Accuracy of Linear Depolarisation Ratios in Clean Air Ranges Measured with POLIS-6 at 355 and 532 NM

Linear depolarization ratios in clean air ranges were measured with POLIS-6 at 355 and 532 nm. The mean deviation from the theoretical values, including the rotational Raman lines within the filter bandwidths, amounts to 0.0005 at 355 nm and to 0.0012 at 532 nm. The mean uncertainty of the measured linear depolarization ratio of clean air is about 0.0005 at 355 nm and about 0.0006 at 532 nm.


INTRODUCTION
Large errors of the linear depolarization ratio (LDR, δ) result from the use of uncertain atmospheric reference values in the relative calibration of the two polarization channels [1]. Several instrumental calibration techniques have been proposed to overcome that, which still can have large uncertainties due to an unknown state of polarization of the emitted laser beam, polarizing optics, rotational misalignment of the optics and of the calibration device, and cross talk of the polarizing beam splitter [2] . In this work we show how those uncertainties have been minimized in the design of POLIS-6, which is a six-channel upgrade of POLIS [3], developed and manufactured by the Meteorological Institute of the LMU in Munich, Germany, in 2013. Furthermore, we show the validation of the measurement accuracy by means of a comparison with theoretically well known LDRs from air molecules.

LIDAR SETUP AND SPECIFICATIONS
POLIS-6 is a truly portable lidar system (see Fig.  1) with specifications shown in Tab. 1. It is operated on a tripod and can be pointed to any direction. The desired low distance of full overlap of 70 m requires a large field of view of ±2.5 mrad (tilted slit [4]) and an optimized optical design to keep the optical paths in the receiving optics short. The laser is directly mounted on the rigid telescope tube (see Fig. 1) without any emitter optics, which avoids possible elliptical polarization of the emitted laser beam. The pointing is achieved with a high precision and very stable two-axis tilt mount and controlled with a camera module in place of one of the detector modules.
The receiving optics has been selected to yield minimal diattenuation |D O | with total values  Fig. 1) is used for the relative calibration of the polarization channels. The retardation of the optics can be neglected because the rotational alignment of the receiving optics module can be determined and adjusted with better than 0.5° precision with respect to the laser polarization (see day-to-day variability after 25.06. in Fig. 5).  Inside of the receiving optics module of POLIS-6 with the top cover removed. The telescope mount is at the image bottom, indicated by the red circle, which also provides the rotation with the fixed ±45° and 0° positions of the module with respect to the laser/telescope assembly (see Fig.1). The green circle indicates the rotation mount for exact 0° adjustment. At the right and top the detector modules are protruding.

THEORY
For the comparison of the measured LDR of clean air ranges with the theoretical values, the rotational Raman lines (RRL) within the bandwidth of the interference filters have to be considered for the calculation of the theoretical molecular (air) LDR. This depends on the bandwidth (BW) and center wavelength (CWL) of the interference filter (IFF) and on the clean air temperature, but also on the exact laser wavelengths. The latter are usually not measured by the laser manufacturers. The fundamental laser wavelength depends, among others, on the temperature of the Nd:YAG rod [5], which we assume for a first estimation to be in the range between 25°C and 85°C. Assuming that the wavelength in air is 1064.15 nm at a rod temperature of 300 K [6] and shifts about +0.005nm/K [5], the second and third harmonics are between 532.07 and 532.22, and 354.71 and 354.81 nm, respectively. While we have measured transmission values for the used 355 nm IFF, we use the specified CWL and BW of the 532 nm IFF (Tab. 1) to calculate the typical two-cavity IFF transmission shape (Fig. 3).  Table 1 for BW and CWL). We calculate the backscatter coefficients of individual RRLs of N 2 and O 2 (Fig. 3) at different air temperatures according to [7,8] and weight them with the IFF transmissions for the sum of their LDRs (see Fig. 4).

Figure 4
Theoretical LDRs of clean air (with 385 ppmv CO 2 and 0% RH) over air temperature including the rotational Raman lines of O 2 and N 2 within the used IFF bandwidths and considering laser wavelength ranges for rod temperatures between 25°C and 85°C. The red rectangles show the considered variability of air temperature and laser wavelength, and the red arrow the resulting uncertainty of the theoretical LDR.

MEASUREMENTS
POLIS-6 was first deployed during a one-month field campaign in 2013. At several nights, measurements of assumed clean air ranges above the aerosol layers were possible with sufficient high signal-to-noise ratios after temporal averaging. With temporal close ∆90°-calibration measurements it was possible to determine the calibration factor and from that the calibrated signal ratio δ* [2,3] with an accuracy better than ±2%, and to estimate the rotation ε between the plane of polarization of the laser beam and the receiving optics [2] (see Fig. 5). The corrected LDRs (δ) calculated from Eq. (1) [2] are shown in Fig. 6 together with the error bars, derived with Eq. (2).

Dd
Dd eDe After initial system adjustments until 25.06.13, the uncertainty due to ∆ε becomes negligible compared to ∆δ*; the latter mainly stems from signal noise.   between the laser rotation at 355 and 532 is about 0.5° over the whole campaign, with a variability well explainable by signal noise.

CONCLUSIONS
We show that it is possible to measure the linear depolarization ratio of clean air with a lidar with high accuracy, if polarizing optics in the emitter and receiver (before the polarizing splitter) are avoided, if the cross talk of the polarizing splitter is suppressed, if the simple but high accurate ∆90°-calibration with mechanical rotation is used, and if the plane of the laser polarization is well aligned with the incidence plane of the receiving optics. At this accuracy level it becomes necessary to include in the calculation of the molecular linear depolarization ratio the influence of the rotational Raman lines within the interference filter bandwidth and to account for the uncertainty of the laser wavelengths due to the unknown laser rod temperature. Furthermore, we find a difference in the rotation of the plane of polarization of about 0.5° between the second and third harmonic of the employed laser, which might be caused by the third harmonic generator, because this is the only optical component between the second harmonic generator and the ∆90°-calibrator. While the difference between the measured and theoretical LDR at 355 nm is only about 0.0005 with a mean measurement uncertainty in the same range, the difference is 0.0012 at 532 nm with an uncertainty of about 0.0006. Possible reasons are residual aerosol in the assumed clean air range, or/and elliptical polarization of the 532 nm due to the third harmonic generator.