A RECIPE TO OBTAIN LIDAR POLARISATION CALIBRATION PARAMETERS G, H AND K

*Email: Joelle.c.buxmann@metoffice.gov.uk ABSTRACT The accuracy of the polarisation calibration is of prime importance for aerosol classification using lidars. We present a detailed description how to obtain the calibration parameters introduced in 2016 [1] accounting for various effects of non-ideal optics, lasers and atmospheric conditions. We find that crucial parameters such as the rotation angle of the plane of polarisation of the Laser (RotL) as well as the degree of linear polarisation (DOLP) influence the volume linear depolarisation ratio significantly.


INTRODUCTION
In a paper on the effects of polarising optics on lidar signals and the polarisation calibration [1] a set of general analytical equations has been introduced; a major change to the way of calibration used before [2]. This can be applied to a large variety of lidar systems, and will be discussed for one specific lidar within the Met Office Volcanic Ash (VA) network [3,4] in the following. Using this new approach, the linear volume depolarisation ratio δV can be expressed as: The parameters G and H account for effects without and with atmospheric polarisation in the reflected (R) and transmitted (T) channel (explicit definitions can be found in [1]), respectively. The measured range dependent signal ratio is here defined as: The calibration factor η can be determined from the gain ratio η*, which we get with a Δ90calibration, and the theoretical correction K of the gain ratio.

METHODOLOGY
In order to calculate the GR, GT, HR, HT we need to describe the optical set up of the lidar using the Müller-Stokes formalism. The multiplication of Müller matrices is in direction of the propagation of light. In essence our lidar can be represented by the set up as shown in Figure 1.

Application and calculation of the G, H, K parameters with an example
We will now describe how to obtain the needed parameters on the example of the datasheets provided for the Camborne lidar of the VAnetwork [3,4]. The same approach can be applied to other lidar systems.
The correction parameters G, H and K can be easily calculated using a Python code developed by V. Freudenthaler. The latest official version of the open source code is available from https://bitbucket.org/iannis_b/atmospheric_lidar _ghk. The code works with Python 2.x and 3.x. The code reads the lidar system parameters from an input file (as downloaded from bitbucket and edited for a specific lidar). Therefore, we will use the same nomenclature as in the input parameter file for easy application to future studies. The input parameters X are indicated in italic, their uncertainties as dX, and the number of steps in the error calculation as nX. In order to adapt the optical input parameters for our own lidar we need the optical performance values for each element. We define the plane of linear polarisation of the laser as the reference plane of our optical system.

Polarizing beam splitter and cleaning polarizing sheet filters
We start from the left in figure 1 with the PBS transmission TS and TP in the planes perpendicular (S) and parallel (P) to the incidence plane, respectively, which are given by the manufacturer for 355nm as: We use high quality polarisation filters behind the transmitted and reflected path of the PBS, to minimize the cross talk. Their extinction ratio ERaT and ERaR are given by the manufacturer: ERaT, dERaT, nERaT = 0.00014, 0.00002, 1 ERaR, dERaR, nERaR= 0.00014, 0.00002, 1 The Rotation RotaT of the pol.-filter behind the transmitted path is 0°+/-2° and RotaR behind the reflected path is 90°+/-2° with respect to the incidence plane of the PBS.

Receiver optics including telescope
The diattenuation parameter is defined as D = (I -I ) / ( I + I ) (see [1]

Calibrator
We use a mechanical rotator before the receiver optics, which is described by the calibrator and location parameters: LocC = 3 ; TypeC = 1

Emitter optics
For two rotated retarding linear diattenuators (in our case two steering mirrors, one before and one after the beam expander) at 0° and 90° with respect to incident plane, we get for the combined diattenuation (DiE), transmittance (TiE) and retardance (RetE) (adapted from [1], eq. 10.10.10): Both highly reflective mirrors were custom designed (Laseroptik GmbH) so that the phase shift is zero at 355 nm and the reflection (here referred to as TiE > 0.95). The polarisation state, when the laser beam hits the incident plane, is considered as s-polarisation. Because the mirrors are cross aligned, their effects for DiE and RetE cancel each other (DiE=RetE=0). The intensity transmittance is Tmax~0.97 for s-polarisation and Tmin~0.93 for p-pol. (see Figure

RESULTS for G, H and K
We can now add the values from above in the input file for the Python script ver. We further asses the effect of the laser's DOLP and RotL on δV shown in figure 4. We find a δV of 0.0298 for the best case scenario (RotL=0, DOLP=1), which also is in agreement with the former way of calibration [2]. We find that δV ranges between 0.0181-0.0298 for RotL between 4•-0• and DOLP between 0.99-1, respectively and δV =0.0283 assuming DOLP=0.997, RotL=0•, as given by the manufacturer. This means an added uncertainty of up to -0.0102 to +0.0015 of the δV in this case.

CONCLUSION
We show how to practically apply the calibration method as described in [1]. We find, that additional assessment of values such as the rotation angle of the plane of polarisation of the Laser RotL as well as the DOLP need to be measured or additional uncertainty needs to be added to the calculated δV.