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VirtualLab Fusion光学设计软件由德国LightTrans公司研发的一款物理光学数值分析软件,是涵盖几何光学和波动光学的统一光学建模平台[23]。通过图形化的交互接口可以任意设计光学流程图,实现自定义数值仿真。VirtualLab Fusion通过求解麦克斯韦方程组,可以在整个光学系统空间中获得光波场向量信息,在确保所有模式光源与通过光学元件任意传输方法的情况下,获得准确的仿真结果。
如图1所示,基于涡旋光与球面波干涉理论测量物体微位移的光学建模流程图。图中“Gaussian wave”为高斯光束(632.8 nm),光束直径为0.7 mm;“Ideal lens1” 、“Ideal lens2”为理想透镜,实现光束扩束,焦距分别为f1=2 mm,f2=20 mm;“Ideal beam spliter”为分束器,分光比为50:50;“LC SLM”为自定义的空间光调制器,拓扑荷数设置为+1;“Spherical phase”为球面相位,将高斯光束变为球面波;“Ideal plane mirror1”、“Ideal plane mirror2”为理想平面镜,理想平面镜2用于产生微小位移;“Raw data detector”为探测器,记录干涉图像。设置光路的参数,光源与理想棱镜1的距离设置为2 mm,理想棱镜1与理想棱镜2的距离设置为22 mm,分光棱镜与理想棱镜2的距离设置为2 mm,LC SLM与球面相位均距离分光棱镜2 mm,为了便于实现纳米位移,理想平面镜1和理想平面镜2与前一个元件的距离均设置为0,探测器距离理想平面镜1与理想平面镜2均设置为2 mm。
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实验结果如图2所示,改变理想平面镜2的位置参数,获得位移前后的涡旋光与球面波的干涉图像,图2(a)为物体位移前的干涉条纹,图2(b)、(c)、(d)为物体位移后的干涉条纹。从图中可以看到涡旋光与球面波的干涉条纹是螺旋形状,当物体发生位移,整个螺旋条纹相比于位移前,发生角度的旋转,经过图像处理可得到旋转角度变化量为位移变化导致的相位变化量。仿真中,为了计算方便,位移d变化量分别为52.73 、237.30 和316.40 nm,对应于相位变化为
${30^ \circ }$ 、${135^ \circ }$ 和${180^ \circ }$ 。Figure 2. Interference intensity of vortex beams and spherical wave before and after micro-displacement in the simulation
将仿真图像使用matlab进行图像处理,获得相对应的位移量。将位移前后的两幅图二值化处理后,使用位移后的图像减去位移前的图像,得到如图3(a)、(b)、(c)所示的位移前后干涉图相减强度分布图,将明暗两个旋转起点中心位置确定为旋转中心,当如图3(c)中相间条纹,不易分辨中心时,则通过相加模式,将位移前和位移后两幅图的强度相加,由于灰度显示不同,相加后可以看出明暗两个旋转起点中心位置,从而确定旋转中心。两种模式都是基于对称性确定旋转中心。以旋转中心为定点绘制干涉螺旋条纹的起始光斑处的中心切线,得到位移前后两幅干涉螺旋条纹的中心切线,分别如图4(a)、(b)、(c)、(d)所示,根据位移前后两图的切线位置,计算切线的角度即为物体位移前后旋转角度,进一步计算得到物体位移量。通过图像处理仿真位移前后两幅图后得到的结果如表1所示,仿真结果说明基于涡旋光与球面波干涉螺旋条纹旋转角度的变化可以有效计算物体的微位移。
Displacement of theory/nm 52.73 237.30 316.40 Rotation angle of theory/(°) 30 135 180 Rotation angle of simulation/(°) 30.79 136.39 180 Displacement of calculation/nm 54.12 239.74 316.40 Error/nm 1.37 2.44 0 Table 1. Measurement results of simulation
Measurement of micro-displacement based on the interference of vortex beams and spherical wave
doi: 10.3788/IRLA202049.0413005
- Received Date: 2019-12-06
- Rev Recd Date: 2020-01-26
- Accepted Date: 2020-02-25
- Publish Date: 2020-04-24
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Key words:
- vortex beam /
- micrometric displacement /
- spiral phase /
- spatial light modulator
Abstract: Based on the theory of vortex beams and spherical wave interference, an optical measurement method for object micro-displacement was proposed. After improving the Mach-Zehnder interference optical path, a vortex beam was generated as a reference beam, using the spatial light modulator illuminated by a beam of light, and another beam was transformed into a spherical wave through the lens and illuminated to the object. The interference fringes were distributed in a spiral shape as the two beams interfered. When the object has a micro-displacement, the optical path difference of the two beams changes, and the spiral interference fringe rotates. Noticing this phenomenon, the micro-displacement of the object can be determined by the rotation angle of the spiral interference which vortex beams interference with spherical wave. Through theoretical analysis, simulation and experiments have proved that the micro-displacement of the object can be monitored in real time, and effectively calculated by the rotation angle change of spiral fringe based on interference of vortex beams and spherical wave. In the experiment, the displacement of the measured object is 27 nm, the actual measured displacement of the object is 25.75 nm, and the error is 1.25 nm compared with the theoretical value.