Visible polarization characteristics of airport ground material based on BPDF correction
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摘要:
为研究典型机场地物材质的偏振特性，并为偏振成像仪器研制提供所需的理论模型，本文以P-G模型为基础，构建新的二向偏振分布函数(BPDF)模型。本文分析了当大角度光线入射时阴影遮蔽效应更严重的问题，创新性地提出将镜面反射点等效为三维球体的解决方案，并利用球面三角学公式对阴影遮蔽函数进行优化。同时，考虑到不同目标具有独特的色散特征，本研究引入色散模型代替受波长影响的传统二向反射分布函数(BRDF)参量，综合考虑漫反射、体散射，构建了新的BPDR模型。通过多角度BRDF实验，与基于动态TS算法的模型参量拟合，得到典型机场地物材质的线偏振度与模型六参量拟合结果。经过多组测试取均值，得到拟合参量中均方根粗糙度参量的测试值，验证了修正BPDF模型的有效性。在仿真分析阶段，以均方根误差(RMSE)作为精度评价指标，将修正BPDF模型、对照模型、实验结果三者进行对比，系统分析了探测角、方位角、入射角对偏振特性的影响。结果显示：4种实验目标在探测角变化时，修正模型的精度较对照模型分别提升了4.39%、4.00%、4.17%、5.26%，且在大探测角下的RMSE仍小于0.05，充分证明修正后模型可用于机场地物目标等粗糙材质的偏振特性研究。此外，通过仿真分析拟合参量对目标偏振特性的影响，发现线偏振度与折射率呈正比关系，而与表面粗糙程度呈反比关系。实验和仿真证明了修正BPDF模型的准确性，为机场地物目标的偏振特性研究提供了思路。
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关键词:
- 偏振特性 /
- 镜面反射 /
- 色散 /
- 遮蔽效应 /
- 二向偏振分布函数(BPDF)
Abstract:This paper provides a theoretical model for studying typical airport ground materials’ polarization characteristics which is required for the development of polarization imaging instruments. First, serious shadow masking effects were analyzed based on the P-G model. These effects occur when light is incident at a large angle. Then, the shadow masking function was optimized using the spherical trigonometry formula. This optimization equates the specular reflection point to a three-dimensional sphere. Due to the unique dispersion characteristics of different targets, a new bidirectional polarization distribution function (BPDF) model was introduced to replace the traditional BRDF parameter affected by wavelength and body scattering. The new BPDF model integrates diffuse reflection and body scattering. In the experimental stage, the accuracy of the line polarization degree was calibrated. The line polarization degree of typical airport ground material was fitted with model parameters. This fitting was based on the dynamic TS algorithm through multi-angle BRDF experiments. The fitting model's six parameters were used to obtain the root mean square roughness parameter. This process verified the validity of the modified BPDF model. In the simulation stage, the root mean square error (RMSE) was used as the accuracy index. The modified BPDF model, control model, and experimental results were compared to analyze the effects of detection, azimuth, and incidence angles on polarization characteristics. The accuracies of the four experimental targets improved by 4.39%, 4.00%, 4.17%, and 5.26% compared with the control model. The RMSE was less than 0.05 for large detection angles. This allows the modified model to study polarization characteristics of rough materials like airport ground targets. Finally, the effect of fitting parameters on polarization characteristics was simulated. Results show that line polarization is positively related to the refractive index and inversely related to the surface roughness. The accuracy of the modified BPDF model is thus proved. This provides ideas for studying polarization characteristics of airport ground targets.
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图 1 散射三分量的几何关系图
Figure 1. Geometric relationship between the three scattering components
图 6 相对方位角为180°，入射角分别为20°、40°、60°时，探测角与线偏振度的关系
Figure 6. Relationship between detection angle versus line polarization when the relative azimuth is 180° and incident angles are 20°, 40°, and 60°
图 7 入射角为60°下，
$2{\text{π }}$ 范围内线偏振度仿真结果（左侧为对照模型，中间为修正后BPDF模型，右侧为实验测量值）；Figure 7. Simulation results of line polarizability in the range of
$2{\text{π }}$ at an incidence angle of 60° (left: control model; middle: modified BPDF model; right: experimental measurements)
图 8 入射角和探测角均为60°时，修正模型与实验结果对比图
Figure 8. Comparison between the modified model and experimental results when incident angle and detection angle both are 60°
图 9 探测角为60°、相对方位角90°～270°范围内，入射角分别为10°、20°、30°、40°、50°、60°的仿真结果
Figure 9. Simulation results when incidence angles are 10°, 20°, 30°, 40°, 50°, and 60° in the range of detection angles of 60° and relative azimuth angles of 90° to 270°
图 10 相对方位角为180°、探测角为60°时，4种目标的入射角与线偏振度的关系。(a) 45#钢板；(b) A3铁板；(c) 硅酸盐水泥；(d) 环氧树脂
Figure 10. Relationship between incident zenith angle and DOLP for a range of relative azimuth angles of 180° and detection angles of 60°. (a) 45# steel plate; (b) A3 iron plate; (c) portland cement; (d) epoxy resin
图 11 均方根粗糙度
$\delta $ 分别为0.1，0.3，0.5，0.7和0.9时，4种材料的线偏振度随探测角的变化情况Figure 11. Relationship between DOLP of four targets and detection angle when
$\delta $ are 0.1, 0.3, 0.5, 0.7 and 0.9
图 12 当折射率n分别为1.1，1.3，1.5，1.7和1.9时，线偏振度随探测角的变化情况
Figure 12. Relationship between DOLP and detection angle for four kinds of objectives when n are 1.1, 1.3, 1.5, 1.7, and 1.9
表 1 DOLP标定结果
Table 1. DOLP calibration results
Polarized light (DOLP) Incident light (DOLP) Emerging light Maximum error (%) 0° 1 0.966 3.4% 45° 1 0.975 2.5% 90° 1 0.972 2.8% 135° 1 0.969 3.1% 
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表 2 参量拟合结果
Table 2. Fitting results of parameters
材料 ${\varepsilon _{\text{i}}}$ ${\varepsilon _{\text{r}}}$ $\delta/\mu {\mathrm{m}}$ ${\delta ^*}/\mu {\mathrm{m}}$ ${{{k}}_{\rm{s}}}$ ${{{k}}_{\rm{m}}}$ ${{{k}}_{\rm{v}}}$ 45#钢板 4.56 −2.54 0.188 0.195 0.902 0.045 0.003 A3铁板 14.14 −9.55 0.302 0.306 0.521 0.334 0.015 硅酸盐水泥 1.37 1.48 0.318 0.328 0.311 0.327 0.009 环氧树脂 2.69 −1.62 0.120 0.122 0.773 0.202 0.031
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表 3 探测角变化,目标仿真值与实测值的均方根误差
Table 3. Root mean square error of simulated and measured DOLP values of four targets for different detection angles
材料 RMSE1 RMSE2 精度提升/% 45#钢板 0.0634 0.0195 4.39% A3铁板 0.0514 0.0114 4.00% 硅酸盐水泥 0.0859 0.0442 4.17% 环氧树脂 0.0677 0.0151 5.26%
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表 4 入射角变化,仿真值与实测值的均方根误差
Table 4. Root mean square error of simulated and measured DOLP values of four targets when incidence angle changes
材料 RMSE1 RMSE2 精度提升/% 45#钢板 0.0675 0.0214 4.61% A3铁板 0.0583 0.0148 4.35% 硅酸盐水泥 0.0573 0.0264 3.09% 环氧树脂 0.0681 0.0230 4.51%
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