Abstract

Polarization-sensitive detection of elastic backscattered light is useful for detection of cloud phase and depolarizing aerosols. The U.S. Department of Energy’s Atmospheric Radiation Measurement Program has deployed micropulse lidar (MPL) for over a decade, but without polarized detection. Adding an actively-controlled liquid crystal retarder provides the capability to identify depolarizing particles by alternately transmitting linearly and circularly polarized light. This represents a departure from established techniques, which transmit exclusively linear polarization or exclusively circular polarization. Mueller matrix calculations yield simple relationships between the well-known linear depolarization ratio δlinear, the circular depolarization ratio δcirc, and this MPL depolarization ratio δMPL.

©2007 Optical Society of America

1. Introduction

Climate change studies have shown that cloud effects and aerosol-cloud interactions (i.e., aerosol indirect effects) are among the largest uncertainties in simulations of climate change [1–2]. Elastic backscatter lidars are highly sensitive instruments capable of providing profiles of cloud and aerosol structure within the atmosphere. The addition of polarization-sensitive detection provides information pertaining to the phase of cloud particles and to the type of aerosol particles [3–4]. The U.S. DOE Atmospheric Radiation Measurements (ARM) Program has deployed eye-safe micropulse lidar (MPL) for semi-autonomous operation at each of its climate research facilities for over a decade. Recently, polarization-sensitive MPL systems have been deployed by ARM through straightforward modifications of existing designs and equipment. This economical use of existing hardware implicitly carried the challenge of adapting a single-channel instrument to what is generally a two-channel measurement.

2. ARM MPL instrument description

The ARM MPL is a compact, eye-safe lidar designed for full-time unattended operation [5]. Eye-safety is achieved through beam expansion (7”-8” diameter) and low laser pulse energy (∼10 μJ) combined with high pulse rate (2500 Hz). Subject to the limits of optical attenuation, the MPL is capable of detecting cloud and aerosol structure up to 20 km in altitude. High sensitivity is achieved through the use of a pulsed solid-state laser, narrow field of view (∼100 μrad), narrow interference filters (∼0.3 nm FWHM), and photon counting detection. It uses a co-axial “transceiver” design with a telescope shared by both transmit and receive optics. A comprehensive description of the MPL systems originally deployed by ARM is provided by Campbell et al. [6]. ARM MPL systems have subsequently experienced several modifications driven by component availability, vendor changes, design improvements, and so on.

 figure: Fig. 1.

Fig. 1. Basic optical layout corresponding to configuration MPL-4B.

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A simplified optical layout of the MPL-4B configuration is shown in Fig. 1. Additional details regarding this configuration are available from the vendor, as this layout differs in several respects from that described in Campbell et al. [6]. The laser light source is a diode-pumped frequency-doubled solid-state laser (Nd-YLF at 523 or 527 nm, or Nd-YAG/ Nd-YVO4 at 532 nm) yielding pulsed visible green light. After a half-wave plate adjusts the orientation of the linear polarization from the raw beam, a dielectric turning mirror directs the beam through a negative lens with focal point matched to the main transceiver telescope. The weakly diverging beam is reflected through a polarizing beam splitter, and then through a pseudo-depolarizing optic composed of cemented quartz wedges. The linear polarization of light passing through the “depolarizer” is rotated by varying amounts with the net effect that the transmitted beam is composed of stripes or zones of linear polarization each having different orientation. Averaged over the entire area of the beam, the net polarization is essentially zero. This pseudo-depolarized beam is then expanded and collimated by the transceiver telescope and transmitted into the atmosphere.

Some fraction of the transmitted beam is scattered back to the lidar from the atmosphere where it is collected by the transceiver telescope. Because the transmitted beam has no net polarization, the returning 180-degree backscattered light is also un-polarized irrespective of whether or not the scattering medium in the atmosphere is depolarizing. The collected photons pass again through the depolarizer and are incident on the polarizing beam splitter. Approximately 50% of the returning light is reflected by beam splitter towards the laser and is lost. The remaining 50% passes through and converges to the focal point of the transceiver telescope. A 200 μm diameter pinhole at this image plane serves as a field stop to restrict the field of view. Passing through the pinhole, the light is collimated by a focusing lens, passes through narrow bandwidth (< 0.3 nm) interference filter, and is focused into an optical fiber leading to the photon counting detector.

3. MPL design modification.

Replacing the passive depolarizing element with an actively controlled liquid crystal retarder (LCR) provides the capability to conduct polarization-sensitive measurements [7]. This is achieved by alternating between two retardation states. When the LCR is operated with zero retardation (or an integral number of half-waves) the transmitted laser beam will be linearly polarized. Backscattered light returning with identical polarization will not pass through the polarizing beam splitter towards the detection optics. In contrast, “depolarized” backscattered light will have some fraction of polarization orthogonal to the incident beam that will pass through the polarizing beam splitter towards the detector.

When the LCR is operated with quarter-wave retardation, the outgoing light will be circularly polarized. When circularly polarized light undergoes non-depolarizing scattering, the 180° backscattered light returns circularly polarized but with reversed rotational sense [8]. Let us suppose that the outgoing beam has right-hand circular polarization. Singly-backscattered non-depolarized light will return with left-hand circular polarization. After passing back through the LCR, this will again become linearly polarized but with orientation orthogonal to the original laser polarization such that it will be efficiently coupled toward the detection optics. In contrast, the detection of depolarized backscattered light will be suppressed to the extent that it returns with the right-hand circular polarization, orthogonal to the non-depolarized signal.

By toggling between these two modes the MPL alternates between suppressing either depolarized or non-depolarized backscattered light. An advantage of alternating modes with a single detector is that detector field of view, overlap corrections, and range-dependent corrections will cancel in the ratio. However, a disadvantage is that the polarization components are not measured simultaneously which may be a concern if the scene changes rapidly. Optimally, the time between the two measurements should be minimized to ensure that the atmospheric scene is essentially static throughout.

The MPL data acquisition system is “slaved” to the laser such that as soon as a laser trigger signal is generated (indicating a laser pulse is imminent), the multi-channel scalar begins counting. For non-polarized ARM MPL systems, this process is repeated for 30 seconds accumulating the thousands of profiles necessary for sufficient signal to noise. Cloud scenes frequently change too rapidly for 30 second polarization intervals to be of consistent value. To reduce this risk ARM polarized MPL systems are currently configured with approximately 3 second intervals averaged to compose 60 second interleaved averages. Newer MPL systems are capable of intervals as short as 0.1 second.

Of some potential concern is the transition time for the LCR to change states. The LCR used in this application (Meadowlark LRC-200-VIS-TSC) is a variable state retarder with a transition time of between 5 and 20 ms depending on the direction of mode change with the worst case corresponding to the change from quarter-wave to zero retardation. In the slaved data acquisition mode used for the prototype design, this suggests that some lidar profiles may be collected while the retarder is in transition. With 3 second averaging intervals, this constitutes less than a 1% contamination of linear depolarization profiles combining with the circular depolarization. This potential concern has been entirely eliminated in recent designs by actively suppressing collection of profiles during the LCR transition interval.

4. Demonstration of polarization-sensitivity.

Figure 2 shows lidar profiles collected from a polarization sensitive MPL operated in Barrow Alaska since November 2003. Figure 2(a) shows the base-10 logarithm of circularly polarized backscattered light collected with the LCR in quarter-wave mode. Several features are noteworthy: the lidar beam experiences significant attenuation by high clouds at 6-7 km between 0-5 UTC, and some minor attenuation at low altitude around 13:00 UTC and 21:00 UTC. A fairly distinct layer is notable below 1 km for much of the day. The general decrease in signal with height is due in part to rarefaction of the atmosphere and in part due to actual extinction of the beam.

 figure: Fig. 2.

Fig. 2. Polarized MPL profiles from top to bottom: 2(a) “Co-polarized” backscatter profile collected in circularly polarized mode displayed range-corrected in log10(MHz-km2), 2(b) “Depolarized” backscatter profile collected in linearly polarized mode displayed range-corrected in log10(MHz-km2), 2(c) Profiles of log10(effective linear depolarization ratio).

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Figure 2(b) shows the base-10 logarithm of linearly depolarized backscattered light collected while in zero-retardation mode. Much more detail is apparent in the elevated aerosol layers as the reduced molecular scattering yields higher contrast for the aerosol layers. The spatial extent of the cirrus cloud in the first quarter of the day is more evident. Also striking is the correlation between the low altitude signal attenuation and strong depolarized returns from the lower atmosphere which identifies the source as ice crystals or snow.

Figure 2(c) shows the base-10 logarithm of the effective linear depolarization ratio computed from the MPL hybrid measurement as derived from the MPL measurements in Eq. (1.6). The high depolarization ratio values of about 50% confirm that nature of the cirrus cloud in the early part of the day and also of the precipitation below 1 km in the two later parts of the day. While the depolarization ratio from the aerosols is much lower in magnitude (less than 10%) there is still significant variation with increased values observed along the base of a stratified layer. Also, because this is a quantity formed of the ratio of lidar profiles, the depolarization ratio measurement is not strongly perturbed by minor attenuation of the lidar beam as occurs around 13:00 and 21:00 UTC.

5. MPL depolarization ratio defined.

The lidar backscattered signal is essentially incoherent and can be represented accurately as a 4-component Stokes vector and analyzed with Mueller matrix calculus. We can represent the MPL measurement as a sequence of Mueller operators acting on polarization vector Pinitial :

Pfinal(φ)=MLPHMLCR(φ,45)MatmMLCR(φ,+45)MLPVPinitial

where MLPV stands for the polarizing beam splitter acting as a linear polarizer with axis aligned to the vertical, MLCR(φ,+45) stands for the LCR with retardation φ aligned with fast axis at +45° to vertical, Matm represents the interaction with the atmosphere, MLCR(φ,-45) is again the LCR but now with fast axis aligned at -45° to vertical, and MLPH is the polarizing beam splitter now acting as a linear polarizer with axis aligned horizontally. Note that the angles are defined as positive clockwise while facing in the direction of propagation. When the direction of propagation is reversed for the returning light, the angles are also reversed. Mueller matrices do not represent optical components so much as optical interactions explaining why different Mueller matrices are used to represent the same optical component. With the exception of Matm, the other operators represent the actions of elementary optical elements with known form.

The Mueller matrix for the atmosphere is of course a changing quantity and is a subject of intense study [9–10]. For a common simple case of single scattering on particles having a plane of symmetry or random orientation along the line of sight (which includes spheres, randomly oriented ice crystals, and horizontal plates for vertically pointing lidar) we benefit from substantial cancellation of matrix elements based on symmetry arguments to obtain

Matm=a[100001d0000d100002d1].

where a is proportional to the magnitude of the return signal and d is related to propensity of the scattering medium to preserve the incident polarization. Subsequent discussion below is limited to this simplified (but common) case. Specifically, the potential effects of elliptical polarization through multiple scattering or complex geometry are not addressed in here.

Taking vector Pinitial as polarized vertically, Eq. (1.1) together with Eq. (1.2) allows us to compute the MPL measured quantities of P(0) and P(π2) as well as P(0) and P(π2) :

P(0)=d2d200,P(0)=1d2d2100,P(π2)=1d1d00,P(π2)=dd00

The various depolarization ratios may be expressed as

δMPL=P(0)P(π2),δlinear=P(0)P(0),andδcirc=P(π2)P(π2).

Combining Eq. (1.3) and (1.4), we find

δMPL=d2(1d),δlinear=d2d,andδcirc=d1d.

which permits us to explicitly relate these three measurable depolarization ratios as:

δMPL=δcirc.2=δlinear(1δlinear)orδlinear=δMPLδMPL+1andδcirc.=2×δMPL.

This result agrees with previous findings relating linear and circular depolarization ratios [11] and shows how standard linear depolarization values may be obtained from the MPL measurement. Taken together, Eqs. (1.4) and (1.6) lead to

P(0)=P(π2)+P(0)

which permits recovery of the total lidar signal power as:

P=P(π2)+2P(0)

6. Conclusions and future work.

The relationships in Eq. (1.6) and Eq. (1.8) place the MPL hybrid polarization measurements fully within the context of the existing body of polarized lidar work. The Mixed-Phase Arctic Cloud Experiment field campaign [12] presents an exciting opportunity to directly compare the polarized ARM MPL measurements with two other collocated lidar which separately measured δlinear and δcirc depolarization ratios [3, 13].

Definitive comparisons will require careful correction for MPL instrumental polarization artifacts arising from non-normal incidence transmission through the retarder, potential misalignment of the retarder fast axis, and polarization mode purity. These are well-documented phenomena [14–15], but the corresponding corrections have not yet been fully characterized for this system. For quantitative use, especially for aerosols with small but detectable depolarization, it is necessary to address these finer calibration details. It will also be important to identify and exclude instances where the atmospheric sample changes significantly over the measurement cycle, such that the ratio is of dubious value.

Beyond consideration of these measurement artifacts, the complex meteorology and mixed-phase clouds present during this field campaign may underscore the limiting assumptions inherent in the current treatment which give rise to the simplified atmospheric scattering matrix in Eq. (1.2) For example, both theoretical and observational studies report non-zero off-diagonal scattering matrix elements which yield elliptical polarization [9–11, 16]. Depending on the degree of elliptical polarization encountered this may constitute a small correction to, or require a reformulation of, the relationships in Eqs. (1.5), (1.6), and (1.7).

Acknowledgments

This research was supported by the Office of Biological and Environmental Research of the U.S. Department of Energy as part of the Atmospheric Radiation Measurement Program. The authors wish to acknowledge Jim Spinhirne, Ken Sassen, Ed Eloranta, and Wynn Eberhard for their feedback and contributions related to the design and implementation of this ARM MPL technique.

References and links

1. G. L. Stephens, et al., “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” Am. Meteorol. Soc. 47,1742–1753, (1990).

2. G. L. Stephens, et al, “The CLOUDSAT mission and the A-Train,” Bull. Amer. Meteorol. Soc. 83,1771–1790, (2002). [CrossRef]  

3. K. Sassen, “The polarization lidar technique for cloud research: A review and current assessment,” Bull. Amer. Meteor. Soc. 72,1848–1866 (1991). [CrossRef]  

4. G. P. Gobbi, “Polarization lidar returns from aerosols and thin clouds: a framework for the analysis,” Appl. Opt. 37,5505–5508 (1999). [CrossRef]  

5. J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans. Geosci. Remote Sens. 31,48–55 (1993). [CrossRef]  

6. J. R. Campbellet al, “Full-time, eye-safe cloud and aerosol lidar observation at Atmospheric Radiation Measurement Program sites: instruments and data processing,” J. Atmos. Ocean. Tech. 19,431–442 (2002). [CrossRef]  

7. M. Del Guasta, et al., “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt. 45,4878–4887 (2006). [CrossRef]   [PubMed]  

8. Y. X. Hu, et al, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 757–764 (2003). [CrossRef]  

9. J. W. Hovenieret al, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157,301–310 (1986).

10. P. Yang, et al, “Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase,” Appl. Opt. 42,4389–4395 (2003). [CrossRef]   [PubMed]  

11. M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20,1356–1358 (1995). [CrossRef]   [PubMed]  

12. J. Harrington and J. Verlinde, “Mixed-Phase Arctic Clouds Experiment (M-PACE),” http://www.meteo.psu.edu/∼verlinde/sciencedoc.pdf

13. E. W. Eloranta, “High Spectral Resolution Lidar” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, K. Weitkamp, ed., (Springer-Verlag, New York, 2005).

14. J. Biele, et al, “Polarization lidar: Corrections of instrumental effects,” Opt. Express 7,427–435 (2000). [CrossRef]   [PubMed]  

15. A. Behrendt and T. Nakamura, “Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature,” Opt. Express 10,805–817 (2002). [PubMed]  

16. J. D. Houston and A. I. Carswell, “Four-component polarization measurement of lidar atmospheric scattering,” Appl. Opt. 17,614–620 (1978). [CrossRef]   [PubMed]  

References

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  1. G. L. Stephens, et al., “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” Am. Meteorol. Soc. 47,1742–1753, (1990).
  2. G. L. Stephens, et al, “The CLOUDSAT mission and the A-Train,” Bull. Amer. Meteorol. Soc. 83,1771–1790, (2002).
    [Crossref]
  3. K. Sassen, “The polarization lidar technique for cloud research: A review and current assessment,” Bull. Amer. Meteor. Soc. 72,1848–1866 (1991).
    [Crossref]
  4. G. P. Gobbi, “Polarization lidar returns from aerosols and thin clouds: a framework for the analysis,” Appl. Opt. 37,5505–5508 (1999).
    [Crossref]
  5. J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans. Geosci. Remote Sens. 31,48–55 (1993).
    [Crossref]
  6. J. R. Campbellet al, “Full-time, eye-safe cloud and aerosol lidar observation at Atmospheric Radiation Measurement Program sites: instruments and data processing,” J. Atmos. Ocean. Tech. 19,431–442 (2002).
    [Crossref]
  7. M. Del Guasta, et al., “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt. 45,4878–4887 (2006).
    [Crossref] [PubMed]
  8. Y. X. Hu, et al, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 757–764 (2003).
    [Crossref]
  9. J. W. Hovenieret al, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157,301–310 (1986).
  10. P. Yang, et al, “Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase,” Appl. Opt. 42,4389–4395 (2003).
    [Crossref] [PubMed]
  11. M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20,1356–1358 (1995).
    [Crossref] [PubMed]
  12. J. Harrington and J. Verlinde, “Mixed-Phase Arctic Clouds Experiment (M-PACE),” http://www.meteo.psu.edu/∼verlinde/sciencedoc.pdf
  13. E. W. Eloranta, “High Spectral Resolution Lidar” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, K. Weitkamp, ed., (Springer-Verlag, New York, 2005).
  14. J. Biele, et al, “Polarization lidar: Corrections of instrumental effects,” Opt. Express 7,427–435 (2000).
    [Crossref] [PubMed]
  15. A. Behrendt and T. Nakamura, “Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature,” Opt. Express 10,805–817 (2002).
    [PubMed]
  16. J. D. Houston and A. I. Carswell, “Four-component polarization measurement of lidar atmospheric scattering,” Appl. Opt. 17,614–620 (1978).
    [Crossref] [PubMed]

2006 (1)

2003 (2)

Y. X. Hu, et al, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 757–764 (2003).
[Crossref]

P. Yang, et al, “Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase,” Appl. Opt. 42,4389–4395 (2003).
[Crossref] [PubMed]

2002 (3)

A. Behrendt and T. Nakamura, “Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature,” Opt. Express 10,805–817 (2002).
[PubMed]

J. R. Campbellet al, “Full-time, eye-safe cloud and aerosol lidar observation at Atmospheric Radiation Measurement Program sites: instruments and data processing,” J. Atmos. Ocean. Tech. 19,431–442 (2002).
[Crossref]

G. L. Stephens, et al, “The CLOUDSAT mission and the A-Train,” Bull. Amer. Meteorol. Soc. 83,1771–1790, (2002).
[Crossref]

2000 (1)

1999 (1)

1995 (1)

1993 (1)

J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans. Geosci. Remote Sens. 31,48–55 (1993).
[Crossref]

1991 (1)

K. Sassen, “The polarization lidar technique for cloud research: A review and current assessment,” Bull. Amer. Meteor. Soc. 72,1848–1866 (1991).
[Crossref]

1990 (1)

G. L. Stephens, et al., “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” Am. Meteorol. Soc. 47,1742–1753, (1990).

1986 (1)

J. W. Hovenieret al, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157,301–310 (1986).

1978 (1)

Behrendt, A.

Biele, J.

Campbell, J. R.

J. R. Campbellet al, “Full-time, eye-safe cloud and aerosol lidar observation at Atmospheric Radiation Measurement Program sites: instruments and data processing,” J. Atmos. Ocean. Tech. 19,431–442 (2002).
[Crossref]

Carswell, A. I.

Eloranta, E. W.

E. W. Eloranta, “High Spectral Resolution Lidar” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, K. Weitkamp, ed., (Springer-Verlag, New York, 2005).

Gobbi, G. P.

Guasta, M. Del

Harrington, J.

J. Harrington and J. Verlinde, “Mixed-Phase Arctic Clouds Experiment (M-PACE),” http://www.meteo.psu.edu/∼verlinde/sciencedoc.pdf

Houston, J. D.

Hovenier, J. W.

M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20,1356–1358 (1995).
[Crossref] [PubMed]

J. W. Hovenieret al, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157,301–310 (1986).

Hu, Y. X.

Y. X. Hu, et al, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 757–764 (2003).
[Crossref]

Mishchenko, M. I.

Nakamura, T.

Sassen, K.

K. Sassen, “The polarization lidar technique for cloud research: A review and current assessment,” Bull. Amer. Meteor. Soc. 72,1848–1866 (1991).
[Crossref]

Spinhirne, J. D.

J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans. Geosci. Remote Sens. 31,48–55 (1993).
[Crossref]

Stephens, G. L.

G. L. Stephens, et al, “The CLOUDSAT mission and the A-Train,” Bull. Amer. Meteorol. Soc. 83,1771–1790, (2002).
[Crossref]

G. L. Stephens, et al., “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” Am. Meteorol. Soc. 47,1742–1753, (1990).

Verlinde, J.

J. Harrington and J. Verlinde, “Mixed-Phase Arctic Clouds Experiment (M-PACE),” http://www.meteo.psu.edu/∼verlinde/sciencedoc.pdf

Yang, P.

Am. Meteorol. Soc. (1)

G. L. Stephens, et al., “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” Am. Meteorol. Soc. 47,1742–1753, (1990).

Appl. Opt. (4)

Astron. Astrophys. (1)

J. W. Hovenieret al, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157,301–310 (1986).

Bull. Amer. Meteor. Soc. (1)

K. Sassen, “The polarization lidar technique for cloud research: A review and current assessment,” Bull. Amer. Meteor. Soc. 72,1848–1866 (1991).
[Crossref]

Bull. Amer. Meteorol. Soc. (1)

G. L. Stephens, et al, “The CLOUDSAT mission and the A-Train,” Bull. Amer. Meteorol. Soc. 83,1771–1790, (2002).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (1)

J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans. Geosci. Remote Sens. 31,48–55 (1993).
[Crossref]

J. Atmos. Ocean. Tech. (1)

J. R. Campbellet al, “Full-time, eye-safe cloud and aerosol lidar observation at Atmospheric Radiation Measurement Program sites: instruments and data processing,” J. Atmos. Ocean. Tech. 19,431–442 (2002).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (1)

Y. X. Hu, et al, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 757–764 (2003).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Other (2)

J. Harrington and J. Verlinde, “Mixed-Phase Arctic Clouds Experiment (M-PACE),” http://www.meteo.psu.edu/∼verlinde/sciencedoc.pdf

E. W. Eloranta, “High Spectral Resolution Lidar” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, K. Weitkamp, ed., (Springer-Verlag, New York, 2005).

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Figures (2)

Fig. 1.
Fig. 1. Basic optical layout corresponding to configuration MPL-4B.
Fig. 2.
Fig. 2. Polarized MPL profiles from top to bottom: 2(a) “Co-polarized” backscatter profile collected in circularly polarized mode displayed range-corrected in log10(MHz-km2), 2(b) “Depolarized” backscatter profile collected in linearly polarized mode displayed range-corrected in log10(MHz-km2), 2(c) Profiles of log10(effective linear depolarization ratio).

Equations (8)

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P final ( φ ) = M LPH M LCR ( φ , 45 ) M atm M LCR ( φ , + 4 5 ) M LPV P initial
M atm = a [ 1 0 0 0 0 1 d 0 0 0 0 d 1 0 0 0 0 2 d 1 ] .
P ( 0 ) = d 2 d 2 0 0 , P ( 0 ) = 1 d 2 d 2 1 0 0 , P ( π 2 ) = 1 d 1 d 0 0 , P ( π 2 ) = d d 0 0
δ MPL = P ( 0 ) P ( π 2 ) , δ linear = P ( 0 ) P ( 0 ) , and δ circ = P ( π 2 ) P ( π 2 ) .
δ MPL = d 2 ( 1 d ) , δ linear = d 2 d , and δ circ = d 1 d .
δ MPL = δ circ. 2 = δ linear ( 1 δ linear ) or δ linear = δ MPL δ MPL + 1 and δ circ. = 2 × δ MPL .
P ( 0 ) = P ( π 2 ) + P ( 0 )
P = P ( π 2 ) + 2 P ( 0 )

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