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在进行相移测量时,首先将待测光纤放置于载物台上,光源发出的光束传输方向为z 向,与待测光纤的径向垂直。待测光纤在x-y平面的方向为偏振器消光方向的45°。假设光束在待测光纤上的折射很小,光横向透过光纤的光强I和相移分布φ之间的关系可表示为[9]:
$$ - \frac{{2\pi }}{{\bar \lambda }}\frac{{\partial I}}{{\partial {z}}} = {\nabla _ \bot }.(I{\nabla _ \bot }\varphi ) $$ (1) 式中:
${\bar \lambda } $ 为光源的平均波长;$ {\nabla _ \bot } $ =$\dfrac{\partial }{\partial x}+\dfrac{\partial }{\partial y}$ 。当待测光纤处于焦点位置时,可通过CCD 相机得到焦点位置的光强分布图像;当待测光纤处于非焦点位置时,可以得到两幅非焦点位置的光强图像。再利用中心差分公式,可以近似得到光强在z向的微分${\partial I}/{\partial z}$ 。因此利用这三幅光强图像,对方程(1)进行数值求解,就可得到相移分布φ。若需得到光纤折射率的横向分布,则要在不同的θf角度(0≤θf<180o)对相移进行测量。以角度θf的光束通过待测光纤后的相移可以表示为[9]:$$ \varphi (x',{\theta _f}) = \frac{{2\pi }}{\lambda }\int\limits_{ - \infty }^\infty {\Delta n(x',y')} {\rm{d}}y' $$ (2) 式中:λ是光源的波长;
$ \Delta n(x',y') $ =$n\left( {{x'},{y'}} \right) - {n_{oil}}$ 为相对折射率差,公式(2)中的坐标关系如图1所示。由计算机断层扫描理论可知,相移分布的一维傅里叶变换Φ等于横向折射率分布的二维傅里叶变换ΔN (乘以2π/λ)的一个径向切片。定义s为空间角频率,那么计算机断层扫描理论可以描述为[9]:
$$ \varPhi (s,{\theta _f}) = \frac{{2\pi }}{\lambda }\Delta N(s\cos {\theta _f},s\sin {\theta _f}) $$ (3) 首先当θf=0时,对相移进行测量,测量完毕之后,待测光纤轴向旋转一定角度(一般为2°),重新聚焦并确认光纤位置,然后再对相移进行测量。因此,随着角度θf 从0增加到180°,可以得到89组相移数据。利用二维傅里叶反变换,光纤的横截面折射率分布可以表示为[9]:
$$ \Delta n(x',y') = \frac{\lambda }{{2\pi }}\int\limits_0^\pi {\left[ {\int\limits_{ - \infty }^\infty {\varPhi \left(s,{\theta _f}\right)\left| s \right|{{\rm e}^{i2\pi sx'}}{\rm{d}}s} } \right]} {\rm{d}}\theta $$ (4) 由公式(4)可知,通过测得的89组相移分布数据,就可得到待测光纤折射率的二维分布,结合多横截面的计算机断层扫描,即可得出待测光纤的折射率分布。值得注意的是,更大的旋转角度意味着测量时间的减少和精度的降低,而更小的旋转角度则相反。经重构算法优化,后续测试中笔者课题组将采用6°的旋转角,即旋转30次,可在确保精度的前提下进一步缩短测量时间。
对于光纤的几何结构重构,可通过定量相位显微法得到的折射率分布图,利用基于机器视觉的数字化图像处理方法,进一步获得光纤的几何结构,该方法可充分发挥计算机的图像处理优势,使得光纤几何结构图像的重构具有快速、准确的特点。
当使用补偿器法测量光纤内应力时,需要将补偿器插入光路中,补偿器的慢轴处于y方向。待测光纤所处坐标系如图2所示。透过待测光纤、补偿器、检偏器的光强由CCD相机捕获,得到光强图像。其光强可以表示为[11]:
图 2 内应力测量时光纤所处坐标系
Figure 2. The coordinate diagram of optical fiber when measuring the internal stress
$$ I{\text{ = }}\frac{{{\pi ^2}}}{{{\lambda ^2}}}{({R_s} \pm {R_c}\sin 2{\theta _c})^2} $$ (5) 式中:λ是光源的波长;Rs和Rc分别为待测光纤和补偿器与原始无待测光纤时光路的光程差;θc为补偿器从消光位置旋转过的角度。调整光路使得旋转补偿器对应CCD相机捕获的光强尽可能小,此时补偿器的角度为θc,min,公式(5)可简化为[11]:
$$ {R_{s}}{\text{ = }}\left| {{R_{c}}\sin 2{\theta _{c,\min }}} \right| $$ (6) 由于待测光纤在整个CCD相机视场内的应力分布可能是不均匀的,因此,对于视场内的每个像素点,当其达到强度最小时所对应的补偿器的角度θc,min 也不尽相同。为了更精确测量每个像素点的光程差,需要进行全视场光程差测量。其流程为:首先确定补偿器旋转角度的范围为θ1 ~θN,其选取原则是保证在这个角度范围之内,视场内的每个像素点均存在θc,min使得光强足够小;其次,补偿器从θ1开始旋转,每次以0.5°的幅度递增,直到旋转到θN,每旋转一个角度,CCD 相机就拍照一次并存储图像,供后续处理使用。需要指出的是,若θ1 ~θN的间隔范围过大,由于旋转次数增多,测试时间会显著增加。以笔者的经验来看,只要在任意的θ1 ~θN内实现光场的“明-暗-明”的变化,即可确定该范围,一般为30°左右。对于一次全视场测量,共获得N副光强图像,对某个像素点而言,通过该点光强度的多项式拟合算法,就可以计算得到该像素点的最小θc,min的值,从而得到该像素点的光程差。当θf从0旋转到180°时,就得到一组光程差分布数据,然后使用计算机断层扫描技术,可以得到轴向应力的分布图。
Reconstruction technology of refractive index and internal stress distribution of multi-core fibers (Invited)
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摘要: 介绍了一种基于定量相位显微(Quantitative phase microscopy,QPM)法、Brace-Köhler补偿器(Brace-Köhler compensator,BKC)法与机器视觉技术的多芯光纤综合参数测试系统,并利用该系统获得了七芯光纤的折射率分布与几何结构,单模光纤的内应力分布图。采用横向测量方式的QPM法避免了截断光纤造成的损坏,采用改进的BKC法优化了光延迟量的获取方式,结合机器视觉技术,实现了多模块、高空间分辨率、快速准确的光纤参数测量,其中相对折射率差的精度约5×10−4量级,单模光纤内应力测量分辨率约0.5 MPa。通过与既有的光纤产品技术指标对比,证明了该系统具有测量准确性,测试结果为多芯光纤在传输和传感等多领域的应用提供了数据支撑。Abstract: A novel multi-core fiber comprehensive parameter test system based on quantitative phase microscopy method, Brace-Köhler compensator method and machine vision technology was introduced. In order to characterize the test capability of peoposed system, the refractive index distribution and geometric structure of a seven-core fiber from YOFC, and the internal stress distribution of a single-mode fiber from Corning were obtained by this system, respectively. According to the former research, the quantitative phase microscopy method using transverse measurement could avoid the performance damage caused by truncated optical fiber efficiently. The improved Brace-Köhler compensatormethod was used to optimize the acquisition to get the optical delay. Combined with the machine vision technology, the system realized multi-modules, high spatial resolution, fast and accurate fiber parameter measurement. After sample processing, program debugging and optimization, the experiment results show that the accuracy of relative refractive index differencein multicore fiber was about 5×10−4 magnitude and the internal stress measurement resolution of single-mode fiber wasabout 0.5 MPa. The comparison with the technicalindicators of existing optical fiber products proves that the system has measurement accuracy, and the test results provide data support for the application of multi-core fibers in multiple fields such as transmission and sensing.
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Key words:
- multi-core fiber /
- quantitative phase microscopy /
- compensator method /
- machine vision /
- reconstruction
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