-
真实的海平面一般粗糙不平,海面油膜介质表面产生的偏振反射分布在整个观测空间。如果要完整表征整个目标表面的多角度反射和偏振特性,需要建立偏振双向反射分布函数(pBRDF)。图1为pBRDF模型示意图。
$${F_r}({\theta _s},{\varphi _s},{\theta _v},{\varphi _v}) = \frac{{\operatorname{d} {L_{rp}}({\theta _s},{\varphi _s},{\theta _v},{\varphi _v})}}{{\operatorname{d} E({\theta _s},{\varphi _s})}}$$ (1) 式中:
${\theta _s}$ 为太阳天顶角;${\varphi _s}$ 为太阳方位角;${\theta _v}$ 为观测天顶角;${\varphi _\nu }$ 为观测方位角;$\operatorname{d} E$ 为入射辐照度;$\operatorname{d} {L_{rp}}$ 为偏振反射辐亮度。然而在实际的偏振探测中,一般使用偏振双向反射率因子(PBR)来间接地反映目标场景的偏振双向反射分布函数,PBR可以表示为:
$$R({\theta _s},{\varphi _s},{\theta _v},{\varphi _v}) = \frac{{\operatorname{d} {L_{rp}}({\theta _s},{\varphi _s},{\theta _v},{\varphi _v})}}{{\operatorname{d} L({\theta _s},{\varphi _s})}}$$ (2) 式中:R为偏振双向反射率因子;
${\rm{d}}L$ 为入射辐亮度。可以把实际的粗糙海面分解成许多各个方向倾斜、近似地服从高斯分布的微小平面。Kyu Yoshimori等人研究了海面风速与二维粗糙海面微小平面的概率分布函数之间的关系[8]。
$$P({S_{\rm{up}}},{S_{\rm{cross}}}) = \frac{1}{{2\pi {\sigma _{\rm{up}}}{\sigma _{\rm{cross}}}}}\exp \left( - \frac{1}{2}\left(\frac{{S_{\rm{up}}^2}}{{\sigma _{\rm{up}}^2}}{\rm{ + }}\frac{{S_{{\rm{\rm{c}}ross}}^2}}{{\sigma _{\rm{cross}}^2}}\right)\right)$$ (3) 式中:
${S_{\rm{up}}}$ 、${S_{\rm{cross}}}$ 分别为倾斜微小平面逆风和侧风方向的斜率;${\sigma _{\rm{up}}}$ 、${\sigma _{\rm{cross}}}$ 分别为倾斜微小平面逆风和侧风方向斜率的RMS值。Scripps海洋学研究所得出海水和油膜的粗糙度与风速分别满足如下关系[9]。
$$\left\{ \begin{aligned} & \sigma _{\rm{up,water}}^2 = 0.000 + 0.003\;16 \times v \pm 0.004 \\ & \sigma _{\rm{cross,water}}^2 = 0.003 + 0.001\;92 \times v \pm 0.002 \end{aligned} \right.$$ (4) $$\left\{ \begin{aligned} & \sigma _{\rm{up,oil}}^2 = 0.005 + 0.007\;8 \times v \pm 0.002 \\ & \sigma _{\rm{cross,oil}}^2 = 0.003 + 0.008\;4 \times v \pm 0.002 \end{aligned} \right.$$ (5) 倾斜微平面单元坐标如图2所示,以倾斜的微小面元上的入射点和反射点为坐标原点,
$x$ 轴、$z$ 轴分别表示方位角、天顶角基准轴;太阳光入射面与平面$oxz$ 重合;${L_{\rm{wind}}}$ ,${L_n}$ 分别表示海风风向和倾斜微平面单元的法线方向;${L_{\rm{s}}}$ ,${L_\nu }$ 分别表示太阳光线入射角度和探测器观测角度;$w$ 表示太阳照射海面微平面单元的入射角度和反射角度;$\beta $ 表示海面倾斜微面元与平面$oxy$ 的夹角。海面倾斜微平面单元在
$x$ 和$y$ 方向的斜率${S_x}$ ,${S_y}$ 与天顶角以及方位角的关系分别满足下式:$${S_x} = \frac{{ - (\sin {\theta _s} + \sin {\theta _v}\cos {\varphi _v})}}{{\cos {\theta _s} + \cos {\theta _v}}}$$ (6) $${S_y} = \frac{{\sin {\theta _v}\sin {\varphi _v}}}{{\cos {\theta _s} + \cos {\theta _v}}}$$ (7) 海面倾斜的微小面元的倾斜角度
$\beta $ 与方向斜率${S_x}$ ,${S_y}$ 的关系可以表示为:$${\tan ^2}\beta = S_x^2 + S_y^2$$ (8) 粗糙海面微平面单元的概率分布函数关于风速不对称,逆风方向和侧风方向的斜率与小平面体
$x$ 和$y$ 的方向斜率${S_x}$ ,${S_y}$ 满足如下关系:$${S_{\rm{up}}} = {S_x}\cos {\varphi _{\rm{wind}}} + {S_y}\sin {\varphi _{\rm{wind}}}$$ (9) $${S_{\rm{cross}}} = {S_y}\cos {\varphi _{\rm{wind}}} - {S_x}\sin {\varphi _{\rm{wind}}}$$ (10) 海面微平面单元的反射角
$w$ 满足下式:$${\rm{cos}}2w = = \cos {\theta _s}\cos {\theta _v} + \sin {\theta _s}\sin {\theta _v}\cos {\varphi _v}$$ (11) 针对太阳光经过海面介质反射后的偏振分量变化可用菲涅尔反射方程表示:
$$ r_{P}=\frac{n_{2} \cos \theta_{i}-n_{1} \cos \theta_{t}}{n_{2} \cos \theta_{i}+n_{1} \cos \theta_{t}}=\frac{\tan \left(\theta_{i}-\theta_{t}\right)}{\tan \left(\theta_{i}+\theta_{t}\right)} $$ (12) $$ r_{S}=\frac{n_{1} \cos \theta_{i}-n_{2} \cos \theta_{t}}{n_{1} \cos \theta_{i}+n_{2} \cos \theta_{t}}=\frac{\sin \left(\theta_{i}-\theta_{t}\right)}{\sin \left(\theta_{i}+\theta_{t}\right)} $$ (13) 式中:rp为P波反射系数;rs为S波反射系数;n1为空气折射率;n2为海面或油膜介质折射率;
${\theta _i}$ 为入射角;${\theta _t}$ 为折射角。联立公式(2)至公式(13),最终推算出归一化的粗糙海水以及油膜表面的偏振分量反射率。
$$ \left\{ {\begin{aligned} & {R_{P,\rm{water}}}\left( {{\theta _s},{\theta _v},{\phi _v},{\phi _{{\rm{\rm{wind} }}}},{n_{\rm{water}}},v} \right)\\ & \quad = \frac{{r_{P,\rm{water}}^2(w) \cdot {P_{\rm{water}}}\left( {{S_{\rm{up}}},{S_{\rm{cross}}}} \right)}}{{4{{\cos }^4}\beta \cos {\theta _v}}}\\ & {R_{S,\rm{water}}}\left( {{\theta _s},{\theta _v},{\phi _v},{\phi _{{\rm{\rm{wind }}}}},{n_{\rm{water}}},v} \right) \\ & \quad= \frac{{r_{S,\rm{water}}^2(w) \cdot {P_{\rm{water}}}\left( {{S_{\rm{up}}},{S_{\rm{cross}}}} \right)}}{{4{{\cos }^4}\beta \cos {\theta _v}}} \end{aligned}} \right. $$ (14) $$ \left\{ {\begin{aligned} & {{R_{P,\rm{oil}}}\left( {{\theta _s},{\theta _v},{\phi _v},{\phi _{{\rm{\rm{wind} }}}},{n_{\rm{oil}}},v} \right) = \frac{{r_{P,{\rm{ }}\rm{oil}}^2(w) \cdot {P_{\rm{oil}}}\left( {{S_{\rm{up}}},{S_{\rm{cross}}}} \right)}}{{4{{\cos }^4}\beta \cos {\theta _v}}}}\\ & {{R_{S,\rm{oil}}}\left( {{\theta _s},{\theta _v},{\phi _v},{\phi _{{\rm{\rm{wind }}}}},{n_{\rm{oil}}},v} \right) = \frac{{r_{S,\rm{oil}}^2(w) \cdot {P_{\rm{oil}}}\left( {{S_{\rm{up}}},{S_{\rm{cross}}}} \right)}}{{4{{\cos }^4}\beta \cos {\theta _v}}}} \end{aligned}} \right. $$ (15) 式中:Rp,water、Rs,water、Rp,oil、Rs,oil分别为海水和油膜的p光和s光的偏振反射率因子;rp,water、rs,water、rp,oil、rs,oil分别为海水和油膜的p光和s光的菲涅尔反射系数。
可见粗糙海面的偏振双向反射率与太阳入射天顶角等多个物理参量均有关系。因此,在数值仿真时需要分别讨论单一变量对粗糙海面和海面油膜的偏振双向反射率因子的影响。另外,在数值仿真中,文中忽略大气传输链路中的大气散射光对偏振反射分量的影响。
-
为了验证海面油膜的偏振探测识别能力,最后进行原理性实验。实验如图8所示,相机以40°角拍摄,通过旋转镜头前偏振片的方式,分时采集四张不同起偏角度图像。图8(b~e)分别是从0°、45°、90°和135°偏振方向采集的图像。
图 8 偏振成像实验场景图以及采集的4幅海面油膜偏振图像
Figure 8. Polarization imaging experiment scene and four polarization images of oil film on the sea surface were collected
海水使用纯净水加海盐配制而成,折射率约为1.33,密度约为1.03 g/cm3;油膜使用大庆原油,折射率约1.46,密度约为0.88 g/cm3。海水油膜的容器采用黑色塑料材料,在暗室内采用卤素灯照射白色漫反射板来模拟阴天天空背景,产生非偏振光。
当光通过海面大气倾斜照射到海水及油膜表面发生反射辐射时会携带目标场景的偏振维度信息,通常采用Stokes参量来表述[10]。
$$S(x,y) = \left[ {\begin{aligned} {{S_0}(x,y)} \\ {{S_1}(x,y)} \\ {{S_2}(x,y)} \\ {{S_3}(x,y)} \end{aligned}} \right] = \left[ {\begin{aligned} I \\ Q \\ U \\ V \end{aligned}} \right] = \left[ {\begin{array}{*{20}{c}} {{I_0}(x,y) + {I_{90}}(x,y)} \\ {{I_0}(x,y) - {I_{90}}(x,y)} \\ {{I_{45}}(x,y) - {I_{135}}(x,y)} \\ {{I_{RHC}}(x,y) - {I_{LHC}}(x,y)} \end{array}} \right]$$ (16) 式中:
${I_0}$ 、${I_{45}}$ 、${I_{90}}$ 、${I_{135}}$ 分别为0°、45°、90º、135º方向线偏振光强度;${I_{LHC}}$ 、${I_{RHC}}$ 分别为左旋、右旋圆偏振光强度。大部分目标Stokes参量中的表征圆偏振分量的$V$ 为零。因此,常规的偏振系统探测线偏振态强度即可。将获取的4幅线偏振强度图像代入公式(16),可计算出Stokes分量。这里使用线偏振度描述目标场景的偏振特性,大小表征了目标场景线偏振度的高低。线偏振度(DoLP)[10]可以用Stokes参量表示:
$$DoLP = \frac{{\sqrt {{Q^2} + {U^2}} }}{I}$$ (17) 此外,偏振角(AoP)也是描述目标场景偏振特性的另一个物理量[11],大小代表着椭圆偏振光的长轴与入射面之间的夹角,用Stokes参量可以表示为:
$$AoP = \frac{1}{2}\arctan (\frac{Q}{I})$$ (18) 通过图像配准等处理将获取的4幅水面油膜的偏振图转换为Stokes分量图如图9所示,图9(a)~(c)分别表示
${S_0}$ 、${S_1}$ 和${S_2}$ 分量的灰度图像。参考公式(17)和公式(18),得出水面油膜场景图像的线偏振度图(见图9(d))和偏振角图(见图9(e))。从DoLP图可以看出,油膜的线偏振度在0.5~0.7范围内,而海水的线偏振度在0.2~0.4范围内。AoP图中油膜和海水的角偏振度都在0°~10°范围内。将正常拍摄的油膜场景原图像分别与线偏振度图、偏振角图进行对比评价。分别计算3幅图像的信息熵等5个指标,定量比较3幅图像质量[12]。可见偏振度和偏振角图在成像对比度和海面油膜识别精度方面较有优势。
图 9 Stokes分量图以及线偏振度图和偏振角图
Figure 9. Stokes component diagram,the linear polarization degree diagram and polarization angle diagram
表 1 图像质量评价结果
Table 1. Image quality evaluation results
Target Original image Linear polarizaiton diagram Polarization angle diagram Information entropy 5.237 6.579 5.496 Standard deviation 10.146 24.449 11.587 Edge strength 2.341 34.640 16.110 Average gradient 0.212 3.460 1.598 Image definition 0.223 4.418 2.000
Simulation experiment of polarization reflection characteristics of the oil slick
-
摘要: 为了给海面溢油污染识别检测提供理论基础,根据菲涅尔反射公式的偏振反射系数,结合偏振双向反射率因子和粗糙海面的概率密度分布函数,建立了完善的pBRDF模型,仿真在不同太阳入射角度、不同探测器观测角度以及不同海面风速风向等条件下海水和油膜的偏振反射分布函数。结果表明:海水和油膜太阳天顶角为53°和56°时P偏振反射率分别为1.0×10−5和2.5×10−5,S偏振反射率随着太阳天顶角的增加而增加;海面风速越大偏振反射率峰值越小;海面风向只改变pBRDF的空间位置;海水和油膜线偏振度空间分布有明显差异。搭建实验平台相机以40°拍摄时,得出海水和油膜的线偏振度分别在0.2~0.4, 0.5~0.7之间,同时表明利用偏振探测获取目标场景的偏振度和偏振角图可提高图像质量。Abstract: To provide a theoretical basis for identification and detection of oil spill pollution on the sea surface, based on the polarization reflection coefficient of Fresnel reflection formula and combined with polarization bidirectional reflectivity factor and probability density distribution function of rough sea surface, a perfect pBRDF model was established. Then the polarization reflection distribution function of sea water and oil film was simulated under different solar incident angles, different detector observation angles and different sea surface wind speed and wind directions. The results show that, firstly, P-polarization reflectance reaches 1.0×10−5 and 2.5×10−5 respectively when the solar zenith angle of seawater and oil film is 53° and 56°. S-polarized reflectance increases with the increase of the solar zenith angle. Moreover, the higher sea surface wind speed is, the smaller peak value of polarization reflectance is. Additionally, wind direction only changes spatial position of pBRDF. Finally, the spatial distribution of linear polarization degree between seawater and oil film is obviously different. Experiment platform was set up with the camera working at 40°. The conclusion is obtained that the linear polarization of seawater and oil film is between 0.2−0.4 and 0.5−0.7, respectively. It also shows that using polarization detection to obtain the polarization degree and polarization angle of the target scene can improve the image quality.
-
Key words:
- oil slick /
- pBRDF /
- polarization reflection characteristics
-
表 1 图像质量评价结果
Table 1. Image quality evaluation results
Target Original image Linear polarizaiton diagram Polarization angle diagram Information entropy 5.237 6.579 5.496 Standard deviation 10.146 24.449 11.587 Edge strength 2.341 34.640 16.110 Average gradient 0.212 3.460 1.598 Image definition 0.223 4.418 2.000 -
[1] Li Yu, Chen Jie, Zhang Yuanzhi. Research progress of synthetic aperture radar sea surface oil spill detection [J]. Acta Electronica Sinica, 2019, 41(3): 248−259. (in Chinese) [2] Li Chengyang, Liu Zhiwen, Liu Kang, et al. Space hyperspectral remote sensing application research progress[J]. Infrared and Laser Engineering, 2019, 48(3): 9-23. (in Chinese) [3] Gao Jun, Bi Ran, Zhao Lujian, et al. Global optimal reconstruction of fog images using polarization information [J]. Optical Precision Engineering, 2017, 25(8): 2212−2220. (in Chinese) doi: 10.3788/OPE.20172508.2212 [4] Li Shujun, Jiang Huilin, Zhu Jingping, et al. Development status and key technologies of polarization imaging detection technology [J]. Chinese Optics, 2013, 6(6): 803−809. (in Chinese) [5] Zhang Weiguo. Polarization detection technology under the background of sea surface solar flare [J]. Chinese Optics, 2018, 11(2): 231−236. (in Chinese) doi: 10.3788/co.20181102.0231 [6] Lv Yunfeng. Polarization characteristics of water bodies[D]. Changchun: Northeast Normal University, 2012. (in Chinese) [7] Zhang Longli, Ma Shinan, Yang Haoran, et al. Relationship between refractive index and combustion heat of crude oil distillate [J]. Laboratory Research and Exploration, 2016, 35(5): 14−17. (in Chinese) doi: 10.3969/j.issn.1006-7167.2016.05.004 [8] Yoshimori K, Itoh K, Ichioka Y. Optical characteristics of a wind-roughened water surface: a two-dimensional theory [J]. Applied Optics, 1995, 34(27): 6236−6247. doi: 10.1364/AO.34.006236 [9] Cox C, Munk W. Measurement of the roughness of the sea surface from photographs of the suns glitter [J]. Journal of the Optical Society of America, 1954, 44(11): 838−850. doi: 10.1364/JOSA.44.000838 [10] Zhang Jiamin, Shi Dongfeng, Huang Jian, et al. Research on full Stokes polarization correlation imaging technology [J]. Infrared and Laser Engineering, 2018, 47(6): 0624001. (in Chinese) [11] Chen Yongtai, Zhang Ran, Lin Wei, et al. Design and construction of real-time all-polarization imaging detector in the sky [J]. Optics Precision Engineering, 2018(4): 816−824. (in Chinese) [12] Zhang Yang. Design of four-camera real-time polarization imaging system[D]. Xi'an: Xi 'an University of Electronic Science and Technology, 2018: 53−54. (in Chinese)