We present a new formalism to calibrate a three-signal polarization lidar and
to measure highly accurate height profiles of the volume linear
depolarization ratios under realistic experimental conditions. The
methodology considers elliptically polarized laser light, angular
misalignment of the receiver unit with respect to the main polarization plane
of the laser pulses, and cross talk among the receiver channels. A case
study of a liquid-water cloud observation demonstrates the potential of the
new technique. Long-term observations of the calibration parameters
corroborate the robustness of the method and the long-term stability of the
three-signal polarization lidar. A comparison with a second polarization
lidar shows excellent agreement regarding the derived volume linear
polarization ratios in different scenarios: a biomass burning smoke event
throughout the troposphere and the lower stratosphere up to 16
Atmospheric aerosol particles influence the evolution of clouds and the formation of precipitation in complex and not well-understood ways. Strong efforts are needed to improve our knowledge about aerosol–cloud interaction and the parameterization of cloud processes in atmospheric (weather and climate) models and weather forecasts and especially to decrease the large uncertainties in future climate predictions (IPCC, 2014; Huang et al., 2007; Fan et al., 2016). In addition to more measurements in contrasting environments with different climatic and air pollution conditions, new experimental (profiling) methods need to be developed to allow an improved and more direct observation of the impact of different aerosol types and mixtures on the evolution of liquid-water, mixed-phase, and ice clouds occurring in the height range from the upper planetary boundary layer to the tropopause. Active remote sensing is a powerful technique to continuously and coherently monitor the evolution and life cycle of clouds in their natural environment.
Recently, Schmidt et al. (2013a, b, 2015) introduced the so-called
dual-field-of-view (dual-FOV) Raman lidar technique, which allows us to
measure aerosol particle extinction coefficients (used as aerosol proxy)
close to cloud base of a liquid-water cloud layer and to retrieve, at the
same time, cloud microphysical properties such as cloud droplet effective
radius and cloud droplet number concentration (CDNC) in the lower part of
the cloud layer. In this way, the most direct impact of aerosol particles on
cloud microphysical properties could be determined. However, the method is
only applicable after sunset (during nighttime) and signal averaging of the
order of 10–30
Highly accurate observations of the volume linear depolarization ratio are
of fundamental importance for a successful retrieval of cloud microphysical
properties by means of the new polarization lidar technique. In this article
(Part 1 of a series of several papers on the dual-FOV polarization lidar
technique), we present and discuss our new polarization lidar setup and how
the lidar channels are calibrated. The basic product of a polarization lidar
is the volume linear depolarization ratio, defined as the ratio of the
cross-polarized to the co-polarized atmospheric backscatter intensity, and
is derived from lidar observations of the cross- and co-polarized signal
components, or alternatively, from the observation of the cross-polarized
and total (cross-
The article is organized as follows. In Sect. 2, the lidar instrument is described. The new methodology to calibrate the lidar system and to obtain high-quality depolarization ratio observations is outlined in Sect. 3. Section 4 presents and discusses atmospheric measurements performed to check and test the applicability of the new methodology. Concluding remarks are given in Sect. 5.
A sketch of the instrumental setup, providing an overview of the entire
lidar system, is shown in Fig. 1. MARTHA (Multiwavelength Tropospheric Raman
lidar for Temperature, Humidity, and Aerosol profiling) has a powerful laser
transmitting in total 1
Overview of the EARLINET lidar MARTHA. The three-signal
receiver unit of the new polarization lidar setup (details are shown in Fig. 2)
is integrated into the MARTHA telescope construction (left side in both
of the sketches). The outgoing laser beam is 54
Sketch of one of the three identical receiver channels of the three-signal polarization lidar. The different parts are explained in the text.
Figure 2 provides details of the new polarization-sensitive channels. Each
of the small receiver telescopes consists of 2 in. (50.8
A 2
The purpose of the new receiver system is to measure accurate profiles of
the volume depolarization ratio in clouds between 1 and 12
In Sect. 3.1, we begin with definitions and equations that allow us to describe the transmission of polarized laser pulses into the atmosphere; backscatter, extinction, and depolarization of polarized laser radiation by the atmospheric constituents; and the influence of the receiver setup on the depolarization ratio measurements. As a first step in this theoretical framework we will derive three lidar equations for our three measured signal components. In Sect. 3.2, we then present the derivation of the new three-signal method for the determination of the volume depolarization ratio starting from the three lidar equations (one for each channel) defined in Sect. 3.1.
We follow the explanations and part of the notation of Freudenthaler (2016),
Bravo-Aranda et al. (2016), and Belegante et al. (2018) in the description
of the lidar setup, from the laser source (as part of the transmitter unit)
to the detector unit (as part of the receiver block), and regarding the
interaction of the polarized laser light photons with atmospheric particles
and molecules by means of the Müller–Stokes formalism (Chipman, 2009).
A Stokes vector describes the flux and the state of polarization of the
transmitted laser radiation pulses, and Müller matrices describe how the
optical elements of the transmitter and receiver units and the atmospheric
constituents change the Stokes vector. The laser beam is expanded before
transmission into the atmosphere. In most polarization lidar applications it
is assumed that the transmitted laser radiation is totally linearly
polarized. But this is not the case in practice. In our approach, we
therefore take into consideration that the transmitted wave front contains a
non-negligible small amount of cross-polarized light after passing through
the beam expander. Additionally, we consider a small-angular misalignment,
described by angle
The transmitted radiation
The true volume backscatter coefficient
To distinguish the apparent measured volume backscatter coefficient,
determined from the actually measured co- and cross-polarized signal
components which are related to the incident field
It is worthwhile to mention that polarization lidars typically have two
detection channels, either a cross-polarized and a parallel-polarized
channel or a cross-polarized and so-called total channel. A commonly used
method for the calibration is to insert an additional polarization filter
into the optical path of the receiver unit and to rotate or tilt a
As mentioned in the introduction, the concept to calibrate a lidar depolarization receiver by using three channels was proposed by Reichardt et al. (2003). The method consists of an absolute calibration procedure based on the measurement of elastically backscattered light with three detection channels for measuring co-, cross-, and totally polarized backscatter components.
To determine the number of counts that the detection channels measure, Müller matrices representing the optical path of each channel would need to be added to Eq. (6). Nevertheless, in this approach we follow the view adopted by Reichardt et al. (2003), in which the traditional lidar equation is used to characterize the lidar channels.
Let us now introduce the lidar equations for these three signals. Following
Reichardt et al. (2003), the number of photons
Outgoing from Eqs. (24)–(26) we will define instrumental (interchannel) constants which are required to calibrate the lidar in the experimental practice and which are also used in the determination of the volume linear depolarization ratio. The equations for the determination of the depolarization ratios will be given. Three different ways can be used to determine the linear depolarization ratio profiles.
Considering Eq. (26) and the sum of Eqs. (24) and (25), we can write
Let us introduce the interchannel instrumental constants
In the conventional three-signal calibration approach, each signal is normalized
to a reference altitude; by doing so the efficiencies of the three channels
In this extended three-signal calibration procedure, the signals are not
normalized to a reference height
Given the form of Eqs. (35)–(37), observable differences between the height
points
To derive the linear depolarization ratio, we divide Eq. (25) by Eq. (24).
Now Eq. (38) can be rewritten after dividing the numerator and denominator
by
To test the method introduced in Sect. 3, the measurement case from 19 September 2017 was analyzed and the results are presented in this section.
Figure 4 provides an overview of the atmospheric situation. An aerosol layer
reached up to about 2.8
Range-corrected 532
Although the time resolution of the lidar measurements is 30
In the next step of the data analysis and calibration procedure, we selected
the height range from a few meters below cloud base up to 240
Example of a 5
Histograms for the interchannel constants
The mean values of the constants with the respective statistical error based
on Fig. 6 are
Using the constant
Values of the instrumental interchannel constants and cross-talk factor determined for the measurement case presented.
Figure 7 presents the height profiles of the volume linear polarization
ratio computed by means of Eqs. (41), (43), and (44). Good agreement among
the different solutions is visible. However, the depolarization ratios
obtained from the channels
Profiles of the volume linear depolarization ratio for the
3
Volume linear depolarization ratio for the entire
3
Figure 8 presents the volume depolarization ratio with 30
To validate the new system and the calibration procedure a comparison
among the measurements of the volume linear depolarization ratio with the
lidar systems MARTHA and BERTHA (Backscatter Extinction Lidar Ratio
Temperature and Humidity profiling Apparatus) is presented in Fig. 9. The
observations were conducted at Leipzig (51
Volume linear depolarization ratio obtained with MARTHA
(extended three-signal method) and BERTHA (
A second measurement period during a unique event with a dense biomass
burning smoke layer in the stratosphere on 22 August 2017 was considered for
comparison (Haarig et al., 2018). Here very good agreement for the layer
between 5 and 7
The time series of the interchannel constant
Time series of the interchannel calibration constant
Time series of the total cross-talk factor
In Fig. 10 the retrieved values of
In this work a new formalism to calibrate polarization lidar systems based
on three detection channels has been presented. We propose a simple lidar
polarization receiver, based on three telescopes (one for each channel) with
a polarization filter on the front (in the case of the cross- and co-polarized channels). This setup removes the effect of the receiver optics
on the polarization state of the collected backscattered light, simplifying
the measurement concept. The derivation of the volume linear depolarization
ratio considering the instrumental effects on the proposed system was
described in Sect. 3. Here there are three effects considered: the emitted
laser beam (after beam expander) is slightly elliptically polarized (
The methodology does not require a priori knowledge about the behavior of
the instrument in terms of polarization and permits the determination of the
so-called interchannel constants
A case study of a liquid-water cloud observation was presented. The
3
The lidar data used for this research can be accessed by request to the Leibniz Institute for Tropospheric Research.
For the derivation outlined in Sect. 3 it is assumed that the polarization
filters in front of the cross- and co-polarized telescopes are pointing
We define the angles
Scheme of the observation of the polarization state of
the backscattered light (similar to Fig. 3). The co-polarized and cross-polarized channels are
misaligned with respect to their components at angles
Calculating the three ratios among Eqs. (A1), (A2), and (A3), we can obtain
the volume linear depolarization ratio, similarly to how it was performed for
Eqs. (41), (43), and (44).
In this measurement case we found a value for
Instrumental channels obtained with an iterative procedure. We did not include the error bars since they are much larger than the variations among runs.
This general solution for the lidar three-signal problem converges to the
same results when we also consider that the receiver cross talk can eventually be
different for the channels P and S. In that case we would have
Results of the instrumental constants after using the iterative procedure (six runs).
The extinction coefficient is assumed to be independent of the polarization
state of the light. This assumption permits the simplification of the three
lidar equations, making possible the determination of the instrumental
constants. The effects of the emission and reception in terms of polarization can be
summarized into one total cross-talk constant Differences with previous studies in terms of the nomenclature are present:
In our approach No diattenuation and retardation are considered in the emission and reception
units.
The theoretical framework was developed by CJ in close cooperation with AA, MH, and UW. RE, JS, and CJ contributed in the setup of the lidar instrument. CJ wrote the computing code for the analysis. CJ and MH performed the measurements and analyzed the data of the MARTHA and BERTHA systems, respectively. CJ and AA prepared the paper in cooperation with MH.
The authors declare that they have no conflict of interest.
This research was partially funded by the program DAAD/Becas Chile, grant no. 57144001. This activity is supported by the ACTRIS Research Infrastructure (EU H2020-R&I), grant agreement no. 654109.
We thank Ilya Serikov for the fruitful discussions on the topic. We would like to acknowledge the three anonymous referees for their valuable feedback given during the revision process. The publication of this article was funded by the Open Access Fund of the Leibniz Association. Edited by: Vassilis Amiridis Reviewed by: three anonymous referees