Polarization lidar for detecting dust orientation: System design and calibration

Dust orientation is an ongoing investigation in recent years. Its potential proof will be a paradigm shift for dust remote sensing, invalidating the currently used simplifications of randomly-oriented particles. Vertically-resolved measurements of dust orientation can be acquired with a polarization lidar designed to target the off-diagonal elements of the backscatter matrix which are non-zero only when the particles are oriented. Building on previous studies, we constructed a lidar system emitting linearlyand elliptically-polarized light at 1064 nm and detecting the linear and circular polarization of the backscattered light. 5 Its measurements provide direct flags of dust orientation, as well as more detailed information of the particle microphysics. The system also employs the capability to acquire measurements at varying viewing angles. Moreover, in order to achieve good signal-to-noise-ratio in short measurement times the system is equipped with two laser sources emitting in interleaved fashion, and two telescopes for detecting the backscattered light from both lasers. Herein we provide a description of the optical and mechanical parts of this new lidar system, the scientific and technical objectives of its design, and the calibration methodologies 10 tailored for the measurements of oriented dust particles. We also provide the first measurements of the system.


Introduction
Dust particles have non-spherical irregular shapes and they have been reported to present preferential orientation (Ulanowski et al., 2007).If present, particle orientation will play a role in the radiation reaching the surface of the Earth and the top of the atmosphere, as well as in the interpretation of the remote sensing observations used for dust monitoring from space, that cannot be described using the long-established assumption of randomly-oriented particles.The phenomenon of dust orientation has been extensively studied for space dust (e.g., Whitney and Wolff, 2002), whereas the investigation for the Earth's atmosphere is a relatively new field of research.Specifically, the only signature of dust orientation in the Earth's atmosphere comes from astronomical polarimetry measurements of dichroic extinction during a dust event at the Canary islands (Ulanowski et al., https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.presented herein are provided in the Appendices A, B and C, as well as in the Supplement.Moreover, a table containing all acronyms and symbols is also provided in the Supplement.
2 Overview of the lidar components The lidar system is equipped with two emission units, and two detection units.The lasers in the emission units emit interleaved light pulses, and their backscattered light is measured interleavingly for each laser at the detectors of the detection units.Each of the detection units is comprised of a telescope, polarizing optics and two detectors.The system uses this "two-laser/twotelescope/four-detector" setup to record eight separate signals.
The lidar has been developed by Raymetrics S.A. and it is housed in a compact enclosure that permits the system to perform measurements in the field, under a wide range of ambient conditions.As shown in Fig. 1, it is comprised by the upper "head" part, containing the lasers, the telescopes and the detection units of the system, the bottom "electronics compartment", containing the power supplies of the lasers, the Transient Recorders (TRs), the Master Trigger Control Unit and the Lidar Peripheral Controlling unit (LPC), and the "positioner" which holds the head and facilitates its movement along different zenith and azimuth angles.The electronics compartment and the head are connected with two umbilical tubes that contain the cooling lines of the lasers and the power and communication cables.

The head
The head of the system contains the lasers, the telescopes, and the rest of the detection units.The lasers and telescopes are placed in a diamond-shaped layout (Fig. 2, right), that ensures equal distances of both lasers from both telescopes, for the proper alignment of the laser beams with the field-of-view of both telescopes.
We expand the laser beams by 5 times with beam expanders of Galilean type.Each laser and beam expander are mounted on a metallic plate which ensures their alignment and proper expanding of the outgoing expanded laser beam.In front of the lasers we place appropriate optical elements in order to change the polarization state of the emitted light, as described in Section 3. Specifically, in front of the "laser A" we place a Half Wave Plate (HW P ) to change the plane of its linear polarization to the plane at 45 o with respect to the horizon, and in front of the "laser B" we place a Quarter Wave Plate (QW P ) followed by a HW P , to change its linear polarization to elliptical polarization, with the angle of the polarization ellipse at 5.6 o with respect to the horizon, and degree of linear polarization of 0.866.The QW P and the HW P s are mounted on stepping-index rotational mounts (with accuracy of 0.1 o ), which enable us to accurately rotate them to the desired positions and produce the desired polarization states, as described in Section 4.
The telescopes are of Dall-Kirkham type, with an aperture of 200 mm and focal length of 1000 mm (F#5).The full overlap of the laser beams to the telescope field-of-views is achieved above 400-600 m.The detection units after the telescopes (Fig. 3) contain the optical elements (e.g.HW P , QW P , Polarizing Beam Splitter cube P BS) that alter the Stokes vector of the collected backscattered light, so as to measure its polarization state effectively, as   1).It also contains a P BS cube (2), followed by cleaning polarizing sheet filters (3), a shutter for dark measurements (4), a camera for the alignment (5), a turning mirror for redirecting the light to the camera (6), an interference filter for the reduction of the background light (7), and a mechanical rotator (8) for accurately rotating a HW P for the system calibration (Section 4).The detection unit after telescope B is the same, with a QW P placed before the P BS.
The lidar head is protected from rain and dust with covers and with special glass windows in front of the lasers and the 90 telescopes (Fig. 2, left).The covers can be easily removed to allow access to the internal parts of the head.Moreover, thermoelectric coolers are installed inside the head in order to stabilize the internal temperature, and to provide tolerance to ambient temperatures up to 45 o C.

The positioner
The positioner enables the lidar head to move along different zenith and azimuth angles.Due to constrains from the umbilical 95 tubes, the head can be moved along −10 o to +90 o from the zenith, and at −150 o to +150 o around the vertical.The positioner consists of two side arms and a base (Fig. 4) which can be manually rotated.For changing the zenith angle, the one of the side arms is driving and the other is free.A break on the free arm reduces the backlash.

The electronics compartment
The electronics compartment (Fig. 5) contains the power supplies of the two lasers, the LPC, the LICEL rack containing the  The synchronization of this complicated lidar system with two lasers emitting interleavingly and with their backscattered signals recorded interleavingly, requires a sophisticated triggering system.We use a master trigger control unit, produced by Licel GmbH (Fig. 6) that utilizes two trigger generators for the synchronization of the emission of the lasers and of the  The lidar system is controlled from the LPC unit.This is an "enhanced" embedded computer with specific I/Os that fits the lidar requirements, providing several ethernet interfaces that makes the controlling (local or remote) of the lidar easy and safe.Temperature and humidity conditions inside the enclosure and the head can be recorder with the LPC.Additionally, the 3 Emission and detection design based on the measurement strategy The core of the new lidar system is its emission and detection design, based on our measurement strategy for monitoring the oriented dust in the atmosphere.Our approach is different from the measurement strategy of previous works, which either focus on the retrieval of the individual elements of the backscatter matrix of the oriented particles utilizing moving elements in the system (e.g., Kaul et al., 2004), or use complicated designs that are difficult to be calibrated effectively (e.g., Geier and Arienti, 2014).We choose to avoid both, in order to achieve robust measurements along with their effective calibration.Moreover, most of the previous works utilize visible light measurements whereas we use near infrared light measurements at 1064 nm, to better probe the larger dust particles (a more detailed discussion is provided in Tsekeri et al. (2021)).
Figure 7 shows the simplest design of a "two lasers/two telescopes/four detectors" lidar system that is able to detect the elliptically-polarized backscattered light from oriented particles in the atmosphere without using any moving parts.The linear polarization of the backscattered signal is detected using a linear-polarization-analyzer (a P BS) in the detection unit after telescope A, and the circular polarization of the backscattered signal is detected using a circular-polarization-analyzer (a QW P followed by a P BS) in the detection unit after telescope B. The calibration methodology is based on the solutions introduced by Freudenthaler (2016) for EARLINET lidar systems, as well as on new methodologies tailored for the detection of oriented particles, presented in Section 4.
Instead of retrieving the individual off-diagonal elements of the backscatter matrix F (Eq. 1), we aim for measurements that are combinations of only the off-diagonal elements of the backscatter matrix that will be nonzero only in case of oriented particles.This way we acquire direct measurements of dust orientation, in the form of flags of "yes" or "no" particle orientation.
This first-level information of the oriented dust in the atmosphere is straightforward to achieve, since it does not require any inversion procedure.Moreover, it is important to have, considering that the phenomenon of dust orientation has not been extensively observed in the Earth's atmosphere, even at this elementary level.To achieve this, laser A should emit linearlypolarized light at 45 o , as discussed in detail below.
Where, f ij = Along with the measurements of "orientation flags", we aim for measurements that provide additional information for the particle orientation properties, as the particle orientation angle and the percentage of oriented particles in the atmosphere, as well as information on dust microphysics, i.e. an estimation of the particle size and refractive index.These are parameters that are necessary to have in order to explain the phenomenon of dust orientation in more detail.The methodology for defining the optimum measurements includes simulated atmospheric scenarios and machine learning tools, and is presented in Tsekeri et al. (2021).Briefly, the backscattered light is simulated for different orientation angles and mixtures of random and oriented particles, as well as irregular shapes and realistic sizes for dust particles.In order to derive signals that provide additional information for the dust orientation and microphysics, the light of laser B should be elliptically-polarized so as the backscattered  The HW PT A at telescope A is used to correct the rotation of the P BST A (Section 4.1).The HW PT B at telescope B is used to check the position of the QW PT B with respect to the P BST B (Section S4 in Supplement)).The shutter at each telescope is used for performing dark measurements.The camera at each telescope is used for the alignment of the laser beams with the field-of-view of the telescope.
This Section provides the methodology we followed to define the properties of the optical elements in the emission and the detection units of the lidar system, so as to fulfil the technical and scientific objectives of our measurement strategy.Considering the layout in Fig. 7 the only "free" parameters that we need to define are the polarization state of the light from the emission The measured signal I * i_k_S for laser i = LA, LB, at the detection unit after telescope k = T A, T B, at the detector S = T , R ("Transmitted" and "Reflected" channel after the P BS k , respectively), is shown in Eq. 2-4.
In Eq. 2, is the Mueller matrix of the QW P T B .F and G are the backscatter Stokes phase matrices of the dust particles and of the gas molecules, respectively, at a certain range in the atmosphere.For the explicit definition of the Muller matrices in Eq. 2, 3 and 4, see Section S1 in the Supplement.i i is the Stokes vector of the light from the emission unit of laser i, and i g is the Stokes vector of the background skylight.y N i_k_S is the electronic background of the S = T or R detector at the detection unit after telescope k, for detecting the backscattered signal of laser i.
After subtracting the background skylight signal offset, and considering noise-free measurements, the signals I i_T A_S and I i_T B_S , are provided in Eq. 5 and 6, respectively.
T , the fast-axis-angle φ T B of the QW P T B with the reference plane, and the backscatter Stokes phase matrix elements (all highlighted in Eq. 7 and 8).In Eq. 7 and 8 we consider ideal receiver optics (i.e.telescope, collimating lenses, bandpass filter), with no diattenuation, retardation and misalignment effects. ) Where, ), T S_k is the unpolarized transmittance (S = T ) or reflectance (S = R) of the P BS k , and D S_k is the diattenuation parameter of the transmitted or reflected channels of the P BS k followed by the cleaning polarizing sheet filters (D T _k = 1 and D R_k = −1, respectively, see Section S1 in Supplement).
As can be deduced by Eq. 7 and 8, in order to use laser A to achieve measurements that contain only the off-diagonal elements of the backscatter matrix, the following conditions must be met: Q LA = 0 for I LA_T A_S , V LA = 0 for I LA_T B_S , and φ T B = 45 o .Thus, the Stokes vector of the light from the emission unit of laser A should be 45 o -linearly polarized, i LA = [1, 0, 1, 0] T .This is achieved using the HW P LA in front of laser A (Fig. 7), as discussed in Section 4.2.Moreover, the fast-axis-angle of the QW P T B should be at φ T B = 45 o .
For calibration reasons, we use the ratios of the measurements of the reflected and transmitted channels after the P BS k (Eq. 9 and 10).The calibrated backscatter signal ratios of laser A provide a direct flag of particle orientation (F LA_T A and F LA_T B in Eq. 12 and 13, respectively), when their values are = 1.discussed in Section S4 in the Supplement)), Eq. 10 changes to Eq. 11.
The orientation flags F LA_T A and F LA_T B are provided in Eq. 12 and 13.
Having achieved the orientation flags with laser A, we use laser B to increase the information content of the measurements in terms of dust orientation properties (e.g.angle and percentage of oriented particles in the atmosphere) and of dust microphysical properties (e.g.size and refractive index).For this reason, the light from the emission unit of laser B is elliptically-polarized with the angle of the polarization ellipse at 5.6 o and Stokes vector i LB = [1, 0.85, 0.17, 0.5] T .The derivation of the optimum polarization state of i LB is provided in detail in Tsekeri et al. (2021), using an extended simulated dataset for various atmospheric scenes with oriented dust particles.In their work, the backscattered light is simulated for different orientation angles and mixtures of random and oriented particles, as well as irregular shapes and realistic sizes for dust particles.The elliptical polarization of i LB is set with the QW P LB and the HW P LB in front of laser B (Fig. 7), as discussed in Section 4.3.The corresponding signal ratios are shown in Eq. 14 and 15. 4 Definition of the polarization of the emitted and detected light with respect to the horizon The polarization of the light emitted and detected by the system should be defined with respect to the horizon, so as the retrieved properties of the oriented particles are defined with respect to the horizon.This is done by first leveling the head of the lidar along the horizon using a spirit level, which then enables us to use the frame of the lidar head as the reference coordinate system.The "frame coordinate system" (Fig. 8a) is a right-handed coordinate system, with x F -axis parallel to the horizon and the z F -axis pointing in propagation direction of the emitted light from lasers A and B, considering that both lasers are parallel.
The optical elements are considered to be perfectly aligned with eachother in the detection units after telescopes A and B (because their holders are manufactured and assembled in a mechanical workshop with high accuracy), but the detection units are possibly rotated around the optical axis with respect to the frame coordinate system by angles ω T A and ω T B , respectively (Fig. 8b and c).The Stokes vectors of the light collected at telescope A and B are consequently described including a multiplication with the rotation matrices R TA (−ω T A ) and R TB (−ω T B ), respectively (see Eq. S.5.1.7 in Freudenthaler ( 2016)), which affects the measurements of the polarized components after P BS T A , but not after P BS T B , as shown in Appendix A.
The rotation of the detection unit after telescope A is corrected using the HW P T A , as shown in Section 4.1.
The "DU T A coordinate system" and the "DU T B coordinate system" in Fig. 8b and c are the right-handed coordinate systems of the detection units after telescopes A and B, respectively.The x DU T A and y DU T A axis coincide with the incidence plane of P BS T A , and the x DU T B and y DU T B axis coincide with the incidence plane of P BS T B .
Equations A1-A6 in Appendix A show the formulation of Eq. 7 and 8 for I i_k_S with respect to the frame coordinate system, taking into account all the optical elements of the system, along with the rotation of the detection units after telescopes A and B. The analytic derivations of Eq.A1-A6 are provided in Section S2 of the Supplement.with unknown angle of polarization αLA.As shown in Eq. 17, using the HW PLA with fast-axis-angle θLA = 22.5 o + α LA 2 , we produce the light emitted from the emission unit of laser A with angle of polarization 2ϑLA = 45 o .e) The light emitted directly from laser B is linearlypolarized with unknown angle of polarization αLB.As shown in Eq. 18, using the QW PLB with with fast-axis-angle φLB = αLB − 30 o , and the HW PLB with fast-axis-angle θLB = α LB 2 − 12.2 o , we produce the elliptically-polarized light emitted from the emission unit of laser B with angle of polarization 5.6 o and degree of linear polarization 0.866.
The Stokes vector of the light from the emission unit of laser A and B is provided by i LA (Eq.17) and i LB (Eq.18), respectively.The light emitted directly from laser A (i lsr_LA ) and laser B (i lsr_LB ) is considered to be 100% linearly-polarized, with angle of polarization ellipse with respect to the frame coordinate system α LA and α LB , respectively, i.e. i lsr_LA (α LA ) = 1 c 2α LA s 2α LA 0 T in Eq. 17 unknown a-priori.The polarization of the light from the whole emission unit is defined according to the position of the optical elements in front of the lasers with respect to the frame coordinate system, i.e. the fast-axis-angle θ LA of the HW P LA in front of laser A, and the fast-axis-angle φ LB of QW P LB followed by the HW P LB with fast-axis-angle θ LB in front of laser B (Fig. 8d and e; Eq. 17 and 18).
4.1 Correction of the signal I i_TA_S , due to the rotation of the detection unit after telescope A Equations A1 and A3 in Appendix A show that the rotation of the detection unit after telescope A changes the signals I LA_T A_S (Eq.9) and I LB_T A_S (Eq.14), respectively.In order to correct for this effect, we have to set the fast-axis-angle of the HW P T A at θ T A = − ω T A 2 with respect to the x DU T A -axis (Fig. 8b), so that c (4θ T A +2ω T A ) = 1 and s (4θ T A +2ω T A ) = 0 in Eq.A1 and A3.Since the value of θ T A with respect to the x DU T A -axis is unknown a priori, we assume that it deviates from the desired value by an unknown angle ε T A , thus θ T A = −ω T A 2 + ε T A .We derive ε T A by using the measurements from laser A, after placing a linear polarizer in front of the window of laser A at 45 o from x F -axis (Fig. 9), and rotating the HW P T A in order to perform a methodology similar to the "∆90 o calibration" of Freudenthaler (2016), as in Fig. 10 and described in detail in Appendix B.
The methodology is applicable only when there are only randomly-oriented particles in the atmosphere.

Definition of the polarization of the light from the emission unit of laser A with respect to the horizon
In order to set the linear polarization of the light from the emission unit of laser A at 45 o -degrees with respect to the horizon, as discussed in Section 3, we have to set ϑ LA = 22.5 o with respect to x F -axis (Eq.17; Fig. 8d).Since the value of ϑ LA is Our methodology is described in Fig. 12.We consider randomly-oriented particles in the atmosphere and we use the measurements of laser B at the detection unit after telescope A. The detection unit is aligned with the frame coordinate system 275 (Section 4.1).First, we consider that the polarization of the light from the emission unit of laser B with respect to the frame coordinate system is unknown, with unknown angle of the polarization ellipse α and degree of linear polarization b.In order to set them to α em , b em , we perform the following steps: .The calibration factors η T A and η T B are derived considering randomly-oriented particles in the atmosphere.We calculate η T A using the ratio of the signals from laser A at the detection unit after telescope A, considering that the effect of its rotation on the signals is corrected (Section 4.1).The η T A is calculated as shown in Eq. 20 (using Eq.A2 in Appendix A).
We derive the calibration factor η T B using the ratio of the signals from laser A at the detection unit after telescope B, as shown in Eq.21 (using Eq.A5 in Appendix A).
6 The derivation of the volume linear depolarization ratio The volume linear depolarization ratio (VLDR) is a useful optical parameter for comparing the measurements of the new polarization lidar with measurements from the commonly-used polarization lidars, which emit linearly-polarized light and measure the corresponding cross-and parallel-polarized components of the backscattered light.The VLDR is calculated using the atmospheric polarization parameter a as shown in Eq. 22.
We derive VLDR considering an atmosphere containing only randomly-oriented particles.Moreover, we consider that the effect of the rotation of the detection unit after telescope A with respect to the frame coordinate system is corrected (Section 4.1) and that the calibration factor η T A is calculated using measurements of laser A, as shown in Section 5.
We turn HW P T A by 22.5 o , so as θ T A = − ω T A 2 + 22.5 o .Then, the measurements from laser A at the detection unit after telescope A are provided from Eq. 23, and the VLDR is calculated as shown in Eq. 24, using Eq.22.
Due to the rotation of HW P T A , the VLDR measurements cannot be acquired simultaneously with F LA_T A (Eq. 12) and I LB_T A_T (Eq.14), but they are acquired simultaneously with F LA_T B (Eq. 13) and I LB_T B_R I LB_T B_T (Eq.16).

First measurements
We present measurements from Athens, Greece, on November 16, 2020, showing a dust layer.Figure 13 After correcting I LA_T A_S for the rotation of the detection unit after telescope A, by setting the fast-axis-angle of HW P T A at θ T A = − ω T A 2 (Section 4.1), Eq.A1 is written as Eq.A2. 2 (Section 4.1), Eq.A3 is written as Eq.A4.
365 After placing a linear polarizer in front of the window of laser A at 45 o from x F -axis (Fig. 9), we acquire the measurements as shown in Eq.B1.
We derive ε T A in a similar way as the "∆90 o calibration" (Section 11 in Freudenthaler ( 2016)), by rotating the HW P T A by an additional angle of 0 o and 45 o with respect to the x DU T A -axis (Fig. 10).The respective calculations are provided in Eq.
As a first approximation of ε T A we calculate ε T A l with Eq.B7.
After adjusting the HW P T A by −ε T A l , which results in θ

I LA_T A_S(θ
Where, ϑ LA = ε LA and a is the atmospheric polarization parameter, a = f22+g22 f11+g11 . We rotate the HW P LA by +22.5 o and −22.5 o with respect to the x F -axis and we derive ε LA by performing the "∆90 o calibration" of Freudenthaler (2016), as shown in Eq.C2-C8.
As a first approximation of ε LA we calculate ε LA l with Eq.C6.
After adjusting the HW P LA by −ε LA l , which results in ϑ LA = ε LA −ε LA l with respect to the x F -axis, we derive Y (ε LA − ε LA l , a) (Eq.C7).Then, ε LA is calculated by Eq.C8.The signals I LB_T A_S (Eq.A4) are provided by Eq.D1, considering an atmosphere with randomly-oriented particles (all offdiagonal elements of the backscatter matrix are zero), and that the detection unit after telescope A is aligned with the system 430 frame (Section 4.1).Note that in Eq.D1 "a" is the atmospheric polarization parameter, whereas "α" is the the angle of the polarization ellipse of the light from the emission unit of laser B. Then, b is derived from Eq. D9-D11 (using Eq.D1), considering that we have already derived the atmospheric polarization parameter a using the measurements of laser A at the detection unit after telescope A, as shown in Section 6.

Figure 1 .
Figure1.The lidar system, with the "head" part at the top (1), the "electronics compartment" at the bottom (2), and the "positioner" of the head (3).

Figure 2 .
Figure 2. The lidar head.Left: Cover of the lidar head, showing the windows in front of the two lasers and the two telescopes.Middle: Photorealistic image of the internal parts of the head, showing the lasers and their beam expanders, the telescopes and the rest of the detection units.Right: Front view of the head, showing the diamond-shaped layout of the lasers (LA and LB) and telescopes (TA and TB).

85
discussed in detail in Section 3. The signals are recorded by two cooled Avalanche PhotoDiodes (APDs) at each detection unit, which contain remote-controlled power supplies and cooling units.Each detection unit contains also a shutter for performing dark measurements, a camera for the alignment of the lasers with the telescopes, and an interference filter for reducing the background light in the measurements.https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.

Figure 3 .
Figure 3.The detection unit after telescope A, containing the optical elements that are used for the detection of the polarization state of the backscattered light, with the signals recorded at the two APDs (1).It also contains a P BS cube (2), followed by cleaning polarizing sheet

Figure 4 .
Figure 4.The fork-type positioner of the lidar head.

100
TRs for digitizing and recording the signals from the APDs, and the Master Trigger Control Unit that synchronizes the emission of the two lasers and the acquisition of the backscattered signals.Moreover, it contains a UPS and a precipitation sensor.

Figure 5 .
Figure 5.The enclosure with 1) the LPC unit, 2) the LICEL rack with the TRs and the Master Trigger Control, 3) the UPS, 4) the power supplies of the lasers, and 5) the precipitation sensor.
https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.acquisition of the signals.As shown in Fig. 6b, the first trigger generator produces a pulse that starts the flash lamp.The laser builds up its maximum energy for 160 µsec, and then a second pulse turns on the active Q-switch, which allows the release of the laser beam pulse.In the meantime, a third pulse triggers the acquisition of the backscattered light from laser A. Pre-trigger measurements are acquired until the emission of the laser A beam pulse.The same sequence is performed from the second trigger generator for laser B, starting 10 ms later, in order to avoid the recording of overlapping photons from the backscattered 110 light of laser A. The duty cycle of lasers A and B is ∼ 12 ms and the time between each cycle is 50 ms (fixed due to the repetition rate of the lasers of 20 Hz), with 38 ms idle time.

Figure 6 .
Figure 6.a) The LICEL rack with the TRs and the Master Trigger Control Unit.b) The pulses from the Master Trigger Control Unit that synchronize the emission of the two lasers and the acquisition of the backscattered signals.The lengths of the pulses are in µs.
https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.connected to the LPC and shut down the lasers in case of emergency.The LPC also controls the mechanical rotators of the optical elements used for calibration purposes (Section 4).

Figure 7 .
Figure 7. Sketch of the system design: two lasers shooting alternatively (LA and LB), with the backscattered signals correspondingly alternatively collected by two telescopes (TA and TB) and then redirected at two detectors for each telescope (D_Sj, S = T, R as of "Transmitted" and "Reflected" channels, j = A, B).The polarization of the light emitted from each laser is changed appropriately, using the HW PLA for laser A and the QW PLB followed by the HW PLB for laser B. The laser beam of each laser is expanded with a beam expander (BEX).After the first telescope the light goes through P BST A and after the second telescope the light goes through QW PT B and P BST B .
https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.units of laser A and B, and the position of the QW P T B in the detection unit after telescope B (the HW P T A and HW P T B are used for calibration purposes (see Section 4 and Section S4 in the Supplement)).
where A k is the area of the telescope k, O i_k is the overlap function of the laser beam receiver field-of-view with range 0-1 (for laser i and telescope k), T (0, r) is the transmission of the atmosphere between the lidar at range r = 0 and a specific range in the atmosphere, and E oi is the pulse energy of laser i. η S_k is the amplification of the signals at S = T or R detector of the detection unit after telescope k. e = [1, 0, 0, 0] T is used to select the first component of the Stokes vector, which corresponds to the signal intensity measured at the APDs.M k is the Mueller matrix of the detection unit after telescope A (Eq. 3) and B (Eq. 4): M S_k is the Mueller matrix of the P BS k followed by cleaning polarizing sheet filters, M O_k is the Mueller matrix of the receiver optics (i.e.telescope k, collimating lenses, bandpass filter), and M QW _T B 6) https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.Performing the Mueller matrix calculations, I i_T A_S and I i_T B_S can be written as a function of the Stokes parameters of the light from the emission units of the lasers i 10) https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.The calibration factors η T A = η R_T A T R_T A η T _T A T T _T A and η T B = η R_T B T R_T B η T _T B T T _T B are derived as shown in Section 5. Due to the HW P T B in the detection unit after telescope B (used for checking for systematic errors in measurements, as

Figure 8 .
Figure 8. a) The "frame coordinate system" (black) is the reference coordinate system with xF -axis parallel to the horizon.b) The "DUT A coordinate system" (light blue) is the coordinate system of the detection unit after telescope A, which is rotated with respect to the frame coordinate system by an angle ωT A. The effect of this rotation on the signals is corrected using HW PT A, placed at θT A = − ω T A 2 (red) with respect to the xF -axis.c) The "DUT B coordinate system" (orange) is the coordinate system of the detection unit after telescope B, which is rotated with respect to the frame coordinate system by an angle ωT B .The rotation does not affect the measured signals.The QW PT B before P BST B , is placed at φT B = 45 o with respect to the xDU T B -axis.d) The light emitted directly from laser A is linearly-polarized , and i lsr_LB (α LB ) = 1 c 2α LB s 2α LB 0 T in Eq. 18.The angles α LA and α LB are https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.

Figure 9 .
Figure 9. Linear polarizer in front of the window of laser A, placed at 45 o from xF -axis.

Figure 10 .
Figure 10.Methodology for correcting the measurements ILi_T A_S due to the rotation of the detection unit after telescope A.

Figure 11 .
Figure 11.Methodology for defining the polarization of the light from the emission unit of laser A, with respect to the horizon.
23) https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.I LA_T A_R_(θ T A =− ω T A 2 +22.5) Fig. 13b.The instrument points vertically.The minimum height of 600 m of the signals in the plots is the full-overlap height,derived by the telecover test(Freudenthaler et al., 2018).The dust layer is at 1 − 2.5 km, as shown in the VLDR profile in Fig.13d.The orientation flag shows no indication of particle orientation for this case.The VLDR values are 0.1 for the dust layer and 0.003 at aerosol-free heights of 5 − 6 km (not shown here), in accordance to the value of 0.0035 provided in literature for molecular atmospheres(Freudenthaler et al., 2018).

Figure 13 .
Figure 13.Lidar measurements at 1064 nm during a dust case at Athens, Greece, on 16 November 2020.The legend shows the time range in UTC for the 15−min averaged signals: a) ILA_T A_T , b) ILB_T A_T and c) FLA_T A. d) The VLDR measurements at 18 : 27 − 18 : 41 UTC.The heights are above the surface level.
g 33 https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.(A3) After correcting I LB_T A_S for the rotation of the detection unit after telescope A, by setting the fast-axis-angle of HW P T A at θ T A = − ω T A A6) https://doi.org/10.5194/amt-2021-30Preprint.Discussion started: 15 February 2021 c Author(s) 2021.CC BY 4.0 License.Appendix B: Derivation of ε T A for correcting I LA_TA_S and I LB_TA_S , for the rotation of the detection unit after telescope A.
Figure B1 shows the test performed for zeroing ε T A and setting θ T A = −ω T A 2 (step 3 in Fig. 10), by the successive steps described above.Specifically, with zero rotation of the HW P T A , ε T A l = 4.69 o , with −4.69 o rotation of the HW P T A , ε T A l = −0.22o , and finally with −4.69 o + 0.22 o = −4.47o rotation of the HW P T A , ε T A l = 0 o .

Figure C1 .
FigureC1shows the test performed for zeroing ε LA and setting ϑ LA = 22.5 o (step 2 in Fig.11), by the successive steps described above.Specifically, with zero rotation of the HW P LA , ε LA l = 4.03 o , with −4.03 o rotation of the HW P LA , ε LA l =