MULTICHANNEL POLARIZATION LIDAR MEASUREMENTS OF AEROSOLS AND CIRRUS CLOUDS

In this paper we report using a 6-channel polarization detector to measure optical properties of aerosols and clouds. The polarization lidar system is designed to measure Stokes vectors and Mueller matrices from back-scatterings of air, aerosols and clouds by using several polarizers of setting at different angles, and a retarder to measure circular polarization. The 4 components Stokes vectors of the scattering media are constructed and a case of tropopause cirrus cloud and stratospheric aerosols are measured with the Mueller matrix derived.


INTRODUCTION
Polarization lidar system is an important tool to measure aerosols and clouds by deriving the depolarization ratios based on two component parallel and perpendicular polarization states. However, as demonstrated a century ago, the 4 component Stokes vector is a more complete description of the polarization state which can be used to derive the Mueller matrix to provide information about optical properties of various subjects. Stokes vector consists of four parameters S=[I, Q, U, V] T defined in terms of the components of the electric fields of the light waves. Here a vector A T indicates the transpose of the A.  The components of T are determined by the polarization filters and the retarder of the lidar system as will be describe later.
The Mueller matrix Mc describes the state of the cloud which consists of randomly oriented particles, As shown in previous works [3][4][5] the Mueller matrix for randomly oriented particles can be simply shown as EPJ Web Conferences 237, 07020 (2020) ILRC 29 https://doi.org/10.1051/epjconf/202023707020 which can be further simplified as: where d is the depolarization ratio [3][4][5].

The lidar system
The lidar system include a 532 nm laser and a Cassegrain telescope of 20 cm diameter. Signals are measured by the detector system which consists of a photomultiplier tube (Hamamatsu R9880) and filter systems which include polarizers and interference filters (0.3 nm FWHM at 532 nm). Signals are treated by a transient recorder (Licel system) with a spatial resolution of 7.5 m. Each profile is accumulated for 30-60 sec.
The lidar system has been described in previous papers [1][2]. The signals are accumulated 1 min for each channel and takes about 5 min for a complete measurements of 5 channels.
The 5 polarization channels are defined by using linear polarizers at orientations of 0 o (#6), ±45 o (#3,4), 90 o (#5), which are arranged by comparing their intensities with the laser emission whose polarization direction exiting to the sky is set by using a half-wave plate. The 532 nm filter is put in front of the polarizing filter system to receive the laser backscattering light. The sixth channel is a dark channel to check the background. Signals are recorded by a multichannel analyzer LICEL system. The telescope and photomultiplier system are considered as mainly constant in response to any polarizer.
We assume Sout=[I0,Q0,U0,V0] as the Stokes vector of the back-scattered signals from the cirrus clouds. As shown previously, the measurements produce another Stoke vector T: The combined Mueller matrix for the detector as Mx=M1(T) M2(I) ,with M2 and M1 the Mueller matrices for the retarder and linear polarizer at a specific angle (T=0,90,45). When the measurement involves only linear polarizer without retarder (such as channels 1 and 2) we have I=0.

T=M1M2Sout
(3) For example, M1= 1 0 0 0 The four component of T=[To,T1,T2,T3] are measured by the lidar system as shown in Fig. 1. The 1st term, To is the most interesting since it is the intensity term [6]. We can derive T0 for a liner polarizers at angle T and a retarder of phase I S/2. After the expansion, we get: To(TI)= (1/2)(I0+Q0 cos 2T + U0 sin2 T cos I + V0 sin 2T sin I) where T is the orientation of the linear polarizer. Again, I =0 means without the retarder. To(TI) is the signals read from the transient recorder shown in Fig. 2. Therefore, a complete determining of the Stoke Vector of Sout can be made by a few measurements with a quarter wave plate and a linear polarizer setting at 0 o , 90 o , ±45 o . Normally, we will normalize these quantities to set Io=1. So the measurements are relative. In order to determine a3, b4, we have to use circular polarization as the light source.

a2-a3+a4=1
For atmospheric application, the circular polarization is very small as shown in Hansen and Travis [7]. In practice, the 4th row and column can be ignored with Mc left as 3x3 matrix. Under this condition, we find a3=a2~0.5. So the Mueller matrix of the 16 km cloud is: