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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 12 — Jun. 17, 2013
  • pp: 14583–14590
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Improved calibration method for depolarization lidar measurement

Bo Liu and Zhien Wang  »View Author Affiliations


Optics Express, Vol. 21, Issue 12, pp. 14583-14590 (2013)
http://dx.doi.org/10.1364/OE.21.014583


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Abstract

An improved calibration method for lidar depolarization measurement is described. With this method the system constants including the electronic gain ratio of the parallel and perpendicular channels, the optical reflectance and transmission parameters of the polarizing beam splitter, and the linear polarization ratio of the emitting laser beam can be determined conveniently by using lidar measurements with a half-wave plate oriented at selected angles.

© 2013 OSA

1. Introduction

The polarization lidar technique first described by Schotland et al in the early 1970s [1

1. R. M. Schotland, K. Sassen, and R. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10(5), 1011–1017 (1971), http://journals.ametsoc.org/doi/abs/10.1175/1520-0450(1971)010%3C1011%3AOBLOLD%3E2.0.CO%3B2. [CrossRef]

] is a powerful tool for distinguishing ice clouds from water clouds and identifying non-spherical aerosol particle. This technique is based on the principle that backscattered radiation from spherical particles does not significantly differ from its original polarization state. Partial depolarization of backscattered light is caused by non-spherical particle scatters, or by multiple scattering effects, which allow non-backscatted light scatters back into the instrument filed-of-view. Traditional linear polarization measurements determine the ratio of the parallel and perpendicular polarized (with respect to the linearly polarized source) return signals. Unfortunately, other factors contributing to observed depolarized signals, such as an incomplete polarization of the laser source, non-ideal behavior of the polarizing beam splitter, and different gain factors between the parallel and perpendicular channels, have to be considered to determine depolarization due to atmospheric particles and molecules. Therefore, calibration of a polarization lidar is important to provide accurate atmosphere measurements.

Usually, the instrument gain ratio of the two polarization channels is determined through observations in aerosol and cloud free regions, by assuming that the observed ratio in these cases is equal to the molecular depolarization ratio obtained with theoretical calculations [2

2. A. Behrendt and T. Nakamura, “Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature,” Opt. Express 10(16), 805–817 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?id=69680. [CrossRef] [PubMed]

] or with observational data [3

3. H. Adachi, T. Shibata, Y. Iwasaka, and M. Fujiwara, “Calibration method for the lidar-observed stratospheric depolarization ratio in the presence of liquid aerosol particles,” Appl. Opt. 40(36), 6587–6595 (2001), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-40-36-6587. [CrossRef] [PubMed]

]. The drawback of this method is low concentrations of undetected aerosols can cause significant errors. Furthermore, molecular depolarization must be known with high accuracy. Considering that lidar measured molecular depolarization ratio can range from 0.36% to 1.4% depending on lidar receiver spectral width and may exhibit temperature dependency [2

2. A. Behrendt and T. Nakamura, “Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature,” Opt. Express 10(16), 805–817 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?id=69680. [CrossRef] [PubMed]

], errors can be significant due to assumed molecular depolarization ratio. Another calibration method uses unpolarized light to generate equal signals on both channels [4

4. K. Sassen, “The polarization lidar technique for cloud research: A review and current assessment,” Bull. Amer. Meteor. Soc 72, 1848–1866 (1991). http://journals.ametsoc.org/doi/abs/10.1175/1520-0477(1991)072%3C1848%3ATPLTFC%3E2.0.CO%3B2. [CrossRef]

, 5

5. K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58(15), 2103–2112 (2001), http://journals.ametsoc.org/doi/abs/10.1175/1520-0469(2001)058%3C2103%3AAMCCCF%3E2.0.CO%3B2. [CrossRef]

]. But unpolarized light is not easily to obtain, especially in the field. A single detector technique can also be used, switching optics to detect the two polarizations for alternate laser pulses [6

6. C. M. R. Platt, “Lidar observation of a mixed-phase altostratus cloud,” J. Appl. Meteorol. 16(4), 339–345 (1977), http://journals.ametsoc.org/doi/abs/10.1175/1520-0450%281977%29016%3C0339%3ALOOAMP%3E2.0.CO%3B2. [CrossRef]

, 7

7. E. W. Eloranta and P. Piironen, “Depolarization measurements with the high spectral resolution lidar,” in 17th International Laser Radar Conference, (Laser Radar Society of Japan, ICLAS, NASDA, and NIES, Sendai, Japan, 1994). pp. 127–128.

]. However, one must accordingly know the optical reflectance and transmission parameters of a polarizing beam splitter (PBS) in this method. These properties are not easily determined and could change significantly, not only by misalignment of the polarizing cube but also by non-ideal collimation of the light beam, especially for broad spectral band prisms [8

8. J. Larry Pezzaniti and R. A. Chipman, “Angular dependence of polarizing beam-splitter cubes,” Appl. Opt. 33(10), 1916–1929 (1994), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-33-10-1916. [CrossRef] [PubMed]

10

10. R. P. Netterfield, “Practical thin-film polarizing beam-splitters,” Opt. Acta (Lond.) 24(1), 69–79 (1977), http://www.tandfonline.com/doi/abs/10.1080/713819379. [CrossRef]

].

2. Polarization lidar calibration method

Assuming that there is no multiple scattering (which is true for observations with optical depth smaller than 0.5 [14

14. Y. You, G. W. Kattawar, P. Yang, X. H. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 470–482 (2006), http://www.sciencedirect.com/science/article/pii/S0022407305004097. [CrossRef]

]), the total backscattered power P(r) from distance r is described with the single-scattering lidar equation:
P=ηPLβ(r)τ2(r)r2.
(1)
where η is the system constant, PL the laser power, β the backscatter coefficient, and the factor τ2 accounts for the atmospheric two way transmittance.

For polarization lidars, atmospheric backscatter signals are separated into parallel and perpendicular polarization components by using a PBS. The angle between the plane of polarization of the laser and the incident plane of the PBS(φ) can be adjusted by rotating a half-wavelength-plate(HWP) which is inserted in the optical path of the transmitting laser beam(as shown in Fig. 1
Fig. 1 Schematic of the signal power components for the lidar transmitter and receiver. See text for different symbols and variables.
). Assuming the laser beam is perfectly linearly polarized, for φ = 0°, the received power components before the PBS with respect to parallel (PP) and perpendicular (PS) to the incident plane of the PBS (see Fig. 1) can be written respectively as
PP=ηPLβτ2r2.PS=ηPLβτ2r2.
(2)
where the backscatter coefficients are split up into parallel (β||) and cross-polarized (β) components. The ratio of the total orthogonally to the total parallel-polarized backscatter coefficient is called the linear volume depolarization ratio δv:

δV=ββ=PSPP.
(3)

Here, we denote the power measured in the reflected and transmitted channels after PBS with the subscripts R and T, respectively. The total reflected (PR) and transmitted (PT) power components actually recorded by the data acquisition can be written as
PR=(PPRP+PSRS)VR.PT=(PPTP+PSTS)VT.
(4)
where VR and VT are the amplification factors including the optical transmittances and the electronic amplification in each channel. RP, RS and TP, TS are reflectivities and transmittances for linearly polarized light parallel (p) and perpendicular (s) to the incident plane of the PBS. It is notable that here the PBS should be considered not only as the polarizing beam splitter cube but also as Polarizing Beam-splitting System including all the optics in the two channels. Figure 1 should be considered as a schematic with key components to represent the effects of other optical components on lidar transmitting and receiving system.

Then, according to the ‘ ± 45°calibration’ method, the relative amplification factor ratio V*(V* = VR / VT) can be calculated from two subsequent measurements by setting φ at ± 45° by [13

13. V. Freudenthaler, M. Esselborn, M. Wiegner, B. Heese, M. Tesche, A. Ansmann, D. Müller, D. Althausen, M. Wirth, A. Fix, G. Ehret, P. Knippertz, C. Toledano, J. Gasteiger, M. Garhammer, and M. Seefeldner, “Depolarization ratio profiling at several wavelengths in pure Saharan dust during SAMUM 2006,” Tellus 61B, 165–179 (2009), http://www.tellusb.net/index.php/tellusb/article/view/16821.

],
V*=TP+TSRP+RSδ*(+45°)×δ*(45°).
(5)
where δ*(δ* = PR / PT) is the measured signal ratio between the parallel and perpendicular channels.

For φ = 0°, from Eqs. (3) and (4) we can get

δ*(0)=PRPT=(PPRP+PSRS)VR(PPTP+PSTS)VT=V*RP+δVRSTP+δVTS.
(6)

For φ = 90°, the polarization plane of the laser has been rotated by 90°, which meanPS'=PP, PP'=PS, then Eq. (4) change to

PR'=(PSRP+PPRS)VR.PT'=(PSTP+PPTS)VT.
(7)

Following Eqs. (3) and (7) we get
δ*(90)=PR'PT'=V*δVRP+RSδVTP+TS.
(8)
Assuming RP + TP = 1, RS + TS = 1, which is reasonable for commercial PBS, and combing with Eqs. (6) and (8) the followings can be derived:
RS=(BAδV)/(1δV).RP=A(1+δV)δVR.STS=1RS.TP=1RP.
(9)
with

A=δ*(0)δ*(0)+V*.B=δ*(90)δ*(90)+V*.
(10)

Thus, we can set initial values for RP, TP, RS, TS and iterate following Eqs. (5), (9), and (10) until the relative residual difference between two iterations is less than 0.1%. For calibration, the value of δv in Eq. (9) can be calculated theoretically for clean air [2

2. A. Behrendt and T. Nakamura, “Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature,” Opt. Express 10(16), 805–817 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?id=69680. [CrossRef] [PubMed]

]. We can then calculate the linear volume depolarization ratio δv from Eq. (6) as,

δV=δ*(0)V*TPRPRSδ*(0)V*TS.
(11)

Figure 2
Fig. 2 Iterative determinations of RP, TP, RS, and TS with simulated lidar signals.
shows the iterated solutions of RP, TP, RS, and TS based on simulated lidar signals generated with RP = 0.04, TP = 0.96, RS = 0.98, TS = 0.02, and V* = 1.67. The initial values for the iteration were arbitrarily set to: RP = 0.01, TP = 0.99, RS = 0.99, TS = 0.01. The errors in determined V* and the other optical parameters are not sensitive to the errors of orientation angle φ, as shown in Fig. 3
Fig. 3 Relative errors of V* and Tp as a function of orientation angle φ uncertainties.
. The errors of the solutions are also insensitive to the assumption error of δv. As illustrated in Fig. 4
Fig. 4 Relative errors of Tp and Rs as a function of uncertainties in assumed δv
, the relative errors in derived RP, TP, RS, and TS are only ~0.3% of the assumption error of δv.

PP=η(Pβ+Pβ)τ2r2.PS=η(Pβ+Pβ)τ2r2.
(12)

Here, we introduce an outgoing laser power linear depolarization ratio δL .

δL=PP.
(13)

P|| and P are components of the outgoing laser power, thus δL is a factor including all the transmitting system effects. Such as the laser source is not perfect linearly polarized, possible depolarization/diattenuation by the beam transmitting optics and the HWPs rarely are able to provide a perfect π phase shift.

In this circumstance, Eq. (3) is rewritten as
δV=PSPP=δL+δA1+δLδA,δA=ββ.
(14)
where δA is the true atmospheric linear depolarization ratio.

Then, we have
δL=δVδA1δAδV.
(15)
δV can be calculated with Eq. (11). For an aerosol-free lidar range in the free troposphere, δA = δm, the linear depolarization ratio δm of air molecules can be calculated theoretically [2

2. A. Behrendt and T. Nakamura, “Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature,” Opt. Express 10(16), 805–817 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?id=69680. [CrossRef] [PubMed]

]. We then solve all the system constants V*, RP, TP, RS, TS and δL in a manner consistent with the iteration process described above, which can then be used for regular measurements. Finally, the linear volume depolarization ratio δv can be calculated by:

δV=δL+PRPTV*TPRPRSPRPTV*TS1+δLPRPTV*TPRPRSPRPTV*TS.
(16)

3. Calibration of the UW Airborne Raman lidar

The University of Wyoming (UW) compact airborne Raman lidar was developed for aerosol and short range (within 1km) water vapor measurements from the UW King Air. The transmitter is a flashlamp-pumped Nd: YAG laser which emits about 50 mJ per pulse at 355 nm with a repetition rate of 30 Hz. A HWP is installed close to the laser emitting window to adjust the polarization direction of the outgoing laser. The receiver is a Cassegrain telescope with aperture of 300 mm, which is mounted on a rigid optical table together with the laser. The lidar has four receiving channels; two channels for elastic scattering parallel and perpendicular respectively, and the other two for Raman scattering from water vapor and nitrogen respectively. All of the channels use narrow band filters with FWHM (full width at half maximum) of 0.3 nm. A four-channel 12-bit data acquisition card with 100M sampling frequency is used to record the signals. A simplified instrument layout is shown in Fig. 5
Fig. 5 Layout of UW airborne Raman lidar. HWP is a half-wavelength-plate. RF1-RF5 are reflecting mirrors. BS1, BS2 are dichroic beam splitters. PMT1-PMT4 are photomultipliers.
.

A calibration exercise was carried out under a clear sky condition after snowing event on Feb 3, 2010. The lidar was aligned for zenith observation from the ground. First, we rotated the HWP to + 22.5°to set the angle φ (see Fig. 1) to be + 45°. After 900 shots of accumulating (30 seconds), the HWP was rotated to −22.5°to set the angle φ to be −45°, then φ = 0° and φ = 90°. Thus, we collected measurements of δ*( ± 45), δ*(0) and δ*(90) to use the method described in Section 2 to calibrate the system. The signals at an aerosol-free range with good signal to noise ratio at about 4 km altitude were chosen to for the calculation. The initial values were set as RP = 0.01, TP = 0.99, RS = 0.99, TS = 0.01 (based on the factory specifications of the PBS) and δV = 0.0045 (calculated based on 355nm and 0.3 nm filter FWHM for clear air), and the solutions are achieved after 9 iteration loops. The solutions are RP = 0.077, TP = 0.923, RS = 0.957, TS = 0.043, δL = 0.0031, V* = 1.745.

4. Conclusion

An improved depolarization lidar calibration method, which just requires a HWP in the emitting optical path, is described in detail. The method is based on lidar measurements at φ(see Fig. 1) = 0°, ± 45° and 90° respectively. With an iteration based processing algorithm and the observations within an aerosol-free range, the optical reflectance and transmission parameters of the polarizing beam splitter and the gain factor ratio of the parallel and perpendicular channels can be determined. The linear depolarization ratio of emitting laser power can also be determined. The lidar can be well calibrated for atmospheric depolarization measurement with these system parameters, which has been demonstrated on the University of Wyoming airborne Raman lidar. This calibration method can be applied to all of the polarization-sensitive lidars if there is a HWP in the emitting optical path, which is true for most systems.

In this method, the assumption of molecular depolarization δv is used in an iteration process rather than directly used for the calibration. The calibration errors in the relative amplification factor ratio and the other optical parameters are only ~0.3% of the error in assumed δv which makes the calibration method more accurate.

Acknowledgments

This work is supported by National Science Foundation (NSF) under Award AGS-0645644.

References and links

1.

R. M. Schotland, K. Sassen, and R. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10(5), 1011–1017 (1971), http://journals.ametsoc.org/doi/abs/10.1175/1520-0450(1971)010%3C1011%3AOBLOLD%3E2.0.CO%3B2. [CrossRef]

2.

A. Behrendt and T. Nakamura, “Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature,” Opt. Express 10(16), 805–817 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?id=69680. [CrossRef] [PubMed]

3.

H. Adachi, T. Shibata, Y. Iwasaka, and M. Fujiwara, “Calibration method for the lidar-observed stratospheric depolarization ratio in the presence of liquid aerosol particles,” Appl. Opt. 40(36), 6587–6595 (2001), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-40-36-6587. [CrossRef] [PubMed]

4.

K. Sassen, “The polarization lidar technique for cloud research: A review and current assessment,” Bull. Amer. Meteor. Soc 72, 1848–1866 (1991). http://journals.ametsoc.org/doi/abs/10.1175/1520-0477(1991)072%3C1848%3ATPLTFC%3E2.0.CO%3B2. [CrossRef]

5.

K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58(15), 2103–2112 (2001), http://journals.ametsoc.org/doi/abs/10.1175/1520-0469(2001)058%3C2103%3AAMCCCF%3E2.0.CO%3B2. [CrossRef]

6.

C. M. R. Platt, “Lidar observation of a mixed-phase altostratus cloud,” J. Appl. Meteorol. 16(4), 339–345 (1977), http://journals.ametsoc.org/doi/abs/10.1175/1520-0450%281977%29016%3C0339%3ALOOAMP%3E2.0.CO%3B2. [CrossRef]

7.

E. W. Eloranta and P. Piironen, “Depolarization measurements with the high spectral resolution lidar,” in 17th International Laser Radar Conference, (Laser Radar Society of Japan, ICLAS, NASDA, and NIES, Sendai, Japan, 1994). pp. 127–128.

8.

J. Larry Pezzaniti and R. A. Chipman, “Angular dependence of polarizing beam-splitter cubes,” Appl. Opt. 33(10), 1916–1929 (1994), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-33-10-1916. [CrossRef] [PubMed]

9.

J. Mouchart, J. Begel, and E. Duda, “Modified MacNeille cube polarizer for a wide angular field,” Appl. Opt. 28(14), 2847–2853 (1989), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-28-14-2847. [CrossRef] [PubMed]

10.

R. P. Netterfield, “Practical thin-film polarizing beam-splitters,” Opt. Acta (Lond.) 24(1), 69–79 (1977), http://www.tandfonline.com/doi/abs/10.1080/713819379. [CrossRef]

11.

J. D. Spinhirne, M. Z. Hansen, and L. O. Caudill, “Cloud top remote sensing by airborne lidar,” Appl. Opt. 21(9), 1564–1571 (1982), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-21-9-1564. [CrossRef] [PubMed]

12.

J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winkler, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol. 23(5), 683–699 (2006), http://journals.ametsoc.org/doi/abs/10.1175/JTECH1872.1. [CrossRef]

13.

V. Freudenthaler, M. Esselborn, M. Wiegner, B. Heese, M. Tesche, A. Ansmann, D. Müller, D. Althausen, M. Wirth, A. Fix, G. Ehret, P. Knippertz, C. Toledano, J. Gasteiger, M. Garhammer, and M. Seefeldner, “Depolarization ratio profiling at several wavelengths in pure Saharan dust during SAMUM 2006,” Tellus 61B, 165–179 (2009), http://www.tellusb.net/index.php/tellusb/article/view/16821.

14.

Y. You, G. W. Kattawar, P. Yang, X. H. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 470–482 (2006), http://www.sciencedirect.com/science/article/pii/S0022407305004097. [CrossRef]

OCIS Codes
(010.3640) Atmospheric and oceanic optics : Lidar
(260.5430) Physical optics : Polarization
(280.1310) Remote sensing and sensors : Atmospheric scattering
(290.1090) Scattering : Aerosol and cloud effects
(010.1615) Atmospheric and oceanic optics : Clouds

ToC Category:
Remote Sensing

History
Original Manuscript: April 4, 2013
Revised Manuscript: June 2, 2013
Manuscript Accepted: June 3, 2013
Published: June 11, 2013

Citation
Bo Liu and Zhien Wang, "Improved calibration method for depolarization lidar measurement," Opt. Express 21, 14583-14590 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14583


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References

  1. R. M. Schotland, K. Sassen, and R. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol.10(5), 1011–1017 (1971), http://journals.ametsoc.org/doi/abs/10.1175/1520-0450(1971)010%3C1011%3AOBLOLD%3E2.0.CO%3B2 . [CrossRef]
  2. A. Behrendt and T. Nakamura, “Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature,” Opt. Express10(16), 805–817 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?id=69680 . [CrossRef] [PubMed]
  3. H. Adachi, T. Shibata, Y. Iwasaka, and M. Fujiwara, “Calibration method for the lidar-observed stratospheric depolarization ratio in the presence of liquid aerosol particles,” Appl. Opt.40(36), 6587–6595 (2001), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-40-36-6587 . [CrossRef] [PubMed]
  4. K. Sassen, “The polarization lidar technique for cloud research: A review and current assessment,” Bull. Amer. Meteor. Soc 72, 1848–1866 (1991). http://journals.ametsoc.org/doi/abs/10.1175/1520-0477(1991)072%3C1848%3ATPLTFC%3E2.0.CO%3B2 . [CrossRef]
  5. K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci.58(15), 2103–2112 (2001), http://journals.ametsoc.org/doi/abs/10.1175/1520-0469(2001)058%3C2103%3AAMCCCF%3E2.0.CO%3B2 . [CrossRef]
  6. C. M. R. Platt, “Lidar observation of a mixed-phase altostratus cloud,” J. Appl. Meteorol.16(4), 339–345 (1977), http://journals.ametsoc.org/doi/abs/10.1175/1520-0450%281977%29016%3C0339%3ALOOAMP%3E2.0.CO%3B2 . [CrossRef]
  7. E. W. Eloranta and P. Piironen, “Depolarization measurements with the high spectral resolution lidar,” in 17th International Laser Radar Conference, (Laser Radar Society of Japan, ICLAS, NASDA, and NIES, Sendai, Japan, 1994). pp. 127–128.
  8. J. Larry Pezzaniti and R. A. Chipman, “Angular dependence of polarizing beam-splitter cubes,” Appl. Opt.33(10), 1916–1929 (1994), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-33-10-1916 . [CrossRef] [PubMed]
  9. J. Mouchart, J. Begel, and E. Duda, “Modified MacNeille cube polarizer for a wide angular field,” Appl. Opt.28(14), 2847–2853 (1989), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-28-14-2847 . [CrossRef] [PubMed]
  10. R. P. Netterfield, “Practical thin-film polarizing beam-splitters,” Opt. Acta (Lond.)24(1), 69–79 (1977), http://www.tandfonline.com/doi/abs/10.1080/713819379 . [CrossRef]
  11. J. D. Spinhirne, M. Z. Hansen, and L. O. Caudill, “Cloud top remote sensing by airborne lidar,” Appl. Opt.21(9), 1564–1571 (1982), http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-21-9-1564 . [CrossRef] [PubMed]
  12. J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winkler, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol.23(5), 683–699 (2006), http://journals.ametsoc.org/doi/abs/10.1175/JTECH1872.1 . [CrossRef]
  13. V. Freudenthaler, M. Esselborn, M. Wiegner, B. Heese, M. Tesche, A. Ansmann, D. Müller, D. Althausen, M. Wirth, A. Fix, G. Ehret, P. Knippertz, C. Toledano, J. Gasteiger, M. Garhammer, and M. Seefeldner, “Depolarization ratio profiling at several wavelengths in pure Saharan dust during SAMUM 2006,” Tellus61B, 165–179 (2009), http://www.tellusb.net/index.php/tellusb/article/view/16821 .
  14. Y. You, G. W. Kattawar, P. Yang, X. H. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transf.100(1-3), 470–482 (2006), http://www.sciencedirect.com/science/article/pii/S0022407305004097 . [CrossRef]

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