Aerosol depolarization ratio measurement 2 capabilities for an elastic LIDAR : implementation 3 and first measurements 4

1 CommSensLab, Unidad de Excelencia María de Maeztu, BarcelonaTech University (UPC), Spain 8 2 Ciències i Tecnologies de l'Espai Centre de Recerca de l'Aeronàutica i de l'Espai / Institut d'Estudis Espacials de 9 Catalunya (CTE-CRAE / IEEC), BarcelonaTech University (UPC), Spain 10 3 Politecnico di Torino, Italy. 11 4 UTC Fire & Security España SL, Spain 12 * Correspondence: alejandro@tsc.upc.edu; Tel.: +34-93-4137237 13 14 Abstract: A new approach to the measurement with elastic lidar of depolarization produced by 15 atmospheric aerosols is presented. The system uses two different telescopes: one for depolarization 16 measurements and another for total-power measurements. The system architecture and principle of 17 operation are described. The first experimental results are also presented, corresponding to a 18 collection of atmospheric conditions over the city of Barcelona. 19


Introduction
Multi-wavelength lidars provide a number of measurements that can be used to characterize the nature and origin of the aerosols present in the atmosphere.The most relevant [1] are: the lidar ratio, defined as that between the retrieved extinction and backscattering at a given wavelength; the ratio of lidar ratios at two different wavelengths and the color ratio (also known as the Ängstrom coefficient [2]), also computed by comparing the retrieved backscattering and extinction at different wavelengths.
Additionally, since the 1970s the use of the lidar depolarization technique has proven to be a valuable tool for atmospheric sciences, e.g.[3] or [4].Regarding aerosol characterization, the depolarization information has been widely used for aerosol typing when combined with additional optical properties (e.g.[5][6][7][8][9][10]).In this sense, it can also be very useful in the retrieval of the planetary boundary layer (PBL) height since it allows to discriminate between the aerosol within this layer and different aerosol types coupled to the PBL height based on aerosol data [11].Fig. 1 shows, in a very visual manner, how the depolarization data combined with the color ratio allow for discriminating among different kinds of aerosols and clouds.So depolarization information can be added to the set of parameters to be considered in aerosol classification [12,13].
Besides aerosol typing, the depolarization technique also provides relevant information for the retrieval of aerosol microphysical properties.Due to the particle shape information associated to lidar depolarization, retrievals of non-spherical particles by inversion methods can be highly improved (see e.g.[14][15][16][17]).Figure from [18] with information from [1].Reproduced with permission from the authors.
Because of the importance of depolarization measurements for aerosol science, a new depolarization measurement channel [19] has been developed and implemented for the BarcelonaTech (UPC) 6-channel elastic/Raman lidar [20].The main difference with other present lidar systems with depolarization measurement capability (see, for instance, [21] or [22]) is the use of an additional telescope (in fact, a telephoto lens) to measure the cross-polarized return signal, without altering the rest of the original system.Section 2 describes the system architecture; section 3 contains the basic formulation for retrieving the information about depolarization profiles; section 4 details the calibration process and section 5 presents some measurements corresponding to a collection of atmospheric conditions over the city of Barcelona.

System architecture
A complete description of the UPC main lidar instrument can be found at [20].The transmitter is based on a Quantel® Brilliant® laser, equipped with second and third harmonic generators.The laser produces 3.6-ns pulses at with energies 130 mJ at 1064 nm and 532 nm and 40 mJ at 355 nm.The 6-channel main receiver unit is sketched in Fig. 2. A 356-mm diameter telescope (CELESTRON® C14-A XLT) collects backscattered light and couples it (with the help of a field lens) to a 3-mm diameter fiber bundle (manufactured by CeramOptec®, custom-made).This bundle delivers the light to a poly-chromator, which splits the beam to the different channels.They include: three elastic backscattering channels (1064, 532 and 355 nm) and three Raman channels (607 and 387 nm for nitrogen and 407 nm for water vapor).
The axes of the laser beams and the telescope are parallel, with an approximate distance of 30 cm between them.This fact causes the partial overlap between the part of the atmosphere illuminated by the laser beams and that "seen" by the receivers, which affects to the amount of light collected from short distances [23].
We have tested the polarization performance of the fiber bundle [24], finding that, for a linearly polarized input, the circularity of the polarization ellipse of the light at the output is better than 93% (in power terms).This fact permits to consider that the 6 channels (including the 532-nm one) are basically sensitive to the total collected power, without any polarization discrimination, even though the poly-chromator includes several beam-splitters that could cause diattenuation.The overall calculated transmission of the fiber bundle and the poly-chromator at the 532-nm output is 6.18% [20].Further measurements (see section Error!Reference source not found.)suggest that the 532-nm channel transmission could be lower.The signal collected in the different channels is detected by means of an APD photo-receiver (for the 1064 nm channel) and five photo-multiplier tube modules (for the remaining channels) and digitized by a parallel Licel® Transient Recorder [25] with analog and photon-counting capabilities.
The aerosol depolarization ratio measurement requires the comparison of the signals recovered by two channels in the system: one proportional to the total power and another proportional to either the co-polar or cross-polar component of the signal collected [26].These two channels operate at 532 nm.
The depolarization auxiliary channel [19,24,27] is shown in Fig. 3.The different distances are indicated in Table 1.Some of the parameters provided in Table 1 have been experimentally determined and adjusted for an optimal performance of the depolarization channel.Every component (except for the telephoto lens) has a diameter of 2.54 mm.The collected light is detected by the active surface of a Licel® R9880U PMT module (PMT in Fig. 4) [28], which feeds the detected current to a dedicated Licel® transient recorder.
The iris is located at the focal plane of the telephoto lens and limits the field of view to a theoretical value of 3.33 mrad (reduced partially due to building compromises, as it will be pointed out later), which is essential to limit the amount of background diffuse light that reaches the PMT active surface, as it is the reduced value of the filter spectral width; the eye-piece produces an image of the telephoto lens input aperture onto the PMT detection surface, optimizing the detection process.
A ray-optics simulation of the receiver has been performed, using the software ZEMAX®.Fig. 5 plots the axial ray distribution over the plane of the active surface of the photo-multiplier tube.The plot shows the impinging points of the rays parallel to the optical axis.The PMT active surface has an 8-mm diameter.According to the optical analysis, the r.m.s.diameter of the ray distribution is 6.2 mm, while all the traced rays lay within a 8.6-mm diameter, which leads to an expected 16% overspill.Fig. 6 shows the ray distribution of those entering the telephoto lens with the maximum effective field of view which, according to the simulation has been reduced to 0.09 degrees (equal to a maximum effective field of view of the optical system of approximately 3.14 mrad).For these rays, the r.m.s.diameter is 6.15 mm and the maximum deviation from the center of the PMT active surface  The telephoto lens axis is approximately 40 cm from the laser beams (refer to the laser description above), which affects to the partial overlap at short distances as indicated earlier in the text.Fig. 7 shows the complete system in our laboratory.The lidar is pointed in a vertical direction; whenever it is not been used, a motorized hose covers the equipment.The nominal position of the polarization analyzer is 90-degrees from the transmitted beam polarization plane.In this way the channel is sensitive to the cross-polarized fraction of the light backscattered by the atmosphere.

Theory of operation
The lidar measures along a vertical axis, so in every expression the distance R to the lidar is equivalent to the height over the system.
The voltage signal obtained at the total-power PMT output can be written: Where: ( ) V R is the total-power 532-nm channel responsivity, as a function of the distance to the lidar system R , including the effect of the partial overlap (see section Error!Reference source not found.).

( )
Tot P R is the backscattered light power collected by the main telescope @532 nm.
The voltage signal obtained at the depolarization channel PMT output can be calculated: Where: We will define the depolarization channel system function as: While it is extremely difficult to determine ( ) V R by means of a calibration process that compares the output signals of the total-power channel and the cross-polar channel, when the polarization analyzer of the latter is set successively + and -45 degrees from its nominal position [21]: The factor 2 takes into account that, at the calibration positions, the auxiliary channel is detecting half of the total backscattered power.
The volume depolarization is usually defined [21]: Accepting that ( ) ( ) ( ) , and operating with the previous results, we can calculate the volume depolarization [24] as: Where: Finally, the particle depolarization ratio can be computed by combining the volume ratio with the molecular and aerosol backscattering profiles [21]: Where: , molecular and aerosol backscattering profiles retrieved by means of a , [30]) or Raman ( [31], [32]) inversion performed over the signal of the total-power channel.

Finally, the molecular volume depolarization ratio
was computed by Behrendt and Nakamura [33] and has an approximately constant value of 3.8×10-3 for a receiver with a spectral width of 0.5 nm.The error analysis of the different magnitudes obtained in the data analysis is detailed in the appendix.

Calibration process
The determination of the depolarization channel system function is made by means of a calibration procedure that compares the outputs of the depolarization and the total power channels [21,35,36]; during the calibration the polarization analyzer of the depolarization channel is set first at +45 degrees, and second at -45 degrees from the nominal (cross-polar) position.Each one of the calibrations runs for 15 minutes, which amounts 18000 laser pulses.
The outputs of the two channels are divided and then a geometrical average is computed (as indicated in equation ( 4)) between the system profiles obtained at the two positions; after that a zero-phase low-pass spatial filter is applied to the average, to reduce noise effects; finally, the values obtained for heights over ~10km are discarded, also due to noise effects, considering the value obtained at 10 km for greater height values.
A number of calibrations have been performed since the implementation of the depolarization channel, and the historic is presented in Fig. 8.The color sequence shows the time evolution of the estimated system functions.As the colder colors point out, the early functions were affected by misalignments between the laser and the receiver.The most recent calibrations are stabilized to a medium-height value around 4.  The system function includes the effect of the different overlap functions of the two channels; it also draws attention on the fact that, even though the ratio of the main telescope and the telephoto lens collecting surfaces is approximately 25, the depolarization channel optics has a higher transmission and a more responsive PMT receiver.This result also suggests that the transmission of the 532-nm total-power channel must be lower than that indicated in section Error!Reference source not found..These uncertainties make the periodic calibrations unavoidable.

Depolarization ratio measurements
Some depolarization measurements are presented next for different aerosol loads.The volume depolarization ratio is retrieved from both total and perpendicular signals with Eq. ( 6) and a calibration depolarization channel system function, * V .In all cases the depolarization channel system function is taken from the closest (in time) calibration performed prior to the measurement considered.The particle depolarization ratio is then retrieved with Eq. ( 8) from the volume depolarization ratio and the particle backscatter coefficient, p β .All cases presented are daytime measurements, so that no Raman inversion is possible and thus p β is retrieved with the Klett - Fernald ([29], [30]) method and a constant lidar ratio of 50 sr, except in the cirrus cloud case.In this case, as there is a molecular region below and above the cloud, the iterative backward-forward method [36] was applied to invert the cloud backscatter and extinction coefficients without the need to assume a lidar ratio.All profiles of the molecule backscatter coefficient, m β , are calculated with the closest (in time) radiosoundings either at 12 or 00 UT.The error bars are calculated following the equations detailed in the appendix.For the sake of clarity, the points of the profiles of the particle depolarization ratio for which the error bar is larger than 50 % are not represented.
Fig. 10 shows the retrieval of volume and particle depolarization for different aerosol loads: pollen, mineral dust, fire smoke and a case of local urban aerosol, as well as a cirrus cloud case.In the case of pollen (Fig. 10a) the atmospheric boundary layer (ABL) extends up to ~1.5 km.In this layer V δ is rather constant ~0.055 while p δ varies slightly between 0.10 and 0.13.These values are in agreement with depolarization ratios measured during another pollen event in Barcelona by [37] who found mean values of For the day considered here, 14th March, 2017, [38] counted a total pollen near-surface concentration in Barcelona of 1746 grains per cubic meter, being 90 % of them Platanus, which is in the lower range of values 1082-2830 found in [37].The second case (Fig. 10b) gives typical values of depolarization for mineral dust.It is taken from an outstanding desert dust intrusion over Iberia with aerosol optical depths as large as 2 [39].Above 1 km V δ is in the range 0.17-0.24and p δ in the range 0.23-0.28.The small differences between km with a rather clean troposphere below.The application of the iterative backward-forward method [36] gives a mean cirrus lidar ratio of 19 sr and a cirrus optical depth of 0.19.The cirrus cloud is quite heterogeneous in time and vertical range during the 60 min. of the measurements, which results in a large variability of the particle depolarization ratio which varies between 0.20 and 0.52, being the mean value 0.39±0.11.This high value of p δ is in agreement with former studies such as [41] who found values in the range 0.30-0.45for cirrus clouds at ~9.5-11.5 km height observed in north-central Oklahoma.Finally to give an idea of the particle depolarization ratio in background conditions in Barcelona, i.e. when the aerosol is from local urban origin and probably mixed with marine particles, a case without long-range transport is selected (Fig. 10e).The ABL is developed up to 1.25 km.
p δ is nearly constant and its mean value is 0.066±0.005.If we compare this value to the collection of depolarization ratios of [40] measured around the globe for anthropogenic pollution (0.06-0.10) and marine aerosols in different relative humidity conditions (0.01-0.10) we find a good agreement.However, at this point, from the depolarization ratio alone it does not seem possible to distinguish the fractions of anthropogenic pollution and of marine particles.

Conclusions
A new depolarization sensing subsystem has been implemented to a 6-channel elastic/Raman lidar.The architecture is based on a dedicated sub-telescope (a telephoto lens).The theory of operation has been presented, including the calibration procedure.Measurements performed during two Saharan dust intrusion events are used to test the new channel.Particle depolarization ratios varying between 10 and 40 % are found in the dust layers.Comparisons of the volume depolarization with an MPL system show a good agreement between both systems and demonstrate the reliability of the new depolarization channel of the UPC multi-wavelength lidar.
( ) , ,..., n y f x x x = (11) Which are known with a standard deviation i x Δ The most reliable value of y can be computed as: , ,..., n y f x x x = (12) With a standard deviation that can be computed as [43,44]: Where is the partial derivative of function f with respect to variable xi, evaluated in the average value i x .
According to this method, the following standard deviations can be obtained for the observable ( ) * 90º , R δ , defined in equation ( 7): Where According to the calibration method, the uncertainty associated to the estimation of the depolarization channel system function is reduced by the signal smoothing that is performed.
According to the different calibrations presented in Fig. 8, an absolute error around ( ) will be considered in the computation of the error of the volume depolarization ratio, defined in equation ( 6): The computation of the error of the backscatter ratio, defined in equation ( 9), considers only the random variations of the retrieved particle backscatter ( [30][31][32][33]): ( ) ( ) ( ) ( ) Finally, for the computation of the error of the particle depolarization ratio, defined in equation ( 8), we will simplify the expression by defining:

Fig. 1 .
Fig. 1.Color ratio vs lidar ratio and particle depolarization ratio for different aerosol and cloud types.

Fig. 3 .Fig. 4 .
Fig. 3. Auxiliary channel for depolarization measurements, where the most relevant elements are labelled The depolarization channel uses a separate telescope (a 70-mm aperture, 300-mm focal distance TAIR-3S telephoto lens).The rest of the optical arrangement, sketched in Fig. 4, includes a 1-mm field-of-view stop iris (D) in the focal plane, a polarization analyzer (P), and eye-piece lens (L4) and aBarr® interference filter (IF) centered at 532 nm, with 0.5-nm spectral width.The polarization analyzer is made by a linear polarizer mounted on a goniometric mount that can be seen in Fig.3.

Fig. 5 .
Fig. 5. Spot diagram of the distribution of the collected rays, parallel to the optical axis, over the 8-mm diameter active surface of the photo-multiplier detector tube calculated with ZEMAX® software.

is 4 .Fig. 6 .
Fig. 6.Spot diagram of the distribution of the collected extreme rays, entering the optical system with an angle equal to half the effective field of view (0.09 deg), over the 8-mm diameter active surface of the photo-multiplier detector tube calculated with ZEMAX® software.

Fig. 7 .
Fig. 7. Complete view of the UPC lidar system: the laser on the left (including 2nd and 3rd harmonic generators), the main telescope in the middle and the depolarization auxiliary channel on the right.

⊥
(www.preprints.org)| NOT PEER-REVIEWED | Posted: 13 October 2017 doi:10.20944/preprints201710.0095.v1( )Dep VR is the depolarization channel responsivity, as a function of the distance to the lidar system R , including the effect of the partial overlap.is the cross-polar fraction power of the depolarized backscattered light, function of R .

Fig. 8 .
Fig. 8. Historic of the calibrations of the depolarization channel system function obtained from March 2016 to June 2017.The colder colors refer to early calibrations while the warmer ones to the recent ones.

Fig. 9 Fig. 9 .
Fig.9shows the temporal evolution of the far range value of * V for the different calibrations presented in Fig.8with the values obtained between realignment procedures grouped.The first group of calibrations shows a deviation of more than 30%.After this period, an improvement in the anchorage of the receiving optics was implemented and the deviation was reduced to less than 10%, which was maintained after following realignment procedures.Anyway this diagram points out that different phenomena (thermal changes, mechanical relaxation, state of the atmosphere) affect * V in a way that cannot be ignored.

δ
are due to the high values of the particle backscatter coefficient (~15 Mm-1sr-1) in the dust layer.According to[40] the values of p δ found in our work are in the upper range of desert dust mixtures (0.14-0.28) and below the values of pure desert dust (0.30-0.35).The example shown in Fig.10cillustrates the transport of Canadian fires over the Iberian Peninsula on 24th May, 2016, at 15 UT.The smoke layers were first detected on the /mplnet.gsfc.nasa.gov/data?v=V3&s=Barcelona&t=20160522)and lasted until the evening of 24th May.In Fig.9bone sees the fire smoke layer at ~2 km and a dust layer above 3 km.To illustrate a case of fire smoke, we looked into our short database but unfortunately we could not find a situation clearly identified as fire smoke and with no other aerosol type.In the fire smoke plume p δ varies in the range 0.05-0.10.Here again our findings are in agreement with the literature, in particular with[40] which collects values of p δ for pure biomass burning measured in several places around the globe in the range 0.02-0.08,being values of fresh smoke slightly lower than for aged smoke.Our values fall into the interval representative of aged smoke.We extend now the illustration of particle depolarization ratios retrieved with the UPC new depolarization channel to ice particles in cirrus clouds.Fig.10dshows a case of cirrus clouds extending between 10 and 12.2

Fig. 10 .
Fig. 10.Some examples of volume and particle depolarization ratio retrievals showing (left) time-height plots of range-square corrected signals in arbitrary units, (center) particle backscatter coefficient at 532 nm, (right) volume and particle depolarization ratios at 532 nm for (a) pollen, (b) dust, (c) dust and fire smoke, (d) cirrus cloud, (e) local urban.The points of the particle depolarization ratio profiles for which the associated error is larger than 50 % are not represented.
average value of the signal detected by the total power channel, as a function of range, average value of the signal detected by the depolarization channel (with the polarizer oriented 90o from the transmitted beam polarization, the standard deviation of the signal detected by the total power channel.the standard deviation of the signal detected by the depolarization channel.

Table 1 .
Parameters of the different optical elements of the depolarization channel.