多模光纤扩展光源抑制干涉仪相干噪声的研究
Defects such as scratches and dust on the surfaces of optical components in interferometers can generate diffraction ring coherent noise in interferograms, which can significantly affect measurement accuracy. To address this issue, this study introduces an extended-light-source method in which the coupling angle of a multimode fiber is altered. By controlling the coupling angle of the multimode fiber after the parallel beam passes through the rotating frosted glass, the proposed method effectively minimizes the effects of scattering and coherent noise. This approach provides a valuable contribution to the theory of extended light sources based on multimode fibers. The derivation and validation of the range of fiber incident angles at the location exhibiting the strongest signal-to-noise ratio (SNR) of the interferometric signal offer important guidance for installing and calibrating interferometers and other optical instruments utilizing this light-source configuration.
In this study, the objectives of eliminating coherent noise and improving the SNR of interference fringes in a composite extended source based on multimode fibers are explained. With a change in the coupling angle in the multimode fiber, the shape and size of the light beam emitted from the fiber end change accordingly. When the coupling fiber angle is adjusted, the free degree of the composite-light-source speckle increases, leading to a decrease in system speckle contrast. However, the size of the extended source affects the contrast of the interference fringes. Based on the formula for obtaining the interferometric SNR, it is known that changes in the scattering contrast and interference fringe contrast affect the SNR of the entire extended light source. In this study, the critical incident angle at which the light beam emitted from the fiber end becomes a hollow beam is derived through calculations.
The Zemax OpticStudio software is used to simulate the fiber-end optical field. In the non-sequential mode, a Gaussian light source is set to enter at different incident angles along the x axis. A detection viewer is used to observe changes in light-field distribution. The change in the output field is calculated at different incident angles based on the formula of the light beam emitted from the fiber end. Simulations and calculations are performed to investigate the effects of different fiber incident angles on the fiber output light-field distribution. The detector parameters are then adjusted, the light-field distribution emitted from the fiber end is recorded, and the number of speckle fields is characterized using the average value of the image gradient magnitude.
To verify further the correctness of the theoretical and simulation results, an experiment is conducted on an interferometer with a diameter of 25.4 mm using a multimode fiber with a core diameter of 1 mm. The light-field distribution at the fiber output port is analyzed at different incident angles using a beam quality analyzer, and a wavelength phase-shifting measurement is performed on the measured mirror.
When light is coupled via a multimode fiber at different incident angles, the changing rules of the optical field distribution at the fiber output are the same in the simulation and experiment, as shown in Figs. 5 and 10, respectively. As the incident angle increases, the output light beam changes from a Gaussian distribution to a hollow disc. The interference SNR is maximized when the speckle contrast exhibits a minimum value, and the position of the minimum point is approximately midway between the calculated critical angle of the hollow beam and the normal incident angle. As Table 3 shows, when the angle of the incident multimode fiber is within the range of -3°?2° following a reduction in the temporal coherence of the beam (accomplished by rotating the ground glass), the SNR of the interferometric signal increases from 4.433 dB at normal incidence (0°) to 6.219 dB, which is an increase of 40.3%. In addition, the scattering contrast decreases from 0.333 (the highest level) to 0.204, and the coupling angle is -2° at the highest SNR. This coupling angle is also between the positive incident angle and the critical angle of emergence of the hollow beam, which is consistent with the calculation. It should be noted that the actual position of the hollow beam may deviate from the calculated value because of the fiber status. However, this does not affect the position of the maximum point of the speckle contrast. This position is used to approximate the position of the hollow beam, which in turn is used to determine the position of the minimum point.
Theoretical derivation and simulation experiments prove that when the angle of parallel beam coupling in a multimode fiber is adjusted to the approximate middle position between the normal incidence and critical value, scatter and coherent noise can be suppressed and the SNR of the interferometric signal can be improved. This study also refines the theory of extended light sources based on multimode fibers. In addition, the derived calculation of the position range at the highest SNR provides a useful reference and guidance for mounting optical instrument systems such as interferometers.
1 引言
激光光源具有单色性好、波长稳定、亮度高等诸多优点,常被用作干涉仪的光源。然而,激光的相干性会将干涉仪光学元件中的划痕、灰尘或者气泡等瑕疵以衍射环的形式成像在干涉图中,极大地影响了测量结果和精度。为了降低系统的相干噪声,提高干涉系统的信噪比,通常需要破坏光源系统的相干性。目前常用的方法之一是通过生成扩展光源来破坏光源的空间相干性,研究人员对扩展光源生成方法开展了大量研究。1999年,Schwider[1]提出了生成扩展光源的方法,在该方法中,点光源经过光源焦点位置处的旋转毛玻璃。这种方法简单有效且在实验中使用较多。2003年,Zygo公司提出环形扩展光源理论[2]。在该理论指导下,Zygo公司基于全息相位板元件[3]成功生成了环形光源并将其应用于干涉系统,有效降低了相干噪声,目前这些技术已被广泛应用于该公司系列干涉仪产品。Kumar等[4]使用锥形镜产生了环形光源,降低了相干噪声。徐建程等[5-8]也对环形光源进行了研究,并提出了产生的新方法。陈秋白等[9]使用环形透镜产生了环形光源,成功抑制了干涉系统的相干噪声。除了使用环形扩展光源外,Freischlad[10]使用旋转毛玻璃与多模光纤扩展光源的组合,同样实现了相干噪声的抑制。动态偏振移相干涉仪[11]以及双移相斐索干涉系统[12]也都在使用类似光源结构。胡晨辉等[13]对透镜会聚光耦合多模光纤的扩展光源系统进行了研究,发现多模光纤的纤芯直径大小、干涉腔长以及成像相机曝光时间等因素会对干涉系统相干噪声的抑制产生影响。然而,透镜会聚光束很难完全准确耦合进入多模光纤,且多模光纤的纤端出射光场受耦合入射光角度的影响[14],因此干涉系统的信噪比受到影响。
本文研究了平行光束以不同角度耦合进入多模光纤纤芯时,光纤出射端的扩展光源的形态变化及其对干涉系统信噪比的影响,提出了一种基于多模光纤耦合角度变化的生成扩展光源的新方法。该方法有效抑制了多模光纤产生的散斑噪声,提高了干涉系统的信噪比。
2 基本原理
2.1 光纤纤端空心光束临界角的推导
光纤中的纤芯和包层是两种折射率存在差异的介质,在入射角小于最大入射孔径角时[15],光在光纤中几乎以全反射和直线两种方式传播。根据几何光学,在光纤直径不变且假设没有任何弯曲的情况下,当入射光沿光纤子午方向入射时出射光方向不变。但在实际使用中,光纤不可能完全没有弯曲,所以出射方向会发生改变,且当光纤较长时出射光场基本沿光纤光轴对称分布。当入射光斜入射时,光束出射角不变,且由于斜光线和光纤纤轴不在一个平面,实际出射光投影为一空心圆盘[14],如
式中:
根据实际光纤的模式传播理论,纤端出射光场的场强分布是由不同权重的自由空间中传输的准高斯光束和准平面波的圆孔衍射场叠加而成的[16]。通常对于纤芯较粗的多模光纤,衍射效应基本被匀化,可使用几何光学对其进行分析。当入射光沿着光纤轴向入射时,其出射场通常可以表述为
式中:
图 1. 不同入射角下平行光束经过光纤后的传播示意图。(a)正入射;(b)斜入射
Fig. 1. Schematics of parallel beam propagation through optical fibers under different incidence angles. (a) Normal incidence; (b) oblique incidence
2.2 组合扩展光源消相干噪声原理
干涉仪中的相干噪声主要是由系统中光学元件的各种缺陷引起的,在元件表面来回反射的“鬼像光”以表面瑕疵作为散射的中心,最终成像在相机中,形成类似“牛顿环”的条纹。因此通过对光源进行“改造”,可以在一定程度上破坏光束的相干性,减少相干噪声。对于散斑噪声,散斑对比度公式[17]为
式中:
多模光纤是一种有多个光传输路径的光纤,允许多个光模式同时传输光信号,不同传输模式下的传输特性和横向光密度分布不同,因此可能会出现模式间的干涉,导致相干噪声的出现。从单模光纤激光器发出的光通过多模光纤时,多模光纤生成的散斑场个数(
式中:
图 3. 不同入射角度下的散斑示意图。(a)正入射;(b)斜入射
Fig. 3. Schematics of speckle patterns under different incidence angles. (a) Normal incidence; (b) oblique incidence
在一定积分时间(
式中:
由上述分析可知,为了使干涉图的背景分布均匀,利用组合光源生成的扩展光源应当避免空心光束,当使用圆形扩展光源照明时,扩展光源的干涉条纹对比度(
式中:
从式(9)可知,干涉信号的信噪比与扩展光源的大小和散斑自由度的数量等均有关联,而光纤入射角度的改变会影响这两个参数,因此无论是为了控制光纤出射场的分布,避免空心光束出现,还是为了增加整个系统散斑自由度的数量,都可以通过改变光纤的入射角度来实现。
3 仿真与实验
3.1 光纤纤端光场仿真
为了研究光路中光束入射角的改变对多模光纤出射的纤端光场分布的影响,使用Zemax OpticStudio软件在非序列模式(NSC)下对光纤出射光场进行仿真实验。鉴于光束在光纤中几乎以全反射和直线方式传播,为了简化模型,该仿真实验仅对多模光纤的纤芯进行仿真,将其等效为一个圆柱体。选择高斯光源,光斑半径为0.75 mm,能量为3 mW,分析光线数量设置为105条,波长设置为632.8 nm,多模光纤纤芯直径设置为1 mm,长度设置为市面上的常用值1 m。在光路中放置矩形探测器(像素点个数为201×201,面积为10 mm×10 mm),记录光束经过多模光纤后出射端场强度分布,仿真参数如
表 1. 多模光纤仿真参数
Table 1. Multimode fiber simulation parameters
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当在x方向上改变光纤与入射光的夹角时,通过NSC光线分裂和光线散射以及偏振光分析对整个光路进行光线追迹,在距离光纤端口20 mm处放置矩形探测器接收光纤出射端的光场信息。在Zemax软件中,记录相干照度下探测查看器的光斑数据并进行分析。为了便于观察光斑强度分布,对数据进行平滑处理,结果如
图 5. 不同入射角下光纤出射端光场分布的仿真结果。(a)0°;(b)1.5°;(c)1.75°;(d)2°;(e)3°;(f)4°
Fig. 5. Simulation results of optical field distributions at fiber outlet under different incidence angles. (a) 0°; (b) 1.5°; (c) 1.75°; (d) 2°; (e) 3°; (f) 4°
仿真结果表明:随着入射角度的改变,光纤端口的出射场光场分布会发生明显的变化。当入射角度为0°时,出射光斑呈高斯分布,随着入射角度的增大,光斑的半径逐渐变大,且形状也逐渐发生变化。当入射角度变为2°时,光斑中心区域的能量开始变小,随着入射角度的继续增大,光斑形状变为空心圆盘,与计算结果吻合。
当固定光纤与入射光束之间的夹角为0°、1°、3°时,改变探测器与多模光纤纤端之间的距离,记录探测器上的光斑信息,其中Zemax软件分析的光斑信息是非相干空间照度数据,未作任何平滑处理,结果如
图 6. 光斑x方向上的半径与传播距离的关系
Fig. 6. Relationship between radius of spot in x direction and propagation distance
给定入射角度,确保光纤出射光斑中未出现空心光束,此时光束传播可以近似为沿着光轴线传播。当光在光纤中以全反射或直线方式传播时,出射角度等于入射角度,因此当光纤直径为1 mm时,调和参数设置为1.5。当光束传输距离为2 mm时,利用
3.2 光纤散斑仿真
多模光纤的散斑场是模式之间的干涉引起的,为了研究光束入射角度对光纤出射场中散斑场个数的影响,对上述仿真模型进行了修改。在相干照度模式下改变光束入射角度,通过NSC光线分裂和光线散射以及偏振光分析等对光路进行光线追迹,分析光束经过光纤传输后在距离光纤端口20 mm位置处的光场强度,对探测器的原始数据不作任何平滑处理。如
图 8. 不同入射角度下的仿真结果。(a)0°;(b)1°;(c)2°;(d)3°
Fig. 8. Simulation results under different incident angles. (a) 0°; (b) 1°; (c) 2°; (d) 3°
所示,分别选取了入射角度为0°、1°、2°和3°时探测器记录的光场信息。
为了更好地说明探测器记录的光场分布中的散斑场个数的变化,引入判断图像模糊程度的评价因子
式中:
表 2. 光场梯度幅值平均值
Table 2. Average value of light field gradient amplitude
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由
4 实验与分析
为了进一步研究所提组合光源抑制相干噪声的效果,在搭建的一套直径为25.4 mm的泰曼-格林干涉仪上开展了实验。波长调谐光纤激光器发出的光束经过准直镜准直后穿过旋转毛玻璃。多模光纤(纤芯直径为1 mm,长度为1 m,NA=0.39)作为入射端口的一端被固定在旋转位移台(分辨率为0.0005°)上,并正对着毛玻璃。光束垂直入射光纤端口,上位机软件将此时位移台示数置零。光纤另一端是出射端口,出射光是整个干涉仪系统的光源。实验过程中固定好光纤位置,避免光纤晃动影响光束传播,旋转万向调节支杆,将光束质量分析仪(分辨率为1360 pixel×1024 pixel,像素尺寸为6.45
图 9. 实验装置图。(a)研究入射角对多模光纤出射场的影响;(b)研究入射角对干涉测量的影响
Fig. 9. Schematics of experimental setup. (a) Studying effect of incidence angle on exit field of multimode fiber; (b) studying effect of incidence angle on interferometry
首先,将光束质量分析仪放在光路中,通过控制转台来调节光束入射多模光纤的角度,旋转角度在-6°~5°范围内,规定顺时针方向为正方向,观察光纤出射端口的光场分布信息,光束质量分析仪采集到的光束光强分布结果如
图 10. 不同入射角度下光束质量分析仪的测量结果。(a)-5°;(b)-3.5°;(c)-2°;(d)-0.5°;(e)0°;(f)1.5°;(g)3°;(h)4.5°
Fig. 10. Measurement results of beam quality analyzer under different incidence angles. (a) -5°; (b) -3.5°; (c) -2°; (d) -0.5°; (e) 0°; (f) 1.5°; (g) 3°; (h) 4.5°
表 3. 不同入射角度下干涉图信噪比的计算结果
Table 3. Calculated signal-to-noise ratios of interferograms under different incident angles
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利用光束质量分析仪采集的灰度图像计算光束的散斑对比度,结果如
图 11. 不同入射角度下散斑对比度的计算结果
Fig. 11. Calculation results of speckle contrast under different incident angles
在移除光束质量分析仪后,两路光在光路中发生干涉,干涉信号最终经过成像系统被CCD相机接收,随着光束入射角度的增大,干涉图强度也在逐渐减小,结果如
图 12. 不同入射角度下的干涉图。(a)-3°;(b)-2°;(c)-1°;(d)0°;(e)1°;(f)2°
Fig. 12. Interferograms under different incident angles. (a) -3°; (b) -2°; (c) -1°; (d) 0°; (e) 1°; (f) 2°
为了表征平行光束耦合进入多模光纤对干涉测量结果的影响,当入射角度分别为2°和-2°时进行测量,测量结果如
图 13. 不同入射角度下的面形测量结果。(a)-2°;(b)2°
Fig. 13. Surface shape measurement results under different incident angles. (a) -2°; (b) 2°
5 结论
提出了一种基于多模光纤和旋转毛玻璃组合装置抑制干涉系统中相干噪声的方法。通过理论推导和仿真实验,计算出干涉图信噪比最大时光束入射多模光纤的角度范围,并基于纤芯直径为1 mm的多模光纤扩展光源,在直径为25.4 mm的泰曼-格林干涉仪上进行了实验验证。结果表明:通过旋转毛玻璃降低光束的时间相干性后,入射多模光纤的角度在-3°~2°范围内,干涉信号信噪比由正入射(0°)时的4.433 dB提高到6.219 dB,增长幅度达到40.3%,散斑对比度也由最高0.333降至0.204,信噪比最高时的入射角度为-2°,此角度在计算推导的结果范围内。因此理论推导和实验证明,当平行光束耦合进入多模光纤的角度在正入射角度(0°)和临界角度中间时,可实现散斑和相干噪声的抑制,从而提高干涉信号的信噪比。研究结果完善了多模光纤扩展光源理论,为干涉仪等光学仪器的装调提供了有效的指导。
[1] Schwider J. Partially coherent illumination in interferometry for optical testing[J]. Proceedings of SPIE, 1999, 3745: 2-13.
[4] Kumar Y P, Negi S S, Kamath M P, et al. Measurement of surface form error of an optical surface with reduced interferometric spatial coherence artifacts using a ring source and polarization phase-shifting interferometry[J]. Applied Optics, 2016, 55(35): 10053-10059.
[5] 徐建程, 王辉, 柴立群, 等. 抑制相干噪声的环形光源技术[J]. 中国激光, 2010, 37(12): 3081-3085.
[6] 徐建程, 许乔, 邓燕, 等. 环形光源在干涉仪系统中的应用[J]. 强激光与粒子束, 2008, 20(3): 367-370.
[7] 徐燕, 万勇建, 吴永前. 基于空间相干性控制的环形光源技术[J]. 强激光与粒子束, 2011, 23(12): 3245-3249.
[8] 徐燕, 吴永前, 李世芳, 等. 基于Zemax干涉仪建模的环形光源误差分析[J]. 光电工程, 2015, 42(2): 84-88.
[9] 陈秋白, 张齐元, 王艳, 等. 基于环形透镜的菲索干涉仪环形光源设计[J]. 激光与光电子学进展, 2021, 58(1): 0112003.
[11] Morris M N, Naradikian M, Millerd J. Noise reduction in dynamic interferometry measurements[J]. Proceedings of SPIE, 2010, 7790: 226-236.
[12] Kumagai T, Hibino K, Nagaike Y. Dual-phase-shift schemes for internal-reflection noise reduction in a Fizeau interferometer[J]. Proceedings of SPIE, 2016, 9960: 99600C.
[13] 胡晨辉, 陈磊, 黄晨, 等. 抑制移相干涉仪中相干噪声的多模光纤扩展光源研究[J]. 光学学报, 2022, 42(19): 1906001.
[14] 王昭, 朱升成, 谭玉山, 等. 集成光纤束并行共焦测量[J]. 中国激光, 2005, 32(1): 105-109.
[15] 郁道银, 谈恒英. 工程光学[M]. 4版. 北京: 机械工业出版社, 2016. 10.1201/b19880-44
YuD Y, TanH Y. Engineering optics[M]. 4th ed. Beijing: China Machine Press, 2016.
[16] 苑立波. 光源与纤端光场[J]. 光通信技术, 1994, 18(1): 54-56.
Yuan L B. Light source and the optical field formed by an optical fiber end[J]. Optical Communication Technology, 1994, 18(1): 54-56.
[17] Redding B, Allen G, Dufresne E R, et al. Low-loss high-speed speckle reduction using a colloidal dispersion[J]. Applied Optics, 2013, 52(6): 1168-1172.
[18] GoodmanJ W. Speckle phenomena in optics: theory and applications[M]. Englewood: Roberts & Co., 2007.
[19] Egidijus A, Dawid B, Maciej W. Multimode fiber enables control of spatial coherence in Fourier-domain full-field optical coherence tomography for in vivo corneal imaging[J]. Optics Letters, 2021, 46(6): 1413-1416.
[20] 徐建程, 刘志超, 杜雅薇, 等. 带旋转毛玻璃干涉成像系统的统计分析[J]. 强激光与粒子束, 2011, 23(3): 702-706.
Article Outline
张徐, 鲁棋, 公维超, 徐天柱, 王微微, 孙莹, 刘世杰. 多模光纤扩展光源抑制干涉仪相干噪声的研究[J]. 中国激光, 2024, 51(6): 0606004. Xu Zhang, Qi Lu, Weichao Gong, Tianzhu Xu, Weiwei Wang, Ying Sun, Shijie Liu. Coherent Noise Suppression with Multimode Fiber Extended Light Source for Interferometer[J]. Chinese Journal of Lasers, 2024, 51(6): 0606004.