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摘要: 增益比定标误差是影响偏振激光雷达退偏比精度主要的因素之一，观测前必须进行准确的增益比定标。本文分析了现存多种增益比定标方法的基本原理并通过实验对比了+45°法、±45°法、∆45°法、旋转拟合法与退偏器法等增益比定标方法在实践中的定标准确性与优缺点。实验结果表明：∆45°法、±45°法与旋转拟合法在对准偏失角较小的情况下定标相对准确，但±45°法与旋转拟合法操作较为繁琐。+45°法在无对准偏失角的情况下定标误差仍较大。退偏器法操作最简便，但会受到非理想退偏器的制约。通过理论与实验的对比，本文给出了增益比定标方法的最佳选择，即在一般情况下采用∆45°法定标，在有高精度退偏器的情况下采用退偏器法定标。Abstract: Gain ratio calibration error is one of the most significant factors affecting the accuracy of a polarization lidar depolarization ratio. This paper analyzes the basic principles of various existing gain ratio calibration methods and compares the advantages and disadvantages of the +45° method, ±45° method, ∆45° method, rotation fitting method and pseudo-depolarizer method in practice though experiments. Results show that: the ∆45° method, ±45° method and rotation fitting method are relatively accurate when the misalignment angle is small, but the operation of the ±45° method and rotation fitting method are more complicated. The +45° method still has a large calibration error without a misalignment angle. The pseudo-depolarizer method is the easiest to operate, but it is restricted by a non-ideal pseudo-depolarizer. Through comparison of theory and experiment, this paper provides a suggestion for the best choice of gain ratio calibration method. It is recommended that the ±45° method be used for calibration with a half-wave plate, and the pseudo-depolarizer method be used for calibration with a high-precision depolarizer.
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Key words:
- polarization lidar /
- gain ratio /
- calibration /
- depolarization ratio
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图 1 偏振激光雷达系统基本原理与结构图
Figure 1. Basic principle and structure diagram of polarization lidar system
图 2 +45°法原理图。(a)半波片旋转之前；(b)半波片旋转+45°之后
Figure 2. Schematic diagram of +45° method. (a) Before HWP rotation. (b) After HWP rotation by +45°
图 3 ±45°法原理图。(a)半波片旋转之前；(b)半波片旋转+22.5°之后；(c)半波片旋转−22.5°之后
Figure 3. Schematic diagram of ±45° method. (a) Before HWP rotation. (b) After HWP rotation by +22.5°. (c) After HWP rotation by −22.5°
图 4 ∆45°法原理图。(a)半波片旋转之前；(b)半波片旋转45°之后
Figure 4. Schematic diagram of ∆45° method. (a) Before HWP rotation. (b) After HWP rotation by 45°
图 7 五种定标方法相对误差随对准偏失角的变化曲线。其中绿色圆圈，蓝色三角，红色方块，紫色五角形与黄色菱形分别代表+45°、±45°、∆45°、旋转拟合与退偏器法
Figure 7. Curves of the relative errors of the five calibration methods changing with the misalignment angle, where the green circle, blue triangle, red square, violet pentagon and orange diamond represent ∆45°, ±45°, +45°, rotation fitting and pseudo-depolarizer methods, respectively
图 8 实际测量退偏比随对准偏失角的变化曲线图。其中蓝色圆圈代表在不同
$\theta $ 情况下测量的${\delta ^{\rm{*}}}\left( \theta \right)$ ，红色虚线代表拟合曲线，绿色虚线代表${\theta _{init}}$ Figure 8. Curve of the actually measured depolarization ratio changing with the misalignment angle, where the blue circle represents the
${\delta ^{\rm{*}}}\left( \theta \right)$ values measured at different$\theta $ angles, and the red and green dotted lines represent the fitting curve and${\theta _{init}}$ , respectively
图 9 退偏器法增益比定标结果。蓝色圆圈代表半波片在不同角度的情况下测量的增益比，红色虚线代表余弦函数多项式拟合曲线
Figure 9. Gain ratio calibration result of pseudo-depolarizer method. The blue circles represent the gain ratios measured at different misalignment angles, and the red dotted line represents the cosine polynomial fitting curve
图 5 旋转拟合法原理图。(a)半波片旋转之前；(b)半波片旋转
${\theta _{h,j}}$ 角之后Figure 5. Schematic diagram of rotation fitting method. (a) Before HWP rotation. (b) After HWP rotation by
${\theta _{h,j}}$ 表 1 Main parameters for polarization lidar system
Table 1. Main parameters for polarization lidar system
Main parameters Value Laser center wavelength 532 nm Laser energy 5 mJ Repetition frequency 10 Hz Pulse width 8 ns Diameter of telescope primary mirror 210 mm Field of view of telescope 1 mrad Focal length of telescope 2000 mm Filter bandwidth 3 nm 
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表 2 Calibration results of five methods at
${\theta _h}{\rm{ = }}{0^\circ }$ Table 2. Calibration results of five methods at
${\theta _h}{\rm{ = }}{0^\circ }$ Calibration method +45° ±45° △45° Rotation fitting Pseudo-depolarizer Calibration result 1.2185±0.1379 1.2679±0.1518 1.2676±0.1524 1.2716±0.0250 1.1977±0.1483
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