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nm, is low, thus smoothing of the lidar signals is required. Typically, smoothing of the order of several hundreds of meters is adequate. As a consequence, the vertical resolution of the retrievals is signicantly reduced compared to the raw signals.

2.4 Depolarization

2.4.1 Polarization lidar method

The linear depolarization ratio is dened as the ratio of the cross- and co-polarized backscat- tered light with respect to the plane of polarization of the transmitted linearly polarized laser beam. Both components are separated by a polarizing beam-splitter cube (PBS). It splits the incident beam into two beams of orthogonal planes of polarization. However, for many common PBS the separation is not perfect. Thus one or both output beams contain a mixture of polarization states.

Analog to the lidar equation (Equation 2:1) the powers of the cross- and co-polarized signals before the PBS can be expressed as

Pk = C_r2kkT2 (2.22)

and

P? = C_r2??T2 (2.23)

with the parallel- (k) and cross-polarized (?) component of the total backscatter

coecient , the system constants (including the telescope aparture and the laser power) Ck and C?, and the atmospheric transmittance T2.

In praxis the determination of the signals described in equations 2:22 and 2:23 is tech- nically dicult and therefore subject to uncertainties. One reason is that the PBS might be misaligned with respect to the plane of laser polarization under an angle ' (see Fig. 2:3). Thus the power components with respect to the plane of the PBS are

Pp = Pkcos2(') + P?sin2(') (2.24)

Figure 2.3: Signal power components in a receiver of a depolarization lidar with a polarizing beam-splitter cube with reectivity Rp and Rs and transmittances Tp and Ts for linearly

polarized light parallel (p) and perpendicular (s) to the incident plane of the polarizing beam-splitter. PR and PT are the measured quantities in the reected and transmitted

path, respectively, and VR and VT are the corresponding amplication factors including

the optical transmittances. - Plot from Freudenthaler et al., 2009

Ps = Pksin2(') + P?cos2(') (2.25)

' is the angle between the plane of polarization of the laser beam and the plane of the PBS, it is ' = 0 _{when the co-polarized signal P}

k is measured in the transmitted

path and ' = 90 _{when it is measured in the reected path. Regarding the dierent}

optical transmittances and electronic amplication of each channel (with VR and VT the

amplication factors resulting from the dierent system constants of the two detector optics), the components of the total reected (PR) and total transmitted (PT) power, that

are actually measured behind the PBS are

PR = [Pp(')Rp+ Ps(')Rs]VR (2.26)

and

24 2.4. DEPOLARIZATION with reectivities Rp and Rs and transmittances Tp and Rs of the PBS, resulting from

insucient separation of both planes of polarization. In the following the signal ratio _{= P}

R(')=PT(') and a relative amplication factor V = VR=VT are used.

Volume linear depolarization ratio

In a rst step the volume linear depolarization ratio v is calculated. It describes

the polarization ratio of the total backscattered light from molecules and aerosols. It is increasing with increasing amount of non-spherical particles. v is the ratio between the

cross- and co-polarized signals

v = P_P?

k =

Ps

Pp; ' = 0

_(2.28)

As for a commercial PBS Rs is closer to 1 than Tp, the high parallel signal is detected

in the reected branch of the PBS (' = 90_{) to reduce cross-talk.}

v = P_P? k = Pp Ps; ' = 90 _(2.29) It follows v = P_Pp s = Rs _VTs V Tp Rp (2.30) as for the measurements of additional polarizing lters were used behind the PBS to suppress cross-talk (Ts = Rp = 0) equation 2:30 is reduced to

v = _PPk

? = V

PR

PT (2.31)

The relative amplication factor V has to be determined from additional measurements (see Section 2:4:2).

Particle linear depolarization ratio

From v the particle linear depolarization ratio p can be calculated. It describes the

linear depolarization ratio resulting only from aerosols. It is an intensive property of aerosols and aerosol mixtures, and provides information about the shape of the aerosols. p can be calculated according to Biele et al. (2000)

p = (1 + _{(1 +} m)R (1 + v)m

m)vR (1 + v) (2.32)

with the backscatter ratio R

R = m+ p

m (2.33)

and the molecular linear depolarization ratio m, resulting only from molecules. It can

be calculated with high accuracy (Behrendt and Nakamura, 2002).

2.4.2 Depolarization calibration

The relative amplication factor V = VR=VT can be retrieved from a calibration measure-

ment using equations 2:28, 2:26 and 2:27.

V = _{((1 +} ((1 + vtan2(')) Tp) + (tan2(') + v) Ts

vtan2(')) Rp) + (tan2(') + v) Rs

PR(')

PT (') (2.34)

In the following three methods to determine V are presented and shortly discussed. 0_-calibration For '=0 _{it follows} V = _RTp+ vTs p+ vRs PR PT (0 _{) (2.35)}

If v is known in a certain range of the lidar signal (e.g. in the free troposphere where

v=m), V can be determined from a regular measurement. However, this method suers

from severe error sources. Already a small amount of depolarizing aerosols in the assumed aerosol free region leads to large errors. Second, the signal-to-noise ratio in the calibration range is insucient for accurate analysis. Furthermore, especially for small cross-polarized

26 2.5. ERROR CALCULATION