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在实际成像环境中,复杂的干扰因素会影响光信号的检测,进而影响关联成像的质量。图1给出了复杂环境下的关联成像模型。随机光源被分束成参考光和信号光,参考光自由传输Z0距离后被CCD记录为
$ {I_r}\left( \rho \right) $ ,信号光在复杂信道中传输Z1距离后到达目标物体表面,经物体透射或反射后被桶探测器记录为$ {I_B} $ 。其中,物体前表面光场分布为$ {I_t}\left( \rho \right) $ ,物体透射或反射率为$ t\left( \xi \right) $ ,桶探测器前总光强为$ {I_{{\text{signal}}}} $ ,探测噪声强度为$ {I_{{\text{noise}}}} $ 。值得注意的是,此模型只考虑了信号光处在复杂环境中的情况,在计算关联成像中参考光可通过预置或者计算的方式获得,因而不需考虑实际环境的影响。通过对两个探测器接收到的信号进行二阶强度涨落关联便可恢复目标物体的图像,可表示为:$$ G\left( \rho \right) = \left\langle {{I_r}\left( \rho \right){I_B}} \right\rangle - \left\langle {{I_r}\left( \rho \right)} \right\rangle \left\langle {{I_B}} \right\rangle $$ (1) 式中:
$ \left\langle { \cdot \cdot \cdot } \right\rangle $ 表示系综平均。桶探测器信号可表示为:$$ {I_B} = {I_{{\text{signal}}}}{\text{ + }}{I_{{\text{noise}}}} $$ (2) 其中,
$$ {I_{{\text{signal}}}}{\text{ = }}\int {{I_t}\left( \rho \right)} t\left( \xi \right){\rm d}\xi $$ (3) 在理想的关联成像系统中,
$ {I_t}\left( \rho \right){\text{ = }}{I_r}\left( \rho \right) $ ,$ {I_{{\text{noise}}}}{\text{ = }}0 $ ,${I_B} = {I_{{\text{signal}}}}{\text{ = }}\int {{I_r}\left( \rho \right)} t\left( \xi \right){\rm d}\xi$ 。在实际应用中,公式(1)~(3)表明物体前表面光场$ {I_t}\left( \rho \right) $ 、探测噪声$ {I_{{\text{noise}}}} $ 会影响探测器信号$ {I_B} $ 。这里把影响信号光测量的复杂环境归为以下几类:(1)系统失配:距离失配(Z0 ≠ Z1)、角度失配等。距离失配使
$ {I_t}\left( \rho \right) \ne {I_r}\left( \rho \right) $ ;角度失配使$ {I_{{\text{signal}}}} $ 发生变化,其主要存在于粗糙目标的反射成像中。(2)信道干扰:散射介质、大气湍流、水湍流、气流等。他们的存在将引起光束畸变、光强闪烁、信号衰减,导致
$ {I_t}\left( \rho \right) \ne {I_r}\left( \rho \right) $ 。(3)探测噪声:探测噪声
$ {I_{{\text{noise}}}} $ 的存在直接影响了$ {I_B} $ ,尤其在信号光较弱时,探测噪声的存在使信号严重失真。这些对信号光测量产生影响的因素可认为是存在于信号光路中的一种噪声。在关联成像中,信号光通过桶探测器来测量,这种含噪信号光将影响关联成像的质量。文中只讨论距离失配、角度失配、散射介质、大气湍流、探测噪声对关联成像的影响。
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在大气环境中,湍流以噪声的形式影响信号光的测量。由于湍流在大气信道中随时间随机变化,因而这种含噪信号光也将随时间随机变化。为此,笔者所在课题组在不同时刻对大气信道中湍流引起的信号噪声进行测量和分析,期望为大气信道影响下的关联成像提供参考。
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激光在大气湍流中传播引起的光强起伏一般用归一化强度起伏方差(闪烁指数)来表征[88]。
$$ \sigma _I^2 = \frac{{\left\langle {{I^2}} \right\rangle }}{{{{\left\langle I \right\rangle }^2}}} - 1 $$ (4) 式中:I为光斑峰值强度。已有研究表明,满足大孔径条件的光强闪烁激光雷达最终获取的闪烁指数为激光发射路径上湍流效应引起的球面波轴向闪烁指数。在弱起伏条件下,忽略湍流内尺度的影响,球面波闪烁指数与湍流强度
$ C_n^2 $ 的关系可表示为[89]:$$ \sigma _I^2 = 0.492C_n^2{k^{7/6}}{L^{11/6}} $$ (5) 式中:k为波矢;L为传输距离。由公式(5)可得:
$$ C_n^2{\text{ = }}\frac{{\sigma _I^2}}{{0.492{k^{7/6}}{L^{11/6}}}} $$ (6) 激光在大气湍流中传播一定距离后,在与其传播方向垂直的平面内,光束中心位置将作随机变化,即光束漂移。通常以光斑质心位置的变化来描述光束漂移,光斑质心(xc, yc)定义为:
$$ {x}_{\text{c}}=\frac{{\displaystyle \iint xI(x,y){\rm d}x{\rm d}y}}{{\displaystyle \iint \langle I(x,y)\rangle {\rm d}x{\rm d}y}}\text{,}{y}_{\text{c}}=\frac{{\displaystyle \iint yI(x,y){\rm d}x{\rm d}y}}{{\displaystyle \iint \langle I(x,y)\rangle {\rm d}x{\rm d}y}} $$ (7) 设光斑质心在水平和垂直方向的漂移方差分别为
$ r_x^2 $ 和$ r_y^2 $ ,则在水平和垂直方向漂移运动统计特性具有独立性的假设下,光斑质心的漂移方差为:$$ r_{\text{c}}^{\text{2}} = r_x^2 + r_y^2 $$ (8) 已有研究表明,对于无限外尺度
$ {L_0} $ 的准直光束,其光束漂移方差可表示为[89]:$$ r_{\text{c}}^{\text{2}} = 2.42C_n^2{L^3}{W_0}^{ - 1/3} $$ (9) 式中:W0为光束束腰半径。由公式(9)可得:
$$ C_n^2 = \frac{{r_{\text{c}}^{\text{2}}{W_0}^{1/3}}}{{2.42{L^3}}} $$ (10) 由以上理论分析可知,只要测出某时刻激光通过大气信道后的光场强度分布,就可由公式(4)和公式(8)计算出对应的闪烁指数和漂移方差,然后利用公式(6)和公式(10)可分别估计出此刻的湍流强度。这里信号噪声的大小用湍流强度来衡量。湍流强度越大,对信号光测量的影响就越大,即信号噪声越大。
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为了测量大气信道中湍流引起的信号噪声大小,笔者所在课题组进行了80 m的室外激光传输实验。实验装置如图19所示,532 nm的固体激光器输出直径约为1.5 mm的高斯光斑经小焦距透镜f1 (125 mm)、细孔及大焦距透镜f2 (1000 mm)组成的扩束系统准直后在大气湍流中传输80 m,最后由透镜f3 (400 mm)缩束后被CCD接收。
图 19 大气湍流影响下的激光传输实验装置
Figure 19. Experiment setup of laser transmission under atmospheric turbulence
图20给出了中午到傍晚激光在大气中传输80 m后的光斑。在此次测量实验中,激光功率偏大,导致接收光斑中心近乎饱和(峰值强度基本不变),由公式(4)计算的闪烁指数值会偏低,进而造成湍流强度估计不准。因此,在这里通过光束漂移理论来反演实际大气的湍流强度。
图21是与图20相对应的光斑质心分布,可以看出光斑质心位置在一定范围内随机变化。此外,图22给出了不同时刻的接收光斑漂移及由公式(10)计算获得的湍流强度随时间的变化关系。可以看出,光斑在x方向(水平方向)漂移幅度xf略大于y方向(垂直方向)漂移幅度yf,漂移范围在1.8 mm以内,质心漂移幅度rc在0.4 mm以内,计算的湍流强度
$C_n^2 \in $ $ \left( {{{10}^{ - 15}}{{\text{m}}^{{\text{ − }}2/3}},{{10}^{- 13}}{{\text{m}}^{{\text{ − }}2/3}}} \right)$ 。结果表明,湍流引起的信号噪声在一定范围内随时间随机变化。
Research on the effect of noise-containing signal light on correlated imaging in complex environment (Invited)
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摘要: 关联成像是通过对测得的参考光和信号光进行关联计算来获取物体信息的新型成像技术。在复杂环境中,湍流、散射等因素会以噪声的形式影响信号光的测量。由于关联成像中信号光是以桶探测器来测量的,因此,对这种含噪信号光的处理及其在关联成像过程中的影响有必要进行系统地研究。文中系统地回顾了笔者所在课题组在上述背景下的相关研究。首先,简述了复杂环境下的关联成像模型;然后,分析了含噪信号光对二值目标和灰度目标关联成像的影响;接着,对大气信道中湍流引起的信号噪声进行了测量和分析,最后,对关联成像的应用进行了展望。Abstract: Correlated imaging is a kind of novel imaging technology which can reconstruct the target information on the optical path through intensity correlation calculation. In complex environments, turbulence, scattering and other factors will affect the measurement of signal light in the form of noise. Since the signal light in correlated imaging is measured by bucket detector, it is necessary to systematically study the processing of noise-including signal light and its influence on the process of correlated imaging. Under this background, this paper systematically reviewed the related research of our research group. Firstly, the correlated imaging model in complex environment was briefly introduced. Then, the influence of noise-including signal light on correlated imaging of binary target and gray target was analyzed. Then, the signal noise caused by turbulence in the atmospheric channel was measured and analyzed. Finally, the application of the correlated imaging was prospected.
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Key words:
- quantum optics /
- imaging system /
- complex environment /
- imaging quality /
- correlated imaging
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图 8 在(a)无散射和(b)散射介质浓度为1.9%的情况下入射角为θi = π∕12的关联结果;(c) 无散射和(d)散射介质浓度为1.9%的情况下入射角为θi = π∕4的关联结果;(e) 散射介质浓度为2.4%,θi = π∕4条件下的关联结果;第一列为传统关联成像的结果,第二列为对应条件下二值化关联成像的结果[76]
Figure 8. Acquired images with θi = π∕12 under (a) no scattering and (b) 1.9% scattering medium; The corresponding results when a large incident angle θi = π∕4 is chosen under (c) no scattering and (d) 19% scattering medium; (e) The ghost-image under the same parameters as those in (d) except for the 2.4% scattering medium. Here, the first column is the result from traditional correlated imaging, and the second column corresponds to the case in binary correlated imaging[76]
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