Sensitive and accurate dual-wavelength UV-VIS polarization detector for optical remote sensing of tropospheric aerosols

Abstract

An UV-VIS polarization lidar has been designed and specified for monitoring aerosols in the troposphere, showing the ability to precisely address low particle depolarization ratios, in the range of a few percent. Non-spherical particle backscattering coefficients as low as 5×10⁻⁸ m⁻¹⋅sr⁻¹ have been measured and the particle depolarization ratio detection limit is 0.6 %. This achievement is based on a well-designed detector with laser-specified optical components (polarizers, dichroic beamsplitters) summarized in a synthetic detector transfer matrix. Hence, systematic biases are drastically minimized. The detector matrix being diagonal, robust polarization calibration has been achieved under real atmospheric conditions. This UV-VIS polarization detector measures particle depolarization ratios over two orders of magnitude, from 0.6 up to 40 %, which is new, especially in the UV where molecular scattering is strong. Hence, a calibrated UV-VIS polarization-resolved time-altitude map is proposed for urban and free tropospheric aerosols up to altitude of 4 kilometers, which is also new. These sensitive and accurate UV-VIS polarization-resolved measurements enhance the spatial and time evolution of non-spherical tropospheric particles, even in urban polluted areas. This study shows the capability of polarization-resolved laser UV-VIS spectroscopy to specifically address the light backscattering by spherical and non-spherical tropospheric aerosols.

Appendices

Appendix A: Depolarization ratio δ ^∗ in the presence of a dichroic beamsplitter misalignment

In this appendix, we investigate the effect of a misalignment of the dichroic beamsplitter on the measured depolarization ratio δ∗. To parameterize the magnitude and the direction of this misalignment, we introduce an offset angle θ ₀ defined in Fig. 1(d) as the angle between the parallel laser linear polarization and the p-axis of the dichroic beamsplitter (defined with respect to the dichroic beamsplitter plane of incidence). The aim of this appendix is to derive the relationship between the measured depolarization δ ^∗ and the atmosphere depolarization δ as a function of the θ ₀ offset angle and the R _p, R _s-reflectivity coefficients of the dichroic beamsplitter, hence justifying Eq. (9).

The incident electric field E _i on the dichroic beamsplitter can be written in the two involved mathematical bases, namely the (//,⊥)-lidar polarization basis and the $(\mathrm{p,s})$-dichroic beamsplitter basis. As shown in Fig. 1(d), a θ ₀ rotation angle enables to change from one basis to the other. We projected the incident electric field vector E _i of backscattered photons on the $(\mathrm{p,s})$-polarization basis to express the electric field vector E _r of the reflected wave:

$$ \left[\begin{array}{c} E_{\mathrm{r},//}\\E_{\mathrm{r},\bot} \end{array}\right] \left[\begin{array}{c@{\quad}c} r_{\mathrm{p}}\cos(\theta_0) & -r_{\mathrm{s}}\sin(\theta_0)\\ r_{\mathrm{p}}\sin(\theta_0) & r_{\mathrm{s}}\cos(\theta_0) \end{array}\right] \left[\begin{array}{c} E_{\mathrm{i,p}}\\E_{\mathrm{i,s}} \end{array}\right]. $$

(13)

In this expression, we have introduced amplitude field reflectivity coefficients r _p and r _s defined as $r_{\mathrm{p}} = E_{\mathrm{r,p}}/E_{\mathrm{i,p}}$ and $r_{\mathrm{s}} = E_{\mathrm{r,s}} / E_{\mathrm{i,s}}$ where E _i,p and E _i,s are the components of E _i in the $(\mathrm{p,s})$-dichroic beamsplitter basis (the same notation is used for the reflected field E _r ). Then, by projecting the incident electric field in the (//,⊥)-polarization basis, Eq. (13) becomes:

(14)

where the m _DB -matrix relates the incident and reflected electric fields in the (//,⊥)-polarization basis and the two coefficients, $a = r_{\mathrm{p}} - r_{\mathrm{s}} = \sqrt{R_{\mathrm{p}}}- \sqrt{R_{\mathrm{s}}}$ and $b = r_{\mathrm{p}} =\sqrt{R_{\mathrm{p}}}$, are determined by the dichroic beamsplitter R _p, R _s-reflectivity coefficients. Hence, reflection (or symmetrically transmission) on the dichroic beamsplitter induces a rotation of the linear polarization state of the light. In the ideal case, the dichroic beamsplitter is vertical, so that the p-axis is horizontal and θ ₀ is π/2. If we exchange the //- and ⊥-polarization channels, θ ₀ is then 0. In both cases (θ ₀=0 or π/2), the m _DB -matrix is diagonal so that no cross-talk is induced. To derive the measured depolarization ratio δ ^∗ as a function of δ, we now introduce intensities proportional to the square of the electric field. Hence, Eq. (14) can be written for laser intensities vectors I _r and I _i . By removing proportionality constants (which disappear in the δ ^∗-calculation), we obtain:

(15)

by noting that the (//,⊥)-polarization basis is orthogonal. As expected, the M _DB -matrix is diagonal in the absence of offset angle θ ₀ (i.e. if θ ₀=0 or π/2). By noting that δ ^∗=I _r,⊥/I _r,// while δ=I _i,⊥/I _i,//, we obtain the following relationship between δ, δ ₀ and θ ₀, which is identical to Eq. (9):

$$ \delta^* =\frac{a^2\cos^2\theta _0\sin^2\theta _0+\delta _0(b-a\cos^2\theta _0)^2}{(b-a\sin^2\theta _0)^2+\delta _0a^2\cos^2\theta _0\sin^2\theta _0} $$

(16)

where the two coefficients, $a = r_{\mathrm{p}} - r_{\mathrm{s}} = \sqrt{R_{\mathrm{p}}}- \sqrt{R_{\mathrm{s}}}$ and $b = r_{\mathrm{p}} =\sqrt{R_{\mathrm{p}}}$, are determined by the dichroic beamsplitter R _p, R _s-reflectivity coefficients.

Appendix B: Notation and abbreviations used

To ease the reading, the notation and abbreviations used in the article are defined in Table 3.

Table 3 Notation and abbreviations used in the article