3.1 Coinciding polarization planes

One of the main sources of errors in polarization measurements is a discrepancy between the polarization planes of the emitting and receiving channels. The Glan prism (GP in Fig. 2) is installed in a rotating frame and allows aligning the planes of emitter and receiver. The accuracy of installation angle is $\mathit{\theta }=\mathrm{34}{}^{\prime }=\mathrm{0.0125}$ rad. Figure 3 shows the measured value of the cross-polarized component (equal to 1 when normalized to the minimum), depending on the angle of the prism rotation. A signal from a uniform aerosol layer with a constant value of δ∼1 % was recorded, with averaging over the 4.2–5 km range and a 3 min interval.

Figure 3Adjusting the position of the Glan prism. The dependence of the cross-polarized component P_cros (normalized to the minimum is 1) on the angle θ of the prism rotation is shown. Measured values P_cros (circles) and fitting curve (red line).

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Let us use the signal components P_∥ and P_⊥ and a true depolarization ratio $\mathit{\delta }=P_{\perp }/P_{\parallel }$. The signal at the cross-polarization receiver, when the prism position is inaccurate, will be $P{{}^{\prime }}_{\perp }=P_{\perp }{\cos }^{\mathrm{2}}\mathit{\theta }+P_{\parallel }{\sin }^{\mathrm{2}}\mathit{\theta }\approx P_{\perp }+P_{\parallel }{\mathit{\theta }}^{\mathrm{2}}$ (θ is a small setting angle error). Hence, the measured depolarization ratio will be $\mathit{\delta }{}^{\prime }=P{{}^{\prime }}_{\perp }/P_{\parallel }=\mathit{\delta }+{\mathit{\theta }}^{\mathrm{2}}$, and the error of the measured depolarization ratio (due to the inaccurate prism position) is $\mathrm{\Delta }\mathit{\delta }={\mathit{\theta }}^{\mathrm{2}}=\mathrm{0.000156}\approx \mathrm{0.016}$ %.

3.2 Phase plate setup

Phase quarter-wave plates are mounted on a rotating platform driven by a stepper motor, working 1200 steps per revolution. One step of the platform is 0.3^∘ and takes 0.68 ms of time, which allows the plate to rotate 45^∘ in the time period between two laser pulses (about 100 ms). During one revolution of the platform, eight laser shots are taken. Positions of the plates A (transmitter) and B (receiver) for four consecutive pulses are shown in Fig. 4. The bold line shows the direction of a fast axis of the plates. With such an arrangement of axes, the signals of the cross-polarized component with both linear and circular polarization are recorded by the same photodetector.

Figure 4Diagram of the rotation of the phase plates. Plate mounting angles for the four consecutive laser pulses are shown. The bold line shows the direction of a fast axis of the plates.

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The rotation angle setting is monitored by the zero position sensors of platforms. When installing the plates in the platform frame, the plate axis can be shifted relative to the sensor at a certain angle, which is initially unknown. However, a laser pulse must be produced at the moment when the axis of the plates coincides with the reference plane of the lidar. The exact positions of the plates in the frame are set separately for plate A and B. We set one plate (e.g., plate B) in its channel (receiver for plate B) and turn on the rotation. A section of a homogeneous atmosphere with small aerosol content is selected. Figure 5a shows the lidar signals from two photodetectors (P_co and P_cros), summarized over all positions of plate B (red and green lines). A height range from 6 to 9 km was chosen, on which the depolarization ratio (blue line) is constant.

Figure 5(a) Lidar signals from two photodetectors (P_co and P_cros), summarized over all positions of plate B (red and green lines). A height range of 6–9 km with constant depolarization ratio (blue line) is chosen to adjust the plates. (b) Depolarization ratio for each pulse (bottom) and averaged over a 30 min record (top).

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For each pulse, the rotation angle of the plate was recorded and the average value of the depolarization ratio over the range of 6–9 km was calculated. These values are shown in Fig. 5b (bottom frame). The dependence averaged over 30 min is shown in the upper frame in Fig. 5b. Minimal depolarization is observed at the 34th step of the platform. The accuracy of platform setting is ±1 step, which corresponds to 0.03 % error with respect to depolarization ratio. A similar adjustment of the plate A gives an exact position at the 45th platform step.

A timing diagram in Fig. 6 shows the position of the laser pulses relative to the zero position of the plates. A 31 ms interval (45 steps) for plate A and 23 ms interval (34 steps) for plate B pass before the first laser pulse. The situation repeats every eight pulses. As already mentioned, the frequency of laser pulses is strictly synchronized with the rotation of the plates.

Figure 6Time positions of the laser pulses relative to the zero positions of the plates. The situation repeats every eight pulses.

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The diagrams indicated in Figs. 4 and 6 refer to the cases of registration for only the far-range signals. If we register both near- and far-range signals, the plates rotate through the angle 22.5^∘ between laser pulses. Intermediate positions correspond to the near-range signals and have an undefined polarization.

3.3 Calibration of the polarization channels

Measurements of the polarization of backscattered radiation require careful consideration of polarization distortions in the receiving paths and sensitivity of photodetectors in the channels of original and cross polarization (Freudenthaler, 2016; Belegante et al., 2018; McCullough et al., 2018). The task of observations in lidar networks is to monitor the optical and microphysical properties of aerosol, which requires restoring not only the backscattering coefficient but also the lidar ratio and attenuation. Therefore, a large number of lidars are designed as aerosol-Raman (Althausen et al., 2000; Whiteman et al., 2007; Reichardt et al., 2012; Groß et al., 2015; Haarig et al., 2017; Madonna et al., 2018) or multiwave high-spectral-resolution lidars (HSRLs; Eloranta, 2005; Burton et al., 2015). Most of these lidars use dichroic beam splitters as wavelength dividers, and polarizing elements (film polarizers) are installed after the beam splitters and deflecting mirrors (Nott et al., 2012; Engelmann et al., 2016; McCullough et al., 2018). This leads to distortions in recording polarization components, which require complex procedures for determining the eigenvectors of polarization of the lidar and taking them into account when restoring the polarization state of scattered radiation (Alvarez et al., 2006; Haymann et al., 2012; Freudenthaler et al., 2009; Bravo-Aranda et al., 2016; Di et al., 2016; Freudenthaler, 2016).

Measurements of polarization characteristics of backscattered radiation were carried out, simultaneously for several wavelengths, by different groups: 347+697 nm (Pal and Carswell, 1978), 355+532 nm (Althausen et al., 2000; Summa et al., 2013; Groß et al., 2015; Engelmann et al., 2016) and $\mathrm{355}+\mathrm{532}+\mathrm{1064}$ nm (Burton et al., 2015; Haarig et al., 2017; Hu et al., 2019). The LOSA-M3 lidar measures polarization components at wavelengths of 532 and 1064 nm. At the same time, the polarization components are separated directly behind the receiving telescope, before the radiation is separated according to wavelength. This scheme has no distortions of the polarization state from dichroic mirrors reflection; therefore, there is no need to use laborious calculations for the instrumental vector of the transmitting-receiving channel and correction of the measured polarization. In this case, it is sufficient to determine the relative sensitivity of detectors in both lidar channels to measure the magnitude of the depolarization ratio. The channel calibration problem is solved in most devices for polarization measurements. An exception is devices where signals of different polarization are sequentially directed to one photodetector (Platt, 1977; Eloranta and Piironen, 1994; McCullough et al., 2017).

The relative sensitivity of photodetectors can be determined by observing the source with known polarization – it can be a non-polarized source (Sassen and Benson, 2001) or an atmospheric layer with purely molecular scattering (Biele et al., 2000; Noel et al., 2002; Volkov et al., 2002; Kaul et al., 2004; Noel and Sassen, 2005). However, the depolarization ratio for molecular scattering depends significantly on the bandwidth of interference filter used, since rotational Raman lines can contribute to the signal (Young, 1980; She, 2001). For pure Rayleigh scattering, the depolarization ratio is δ=0.00365, with a wide filter, δ=0.015. This leads to an ambiguous lidar calibration.

The most common calibration is associated with rotation of the separation plane for polarization components by 90^∘ (Freudenthaler, 2016). In this case, the photodetectors change places with respect to the polarization components. Turning by 90^∘ can be carried out physically by rotating the entire photodetector unit (Yoshida et al., 2010; Strawbridge, 2013) or by rotating the half-wave phase plate, which can be installed both in the transmitter channel (Spinhirne et al., 1982) and the receiver (McGill et al., 2002; Reichardt et al., 2012). In previous lidars of the LOSA series (Balin et al., 2009), mechanical rotation of the photodetector unit by 90^∘ was used. The intensity ratios in both channels were taken into account and made it possible to eliminate possible changes in the object brightness during turning. When calibrating with this method, you can choose any stable aerosol-cloud formation as a scattering object, which is characterized by a noticeable (>10 %) and constant depolarization ratio during the measurement period.

To measure the depolarization ratio of backscattered radiation, the relative sensitivity of detectors must be known. Thus, in our lidar we offer a new method for a continuous rotation of the λ∕2 phase plate, temporarily installed in the receiver module instead of the λ∕4 plate PP3 in Fig. 2. For the light backscattering phase matrix (BSPM), we take a 4×4 matrix M relating the Stokes vectors of radiation scattered in the direction toward the source $\mathit{S}=[I,Q,U,V{]}^T$ with the Stokes vector S₀ of radiation, incident on an ensemble of particles. Polarization components are expressed as $I_{\parallel }=(I+Q)/\mathrm{2}$, $I_{\perp }=(I-Q)/\mathrm{2}$. Let us assume that laser radiation is linearly polarized (the initial vector is ${\mathit{S}}_{\mathrm{0}}^L={\left[\mathrm{1},\mathrm{1},\mathrm{0},\mathrm{0}\right]}^T$). Then the scattered Stokes vector is $\mathit{S}=\mathbf{M}{\mathit{S}}_{\mathrm{0}}^L=[m_{\mathrm{11}}+m_{\mathrm{12}},m_{\mathrm{12}}+m_{\mathrm{22}},-m_{\mathrm{13}}-m_{\mathrm{23}},m_{\mathrm{14}}+m_{\mathrm{24}}{]}^T$. If we install the λ∕2 phase plate with matrix

before the polarization prism in the receiver, where ϕ is the rotation angle, the Stokes vector will be

where C₄=cos 4ϕ and S₄=sin 4ϕ. Polarization components I_∥ and I_⊥ are different: $\mathrm{2}{I}_{\perp }^{\parallel }=m_{\mathrm{11}}+m_{\mathrm{12}}\pm (m_{\mathrm{12}}+m_{\mathrm{22}})C_{\mathrm{4}}\mp (m_{\mathrm{13}}+m_{\mathrm{23}})S_{\mathrm{4}}$ (the upper sign is for I_∥, and the lower sign is for I_⊥). However, the integral for a complete turn of the plate over the angle $\mathit{\varphi }\underset{\mathrm{2}\mathit{\pi }}{\int }{I}_{\parallel ,\perp }\mathrm{d}\mathit{\varphi }=\mathit{\pi }(m_{\mathrm{11}}+m_{\mathrm{12}})$ is the same for each polarization component, regardless of the values of matrix elements. The ratio of measured values of the integral for two components $K=\underset{I_{\perp }}{\int }\mathrm{d}\mathit{\varphi }/\underset{I_{\parallel }}{\int }\mathrm{d}\mathit{\varphi }$ gives us the value of relative sensitivity of the polarization channels.

The calibration procedure is done separately for 532 and 1064 nm. The method works for any initial state of polarization and for any BSPM of aerosol layer. Unlike the Δ90 method, there is no need to ensure extremely accurate setting of the plate rotation angle, but during the plate turning (about 20 s), the change in the scattering properties of the object should be minimal. Figure 7 shows one of calibration records made on 7 May 2017, demonstrating the errors of the applied method. The upper part (Fig. 7a) shows the record of a signal (1064 nm) integrated by the plate rotation angle, with components I_∥ (green) and I_⊥ (red). Integration was carried out during four revolutions of the plate. Figure 7b shows the value of calibration constant K, calculated in the height range of 1800–8000 m. In this case, the mean value is K=1.91. Similar calibration procedures were carried out before each measurement in April and June 2018. All values of K did not deviate by more than ±0.05.

Figure 7Channel calibration procedure. (a) The record of a signal (1064 nm) integrated by the plate rotation angle, with components I_co (green) and I_cros (red). Integration was carried out during four revolutions of the plate. (b) The value of calibration constant K, calculated in the height range of 1800–8000 m. The mean value is K=1.91.

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4.1 Zenith scanning at 1064 nm wavelength

Below we present the data for polarized components at 1064 nm related to radiation with initial circular polarization. The depolarization of linearly polarized radiation is generally less than that of circularly polarized radiation. For randomly distributed particles, the linear depolarization is 2 times less than that for the circular depolarization (Mishchenko and Hovenier, 1995; Gimmestad, 2008). For oriented particles the difference is smaller, since the BSPM element m₁₂ is not equal to zero (Balin et al., 2011). The low value of depolarization results in the cross-polarized component $I_{\mathrm{cros}}^{\mathrm{Lin}}$ very often not standing out against the background of the photodetector noise in the specular reflection. Therefore, the dependences of polarized components for 1064 nm are presented for initial circular polarization of the laser beam. Dependences I_co(α) for linear and circular polarizations for scan angles 0–4^∘ do not differ within the error limits.

Figure 8 shows the lidar data observed on 6 April 2018. The recording starts at 10:25 LT (UTC+7), and the time from the start is shown on x axis. Figure 8a gives the component $I_{\mathrm{co}}^{\mathrm{circ}}$ (signal intensity; mV), Fig. 8b gives the depolarization ratio ${\mathit{\delta }}^{\mathrm{circ}}=I_{\mathrm{cros}}^{\mathrm{circ}}/I_{\mathrm{co}}^{\mathrm{circ}}$ (%), Fig. 8d gives the zenith scanning angle (arcmin), and the time axis is aligned with Fig. 8a and b. Data of weather sounding (Fig. 8c) are taken from the site of the University of Wyoming (http://weather.uwyo.edu/upperair/sounding.html, last access: 20 February 2020). Radiosonde sounding was carried out at the Novosibirsk station, about 250 km from Tomsk to the SW; two records were made at 07:00 and 19:00 LT. Of course, due to the distant location of the station and the rare launches of probes (once every 12 h), these data do not describe the fine structure of the ice cloud.

Figure 8Lidar data on 6 April 2018 at 10:25 LT (UTC+7) for the initial circular polarization. (a) Intensity of $I_{\mathrm{co}}^{\mathrm{circ}}$ component. (b) Depolarization ratio ${\mathit{\delta }}^{\mathrm{circ}}=I_{\mathrm{cros}}^{\mathrm{circ}}/I_{\mathrm{co}}^{\mathrm{circ}}$. (c) Weather sounding data (Novosibirsk station at 07:00 and 19:00 LT). (d) Zenith tilt angle (arcmin); time axis is aligned with (a, b).

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The duration of recording is 300 s. In the interval from 120 to 250 s, scanning was carried out in the range from 0 to 2^∘. A high-level cloud consists of two layers. The thin bottom layer (6600–7000 m) has a temperature of −26 to −31 ^∘C, and the top layer (7800–9800 m) temperature is −37 to −52 ^∘C . The behavior of these layers is significantly different. Characteristics of the top layer do not change when scanning, which indicates the chaotic orientation of particles in the cloud. In the bottom layer a pronounced modulation of signal intensity and polarization is observed, characteristic of a predominantly horizontal orientation of particles. The maximum intensity of the signal with the vertical sensing direction corresponds to the minimum of the depolarization ratio. An extremely low value δ^circ in the zenith direction ${\mathit{\delta }}_{\mathrm{Zen}}^{\mathrm{circ}}\approx \mathrm{4}$–5 % corresponds to the specular reflection.

The other situation is observed on 2 June 2018 at 09:55 LT (Fig. 9). The duration of this recording is 550 s. The maximum inclination was 4^∘, and the beam passed through the vertical by 1^∘ while scanning. In Fig. 8a we saw clearly expressed the single line of the maximum signal because the vertical position was the edge position when scanning. When we scan our lidar from 4 to −1^∘ and back, vertical positions (0^∘) are close to each other. So in Fig. 9a two lines of maximum signals are close to each other and look like a double line.

Figure 9Lidar data on 2 June 2018 at 09:55 LT. Designations as in Fig. 7.

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A cirrus cloud with a complex structure extends in a layer of 8–11.7 km. The temperature in the cloud varies from −34 to −60 ^∘C. Pronounced modulation of the signal intensity and depolarization ratio is observed throughout the entire height of the cloud. As in the previous case, the maximum intensity of the signal corresponds to the minimum of depolarization ratio. However, the minimum values ${\mathit{\delta }}_{\mathrm{Zen}}^{\mathrm{circ}}$ differ significantly in various parts of the cloud. In the lower part of the cloud, the value ${\mathit{\delta }}_{\mathrm{Zen}}^{\mathrm{circ}}\approx \mathrm{0.6}$ indicates the predominance of chaotically oriented particles and a small proportion of horizontally oriented particles. In the upper part (11.2–11.7 km) ${\mathit{\delta }}_{\mathrm{Zen}}^{\mathrm{circ}}<\mathrm{5}$ % is characteristic of mirror reflection and indicates a pronounced horizontal orientation of particles in this part of the cloud. Values of δ^circ outside the vertical are close to 100 % throughout the entire cloud thickness. This suggests that particles in the cloud differ only in the degree of their horizontal orientation.

4.2 Dependence of the signal intensity on the lidar tilt angle

The ice clouds never constitute a formation uniform in height and constant in time. Pronounced layers with the thickness of hundreds of meters are regularly observed in the structure of ice clouds. They differ in the state of depolarization and signal intensity from the higher and lower regions and are supposedly homogeneous in composition and degree of particle orientation. However, the signal intensity and the depolarization ratio do not remain constant but vary with time rather quickly. The height of layers also varies. Weak values of the backscatter signals lead to the need of averaging the signals over the height of the selected layer and over about 3–5 min. As a result, it is necessary to preselect sections of the cloud, characterized by an approximately constant value of intensity and depolarization ratio and lasting for several scan cycles, to measure the dependence of echo signal characteristics on the tilt angle. An example of such a procedure for selecting the cloud sections to be studied is shown in Fig. 10.

Figure 10Selection of cloud sections for further processing. Recorded on 2 June 2018 at 12:00–12:05 LT. Rectangles highlight areas which have a pronounced dependence on the tilt angle, and there is no signal overflow when the lidar is oriented to zenith.

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In the given 5 min recording, six sections were selected (marked with rectangles), with the duration from three to seven scan cycles. The rest of cloud portions were not analyzed on this record. In total, about 20 records were selected during observations on 2 June 2018, which have a pronounced dependence on the tilt angle, and there is no signal overflow when the lidar is oriented to the zenith.

Figure 11 indicates the typical dependences of signal intensities of parallel $I_{\mathrm{co}}^{\mathrm{circ}}$ (circular initial polarization) and cross-polarized $I_{\mathrm{cros}}^{\mathrm{circ}}$ components on the tilt angle α. The record shown in Fig. 11a was registered at 12:00 LT, with averaging of characteristics over the layer from 11 470 to 11 600 m. The record shown in Fig. 11b was made at 10:00 LT, with averaging of characteristics over the layer from 10 980 to 11 270 m. The signal was accumulated during 10 min. These measurements and all data, obtained in June 2018, are described satisfactorily by the following exponential dependence (red line in Fig. 11):

where I is the signal intensity, I₀ is the offset of dependence determined by a signal without the specular component, A is the constant, depending on the contribution of specular reflection in total intensity, α is the tilt angle, w determines the width of distribution and α₀ indicates the error of lidar targeting to the vertical. For Fig. 11a, w=42 arcmin, and for Fig. 11b, $w=\mathrm{82}{}^{\prime }$. The Gaussian function used in Noel and Sassen (2005; blue line in Fig. 1 is noticeably wider and poorly describes the observed distribution, perhaps because it does not take the intensity peak at α=0^∘ into consideration).

Figure 11Typical angular dependences of the intensity of polarization components on 2 June 2018. Top frames: co-polarized components $I_{\mathrm{co}}^{\mathrm{circ}}$. Bottom frames: $I_{\mathrm{cros}}^{\mathrm{circ}}$. (a) Averaging over the layer from 11 470 to 11 600 m at 12:00 LT. (b) The layer 10 980–11 270 m at 10:00 LT. The record (a) shows low depolarization ratio and narrow (w=42 arcmin) distribution. The record (b) has a wider distribution (w=82 arcmin) and large depolarization.

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Cross-polarized signals $I_{\mathrm{cros}}^{\mathrm{circ}}$ have random variations from pulse to pulse that are comparable with the average value. In most cases the values of $I_{\mathrm{cros}}^{\mathrm{circ}}$ show a weak decline of intensity with the angle, but these variations do not exceed instrumental errors (about 1 % for depolarization ratio). Figure 11a shows the variations even less than 0.5 %. Moreover, a slightly noticeable maximum at $\mathit{\alpha }=\mathrm{0}{}^{\circ }$ looks like signal penetration from the parallel to perpendicular channel. Therefore, we think that the linear trend is not statistically reliable. We can conclude that $I_{\mathrm{cros}}^{\mathrm{circ}}$ is practically independent of the tilt angle.

Figure 12 gives some selected dependences of intensity angle distributions for component $I_{\mathrm{co}}^{\mathrm{circ}}$. We did not find any correlation of the distribution parameters (A, I₀, w) with the height of the selected area inside the cloud. Thus the selection of cloud portions presented in Fig. 12 is rather subjective. The only requirement is that these portions must have a pronounced dependence on the tilt angle, and there is no signal overflow when the lidar is oriented to the zenith. The dependences are normalized to the value I₀ obtained by fitting according to the Eq. (1). Squares indicate the tilt angles, corresponding to the distribution width w. For all measurements the value w is within 40–160 arcmin. The shift α₀ of the curve maximum from 0^∘ is less than 2 min, which indicates a good lidar orientation to the zenith. Since the signal intensity offset I₀ is determined by particles with any orientation (both random and horizontal), the ratio $I_{\mathrm{co}}^{\mathrm{circ}}\left(\mathrm{0}{}^{\circ }\right)/I_{\mathrm{0}}$ may reflect the contribution of mirror particles to the lidar signal. The left frame shows cases of a fairly narrow distribution, and w is within 40–75 arcmin. The ratio $I_{\mathrm{co}}^{\mathrm{circ}}\left(\mathrm{4}{}^{\circ }\right)/I_{\mathrm{0}}$ is less then 1.1. The right frame shows cases with $I_{\mathrm{co}}^{\mathrm{circ}}\left(\mathrm{4}{}^{\circ }\right)/I_{\mathrm{0}}>\mathrm{1.1}$; among these cases there are distributions with a large (up to 159 arcmin) width.

Figure 12Selected cases of observed distributions $I_{\mathrm{co}}^{\mathrm{circ}}$. For all curves the values of intensity are normalized to the values I₀, obtained by fitting according to Eq. (1). Squares indicate the tilt angles, corresponding to the distribution width w. Panel (a) shows cases of a fairly narrow distribution; w is within 40–75 arcmin. The ratio $I\left(\mathrm{4}{}^{\circ }\right)/I_{\mathrm{0}}$ is less then 1.1. Panel (b) shows cases with $I\left(\mathrm{4}{}^{\circ }\right)/I_{\mathrm{0}}>\mathrm{1.1}$; among these cases there are distributions with a large (up to 159 arcmin) width.

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4.3 Angular distributions for green and infrared wavelengths

The obtained dependence I_co(α) in general terms should correspond to the distribution of specularly reflecting particles along the angles of deviation from the horizontal plane (flutter). However, due to the phenomenon of backscattered radiation diffraction on the particle's contour (Borovoi et al., 2008), the distribution is wider than the distribution of particles along the angles of inclination. In addition, the ratio of backscattering coefficients (color ratio) for $\mathit{\alpha }\gg \mathrm{4}{}^{\circ }$ (and for randomly oriented particles in any direction) is not equal to unity (Tao et al., 2008; Vaughan et al., 2010; Borovoi et al., 2014). Therefore, the distribution I_co(α) may depend on the radiation wavelength.

Figure 13Angular dependencies of polarization components for 532 nm (green) and 1064 nm (red). Two cases with the maximum angular differences are shown. In all other cases the distribution width w for 532 nm is equal to or bigger than that for 1064 nm.

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As mentioned in the Sect. 2 the measurements for the wavelength of λ=532 nm were carried out only for linear polarization of radiation, as we used the quarter-wave plates in the transceiver for the wavelength λ=1064 nm. Two cases with the maximum angular differences are shown in Fig. 13. The relative sensitivity of photodetectors at 532 and 1064 nm was not calibrated. Therefore the intensities of polarization components for 532 nm (both $I_{\mathrm{co}}^{\mathrm{Lin}}$ and $I_{\mathrm{cros}}^{\mathrm{Lin}}$) were normalized so that the intensity maximum of $I_{\mathrm{co}}^{\mathrm{Lin}}$ (0^∘) in the vertical position coincided with $I_{\mathrm{co}}^{\mathrm{Lin}}$ (0^∘) for 1064 nm. In Fig. 13a the angle distributions are the same, and in Fig. 13b the distribution for 532 nm is much wider ($I_{\mathrm{532}}\left(\mathrm{4}{}^{\circ }\right)/I_{\mathrm{1064}}\left(\mathrm{4}{}^{\circ }\right)=\mathrm{1.5})$. In all other cases we have intermediate states: the distribution width w for 532 nm is equal to or bigger than that for 1064 nm. The reason for such behavior of dependences is not yet clear for the authors.