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斯托克斯矢量模型是描述偏振光的一种常用方法,斯托克斯矢量S有4个分量,S=(I,Q,U,V)T包含了光波的所有偏振信息,其中,I为总光强,Q、U为线偏振成分的信息,V为圆偏振成分的信息。由于全偏振态的测量比线偏振成分的测量要复杂,文中主要分析斯托克斯矢量的线偏振成分。斯托克斯矢量的线偏振成分可表示为:
$$ {{S}'}=\left( {\begin{aligned} I \\ Q \\ U \end{aligned}} \right)=\left( {\begin{array}{*{20}{c}} {{I_0} + {I_{90}}} \\ {{I_0} - {I_{90}}} \\ {{I_{{\rm{45}}}} - {I_{{\rm{135}}}}} \end{array}} \right) $$ (1) 斯托克斯矢量能够直接和光强测量值联系起来,公式(1)中,I0、I45、I90、I135分别表示光在线偏振0°、45°、90°、135°的分量。定义线偏振度DOLP和偏振角AOP描述光波偏振态的特性[13]:
$$DOLP{\rm{ = }}\frac{{\sqrt {{Q^2} + {U^2}} }}{I}$$ (1) $$AOP{\rm{ = }}\frac{1}{2}{\rm{arctan}}\left( {\frac{U}{Q}} \right)$$ (2) 线偏振度DOLP表示线偏振分量的强度和光波总强度的比值,偏振角AOP描述了光的偏振方向。总光强可以分解为0°和90°光强之和,也可分解成45°和135°光强之和,至少需要三幅图像才能获得入射光的线偏振信息。
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光在介质表面发生反射,反射光偏振态发生改变,反射光的振幅和相位的变化遵循菲涅尔定律。对铜、铁、铝三种金属表面反射偏振变化进行了模拟。金属的折射率如表1所示[15]。
表 1 常见金属的折射率
Table 1. Refractive index of several common metals
Metal λ/nm n k Al 465 0.643 5.585 660 1.488 7.821 Fe 465 2.276 3.279 660 3.000 3.754 Cu 465 1.227 2.554 660 0.214 3.67 根据参考文献[16]理论,模拟了反射光的DOLP和AOP随入射角度变化。在模拟中,入射光为单色平行光,在金属表面发生镜面反射,反射光的DOLP和AOP随入射角度的变化,如图4所示。实际情景中大多数物质的表面粗糙并非发生镜面反射,使得偏振光在表面发生散射而退偏。金属与非金属相比,吸收效应强,吸收效应的增强会抑制甚至完全减弱退偏效应,因此,主要考虑金属表面反射的情况[17]。
图 4 铜、铁、铝金属表面反射光线的DOLP和AOP变化随入射角变化的曲线图
Figure 4. Changes of reflected DOLP and AOP of light from the surfaces of the copper, iron and aluminum material, versus the incident angle of illuminating light
图4中(a)~(c)为样品在非偏振光、30°线偏振光、60°线偏振光入射时,红光(R)、蓝光(B)波长的反射光DOLP随入射角度变化的曲线图,图4(d)~(f)对应AOP的变化。红、蓝曲线分别表示λ=660 nm和λ=465 nm入射光。由曲线图4(a)看出,无偏振光入射时,反射光在入射角度在60~70°时,线偏振度高,其余入射条件下,DOLP低,不利于区分金属和非金属。若用30°和60°线偏振光照射,当入射角度小于30°时,线偏振度接近1;当入射角度在60~70°时,达到极小值;同时,当入射角度在60~70°时,不同金属的DOLP和AOP产生差异,差异的大小与光的波长有关。所以,只要选择适当的接收光波长、入射光线偏振角度和入射角度,就可以利用线偏振成像方法有效地区分金属和非金属,以及不同金属。
根据模拟结果分析,入射角度小于30°时,用30°或60°线偏振光照射在金属表面,反射光的DOLP接近1。图3中给出的金属碎屑位置杂乱,反射面不统一,反射面粗糙导致DOLP小于1,但从图3可看出金属的DOLP明显大于背景值。背景是尺寸远小于金属碎屑的土壤颗粒,表面漫反射导致严重退偏,DOLP很小;对比图3(b)~(d)发现,背景在蓝光下DOLP较大,红光下DOLP最小。同时,在入射角小于30°时,金属表面的DOLP对波长不敏感。在图3中,即便是某些金属碎屑,它的反射角大于30°,DOLP不是很大且随着波长变化,但此时仍然与背景DOLP差别很大而被突显出来。所以,选取红色通道下的DOLP图像更好识别金属。综合图3和图4可知,在适当选择接收光波长、线偏振角度和入射角度时,线偏振成像可在复杂环境中有效检测和识别金属。
同时从图4中注意到,在入射角在60~70°时,不同金属的DOLP和AOP产生差异,可利用这一特性对金属分类。接下来用图1(c)的偏振相机对铜铁铝三类金属进行测试。
为了使金属在同一个入射面内,将平整的金属放在同一平面上,第一列是铜,第二列是铁,第三列是铝。入射角度为60°,偏振相机前装有中心波长为660 nm的滤光片(福州浩蓝光电有限公司,AZURE-BP660)。实验发现:在60°线偏振光入射时,三类金属的偏振图像差异很大,如图5所示。
图5(a)是DOLP图像,图5(b)是AOP图像。选择图5(a)中黑色边框区域来做定量分析,铜、铁、铝各取一块区域。从图5(a)和(b)分别所示的DOLP和AOP中,很明显看出差异。考虑到DOLP和AOP的量纲不一样,为了简单起见,直接采用公式(1)中的Q、U值,图5(c)显示了图5(a)中所选区域像素点的Q、U分布图。从图5(c)可以看出,在同一条件下,三类金属反射光的偏振存在明显差异,展示出线偏振成像区分不同材料金属的潜力。
Rapid identification of metal debris in complicated scenes by using polarization imaging(Invited)
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摘要:
爆炸犯罪杀伤群众,破坏公私财产,对公共安全造成危害。为快速侦破爆破案件,需要在爆炸现场众多残留物中识别金属,找出爆炸装置碎屑。针对在复杂背景中快速识别金属碎屑的需求,提出了一种基于线偏振成像增强金属对比的方法。基于偏振光成像的原理,搭建了两种多波长偏振图像采集装置。针对多种非金属和金属材料进行实验,发现调整入射光的线偏振角度和入射角,多波长偏振成像方法在复杂现场中可以对金属与非金属快速识别和分类。通过模拟研究了多波长下金属表面反射光的线偏振度和偏振角随入射角度变化的情况,给出识别不同金属的最佳角度和照明偏振光。进一步实验结果显示:多波长线偏振成像方法有区分不同种类金属的潜力。
Abstract:Crimes associated to explosives always kill the lives of people, destroy the facilities, and threaten the public security. Rapid identifying the medal debris from the residuals of the explosives in criminal scenes is the key to speed up the detection of these criminal cases. Responding to these applications, in the paper, a method was proposed based on polarization imaging to rapidly identify the medal debris from the complicated scenes. Two setups were built, which can respectively capture polarization images with multiple colors and in a simultaneous imaging manner. Experiments of the medal and non-medal debris and their mixtures show that polarization imaging can effectively identify the medal debris if the incident angle polarization, and wavelength of the illuminating light are appropriately set. Simulations based on Fresnel formula show how the polarization degrees and angles change with the incident angle, polarization, and wavelength of the illumination light. And the results suggest that polarization imaging can identify the types of the medal debris, which is proved by the additional experiments. In summary, it is indicated that polarization imaging has the potential to rapidly identify the medal debris from the complicated scenes which would help for the physical evidence in criminal detections.
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Key words:
- complicated scenes /
- explosive /
- medal debris /
- identification /
- polarization imaging
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表 1 常见金属的折射率
Table 1. Refractive index of several common metals
Metal λ/nm n k Al 465 0.643 5.585 660 1.488 7.821 Fe 465 2.276 3.279 660 3.000 3.754 Cu 465 1.227 2.554 660 0.214 3.67 -
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