Design and optimization analysis of imaging system of polarized skylight pattern of full polarization
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摘要: 全偏振成像能够获取目标更为丰富的信息, 在目标探测、大气特性研究和医学诊断等领域具有广阔的应用前景. 为了实现大视场天空区域全偏振信息的快速获取, 设计了一套全偏振大气偏振模式成像系统; 针对因系统传输矩阵“性态”的不同使得求解的目标Stokes矢量存在误差的问题, 通过分析传输矩阵的特性并建立目标函数, 将传输矩阵的优化转化为目标函数在多组条件下的求解, 确定了最优系统传输矩阵; 并对系统的四分之一波片的延迟量、偏振片的消光比以及传输矩阵进行标定. 通过开展优化前后偏振信息的对比实验, 结果表明: 优化后偏振角误差较优化前降低了10%以上; 偏振度和线偏振度中最大偏振度带的误差和中性区域的误差较优化前也有不同程度的下降. 在此基础上开展了外场全偏振信息测量实验, 结果表明系统满足设计要求, 能够有效地获取天空全偏振信息.Abstract: Full polarization imaging can obtain more information about target, which has a broad application prospect in the target detection, researches of atmospheric characteristics, and medical diagnosis. This paper develops an imaging system of polarized skylight pattern of full polarization for obtaining the information about full polarization rapidly. Meanwhile, aiming at the problem that the error of the light intensity image obtained by the system due to the different “behavior” of the system transmission matrix is brought into the solution of the target Stokes vector, this paper analyzes the condition number and determinant of the system transmission matrix. Firstly, an objective function is established by combining the three sets of condition numbers and the determinant. Therefore, the problem of solving the optimal transmission matrix is transformed into a multi-condition extremal problem. And then the objective function is minimized to determine the optimal angle of the transmission matrix when the 1 norm condition number, 2 norm condition number and ∞ norm condition number reach the minimum value and the determinant reaches the maximum value. In addition, in order to improve the measurement accuracy, the delay components of quarter wave plate, extinction ratio of polarizer, and the transmission matrix of the system are calibrated. Optimization contrast experiment and outfield experiment are performed. The entropy, mean, and standard deviation are used to quantify the optimized results of the angle of polarization, degree of polarization, and degree of linear polarization. ∆Aop is defined as the difference in absolute value of angle of polarization between the two sides of the symmetry axis to verify the optimization performance of angle of polarization. Experimental results show that the polarization angle error after optimization is reduced by more than 10% compared with that before optimization; the error of the band of maximum polarization and the error of the neutral zone in the degree of polarization and linear polarization also decline to different degrees compared with before optimization. On this basis, an experiment on measuring external field full polarization information is carried out. The results show that the system meets the design requirements and can effectively obtain the sky full polarization information.
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图 3
${{{M}}_{{\rm{tran}}}}$ 的$1/{\rm{Cond}}$ 与Det变化趋势 (a)$1/{\rm{Con}}{{\rm{d}}_1}$ 变化趋势; (b)$1/{\rm{Con}}{{\rm{d}}_2}$ 变化趋势; (c)$1/{\rm{Con}}{{\rm{d}}_\infty }$ 变化趋势; (d)$Det$ 变化趋势Figure 3. The change trend of
$1/{\rm{Cond}}$ and Det of the${{{M}}_{{\rm{tran}}}}$ : (a) Change trend of$1/{\rm{Con}}{{\rm{d}}_1}$ ; (b) change trend of$1/{\rm{Con}}{{\rm{d}}_2}$ ; (c) change trend of$1/{\rm{Con}}{{\rm{d}}_\infty }$ ; (d) change trend of Det.
图 5 优化前后偏振信息对比 (a)−(d) 优化前Aop, ∆Aop, Dop和Dolp; (e)−(h) 优化后Aop, ∆Aop, Dop和Dolp
Figure 5. Comparisons of polarization information before and after optimization: (a)−(c) Aop, ∆Aop, Dop and Dolp before optimization; (d)−(f) Aop, ∆Aop, Dop and Dolp after optimization.
图 6 优化前后Dop, Dolp的BMP和NZ对比 (a)−(d) 优化前Dop, Dolp的BMP和NZ; (e)−(h) 优化后Dop, Dolp的BMP和NZ
Figure 6. Comparisons of BMP and NZ of Dop and Dolp before and after optimization: (a)−(d) BMP and NZ of Dop and Dolp before optimization; (e)−(h) BMP and NZ of Dop and Dolp after optimization.
图 7 目标天空区域光强图与偏振模式分布结果 (a) 偏振光强图; (b) Aop; (c) Dop; (d) Dolp; (e) Docp; (f) I分量图; (g) Q分量图; (h) U分量图; (i) V分量图
Figure 7. The light intensity map and polarization mode distribution results of the target sky area: (a) Polarization intensity diagram; (b) Aop; (c) Dop; (d) Dolp; (e) Docp; (f) I component diagram; (g) Q component diagram; (h) U component diagram; (i) V component diagram.
表 1 最大Det、最小Cond与β对应表
Table 1. Corresponding table of maximum Det, minimum Cond and β.
条件数(Cond) 行列式(Det) 角度(β0, β1,
β2, β3)Cond1 8.6084 0.0923(最大) Det: (5°, 45°, 120°, 155°) Cond2 3.4864 Cond∞ 7.837 Cond1(最小) 7.9448 0.0814 Cond1: (0°, 30°, 115°, 150°) –0.0814 Cond1: (25°, 60°, 90°, 120°) Cond2 4.0092 — — Cond∞ 7.0859 — — Cond1 8.4653 — — Cond2(最小) 3.3381 –0.0919 Cond2: (35°, 70°, 100°, 135°) Cond∞ 7.791 — — Cond1 8.5767 — — Cond2 3.4563 — — Cond∞(最小) 6.2275 0.0911 Cond∞: (0°, 40°, 115°, 150°) 
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表 2 系统传输矩阵标定结果
Table 2. Calibration results of system transmission matrix
QWP旋转角度 m11 m12 m13 m14 5° 0.500 –0.44 –0.0775 0.225 10° 0.500 –0.377 –0.137 0.299 40° 0.500 0.0102 0.0577 0.497 45° 0.500 0.001 0.144 0.479 120° 0.500 –0.0574 –0.0994 –0.487 125° 0.500 –0.00975 –0.0268 –0.499 155° 0.500 –0.269 0.32 –0.274 160° 0.500 –0.352 0.295 –0.198
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表 3 优化前后∆Aop数据离散度对比
Table 3. Comparisons of data dispersion of the ∆Aop before and after optimization.
Index 熵 均值 标准差 优化前 优化后 优化前 优化后 优化前 优化后 ∆Aop 1.996 1.7956 4.9553 4.2633 27.7036 24.709
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表 4 优化前后BMP的数据离散度指标对比
Table 4. Comparisons of data dispersion index of BMP before and after optimization.
Index 熵 均值 标准差 优化前 优化后 优化前 优化后 优化前 优化后 $\Delta {\rm{Do}}{{\rm{p}}_{{\rm{BMP}}}}$ 2.6884 2.5550 0.7496 0.7252 0.0476 0.0359 $\Delta {\rm{Dol}}{{\rm{p}}_{{\rm{BMP}}}}$ 2.6933 2.5564 0.7508 0.7256 0.0481 0.0361
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表 5 优化前后NZ数据离散度指标对比
Table 5. Comparisons of data dispersion index of NZ before and after optimization.
Index 熵 均值 标准差 Poa 优化前 优化后 优化前 优化后 优化前 优化后 优化前 优化后 $\Delta {\rm{Do}}{{\rm{p}}_{{\rm{NZ}}}}$ 1.5359 1.5141 0.0446 0.0413 0.0246 0.0222 31.9377 35.3431 $\Delta {\rm{Dol}}{{\rm{p}}_{{\rm{NZ}}}}$ 1.5285 1.5085 0.0441 0.0409 0.0245 0.0223 32.8158 35.9437
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