- A. Belmonte, "Analyzing the efficiency of a practical heterodyne lidar in the turbulent atmosphere: telescopeparameters," Opt. Express 11, 2041-2046 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-17-2041">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-17-2041</a> [CrossRef] [PubMed]
- S. C. Cohen, �??Heterodyne detection: phase front alignment beam spot size and detector uniformity,�?? Appl.Opt. 14, 1953-1959 (1975). [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, �??Effects of refractive turbulence on coherent laser radar,�?? Appl. Opt. 32, 2122-2139 (1993) [CrossRef] [PubMed]
- R.G. Frehlich, M. J. Kavaya, �??Coherent laser radar performance for general atmospheric refractive turbulence,�?? Appl. Opt. 30, 5325-5352 (1991). [CrossRef] [PubMed]
- B. J. Rye, �??Antenna parameters for incoherent backscatter heterodyne lidar,�?? Appl. Opt. 18, 1390-1398 (1979). [CrossRef] [PubMed]
- A. Ishimaru, Wave propagation and scattering in random media, (Academic Press, New York, 1978).
- W.B. Miller, J.C. Ricklin and L.C. Andrews, �??Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,�?? J. Opt. Soc. Am. A 10, 661-672 (1993). [CrossRef]
- See papers presented on the Device Technology�??s session in Proceedings of the Twelfth Biennial Coherent Laser Radar Technology and Applications Conference, Bar Harbor, Maine, 15-20 June, 2003.
- A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily and V. I. Shishov, �??Laser irradiance propagation in turbulent media,�?? Proc. IEEE 63, 790-811 (1975). [CrossRef]
- R. L. Fante, �??Electromagnetic beam propagation in turbulent media,�?? Proc. IEEE 63, 1669-1692 (1975). [CrossRef]
- R.F. Lutomirski, H.T. Yura, �??Propagation of a finite optical beam in an inhomogeneous medium,�?? Appl. Opt. 10, 1652-1658 (1971). [CrossRef] [PubMed]
- H.T. Yura, �??Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium,�?? Appl. Opt. 11, 1399-1406 (1972). [CrossRef] [PubMed]

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