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激光回馈干涉理论模型主要包括Lang-Kobayashi速率方程理论[11-12]和三镜腔理论[13-14]。Lang-Kobayashi速率方程理论能够对激光回馈干涉现象做出完整解释,但解释过程和理论公式相对复杂。
三镜腔理论模型是一种激光回馈干涉的简单有效模型。如图1所示,该模型中激光器的光学谐振腔称为内腔,激光器和外界反射物之间的有效空间称为外腔。根据激光在外腔中的反射过程给出反射光的光程以及相位方程,认为反射光参与激光谐振,并根据模型的稳态条件,得到激光输出功率等特性的表达式。
图1中r1和r2表示激光器的全反镜、输出镜的反射率;r3表示反射物表面的反射率;l表示全反镜和输出镜组成的内腔长度;L表示输出镜和外界反射物之间的外腔长度。内腔产生的激光在外腔中往返一次,被反射物表面反射回内腔,改变激光特性,形成激光回馈干涉。若激光在外腔中往返一次,可利用三镜腔理论得到回馈干涉相位和激光输出功率方程:
$$\varphi_F (\tau ) = \varphi_0 (\tau ){\rm{ - }}C\sin [\varphi_F (\tau ) + \arctan \alpha ]$$ (1) $$P(\varphi_F (\tau )) = \mathop P\nolimits_{\rm{0}} [1 + mF(\varphi_F (\tau ))]$$ (2) $$F(\varphi_F (\tau )) = \cos (\varphi_F (\tau ))$$ (3) 公式(1)称作相位条件。
$\alpha $ 为线宽因子,C为描述反馈程度的反馈因子,当0<C<1时,称为弱反馈;当1≤C≤4.6时,称为适度反馈;当C>4.6时,称为强反馈;随着C的增加,干涉条纹逐渐失真,甚至出现跳模情况。τ为在外腔往返一次所需要的时间,$\tau = {\rm{2}}L{\rm{/c}}$ ,c为光速;φF(τ)和φ0(τ)分别为在有光回馈和无光回馈下的相位。公式(2)为功率方程,P为激光输出功率,P0为初始功率,m为调制系数。无反馈光时$$ {{\varphi }}_{\rm{0}}(\tau )={{\omega }}_{0}\times 2L(\tau )/c$$ (4) 可以被表示为:
$$L(\tau ) = \varphi_0 (\tau )\frac{c}{{2 \omega _0 }} = \frac{{ \lambda _{} }}{{2 \times 2\pi }}\varphi_0 $$ (5) $ \lambda$ 为激光波长,在弱反馈下$ {{\varphi }}_{F}(\tau )\approx {{\varphi }}_{\rm{0}}(\tau )$ ,上式可表示为:$$L(\tau ) = \frac{{ \lambda _{} }}{{2 \times 2\pi }}\varphi_F (\tau )$$ (6) 如果光源为激光二极管,那么激光二极管中的光电二极管能直接对回馈干涉信号进行监测,然后根据已有的理论对回馈干涉信号进行处理,解算外部物体信息。
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激光回馈散斑干涉是指激光照在具有漫反射特性的粗糙表面物体,部分后向散射光耦合至谐振腔内发生激光回馈干涉。如果外界反射物运动,引起反馈光特性的改变,产生动态的回馈散斑干涉信号。
激光回馈散斑干涉理论是以激光回馈干涉系统三镜腔等效模型为基础,差别在于它的反射面不是光滑面,而是粗糙的物体表面。如图2所示。图中,T代表外界反射物。
激光照射在外界反射物T的粗糙表面,部分后向散射光返回谐振腔,外腔长度L影响参与激光回馈干涉的后向散射有效光强以及光程。外界反射物粗糙度和运动特性不同,表现为散斑信号的较大差异,经过对散斑信号的分析,可以测量物体的不平滑度[15]、运动速度[16]。散斑信号具有一定随机性,所采集的激光回馈散斑干涉信号通常包含噪声,进行信息提取前需要对采集信号进行信号处理。基于包络提取过渡检测算法的信号处理方法[17],以顺利处理包含散斑的激光回馈干涉信号并正确提取外界反射物信息。同时该方法还可以区分不同回馈强度的外界反射物运动方向。首先,利用低通滤波器进行滤波,消除所采集信号中的高频噪声,以更好地提取相应信号包络;然后,利用局部最大和最小检测获得过零信号;经过标准化后,从过零信号中得到归一化信号;最后进行位移测量和方向判别。结果表明,散斑干涉信号的调制深度为10.4,所提出算法的测量精度为53 nm。
2018年,东北石油大学的高丙坤等[18]基于自相关谱法对采集到的激光回馈散斑干涉信号进行频谱分析,其自相关谱曲线的峰值对应着外界反射物引起的激光回馈散斑干涉频移,通过对激光回馈散斑干涉频移与外界反射物旋转速度的关系,便可以得出反射物的旋转速度。该方法可以实现粗糙表面外界反射物旋转速度的非接触式测量,其测量误差小于2%。
2019年,东北石油大学的高丙坤等[19]利用快速傅里叶变换(FFT)对激光回馈散斑干涉信号的频谱进行分析,提取激光回馈散斑干涉信号中的拍频,通过回馈干涉散斑干涉拍频与转速的关系,实现对转盘速度的测量,测量误差小于2%。2019年,郑州大学的常玲等[20]采用自适应滤波算法处理激光回馈散斑干涉信号,基于最小均方所改进的算法——归一化最小均方算法,对激光回馈散斑干涉信号进行滤波处理。结果表明,当散斑信号频率发生变化后,归一化最小均方自适应滤波权值系能够在数量级(10−3)迅速调整为合适值,降低了参数估计及测量的响应时间。
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如果外界反射表面为非准直光滑镜面,外界反射物与激光器输出镜构成离轴外腔。激光在外腔中发生多次反射,多次反射光进入光学谐振腔形成多重光反馈,即多重激光回馈干涉[21](MSMI)。由于反射光程的成倍增加,多重激光回馈干涉的干涉条纹数量也会随之成倍增加。
多重激光回馈干涉的形成过程如图3所示。其中,外界反射物和激光的光轴不垂直,输出镜、透镜以及外界反射物构成了非准直外腔。
激光器内腔发出激光,经过透镜聚焦到外界反射物表面,反射后经过输出镜时,一部分光返回内腔形成激光回馈干涉,一部分光被输出镜再次反射到目标物体就形成了二次反射。二次反射光经反射返回内腔,与腔内初始光发生耦合,再次形成激光回馈干涉。由于一次反射光和二次反射光的光程呈近似整数倍关系,它们分别引起激光回馈干涉的时域信号叠加后达到干涉条纹数目加倍的效果。如果激光在外腔中发生三次反射,则干涉条纹数目进一步增加。多重回馈干涉是激光回馈干涉中的一种普遍的现象,发现之初,被认为是一种干扰噪声,但是随着研究的不断深入,发现该现象的时域信号等同于多个激光回馈信号叠加后的细分条纹效果,具备满足光学测量领域更高精度要求的潜力。
多重激光回馈干涉可以在三镜腔理论模型的基础上进行阐述,根据外腔镜面的反射率和反射光程的倍数关系依次得到反射光表达式,进一步结合初始光表达式和系统的稳态条件,得到激光输出功率表达式P(t):
$$ P(t) = P_0 \{ 1 + m[\cos (2\pi \nu_f {\tau _1}) + \cos (2\pi \nu_f {\tau _2})]\} $$ (7) 式中:P0为激光器的初始功率;m为调制系数;
$2\pi \nu_f {\tau _1}$ 和$2\pi \nu_f {\tau _2}$ 为反射光相位;vf为激光光频;${\tau _1}$ 和${\tau _2}$ 为反射光在外腔的往返时间。如果外界反射表面产生随时间t变化的位移,令输出镜到外部反射物的距离为$ L(t)$ ,反射光在外腔往返时间及相互关系可以表示为:式中:${\tau _2} = 2{\tau _1} = \frac{{4kL(t)}}{c}$ (8) 式中:k = 2π/λ;c为光速且
$c = \nu_f \cdot \lambda $ ,$\lambda $ 为波长。可知,图4为一次反射光(SMI)、二次反射光(2 MSMI)、三次反射光(3 MSMI)下激光回馈干涉时域波形。在一个周期内,二次反射光、三次反射光下激光回馈干涉时域波形的干涉条纹分别是一次反射光下的两倍、三倍。
图 4 一次、二次、三次反馈光下的激光回馈干涉时域波形
Figure 4. Waveform in time domain of laser feedback interference with one-order, two-order, three-order feedback light
多重激光回馈干涉近年来正逐渐引起研究者的关注。有研究认为多重激光回馈干涉能够让干涉条纹数目加倍,达到细分条纹的效果,并且已经利用多重激光回馈干涉进行位移[22]、速度[23]、距离[24-25]的高精度测量。现有成果主要关注多重回馈干涉的应用研究,而相关的理论机制研究有待深入。一般认为非准直外腔(即外界反射物与激光光轴存在一定倾角)是多重激光回馈干涉的重要影响因素,但是多重激光回馈干涉的形成机制,特别多重激光回馈干涉与倾角之间的定量关系,尚缺乏进一步研究。
Review of laser feedback interference and its applications in biological medicine
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摘要: 激光回馈干涉具有共光路、精度高等优势,已经成为光学测量领域的研究热点。基于激光回馈干涉的理论及主要模型,根据外界反射物信息分析反射光特性,得到激光回馈干涉的测量方法,通过分析激光输出特性的变化实现外界反射物体的信息测量。针对粗糙表面物体或流体,激光回馈干涉结合散斑技术发展为激光回馈散斑干涉技术;针对光滑表面物体,激光回馈干涉在离轴短外腔下出现多重激光回馈干涉现象。激光回馈干涉技术在位移、角度、速度、成像等检测领域快速发展。激光回馈干涉能够检测粗糙表面的弱反馈光且灵敏度高,同时兼具传统干涉技术的高精度优势,在生物医学领域的非接触测量具有研究价值和应用前景。Abstract: Laser feedback interference has been the research highlight in the area of optical measurements, due to its advantages of common path and high precision. The measurements method of laser feedback interference was obtained according to the external reflective object’s information to analyze the characteristics of reflective light based on the basic theory and the main model of the laser feedback interference. Measurement of external reflective object’s information was realized through the analysis of laser output characteristics change. Laser feedback speckle interference was produced from the laser feedback interference and the laser speckle technology for the objects with the rough surfaces or the fluids. The phenomenon of multiple laser feedback interference arose from the laser feedback interference on condition of a short off-axis external cavity for the objects with smooth surfaces. The laser feedback interference technology achieved rapid development in the areas of displacement, angle, speed, imaging and so on for precisely detecting. The laser feedback interference technology was able to detect the weak feedback light scattered by the rough surfaces with high sensitivities and it also has the advantage of high precision like the traditional interference technology. The conclusion is drawn that the laser feedback interference technology has the research value and the application prospect in the fields of biological medicine for the non-contact detection.
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Key words:
- laser feedback interference /
- speckle /
- biological medicine
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[1] Amin S, Zabit U, Bernal O D, et al. High resolution laser self-mixing displacement sensor under large variation in optical feedback and speckle [J]. IEEE Sensors Journal, 2020, 20(16): 9140-9147. [2] Li Y, Chun W, Yang N, et al. Optically mutual-injected terahertz quantum cascade lasers for self-mixing velocity measurements [J]. Optics Express, 2019, 27(19): 27076-27087. [3] Chen J, Zhu H, Xia W, et al. Self-mixing birefringent dual-frequency laser Doppler velocimeter [J]. Optics Express, 2017, 25(2): 560-572. doi: 10.1364/OE.25.000560 [4] Yang Y, Li X, Li H, et al. Acceleration sensor based on laser self-mixing interference [J]. Acta Optica Sinica, 2013, 33(2): 0228003. (in Chinese) doi: 10.3788/AOS201333.0228003 [5] Chen W, Zhang S, Wu X. Angle measurement with laser feedback instrument [J]. Optics Express, 2013, 21(7): 8044-8050. doi: 10.1364/OE.21.008044 [6] Guo D, Jiang H, Shi L, et al. Laser self-mixing grating interferometer for MEMS accelerometer yesting [J]. IEEE Photonics Journal, 2018, 10(1): 6800609. [7] Zhu W, Chen Q, Wang Y, et al. Improvement on vibration measurement performance of laser self-mixing interference by using a pre-feedback mirror [J]. Optics and Lasers in Engineering, 2018, 105: 150-158. doi: 10.1016/j.optlaseng.2018.01.022 [8] Jiang C, Wen X, Yin S, et al. Multiple self-mixing interference based on phase modulation and demodulation for vibration measurement [J]. Applied Optics, 2017, 56(4): 1006-1011. doi: 10.1364/AO.56.001006 [9] Kou K, Li X, Yang Y, et al. Self-mixing interferometry based on all phase FFT for high-precision displacement measurement [J]. Optik International Journal for Light & Electron Optics, 2015, 126(3): 356-360. [10] Tao Y, Wang M, Guo D. Compound cavity theory of resonant phase modulation in laser self-mixing ultrasonic vibration measurement [J]. Optical Engineering, 2016, 55(7): 0741071. [11] Guo D. Quadrature demodulation technique for self-mixing interferometry displacement sensor [J]. Optics Communications, 2011, 284(24): 5766-5769. doi: 10.1016/j.optcom.2011.08.027 [12] Yu Y, Fan Y, Xi J, et al. Improving the measurement performance for a self-mixing interferometry-based displacement sensing system [J]. Applied Optics, 2011, 50(26): 5064-5072. doi: 10.1364/AO.50.005064 [13] Randone E M, Donati S. Self-mixing interferometer: Analysis of the output signals [J]. Optics Express, 2006, 14(20): 9188-9196. [14] Donati S, Giuliani G. Analysis of the signal amplitude regimes in injection detection using laser diodes[C]//Proceedings of SPIE the International Society for Optical Engineering, 2000, 3944: 639-644. [15] Kong P, Yang H, Zang G, et al. Advances in laser speckle flowgraphy technique [J]. Optical Technique, 2014, 40(1): 21-26. (in Chinese) [16] Alexandrova A S, Tzoganis V, Welsch C P. Laser diode self-mixing interferometry for velocity measurements [J]. Optical Engineering, 2015, 54(3): 034104. [17] Huang Z, Li C, Li S, et al. Speckle affected fringe detection based on three envelope extraction for self-mixing displacement measurement [J]. Optics Communications, 2017, 392: 100-108. doi: 10.1016/j.optcom.2017.01.037 [18] Gao B, Chen Q, Jiang C, Chen P. Rotation speed measurement based on self-mixing speckle interference [J]. Optics Communications, 2018, 428: 110-112. doi: 10.1016/j.optcom.2018.07.056 [19] Gao Binku, Li Haoran, Qing Chen. Measurement of rotation speed based on self-mixing speckle interference [J]. Optical Technique, 2019, 45(2): 188-191. (in Chinese) [20] Chang L, Xue Q, Ye H, et al. Normalized LMS filtering of self-mixing interference signal with varying frequency [J]. Destech Transactions on Computer Science and Engineering, 2019, 27870: 457-461. [21] Jiang C L, Zhang Z H, Li C W. Vibration measurement based on multiple self-mixing interferometry [J]. Optics Communications, 2016, 367: 227-233. doi: 10.1016/j.optcom.2016.01.032 [22] 姜春雷. 基于多重反馈自混合干涉的振动测量技术研究[D]. 哈尔滨工业大学, 2017: 10-18. Jiang C L. Research of vibration measurement technology based on multiple self-mixing interference[D]. Harbin: Harbin Institute of Technology, 2017: 10-18. (in Chinese) [23] Zhang X Y, Gu W Y, Jiang C L, et al. Velocity measurement based on multiple self-mixing interference [J]. Applied Optics, 2017, 56: 6709-6713. doi: 10.1364/AO.56.006709 [24] Zhang Y T, Wang R, Wei Z, et al. Broad Range and high precision self-mixing interferometer based on spectral analysis with multiple reflections [J]. IEEE Sensors Journal, 2019, 19(3): 926-932. doi: 10.1109/JSEN.2018.2879506 [25] Sun H F, Zhang Y T, Chen H Q, et al. Large-range nanoscale self-mixing interferometer based on multiple reflections and even-power fast algorithm [J]. Optics Communications, 2019, 443: 160-165. doi: 10.1016/j.optcom.2019.03.024 [26] Kong L W, Cai W K, Shi L H, et al. Micro-displacement measurement technology based on Littrow-configured laser feedback grating interference [J]. Chinese Journal of Lasers, 2019, 46(4): 224-229. (in Chinese) [27] Zhao Y, Zhang B, Han L. Laser self-mixing interference displacement measurement based on VMD and phase unwrapping [J]. Optics Communications, 2020, 456: 1245881-1245882. [28] Zhang Z H, Sun L Q, Li C W. Laser self-mixing interferometry for micro-vibration measurement based on inverse Hilbert transform [J]. Optical Review, 2020, 27(1): 90-97. [29] Guo C Y, Wu R. Improvement of real-time tracking measurement algorithm for optical feedback self-mixing interference displacement [J]. Modern Electronics Technique, 2018, 41(16): 116-119. (in Chinese) [30] Zhang Z H, Li C W, Huang Z. Vibration measurement based on multiple Hilbert transform for self-mixing interferometry [J]. Optics Communicationa, 2019, 436: 192-196. doi: 10.1016/j.optcom.2018.12.032 [31] Wang X, Song X, Tan R, et al. Micro-vibration measurement based on current modulation and secondary feedback self-mixing interference technology [J]. Optical Review, 2019, 26(2): 241. [32] Zhang Z H, Wang F L, Yuan T, et al. Multiple self-mixing interferometry based on lock-in amplifer analysis for vibration measurement [J]. Optical Review, 2020, 27: 313-320. doi: 10.1007/s10043-020-00600-0 [33] Zhang Z H, Tan Y D. Third-generation laser interference——Breakthrough in solid-state mirochip laser self-mixing measurement technology [J]. Measurement Technology, 2018, 38(03): 43-59. (in Chinese) [34] Tan Y D, Zhang S L, Zhang S, et al. Response of microchip solid-state laser to external frequency-shifted feedback and its applications [J]. Scientific Reports, 2013, 3(1): 1-10. [35] Wu Y, Tan Y D, Zeng Zhaoli, et al. High-performance HeNe laser feedback interferometer with birefringence feedback cavity scanned by piezoelectric transducer [J]. Review of Scientific Instruments, 2013, 84: 0561031-0561033. [36] Zhu K Y, Guo B, Zhang S L, et al. Single-spot two-dimensional displacement measurement based on self-mixing interferometry [J]. Optica, 2017, 4(7): 729-735. doi: 10.1364/OPTICA.4.000729 [37] Li M F, Wang Y F, Jiang X S, et al. Free-space self-interference microresonator with tunable coupling regimes [J]. Applied Physics Letter, 2020, 117: 0311061-0311065. [38] Capelli G, Bollati C, Giuliani G. Non-contact monitoring of heart beat using optical laser diode vibrocardiography[C]//International Workshop on Biophotonics, 2011: 1-3. [39] Arasanz A, Azcona F J, Royo S, et al. A new method for the acquisition of arterial pulse wave using self-mixing interferometry [J]. Optics & Laser Technology, 2014, 63: 98-104. [40] 魏颖斌. 基于激光自混合干涉效应的传感应用研究[D]. 厦门大学, 2017: 44-46. Wei Y B. Researches of sensing applications based on laser self-mixing interference effect[D]. Xiamen: Xiamen University, 2017: 44-46. (in Chinese) [41] Wei Y, Wang X, Huang W. Double-path acquisition of pulse wave transit time and heartbeat using self mixing interferometry [J]. Optics Communications, 2017, 393: 178-184. doi: 10.1016/j.optcom.2017.02.052 [42] Yang B, Wang D, Zhou L, et al. A ultra-small-angle self-mixing sensor system with high detection resolution and wide measurement range [J]. Optics & Laser Technology, 2017, 91: 92-97. [43] Yang B, Wang C, Jun Z, et al. A small-angle self-mixing measurement system with improved detection resolution based on a rotatable pentagonal prism [J]. Optics Communications, 2018, 429: 29-34. doi: 10.1016/j.optcom.2018.07.082 [44] Zhong J G, Liang Z Q, Li S P. Parameter optimization and direction recognition in angle measurement by laser self-mixing interference [J]. Optics and Precision Engineering, 2016, 24(5): 1003-1007. (in Chinese) [45] Zhao Y K, Xiang R, Huang Z T, et al. Research on the multi-longitudinal mode laser self-mixing static angle-measurement system using a right-angle prism [J]. Measurement, 2020, 162: 107906. doi: 10.1016/j.measurement.2020.107906 [46] Zhu C J, Xu H H, Zhang H T, et al. High precision angle measurement method based on laser self-mixing interference [J]. Laser & Infrared, 2020, 50(01): 37-41. (in Chinese) doi: 10.3969/j.issn.1001-5078.2020.01.007 [47] Zhao Y, Fan X, Wang C, et al. An improved intersection feedback micro-radian angle-measurement system based on the Laser self-mixing interferometry [J]. Optics and Lasers in Engineering, 2020, 126: 105866. doi: 10.1016/j.optlaseng.2019.105866 [48] Donati S, Norgia M. Self-mixing interferometry for biomedical signals sensing [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2014, 20(2): 6900108. [49] Kazmi S M S, Faraji E, Davis M A, et al. Flux or speed? Examining speckle contrast imaging of vascular flows [J]. Biomedical Optics Express, 2015, 6(7): 236031. [50] Semyachkina-Glushkovskaya S G O, Abdurashitov A A A, Pavlov A P A, et al. Laser speckle imaging and wavelet analysis of cerebral blood flow associated with the opening of the blood-brain barrier by sound [J]. Chinese Optics Letters, 2017, 15(9): 090002. doi: 10.3788/COL201715.090002 [51] Yanez C, Azcona J F, Royo S. Confocal flowmeter based on self-mixing interferometry for real-time velocity profiling of turbid liquids flowing in microcapillaries [J]. Optics Express, 2019, 27(17): 24340-24352. [52] Zhao Y, Shen X F, Yu J W, et al. Self-mixing interferometry-based micro flow cytometry system for label-free cells classification [J]. Applied Sciences, 2020, 10: 478. doi: 10.3390/app10020478 [53] Tan Y D, Zhang S L, Xu C X, et al. Inspecting and locating foreign body in biological sample by laser confocal feedback technology [J]. Applied Physics Letters, 2013, 103: 1019091. [54] Tan Y D, Wang W P, Xu C X, et al. Laser confocal feedback tomography and nano-step height measurement [J]. Scientific Report, 2013, 2971(3): 1-7. [55] Mowla A, Du B W, Taimre T, et al. Confocal laser feedback tomography for skin cancer detection [J]. Biomedical Optics Express, 2017, 8(9): 4037-4048. doi: 10.1364/BOE.8.004037 [56] Zhu K Y, Zhou B R, Lu Y Y, et al. Ultrasound-modulated laser feedback tomography in the reflective mode [J]. Optics Letters, 2019, 44(22): 5415-5417. [57] Lim L Y, Bertling K, Taimre T, et al. Coherent imaging using laser feedback interferometry with pulsed-mode terahertz quantum cascade lasers [J]. Optics Express, 2019, 27(7): 10221-10233. doi: 10.1364/OE.27.010221 [58] Wang K, Cao M, Liu P. A method of human eye parameter measurement based on laser self-mixing interference [J]. Journal of Russian Laser Research, 2020, 41: 197-206. doi: 10.1007/s10946-020-09865-x [59] Zhou B R, Wang Z H, Shen X J, et al. High-sensitivity laser confocal tomography based on frequency-shifted feedback technique [J]. Optics and Lasers in Engineering, 2020, 129: 106059. doi: 10.1016/j.optlaseng.2020.106059