Echo characteristics of polarized heterodyne lidar in nonspherical aerosol environments

Optik - International Journal for Light and Electron Optics 180 (2019) 302–312

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Original research article

Echo characteristics of polarized heterodyne lidar in nonspherical aerosol environments

T

Xiao Donga,b, Yihua Hua,b, , Nanxiang Zhaoa,b, Xinying Zhaoa,b, Shilong Xub ⁎

a b

State Key Laboratory of Pulsed Power Laser Technology, National University of Defense Technology, Hefei 230037, China Key Laboratory of Electronic Restriction of Anhui Province, National University of Defense Technology, Hefei 230037, China

ARTICLE INFO

ABSTRACT

Keywords: Heterodyne lidar Polarization T-matrix Nonspherical aerosols

Heterodyne lidar echoes in atmospheric detection are greatly affected by the shapes of aerosols. With the aid of T-matrix and vector Monte Carlo simulation, we investigated the properties of lidar echoes backscattered by randomly oriented polydisperse aerosols, including the soot, sea salt and mineral aerosols. The degree of polarization (DoP) and backscattered photon numbers in different range bins are calculated when the launched laser pulses are linearly polarized light and circularly polarized light at 1.55 μm. There are reductions of DoP along the 10 km detection path, which vary with aspect ratios (AR) and aerosol types. The ARs are chosen within 0.5–2.0 for cylinders and 0.3–1.0 for spheroids. The lidar echoes in soot aerosols have the largest DoP which is higher than 0.8. Moreover, the shape fading factor and polarization fading factor are defined and calculated based on the effective backscattered photon numbers, which shows that the mineral aerosols in nuc.mode (MINM) is less affected by aerosol shapes and laser polarization states, and that the LPL is suitable for the heterodyne detection of nonspherical atmospheric aerosols. The results provide echo characteristic deviations from the spherical particle scattering, which can be used in the practical modeling of atmospheric echoes and designs of heterodyne lidars.

1. Introduction Atmospheric aerosols have different scattering abilities due to various complex refractive indexes (CRI), shapes, sizes and orientations, which can affect the properties of heterodyne lidar echoes. Based on the lidar return backscattered by aerosols, many atmospheric parameters can be observed, such as the wind field [1], turbulence [2], constituents [3] and aerosol microphysical properties [4]. To achieve higher signal to noise ratios (SNR) and spatiotemporal resolutions, coherent lidars are widely used in atmospheric observations, especially the coherent Doppler lidar (CDL) [5] and the coherent differential absorption lidar (CDIAL) [6]. Both the degree of polarization (DoP) and the echo intensity are important in the performance analyses of heterodyne lidars used in atmospheric remote sensing. Even though the polarization diversity reception (PDR) can improve the polarization matching between the local oscillator and lidar return [7], the DoP places the upper limit of heterodyne efficiency and only the polarized components of the lidar echoes can be utilized in heterodyne detection because the unpolarized components can be seen as natural light which is incoherent. Generally, the analyses on backscattering properties of polarized light in aerosols are based on spherical particles and the Mie theory. However, the shapes of aerosol particles vary dramatically, and the spherical assumption may cause big errors for certain ⁎ Corresponding author at: State Key Laboratory of Pulsed Power Laser Technology, National University of Defense Technology, Hefei 230037, China. E-mail address: [email protected] (Y. Hu).

https://doi.org/10.1016/j.ijleo.2018.11.071 Received 14 October 2018; Accepted 19 November 2018 0030-4026/ © 2018 Elsevier GmbH. All rights reserved.

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aerosols that are non-spherical in actual atmosphere. Current researches on nonspherical aerosols are concentrated on the sky radiation pattern [8], microphysical properties inversion [9] and environment monitoring [10]. The nonspherical aerosols can be distinguished by the depolarization ratio which can be observed at a few discrete visible and near infrared bands. However, these observation bands do not cover the infrared wavebands around 1.6 μm and 2.05 μm that are widely used in heterodyne lidars for atmospheric detection, and the CRI as well as size parameter are also different from that in the visible/near-infrared wavebands, which lacks sufficient analysis of the backscattering characteristics at these two wavebands. In addition, the photon path change caused by the multiple scattering of aerosols is one of the main errors in concentration inversion [11]. Thus the analyses on aerosol scattering characteristics by considering the multiple scattering and nonspherical shapes are of practical significance to improve the effectiveness of heterodyne lidar system design and the accuracy of atmospheric components inversion. Several studies have been carried out for the nonspherical aerosol scattering. The vector radiative transfer models can provide higher accuracy than the scalar method, which include the RT3/PolRadtran [12], the VDISORT [13] and the Monte Carlo (MC) method [14]. The MC method has preferable practicability and self-adaptability, which can describe the multiple scattering phenomenon, especially when the particle concentration is relatively high [15]. In the modeling of aerosol particle swarms, many observations suggest that there are many differences in the scattering characteristics between the actual non-spherical atmospherical particles and equivalent spherical particles, and most of the dust and soot aerosols can be modeled as rotationally symmetric nonspherical particles [16,17]. Among the nonspherical scattering theories, such as T-matrix [18], DDA [16] and FDTD [19] methods, the T-matrix method is regarded as one of the most efficiency method, which can calculate the scattering characteristics of nonspherical aerosols more rigorously and give consideration to both the accuracy and speed, and thus we use this method in this paper. In this paper, we focus on the influence of shape parameters on the characteristics of heterodyne lidar echoes in randomly oriented polydisperse aerosol environments, and the relative deviations between the non-spherical and spherical aerosols are discussed. The wavelength is 1.55 μm, which can roughly describe the scattering properties in the infrared wavebands from 1.45 μm to 1.6 μm. The CRIs and size distributions are based on the OPAC (Optical Properties of Aerosols and Clouds) database [20]. Then the DoP and backscattered photon numbers are analyzed in detail, which offers the references for understanding the depolarization behavior of atmospheric aerosols better and improving the effectiveness of heterodyne lidar designs. 2. Theoretical background 2.1. T-matrix method for nonspherical particle calculation The T-matrix is a transfer matrix between the incident and scattered light fields, which is only related to the intrinsic properties of aerosols, such as the CRI and particle size. Based on the T-matrix method, the Maxwell equations can be solved analytically and exactly, and there is no need to simulate the scattering properties in different orientations, which can greatly save the computation time. We use the T-matrix method to compute the backscattering characteristics of randomly oriented nonspherical particles. The stokes vectors of scattered light are defined in the meridian plane, which can be written as [21,22],

Ss =

Csca F ( ) Si, 4 R2

(1)

where Ss and Si are the stokes vectors of incident and scattered light respectively, R is the distance between the scattering particles and lidar, F( ) is the normalized scattered matrix, Csca is the scattering cross section. In atmosphere, there are variations in aerosol positions, such as the drifting and rotating, and the particle orientations are randomly distributed, which can be modeled as rotationally symmetric particles. Then Csca can be represented as 〈Csca〉, and the normalized scattering matrix has only six unrelated parameters, which can be expressed as,

F( ) =

4 Csca

F11 ( ) F12 ( ) 0 F12 ( ) F22 ( ) 0 F( ) = 0 0 F33 ( ) k2 0 0 F34 ( )

0 0 F34 ( ) F44 ( )

, (2)

where 〈 ⋯ 〉 is the average results in randomly orientations, 〈Csca〉 is the mean scattering cross sections, the average scattering matrix 〈F(θ)〉 characterizes the spatial distributions of scattered light and the quantitative relationship between Ss and Si, k = 2π/λ, λ is the wavelength, F11(θ) is the phase function,

1 2

0

sin( ) F11 ( )d

= 1.

(3)

The average scattering matrix in randomly orientations is used in the MC simulations of multiple scattering of nonspherical aerosols, which can be calculated as [22],

F( ) =

1 8

2 2

0

d

0

sin d

2 0

Z ( , 0, 0, 0; , , ) d ,

(4)

where (α, β, γ) is the angle of coordinate systems of the particle and the laboratory, the Z(θ, 0, 0, 0 ; α, β, γ) represents that the incident light is along the z axis, scattering matrix Z is defined on the meridian plane. The ensemble-averaged scattering cross section of randomly oriented particles can be calculated based on the normalized size 303

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Table 1 Compositions of aerosol types in typical environments. Aerosols

Ni/cm3

C1

R1/%

C2

R2/%

C3

R3/%

Continental Urban Maritime Desert

15300 15800 9000 2300

WASO WASO WASO WASO

45.75 17.72 42.22 86.96

SOOT SOOT SOOT MINM

54.25 82.28 57.56 11.72

INSO INSO SSAM MIAM

2.6 × 10−5 9.4 × 10−6 0.22 1.32

distribution n(r),

Csca

=

r2 r1

Csca (r ) n (r )dr.

(5)

The logarithmic normal distribution and its superpositions can describe the size distributions of the whole aerosol environments [20]:

dN(r ) N0 = dr r 2 ln

exp

(lg r

lg rmod, N ) 2 , 2(lg ) 2

(6)

where rmod,N is the mean mode radius, σ is the geometric standard deviation, N0 is the particle number density (in cm−3). In the scattering analyses of polarized light in polydisperse aerosols, the bulk optical properties should be calculated. The bulk scattering cross section and bulk scattering matrix elements can be written as [23], (7)

Csca, b = Csca N0,

Pi, j

=

r2 F ( r 1 i, j , r

) Csca (r ) N (r )dr Csca, b

,

(8)

where Fi,j,r(i, j = 1–4) is the element in the scattering matrix 〈F(θ)〉 when the particle radius is r. In this paper, four typical environments are chosen including the continental average, urban, maritime polluted and desert environments. The compositions modeled in OPAC [20] are shown in Table 1. There are mainly 5 aerosol types including the water soluble (WASO), soot, sea salt (SSAM), mineral in nuc.mode (MINM), mineral in acc.mode (MIAM) and insoluble (INSO). Ni(i = 1, 2, 3, 4) is the particle number densities of four aerosol types. Rj(j = 1, 2, 3) and Cj(j = 1, 2, 3) are the main aerosol compositions and the particle number mixing ratios in specific environment. In the above four environments, the particle number mixing ratio of INSO is lower than 0.01%, and thus we neglect the INSO. In addition, the heterodyne lidar usually functions around 1.45 μm to 1.6 μm, and the CRIs at this region changes slowly [24], and we use the CRIs at the 1.50 μm in our simulation which are listed in Table 2, where the subscripts of r and i represent the real part and imaginary part. Moreover, the size distributions in Eq. (6) are also listed in Table 2. Generally, the WASO tends to be spherical [17], and its scattering properties are analyzed in our previous work [24]. The other four kinds of aerosol types can be non-spherical in most situations. Previous studies [25,26] have shown that the complicated scattering properties of nonspherical aerosols can be mimicked by the size-shape distributions of homogeneous spheroids and cylinders, and thus we use the spheroids and cylinders in the nonspherical scattering analyses of soot and mineral aerosols. As for the SSAM, the shape changes with relative humidity (RH) due to the hygroscopic behavior, and the particle radius increase with the growth of RH. Typically, SSAM particles exhibit crystal faces corresponding to effloresced particles, and the particle has a near rounded cross sections when the RH decrease from the 75% deliquescence point to the 42% crystallization point [27]. Considering the high HR in maritime aerosol environments, we focus on situations where RH is higher than 50%, and then the spheroid and cylinder assumption are reasonable. For hygroscopic aerosols, such as WASO and SSAM, the radius and CRI change with RH. Through plenty of theoretical and experimental studies, an empirical formula [28] has been obtained for characterizing the radius rh and CRI of an equivalent uniform spherical particle, which can be written as,

rh = (1

H)

(9)

(1/ d) r , 0

Table 2 Dry aerosol components size distributions and CRIs. Particle type

WASO

SSAM

MIAM

MINM

SOOT

rmod,N σ nr ni

0.021 2.24 1.333 1.595×10−3

0.21 2.03 1.354 2.89×10−4

0.40 2.00 1.53 5.7×10−3

0.07 1.95 1.53 5.7×10−3

0.012 2.00 1.77 0.46

304

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Fig. 1. Schematic of laser scattered by polydisperse nonspherical aerosols.

n ( ) = n w ( ) + [n 0 ( )

n w ( )]

rh r0

3

,

(10)

where r0 is the radius of dry aerosols, d is a constant related to aerosol types, which is 4.16 in this paper, n w and n0 are CRIs of water and dry aerosol. According to the OPAC dataset, the particle distributions are assumed to be unchange with RH. 2.2. Monte Carlo method and simulation The Monte Carlo method solves the scattering process of laser in aerosols by using the statistical mean of photon random motions. Approximate backscattering characteristics can be obtained by tracing the scattering process of large numbers of photons, which is verified by experiments [29]. In our MC simulations, the polydisperse aerosols are assumed to be well mixed and randomly oriented. The pulse lidars can detect the spatial distributions of aerosols. Based on the lidar returns, the information of atmospheric CO2 concentrations and wind field at different range bins can be detected by using the differential absorption method and the Doppler shift respectively. The detection process is shown in Fig. 1, and the length of each range bin can be calculated with ΔR = cτ/2, where τ is the laser pulse width. The initial stokes vectors can be expressed as S0 = [I0, Q0, U0, V0]. The states of polarization (SoP) of incident light are linearly polarized light (LPL) and circularly polarized light (CPL), which corresponds to the two main kinds of heterodyne lidar transceivers [24]. The simulation process mainly includes the photon emission, move step execution, drop, scattering direction calculation and the judgement of termination condition [14]. Backscattering characteristics of polarized light is determined by the scattering matrix and the SoP of incident light. In the polarized lighted MC simulation, the scattering angle α and azimuth angle β are correlated, and the sampling process of these two angles should adopt the cumulative probability distribution function (CDF) and the rejection method [14]. The single scattering phase function for incident polarized light can be expressed as, (11)

( , ) = m11 ( ) + m12 ( )[Q0 cos(2 ) + U0 sin(2 )]/ I0

where m11(α) and m12(α) are the elements of the scattering matrix. There are mainly two ways to achieve the rejection method which include the one-step sampling method and the two-step sampling method. In the former method [14], α and β are chosen randomly, and the final angles can be obtained when ρ(α, β) > ξ, where ξ is a random number between 0 and 1. In the latter method, α is determined firstly based on Eq. (3), and then the β can be obtained based on the Conditional probability distribution (CPD) [24]. These two angle sampling methods can acquire similar angle sampling results, but the former one can save much simulation time. The required time for generating 105 pairs of (α, β) for polystyrene particles are listed in Table 3, where λ = 1.55 μm. As shown in Table 3, the one step method is more efficient especially when the particles are small, and thus we use this method in the next simulations. In traditional MC simulations, only a very small number of photons can exit the aerosols medium exactly in the backscattering direction. To collect enough backscattered photons, tremendous numbers of photons should be launched, which reduces the computation efficiency. As a result, there should be compromises between the calculation efficiency and accuracy [30]. Moreover, the semi-analytical approach is also used to improve the simulation efficiency. For a single scattering process, the stokes vectors can be expressed as,

Sc = L (

(12)

i2) F ( ) L ( i1) Si,

where the L(·) is the rotation matrix. Once scattered, the weight of photon is attenuated by the albedo ω. Then the stokes vectors of the scattered light can be written as, Table 3 Required time in scattering angles selections (in second). Method

0.01 μm

0.1 μm

1 μm

2 μm

4 μm

One step Two step

0.4366 34.1467

0.4582 33.6357

2.1745 32.1198

7.0663 31.9943

21.8248 31.2112

305

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X. Dong et al.

Sc Si (1)· , Sc (1)

Sc =

as

(13)

Considering the multiple scattering [31] and Eq. (1), the final backscattering stokes vectors of a photon can be generally expressed

L( ) R2

Ss =

k

L(

i2, k ) F ( k ) L ( i1, k ) Si,

if( nz ·nb)

cos

(14)

k=0

where L(χ) is the rotation matrix that rotates Stokes vectors to the detector plane, k′ is the maximum scattering number, nz and nb are the direction cosines of the lidar detection direction and the backscattered photons, φ is half of the receiving field of angle. R is the discrete distance between the range bins and lidar, which can be determined by the cumulative scattering path of photons. The scattering process can be terminated when the photon weight is small enough (such as 10−8) or the photon is out of the aerosol region. The backscattered field by aerosols can be regarded as incoherent because the distance between aerosol particles are much larger than the particle radius [32]. Eq. (14) is the basic equation that describes the stokes vectors of lidar returns, and the scattering characteristics of actual aerosol environments can be analyzed based on the superposition of stokes vectors, i.e., Nk, j, i

Sk, j =

Sk, j, i,

(15)

i=0

where Sk,j,i and Nk,j,i are the Stokes vectors and scattering numbers in one simulation group, the subscripts of k and j are the four kinds of nonspherical aerosols and four typical environments shown in Table 3. The final Stokes vectors of the returned photons can be written as Sk,j = [Ik,j, Qk,j, Uk,j, Vk,j]. Then the DoP of backscattered field of certain aerosols in each environment can be expressed as,

Pk, j =

Qk, j 2 + Uk, j 2 + Vk, j 2 Ik, j ,

(16)

where the Ik,j is also the weighted backscattered photon numbers. Typically, the overall reflectivity can be calculated by the average of weight reflection probability, which can be written as,

Rim = Wi exp(

(17)

ext li ),

where σext is the extinction coefficient, li is the ith scattered distance, i is the scattering number, m represents the mth photon, Wi = ωi. Then the reflectivity can be written as,

R =

1 M

M

N

Rim ,

(18)

m=1 i=1

where M is the number of launched photons, N is the scattering numbers. 3. Results and discussion 3.1. Monte Carlo simulation verification We conduct simulations using spherical particles, and the scattering matrixes are calculated by the T-matrix and Mie theory respectively. The total transmittance and reflectivity are simulated from a semi-infinite media and compared with Ref. [14] (vector MC simulation) and Ref. [33] (scalar MC simulation). Three typical radii are considered in this part, which include 0.05 μm, 0.5 μm and 1 μm. The initial stokes vectors is Si = [1,0,0,0]; launched photon numbers are 107; CRI is 1.59, and λ = 0.6328 μm. The length of the particle area is chosen as 4/Csca,b. The results are listed in Table 4. Ri and Ti(i = 0.05, 0.5, 1) are the reflectivity and transmittance. All the errors are below 0.2%, which suggests that the simulation method used in this paper is accurate. To verify the polarization properties, vector MC simulations are also conducted, and the DoPs of backscattered light are calculated under different radii r and SoP, which are shown in Fig. 2. In the vector simulations, the particle radii change from 0.05 μm to 5 μm with the interval of 0.05 μm, and the relative errors RE between our results and Ref. [14] are also calculated and shown in Fig. 2(b). The DoPs of the backscattered field are practically in good agreement with Ref. [14] at different particle radii, and the relative error is below 1%. Fig. 2(a) also shows the influence of SoP of the incident light on the DOP of the backscattered field, and the DoPs are higher with CPL in the radii region from 0.15 μm to Table 4 Accuracy verification of MC simulation. Method

T0.05

R0.05

T0.5

R0.5

T1

R1

Ref. [14] Ref. [33] This code

0.3230 0.3229 0.3233

0.6770 0.6771 0.6767

0.5522 0.5526 0.5529

0.4478 0.4474 0.4471

0.7070 0.7068 0.7067

0.2930 0.2922 0.2933

306

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Fig. 2. The DoP validations of backscattered field. (a)The DoP validations using LPL and CPL. (b)Relative DoP errors.

0.45 μm. 3.2. The influence of aerosol shapes on the DoP of backscattered filed In the lidar detection process, aerosol scattering properties are closely related to the particle shapes. The scattering matrix F( ) , scattering coefficient and extinction coefficient change with shape and aerosol types. In this part, four types of aerosols are analyzed, including the MINM, MIAM, SOOT and SSAM. As mentioned above, non-spherical aerosol shapes are modeled as cylinders and spheroids. The aspect ratios (AR) of cylinders are calculated between 0.5 and 2.0 with the interval of 0.05; similarly, AR values for spheroids are chosen from 0.3 to 1.0 with the interval of 0.025. Considering the size distribution, the particle size range is from 0.001 μm to 0.8 μm for soot and MINM; for the MIAM and SSAM, the radius range is from 0.01 μm to 4.5 μm. The MIAM and MINM have identical CRIs and the difference is only the size distributions. When the single scattering is considered, the linear backscattering depolarization ratio can be written as [34], L

=

F11 ( ) F12 ( ) . F11 ( ) + F12 ( )

(19)

Then δL is calculated under different aerosols shapes, as shown in Fig. 3. Different nonspherical particles have specific δL features. The δL for randomly oriented spheroid particles is same when the ARs are reciprocals. Among the four kinds of aerosols, soot aerosols are less affected by shapes, which has the lowest peak values, as shown in Fig. 2(a) and (b). The peak δL is 0.1224 (@r = 0.41 μm, AR = 0.3) and 0.1266 (@r = 0.63 μm, AR = 0.475) for spheroid model; for cylinder model, the peak δL is 0.1201 (@r = 0.42 μm, AR = 0.5) and 0.1223 (@r = 0.64 μm, AR = 0.6). For most of the non-spherical parameters, δL is small enough especially with smaller particle radii. Similarly, the peak δL for MINM is a bit larger, which is 0.1502(@r = 0.41 μm, AR = 0.3,spheroid) and 0.1562 (@r = 0.5 μm, AR = 0.5, cylinder), as shown in Fig. 2(c) and (d). As for the other two types of aerosols, the δL is much larger and similar, and the δL distributions with AR and particles radii indicate that the aerosol shapes of MINM and SSAM can have great impacts on the overall backscattering properties. The δL is relatively larger at large particle radii for these two aerosol types. For the spheroid model, higher δL are obtained when AR is in the range of 0.7–0.9 and particle radii are typically larger than 1.5 μm. For the cylinder model, higher δL are obtained when the AR near 0.5 or 2.0, and there is a δL trough when AR is close to 1.0 at different radii because the nonsphericity is not significant with this AR. Actually, there are multiple scattering during the transmission of laser in atmospheric aerosols, and the DoP may deviate the δL. In addition, as depicted in Fig. 1, the DoP of transmitted laser at different range bins can also change due to the scattering process in the former range bins, and thus the DoP of backscattered field from different range bins changes, and it is practical and reasonable to take the spatial information into consideration. In our simulation, the detection range is chosen as 10 km with each range bin of 500 m. Considering the simulation efficiency, the bulk scattering matrix in Eq. (8) is used, and the effectiveness of bulk scattering matrix is verified by experiments [30]. In the multiple scattering analyses, the photons may have too large attenuations to detect the aerosols properties at the range bin near 10 km when a fixed N0 is used. As a result, we adjust N0 dynamically with aerosol types and the backscattered intensities are assumed to be proportional to N0. The DoP of the backscattered field in soot aerosols along the detection path is shown in Fig. 4. As we can see, the DoP of the backscattered field decreases along the detection path, which suggests that the performance may be further deteriorated except for the power attenuation along the distance. In addition, the spherical particles have the largest DoP as shown in Fig. 4(b). The DoP decreases with the increase of deviation from sphere. To describe the DoP attenuation caused by nonspherical particles, we define the relative DoP as,

RD =

1 N

i=N i=1

DoPns (i R) , DoPs (i R)

(20) 307

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Fig. 3. The linear depolarization ratios under different shapes. The left and right subgraphs are for the results with spheroids and cylinders respectively. Results of soot, mineral aerosols (MINM and MINM) and SSAM are listed from top to bottom.

Fig. 4. The DoP of the backscattered field in nonspherical soot aerosols. (a) LPL and (b)CPL. N0 = 3.12×104cm−3; the size distributions are chosen form Table 4.

where the subscript ns and s represent the non-spherical and spherical particles, N is the total number of range bins. The RD represents the average DoP attenuation along the detection path. The minimum RD for soot is 95.71% (@AR = 0.5, cylinder) and 91.67% (@AR = 0.3, spheroid) for LPL. When the incident light is CPL, the minimum RD can be reduced further, which is 91.55% (@AR = 0.5, cylinder) and 83.85% (@AR = 0.3, spheroid). 308

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Fig. 5. The DoP of backscattered field in mineral aerosols. (a) and (b) for MIAM, N0 = 28.6 cm−3; (c) and (d) for MINM, N0 = 1608.3 cm−3. The legends in Fig. 5(c) are applicable to all the four subgraphs.

The backscattering properties of polarized laser in MINM and MIAM aerosols are also simulated and the results are shown in Fig. 5. The MIAM has relatively larger particles, and the shape parameters play a leading role in the depolarization process, as shown in Fig. 5(a) and (b). The MINM particles are much smaller than that in MIAM, which is more closer to the Rayleigh scattering, and the shape influence on the DoP of backscattered field is relatively lower as shown in Fig. 5(c) and (d). In MIAM, The spherical particles have the best DoP both for the LPL and CPL. For both MIAM and MINM aerosols, the LPL have higher DoPs. Moreover, larger particles have better scattering abilities and the required N0 can be smaller. The minimum RD for MIAM is 50.88% (@AR = 2.0, cylinder) and 51.18% (@AR = 0.7, spheroid) for LPL, and RD can be much lower with CPL, which is 6.46% (@AR = 0.5, cylinder)and 7.35% (@AR = 0.6, spheroid). The minimum RD for MINM is relatively stable and much higher which is 97.40% (@AR = 2, cylinder) and 95.97% (@AR = 0.7, spheroid) for LPL. When the CPL is used, the minimum RD changes slightly which is 97.21% (@AR = 0.5, cylinder) and 96.92% (@AR = 0.3, spheroid), which suggests the impact of shape is less significant. Similarly, the DoP properties in SSAM aerosols are calculated and shown in Fig. 6. The situations of LPL and CPL are also considered. The SSAM aerosols particles are relatively larger. The spherical particles have better DoP especially when the LPL is launched. The

Fig. 6. The DoP of the backscattered field in nonspherical SSAM aerosols. (a) LPL and (b) CPL. N0 = 108.4 cm−3. RH = 50%. 309

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Fig. 7. Relative scattering cross sections of different aerosols. (a) Cylinder; (b)Spheroids. The scattering properties of SSAM is calculated when RH = 50%.

minimum RD for SSAM is 84.42% (@AR = 2.0, cylinder) and 80.68% (@AR = 0.775, spheroid) for LPL. When the CPL is used, the DoP decreases, and the minimum RD is 65.99% (@AR = 2.0, cylinder) and 51.87% (@AR = 0.775, spheroid). We can see that the AR corresponding to the minimum RD changes with aerosol types. 3.3. The relative effective backscattered photon numbers in different aerosols Aerosol shapes can change the scattering cross sections, and we define the relative cross section to describe the deviations from the spherical assumption, which can be written as,

Cr =

Csca, b Csca, b sp

1.

(21)

The Cr of the four aerosol types under cylinder and spheroid models are shown in Fig. 7, which indicates that the mineral aerosols scattering abilities are obviously affected by AR. Despite the same CRI for MINM and MIAM, the Cr of these two aerosols have opposite trends. The scattering abilities of soot and SSAM are less sensitive to shapes, and the largest deviations are lower than 4% in Fig. 7(a) and (b). The non-spherical shapes will improve the scattering abilities for soot and MIAM aerosols in both cylinder and spheroid models and the Cr are higher when the non-sphericity is more significant. For the SSAM and MINM aerosols, the non-spherical particles have lower scattering abilities than spherical particles. Based on the N0 in Figs. 4–6, 〈Csca,b〉sps of soot, MINM, MIAM, SSAM are 4×10−6/ m, 1.02×10−4/m, 9.67×10−5/m and 1.0×10−4/m. Soot aerosols have the lowest scattering abilities. In heterodyne detection, both the DoP and the intensity should be involved in the performance analyses. In this paper, we mainly analyze the relative deviations from spherical assumptions. Considering our previous work [24], the effective backscattered photon numbers can be defined as, (22)

Ne (k, , P , R) = DoP(k, , P , R) N (k, , P , R),

where k is the four nonspherical aerosols types, ρ is AR, P is the SoP of incident light, N(k, ρ, P) is the backscattered photon numbers in the MC simulations. Considering the Ne deviations caused by nonspherical aerosols and Eq. (20), the shape fading factor can be defined as,

Nre (k, , P ) =

1 N

N i=1

Ne,ns (k, , P , i R) Ne,sp (k, , P , i R)

1,

(23)

where the subscripts of ns and sp are for nonspherical and spherical aerosols. The Nre with LPL are calculated and shown in Fig. 8. Fig. 8 shows the deviations of four typical nonspherical aerosols under the cylinder and spheroid models. The particle radii of MINM aerosols are the smallest, and both the DoP and backscattering intensities are similar to the Rayleigh scattering. Thus the variations of aerosol shapes has little influence on Ne. Among the two shape models, the maximum Nre for MINM is 2.6% (AR = 0.5, cylinder), and Nre is close to 0 at other shape parameters. For the other three aerosol types, the particle size ranges are larger than that of MINM, especially the SSAM aerosol, and the scattering of nonspherical particles will reduce the Ne. The reduction ranges for soot is within 6.78–20% (for cylinder) and 0–28.34% (for spheroid). Similarly, the variations of Nre for the SSAM and MIAM are much higher, and the maximum Nre for cylinder aerosols are acquired when the AR is near 1.1; for the spheroid aerosols, Nre increases with the growth of AR, and the maximum reduction of Ne for SSAM and MIAM are 18.73% (AR = 0.725,speroid) and 60% (AR = 2.0,cylinder) respectively. As we can see, for most aerosol types, the nonspherical aerosols scattering will reduce the heterodyne lidar performance. 310

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Fig. 8. Shape fading factors in different aerosols with LPL. (a) Cylinder; (b) spheroids.

In addition, the SoP of incident light also affects the properties of lidar returns. Given that the Ne is a function of AR and the SoP of incident light, we define the polarization fading factor as,

Pre (k , ) =

1 N

N i=1

Ne (k, , cpl, i R) , Ne (k, , lpl, i R)

(24)

where cpl and lpl represent the SoP of incident light. The polarization fading factors are calculated and shown in Fig. 9. The Pre for MINM is the largest and close to 1 for spheroids, which indicate the results with CPL and LPL are similar. For cylinders, the maximum Pre with CPL is 5.1% (AR = 0.5, cylinder) larger than that with LPL. For the other three aerosols, the minimum Pre can be as low as 13.2% (AR = 0.3, cylinder, MIAM), 64.77% (AR = 0.775,spheroid, SSAM) and 89.96% (AR = 0.3,spheroid, soot). The Pre is lower than 1 with most of AR values including the situation when AR = 1 in the spheroid model, which indicate that the detection with LPL is better for both nonspherical and spherical aerosols. 4. Conclusion The properties of heterodyne lidar echo in randomly oriented polydisperse non-spherical aerosols vary significantly with aerosol types and ARs. Based on the T-matrix, the scattering matrix, scattering cross section and extinction cross section are obtained with laser at 1.55 μm. Then the linear depolarization ratios δL are analyzed. In soot aerosols, the δL is relatively smaller and the peak values is 0.1266 (r = 0.63 m, AR = 0.475, spheroid); the peak δL for mineral aerosol and SSAM aerosols are much larger for spheroids, which can be larger than 0.6 and 0.8. For the cylindrical aerosols, there is a δL trough when AR is around 1.0 at different radii because the nonsphericity is less significant at this AR region. Considering the multiple scattering, the vector Monte Carlo simulations are conducted and verified. The DoPs and intensities of backscattered field are obtained in each range bin using the LPL and CPL, and there are reductions of DoP along the detection path for all the four aerosol types, which indicates the additional reductions of heterodyne lidar performances. The majorities of particles in MINM are relatively smaller, and the scattering abilities is close to the Raleigh scattering to some extent, and thus the DoP and intensity deviations of the backscattered field is less affected by aerosol shapes and the SoP of incident laser. The deviations of effective backscattered intensity caused by nonspherical shapes can be as low as 2.6% in MINM. The other three aerosols are more easily influenced by particle shape and SoP of incident light. The maximum deviations of effective backscattered photon numbers are 28.34% (soot), 18.73% (SSAM) and 60% (MIAM) when the emitted laser pulses are LPL.

Fig. 9. Polarization fading factors under different nonspherical parameters. (a) Cylinder; (b) spheroids. 311

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In addition, the polarization fading factor also defined and calculated, and the maximum deviations caused by the SoP of launched laser are 5.1% (MINM), 10.04% (soot), 35.28% (SSAM) and 86.8% (MIAM), and for most of the AR range, Pre is lower than 1.0, which indicates that the detection with LPL is better in both nonspherical and spherical aerosols. Based on the method in this paper, the scattering properties in different wavelength, humidities and shapes can be calculated further. The results in this paper will help determine the deviation ranges form the MC simulation that is based on the spherical assumption, which can be used in heterodyne lidar performance analyses. Acknowledgements This study is supported by the Natural Science Foundation of Anhui Province, China (Grant No. 1808085QF200). References [1] S. Wu, B. Liu, J. Liu, X. Zhai, C. Feng, G. Wang, H. Zhang, J. Yin, X. Wang, R. Li, Wind turbine wake visualization and characteristics analysis by doppler lidar, Opt. 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