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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 25670–25676
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Investigation of spherical aberration effects on coherent lidar performance

Qi Hu, Peter John Rodrigo, Theis F. Q. Iversen, and Christian Pedersen  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 25670-25676 (2013)
http://dx.doi.org/10.1364/OE.21.025670


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Abstract

In this paper we demonstrate experimentally the performance of a monostatic coherent lidar system under the influence of phase aberrations, especially the typically predominant spherical aberration (SA). The performance is evaluated by probing the spatial weighting function of the lidar system with different telescope configurations using a hard target. It is experimentally and numerically proven that the SA has a significant impact on lidar antenna efficiency and optimal beam truncation ratio. Furthermore, we demonstrate that both effective probing range and spatial resolution of the system are substantially influenced by SA and beam truncation.

© 2013 Optical Society of America

1. Introduction

One of the main considerations in the development of the wind industry is the metrology issues. Essentially, more cost efficient and accurate wind velocity and turbulence mapping systems are highly desired [1

1. The final report of the EU FP6 project UPWIND, http://www.upwind.eu/

]. Since the traditional cup and sonic anemometers require meteorological masts, a detailed turbulence mapping will require a tremendous amount of masts at different locations and heights. For this particular task the laser remote sensing (lidar) technology offers an attractive alternative [2

2. J. Mann, J. P. Cariou, M. Courtney, P. Parmentier, T. Mikkelsen, R. Wagner, P. J. P. Lindelöw, M. Sjöholm, and K. Enevoldsen, “Comparison of 3D turbulence measurements using three staring wind lidars and a sonic anemometer,” Meteorol. Z. 18, 135–140(2009). [CrossRef]

]. In these systems, precise control of multiple lidar units are required in order to acquire the full 3D wind vectors with high a spatial resolution, which is determined by the overlap between the individual lidar weighting function that describes the spatial sensitivity and confinement along each beam direction.

2. Experimental setup

In this work the impact of the SA is measured by probing the lidar weighting function of the system with a rotating belt as the hard target using a 1550 nm CW beam output as shown in the schematic layout in Fig. 1. Both the simulation and the experiment follows the geometry in Fig 1. The distance between L1and L2is adjusted such that the lidar signal is optimized with the hard target (rotating belt) placed at a range of 80 m. Around 0.5 mW of the diode laser output is tapped within the optical ciculator and is used as the local oscillator (LO) for the heterodyne detection. Both the signal from the rotating belt and the LO is focused onto the detector through the optical circulator. The ”virtual” back propagated local oscillator (BPLO) from the detector plane matches the transmit beam with a Gaussian field amplitude profile of radius, w, at the plane of lens L2. This configuration is commonly referred to as the Wang design [7

7. J. Y. Wang, “Optimal truncation of a lidar transmitted beam,” Appl. Opt. 27, 4470–4474(1988). [CrossRef] [PubMed]

]. Different truncation ratios, ρ= w/rL2where rL2is the radius of L2aperture, can be probed by changing the focal length (f1) of lens L1, since the imaging magnification of the beam is dependent on the focal length ratio between L1and L2. Two different L2, both with exit aperture radius of rL2= 35.65 mm (3 inch optics), are used in our experiments in order to evaluate the system under different degrees of SA. The lenses (L2) are respectively a singlet lens (f2= 200 mm) that is not corrected for SA and a doublet lens (f2= 216 mm) designed for reduced SA. The correlation overview between the L1focal lengths and ρcan be found in Table 1. A quantitative illustration of the SA introduced by the L2lenses is shown in Fig. 2(a), where the optical path difference (OPD) is measured in number of waves. The curves in Fig. 2(a)are generated using a Zemax simulation with monochromatic input, zero incident angle and assuming circular symmetry in the transverse plane, i.e. only the symmetrical components of wavefront errors are presented. The first six nonzero Zernike fringe coefficients, generated in Zemax, are listed in Table 2. Those coefficients are used to generate the OPD curves and they differ slightly from the standard Zernike coefficients, which is evident from the polynomials provided in the table. A detailed description of those coefficients can be found in the user’s manual of Zemax [9

9. ZEMAX Optical Design Program User’s Manual (July8, 2011) pp. 196–199.

]. It is evident from the table values that the SA (Z9) is the dominant source of the waverfront errors.

Fig. 1 Schematic layout of the system setup. The size of the exit aperture is the diameter of L2. During the experiments several diffraction limited aspherical lenses, L1with different focal lengths are used in order to probe different ρvalues; while two different L2are used to introduce different degree of aberrations. The rotating belt is used to generated the Doppler signal for our measurements.

Table 1. Relation between focal lengths of L1and ρ

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Fig. 2 a) The OPDs of the two different L2used in our experiments. The OPDs are generated in Zemax with zero incident angle and circular symmetry. b) The calculated transverse irradiance profile of the output beam in different axial distances from the singlet L2. The focal length of L1is 15.6 mm in the simulation.

Table 2. Zernike fringe coefficients from Zemax

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An accurate theoretical prediction of the field or irradiance distribution on the target side of L2is possible using those OPD curves. The SA can be incorporated in the theoretical simulation by introducing an extra phase term, ϕSAto the truncated Gaussian field at L2according to Eq. (1)[8

8. B. J. Rye, “Primary aberration contribution to incoherent backscatter heterodyne lidar resturns,” Appl. Opt. 21, 839–844(1982) [CrossRef] [PubMed]

]
E(r)={E0exp{r2w2+iϕ(r)+iϕSA(r)}for0rrL20forr>rL2,ϕSA=2π*OPD(r)
(1)
where E0is the peak amplitude, ris the radial coordinate, ϕ(r) is the phase of the beam due to field curvature, ϕSAis the phase term induced by the SA and the OPD(r) is either curves shown in Fig. 2(a). Due to the circular symmetry, the field on the target plane can be calculated numerically by a simple Fourier-Bessel transformation of Eq. (1)with an appropriate field curvature [8

8. B. J. Rye, “Primary aberration contribution to incoherent backscatter heterodyne lidar resturns,” Appl. Opt. 21, 839–844(1982) [CrossRef] [PubMed]

].

3. Results and discussions

To illustrate the degree of SA for the singlet L2case, the transverse irradiance profiles in different distances, zafter the singlet L2are calculated and shown in Fig. 2(b). A side by side comparison between the numerical simulation and the experimental counterpart of the beam profiles is displayed in Fig. 3. The observed beam profiles are recorded with aid of an IR-detection card. An intensity clipping level was introduced in the presentation of the numerical results in order to simulate the saturation effect of the IR-detection card. In Fig. 3the consistency between the simulations and the measurements is quite evident, qualitatively validating the accuracy of our theoretical simulations.

Fig. 3 The observed and simulated beam profiles emitted from the singlet L2in different axial distances (10m, 40m, 60m and 80m) The focal length of lens L1is 15.6 mm.

In order to maximize the signal in diffraction limited monostatic lidar systems, ρ≈ 0.8 through the L2is required [3

3. T. Fujii and T. Fukuchi, eds. Laser Remote Sensing(CRC Press, 2005).

]. However, in the presence of SA, optimal ρwill differ from 0.8 and the overall antenna efficiency will decrease compared to the aberration-free case. It is easiest to calculate the antenna efficiency, ηausing the target-plane formalism based on Siegman’s antenna theorem [3

3. T. Fujii and T. Fukuchi, eds. Laser Remote Sensing(CRC Press, 2005).

, 10

10. A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594(1966). [CrossRef] [PubMed]

].
ηa(z)=λ2R2ArItarget2(x,y,z)dxdy
(2)
where λis the wavelength, Ris the intended imaging or probing range (80 m in our case), Aris the area of L2and Itargetis the irradiance distribution of the output beam at the target plane position, zand is normalized by the total beam power before truncation.

In Fig. 4(a)the calculated antenna efficiency at z= Ras a function of ρis shown for both L2lenses and compared with the aberration-free case (the dashed lines). The simulation is constructed such, that the algorithm is imitating the same distance optimization procedure as in the experiments. It is evident that not only the overall antenna efficiency has decreased as the consequence of SA, but the optimum ρalso shifts with different degrees of aberrations. Even for the doublet case where the SA is minimal, there is still a clear shift of the optimal ρand a quite noticeable drop in the maximum antenna efficiency. It demonstrates the importance of considering the aberration effects in designing a lidar system. The result in Fig. 4(a)indicates that optimal ρdecreases with increasing degree of SA.

Fig. 4 a) The dash lines illustrates the numerically calculated antenna efficiency using Eq. (2)as a function of ρ; while the scattered points shows the measured lidar signal as a function of ρ. Both the simulation and the experimental data are acquired at a probing range of 80 m. b) The simulated antenna efficiency for the aberration-free case as a function of distance with and without the truncation effect (ρ= 0.8 for truncated case).

The measured hard target lidar signal as a function of ρ, normalized to the maximum data point of the doublet case, is also shown in Fig. 4(a). The experimental data shows the same tendencies as the numerical calculations. While the singlet data coincides quite well with the simulations, there is a slight deviation for the doublet case. Since the simulation only includes the SA effect, it is reasonable that the doublet data can deviate from the simulation due to other aberration effects in the rest of the system (we do observe small degree of astigmatism from the output of the optical circulator). The singlet data is, on the other hand, dominated by the SA, which explains the good agreement with the simulation.

The weighting function can be acquired experimentally by measuring the lidar signal with a moving hard target. The experimental data of six different combinations of L1and L2are presented in Fig. 5along with their numerical counterparts. In general the numerical results coincide quite well with the experimental data, but the singlet case gives a much better match than the doublet case. As we discussed earlier the simulations only include the SA effect, since the measurement with singlet L2is dominated by SA while the doublet L2case is not, it is expected that singlet lens case will provide a better fit. The simulation results do suggest that the full system (not only L2) potentially suffers from other aberration effects like astigmatism and coma, which are comparable with the SA introduced by the doublet L2, since the experimental data shows a visible broadening of the weighting function compared with their numerical counterparts. Comparing the simulation with the experimental data there is a broadening of 21% for the green dash line (f1= 8.1 mm) while the broadening is 70% for the blue dash line case (f1= 18.8 mm). The residual broadening is likely due to the astigmatism of the beam from the optical circulator, which also explains the observed increase in the degree of broadening with the focal length of L1.

Fig. 5 The measured weighting functions for six different transceiver configurations along with their theoretical counterparts. The simulations are acquired using the numerical integration of the fields including the truncation diffraction effects. The blue solid line represents the optimal ρof 0.3 for the singlet case, while the green dash line corresponds to the optimal ρof 0.8 for the doublet case. The dash lines in the graph to the right are the Lorentzian fit to the experimental data (scattered points).

From Fig. 5it is quite obvious that in general one should reduce SA in the system, since both the spatial resolution/confinement and the maximum signal strength of the optimal doublet case (green dashed line) are much better than the optimal case for the singlet lens (blue solid line). However, the area under the weighting function (estimating the total lidar signal strength for aerosol target) has only increased by around 30% from the optimal singlet case to the doublet one. So for measurements of laminar air flow (i.e. negligible spatial dependence of wind vector), the benefit gained from using the more expensive doublet L2is minor in terms of signal strength enhancement but more on improved spatial resolution. For the more general turbulent air flow in the probing volume, higher signal strength enhancement due to tighter spatial confinement is of course expected.

4. Conclusion

In this paper we have shown both numerically and experimentally that SA has a significant impact on antenna efficiency, optimal truncation ratio and the shape of the weighting function of a CW coherent lidar. If the system suffers from strong SA effect only very limited spatial confinement can be obtained as shown in Fig. 5. It is also evident that the degradation of spatial confinement or broadening of the lidar weighting function due to SA can be reduced by tuning the beam truncation through L2. This corrective measure results from the novel finding in this work that the optimal truncation ratio depends on the degree of SA. Furthermore we have shown that both SA and truncation ratio influence the peak shift and width of the weighting function. In applications where precise probing range and spatial resolution are essential, a weighting function calibration of the lidar system using a hard target might be necessary. It is worth to stress that this study can also be applied to accurately model the weighting function of pulsed coherent lidar systems [2

2. J. Mann, J. P. Cariou, M. Courtney, P. Parmentier, T. Mikkelsen, R. Wagner, P. J. P. Lindelöw, M. Sjöholm, and K. Enevoldsen, “Comparison of 3D turbulence measurements using three staring wind lidars and a sonic anemometer,” Meteorol. Z. 18, 135–140(2009). [CrossRef]

].

Acknowledgments

The authors would like to acknowledge the financial support from the Energiteknologisk Udviklings- og Demonstrations Program (EUDP)J.nr. 641012-0003.

References and links

1.

The final report of the EU FP6 project UPWIND, http://www.upwind.eu/

2.

J. Mann, J. P. Cariou, M. Courtney, P. Parmentier, T. Mikkelsen, R. Wagner, P. J. P. Lindelöw, M. Sjöholm, and K. Enevoldsen, “Comparison of 3D turbulence measurements using three staring wind lidars and a sonic anemometer,” Meteorol. Z. 18, 135–140(2009). [CrossRef]

3.

T. Fujii and T. Fukuchi, eds. Laser Remote Sensing(CRC Press, 2005).

4.

Y. Zhao, M. J. Post, and R. M. Hardesty, “Receiving efficiency of pulsed coherent lidars. 1: theory,” Appl. Opt. 29, 4111–4119(1990). [CrossRef] [PubMed]

5.

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

6.

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]

7.

J. Y. Wang, “Optimal truncation of a lidar transmitted beam,” Appl. Opt. 27, 4470–4474(1988). [CrossRef] [PubMed]

8.

B. J. Rye, “Primary aberration contribution to incoherent backscatter heterodyne lidar resturns,” Appl. Opt. 21, 839–844(1982) [CrossRef] [PubMed]

9.

ZEMAX Optical Design Program User’s Manual (July8, 2011) pp. 196–199.

10.

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594(1966). [CrossRef] [PubMed]

11.

J. Mann, A. Peña, F. Bingöl, R. Wagner, and M. S. Courtney, “Lidar scanning of momentum flux in and above the atmospheric surface layer,” J. Atmos. Oceanic Technol. 27, 959–976(2010). [CrossRef]

OCIS Codes
(280.0280) Remote sensing and sensors : Remote sensing and sensors
(280.3340) Remote sensing and sensors : Laser Doppler velocimetry
(280.3640) Remote sensing and sensors : Lidar

ToC Category:
Remote Sensing

History
Original Manuscript: July 24, 2013
Revised Manuscript: September 3, 2013
Manuscript Accepted: October 10, 2013
Published: October 21, 2013

Citation
Qi Hu, Peter John Rodrigo, Theis F. Q. Iversen, and Christian Pedersen, "Investigation of spherical aberration effects on coherent lidar performance," Opt. Express 21, 25670-25676 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-25670


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References

  1. The final report of the EU FP6 project UPWIND, http://www.upwind.eu/
  2. J. Mann, J. P. Cariou, M. Courtney, P. Parmentier, T. Mikkelsen, R. Wagner, P. J. P. Lindelöw, M. Sjöholm, and K. Enevoldsen, “Comparison of 3D turbulence measurements using three staring wind lidars and a sonic anemometer,” Meteorol. Z.18, 135–140(2009). [CrossRef]
  3. T. Fujii and T. Fukuchi, eds. Laser Remote Sensing(CRC Press, 2005).
  4. Y. Zhao, M. J. Post, and R. M. Hardesty, “Receiving efficiency of pulsed coherent lidars. 1: theory,” Appl. Opt.29, 4111–4119(1990). [CrossRef] [PubMed]
  5. R. G. Frehlich and M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt.30, 5325–5352(1991). [CrossRef] [PubMed]
  6. 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]
  7. J. Y. Wang, “Optimal truncation of a lidar transmitted beam,” Appl. Opt.27, 4470–4474(1988). [CrossRef] [PubMed]
  8. B. J. Rye, “Primary aberration contribution to incoherent backscatter heterodyne lidar resturns,” Appl. Opt.21, 839–844(1982) [CrossRef] [PubMed]
  9. ZEMAX Optical Design Program User’s Manual (July8, 2011) pp. 196–199.
  10. A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt.5, 1588–1594(1966). [CrossRef] [PubMed]
  11. J. Mann, A. Peña, F. Bingöl, R. Wagner, and M. S. Courtney, “Lidar scanning of momentum flux in and above the atmospheric surface layer,” J. Atmos. Oceanic Technol.27, 959–976(2010). [CrossRef]

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