- Email: [email protected]
Implementation of the reflection phase-shift laser self-mixing interferometer for large-scale displacement measurement
Accepted Manuscript Title: Implementation of the reflection phase-shift laser self-mixing interferometer for large-scale displacement measurement Author: Qiang Liu Ming Wang PII: DOI: Reference:
S0030-4026(15)00951-1 http://dx.doi.org/doi:10.1016/j.ijleo.2015.08.184 IJLEO 56108
To appear in: Received date: Accepted date:
1-9-2014 25-8-2015
Please cite this article as: Q. Liu, M. Wang, Implementation of the reflection phase-shift laser self-mixing interferometer for large-scale displacement measurement, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.08.184 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Implementation of the reflection phase-shift laser self-mixing interferometer for large-scale displacement measurement Ming Wang*
(Tel:(086)02583598685; Mobile:15850525102;
Email:[email protected])
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Qiang Liu
Abstract
cr
(Key Laboratory of Optoelectronic Technology of Jiangsu Province, College of Physics Science and Technology, Nanjing Normal University, Nanjing, Jiangsu , China, 210023)
Begining with introducing / 2 phase-shift on the laser self-mixing
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front output signal reflected by the metal-dielectric film , the new measurement technique of laser self-mixing interferometer is studied. Through the glass substrate coated by metal film attenuating the laser intensity while introducing / 2 phase-shift on the reflection self-mixing interference front signal in the electronic domain, it is easy to make the laser self-mixing interferometer system work under weak feedback conditions and to produce two orthogonal interference signals which are used to measure the displacement. The simulation result indicates high measurement accuracy. In order to improve the measurement accuracy and resolution of interferometer in hundred mm level displacement, the collected self-mixing interference signal is dealt with electronics subdivision in the digital domain, improving the noise performance and measurement reliability. Calibration experiments with high precision guide shows that 0.4μm resolution in 100mm displacement measurement process is achieved. As the self-mixing interference signals are acquired directly, the system measurement speed can be high. But subject to sampling rate of the data collection and processing system, the speed can reach close to 100mm/s in hundred mm range displacement measurement theoretically.
Keywords: self-mixing interference, reflection phase-shift, electronics division 1. Introduction
With the development of VLSI technology, ultra-precision machining industry, and bio-medical technology, the displacement measurement technique with hundred mm range and the nm positioning accuracy is needed and the successful implementation of such instruments will have great significance. The laser self-mixing interference (SMI) [1-4] is a novel large-scale high-precision displacement measurement technology different from the conventional two-beam interference, which refers to the output of the laser light is reflected or scattered by an external object where the portion of the light fed back to the laser cavity which carries information of the object and is mixed with light in the cavity, thus modulating output power and frequency of the laser. The laser self-mixing interferometer has the same phase sensitivity as traditional interferometers, and has a great advantage in high-precision displacement measurement owing to its simple
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structure, compact and easy collimation features. With the study on laser self-mixing interference, sinusoidal phase-shifting [5][6] was introduced into it, and various demodulation algorithms have also been proposed accordingly, such as the time domain carrier phase shifting technique, fast Fourier transform (FFT)[7]. They have greater advantages in the field of micro and nano diaplacement measurement and nanoscale precision can be achieved [8]. However, if these modulation and demodulation techniques is used to measure hundred mm level displacement , as the high speed is required in the measurement process , which will cause a large increase in the bandwidth of the modulated self-mixing interference signal. If some of the existing demodulation methods are adopted, the amount of data collected will be very large, demanding the cost of the system hardware and difficult to achieve real-time displacement measurement. This paper presents a phase-shift laser self-mixing interferometer based on reflection by the metal film. The metal-dielectric film is placed in the external laser cavity, which is used not only as an attenuator but also as a reflection mirror. The laser self-mixing interference system can work under weak feedback condition, and front self-mixing interference output signal can obtain / 2 phase-shift relative to the rear output. As phase-shift is sensitive to the direction of external object’s movement, two orthogonal interference signals are obtained for the real-time displacement precision measurement. PC and data acquisition card are used to acquire two orthogonal laser self-mixing interference signals. Electronics subdivision in the digital domain and fringe counting are dealt, so the external cavity’s phase is demodulated and the displacement is recovered simultaneously. The results of the displacement measurement are consistent with precision guide’s movement parameters. Factors affecting the speed in real-time displacement measurement were analyzed. Speed test is also conducted, so the speed limit of the interferometer is derived from theory. The experiment results show that the interferometer in the absence of sinusoidal phase-shifting can obtain 0.4μm error in the 100mm level displacement measurement process, ensuring the measure speed and real-time .
2. Principles
2.1 Optical System
Fig.1 Optical system of the reflection phase-shift laser self-mixing interferometer
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The overall system we have constructed is described as Fig.1, the He-Ne laser tube, the sloping metal-dielectric film (ND), photodetector1 (PD1), photodetector2 (PD2) and other components. The angle of ND is adjusted to make the laser selfmixing interference system works under weak feedback conditions; PD1 will detect this standard cosine wave.From the literature[9], the laser self-mixing interference front and rear output signals are in phase opposition and we observe the inverted laser self-mixing interference signals from PD1 and PD2 in experiments. However, we integrated a phase shifter (PS) in PD2, and thus will be able to detect two orthogonal laser self-mixing signals sensitive to the direction of motion in PD1 and PD2. 2.2 Laser self-mixing effect under weak feedback condition and displacement measurement principles According to the theory of laser self -mixing interference’s three-mirror FP cavity model, the interference wave function is determined by its feedback factor C, when
C<<1, ignoring multiple feedback of external cavity, F (ext ) is the cosine function[10]
an
and the laser output power meets equation (1):
P P0 [1 mF ( ext )] P0 (1 m cos ext )
(1)
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Where P0 is the optical power without feedback , m is the modulation factor, approximately equals 10 3 .
d
ext 4Lext / 4 ( L0 d (t )) /
(2)
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L0 is the initial cavity length of the external cavity, d (t ) is the object’s real motion.
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Assume that the speed of external object is in uniform motion V , the phase change caused by it is: (t ) 2 ( 2V / ) t
(3)
The rear output of the laser self-mixing interference signal can be expressed as:
y1 cos( (t ))
(4)
The front output signal is expressed as:
y2 cos( (t ))
(5)
Obviously, they are in phase opposition, which is meaningless for the displacement measurement. But, if y2 signal is / 2 phase-shifted by electronic circuits, we can get two orthogonal signals, which are important to measure the displacement. The reasons are as follow: i) When the movement direction of the object is positive, V is positive, then
(t ) is positive, the signal y1 remains unchanged,
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y1 cos( (t ))
(6)
but the signal y2 changes to be y2 cos( (t ) / 2) sin( (t ))
(7)
y1 cos( (t )) cos( (t ))
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is negative, because cos function is an even function, the y1 signal
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ii)When the movement direction of the object is negative, V is negative, then (t )
(8)
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still remains unchanged, but y2 signal changes to be
(9)
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y2 cos( (t ) / 2) sin( (t ))
From the above analysis, it can be concluded that: when the y2 signal is phase
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shifted by / 2 , y1 and y2 are quadrature, and the y2 signal is sensitive to the
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direction of the movement object, which is very useful for measuring displacement. We can take advantage of the two signals for displacement precision measurement, similar to optical grating for the displacement measurement. In order to verify the above idea, the rail is controlled in uniform motion, and the self-mixing interferometer system works in weak feedback level. The waveforms of self-mixing interference’s front and rear output signals detected by PD1 (yellow line) and PD2 (red line) are observed when the external object is in positive and negative uniform movement, as shown in Fig.2 & Fig.3,which can be seen that phase-shift is sensitive to the motion direction of the object. Two orthogonal signals allow real-time displacement measurement,because they contain the speed and displacement’s direction and magnitude information.
Fig. 2
Two orthogonal signals detected when in positive motion
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Fig. 3
Two orthogonal signals detected when in negative motion
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2.3 Electronics subdivision: In actual signal processing, in order to improve the measurement accuracy and resolution, the electronics subdivision in the digital domain is adopted. Known from the above theory, a sine wave stripe corresponds to / 2 displacement, and it will be changed to a square wave signal by the zero-crossing comparator, then by n subdivision and counting the number of the square wave, obtaining the actual displacement of the external object. After this processing, the resolution / 2n can be obtained. Shown in Fig.4, in period of a sine wave (the red line), through its zero-crossing comparator, square wave signal is obtained (the green line), wave after five subdivision (as blue line), so it can improve the resolution by counting method. In addition, the interference signal were plastic before subdivision, significantly enhancing the anti-jamming capability to the Gaussian noise superimposed on the self-mixing interference signal, and the measurement result will be more stable and reliable.
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Fig.4
Schematic diagram of five electronics subdivision
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Subdivision in the digital domain is performed as follows (Fig.5): the square-wave signal obtained above is rewritten into binary codes (1111100000), and is right shifted nine times. The odd-shift and even-shift results will be dealt with XOR gate, thus obtaining five subdivision signals (1010101010) and its complementary signal (0101010101), realizing five subdivisions to the original self-mixing interference signal. The above method is simulated; the results are shown in Fig.6 below. First assume that an object moves 1 mm, as Fig.6-a shows, two orthogonal self-mixing interference signals as a result of the movements are obtained as Fig.6-b, subdivision results as Fig.6-c, reconstructed displacement as Fig.6-d. It can be found that the method can accurately recover the movement displacement of the object. (b, c is lateral magnification in 0.5s position)
Fig.5
Scheme of five subdivision in digital domain
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Fig.6
Simulation of the displacement reconstruction
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3. Experimental setup
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The PD1 and PD2 detect two weak quadrate signals which will be converted into a voltage signal after current-voltage (IV) transformation, and the DC offset will also be derived by the high-pass circuits. After being processed by the amplifier circuit, the two SMI signals will be acquired by the NI’s data acquisition card USB-6251, preparing for subdivision and counting by LabVIEW program on PC. Since the phase of two SMI signals differs 90°, it can reconstruct and display the displacement of external object real-time after electronics subdivision in the digital domain and counting backwards. The signal processing process is shown as Fig.8.
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Fig.7 Flow diagram of the signal processing for laser self-mixing interference
Fig.8
Diagram of real-time displacement recovery
4. Experimental results
4.1 Calibration experiments 4.1.1 Experimental method: The M-521.DD precision guide is adopted. Its unidirectional repeatability of positioning resolution: 0.1μm, straightness parameters: 1μm/100mm, maximum operating speed: 50mm/s, range: 200mm. The M-521.DD drives the cat mirror target, and the movement range is set to 100mm, each uniform step: 10mm, the movement speed: 10mm/s, 10 times, each step displacement showing as a standard; this process is finished automatically, and the
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self-mixing interferometer measures and records each step displacement , giving the real-time error automatically. The experiment is repeated dozens of groups, and the data is saved. Four experiments data are chosen to analyze , which NO.1, NO.2 NO.3 are carried out in the same environmental conditions (optical vibration isolation units, thermostat:20℃ 1℃, humidity :50% 3% ,the laser preheating for two hours , laser wavelength :632.8334nm) , and the NO.4 results are obtained in other test field. 4.1.2 Data analysis: The result of the four experimental groups (NO.1, NO.2, NO.3, and NO.4) is shown as the following Fig.9: 4
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m u/ t n e m e c al p si D d er u s a e M
NO.1 NO.2 NO.3 NO.4
2
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0 0
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3
4 5 6 PI Displacement/um
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Diagram of comparison between the measured and PI’s displacement
Experimental results show that the interferometer’s maximum standard deviation compared with the precision guide is 0.3μm, the maximum error is 0.4μm, and the worst linear fit parameter is 0.9999. Measurement results of the laser self-mixing interferometer is consistent with the guide’s setting parameters, indicating that affected by the measurement environment and circuit noise restrictions, the interferometer has the ability of measuring hundred mm large-scale displacement with 0.4μm error real time and has good repeatability .
5. Analysis of error and speed limit 5.1 wavelength stability: In this interferometer, the laser is part of the measurement optical path and not a separate wavelength stabilized light source, whose stability has a great influence on measurement accuracy. The center wavelength of the He-Ne laser is 632.8334nm, and the short-term frequency stability is 1.5ppm [11].Therefore, in the
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absence of feedback, the laser wavelength stability is 0
v 0.9492 10 6 μm, v
showing a good performance. When the laser is used for self-mixing interference measurement, the frequency equation can be described as equation (10): ( 0 ) C sin( arctan( ))
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(10)
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Fig.10 The frequency fluctuation of the laser self-mixing interference signal changes along with the feedback coefficient C
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Fig.10 shows that: when the feedback coefficient C is very low, the frequency fluctuation is also small. The metal-dielectric film in the optical path can be adjusted to make the feedback level be very low, making the value of C very small, increasing the frequency stability. Theoretical calculations show that when the external cavity length is in one hundred mm, the measurement accuracy of wavelength stability can achieve 10 8 .
5.2 The analysis of speed limits [12]: A. Response bandwidth of PD: PD’s response bandwidth is consistent with the upper frequency of the laser self-mixing interference. The self-mixing interference signal is very weak, to increase the signal to noise ratio and facilitate the subsequent signal processing, so an external resistor should be selected to amplify the signal’s amplitude. PD’s response bandwidth depends on the external resistor and junction capacitance, as formula (11) shows, RLOAD is the load resistance of the PD, C j is
the junction capacitance of the PD. f BW
1 2 R LOAD C j
(11)
B. The sampling rate of data acquisition and processing system: Due to maximum sampling rate of the data acquisition card is 1.25M/s, and dual-channel simultaneous acquisition is required, so each channel sampling rate is 625K/s. According to the
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Nyquist sampling theory, it can meet the acquisition of the dual quadrate signals containing motion phase information. From the formula (3), the real-time measurement speed of self-mixing interferometer can reach close to 100mm / s. C. The actual noise level in the circuit: Due to the laser intensity fluctuations and environmental factors, noise level will become sensitive to the increased speed, affecting the measurement accuracy greatly. It is necessary to rationalize the circuit design system and adopt high-performance PD and high-precision data acquisition and processing system to reduce noise in the interferometer.
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6. Conclusion
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This paper presents reflection phase-shift laser self-mixing interferometer which has a more simple, compact and easy collimation structure. By introducing / 2 phase-shift to the self-mixing interference front output signal reflected by the metal film, and two orthogonal laser self-mixing interference signals are obtained for the real-time displacement measurement directly, which greatly reduces the cost and enhances the reliability of the measurement system, owing to no modulation and demodulation. Through the subdivision method in the digital domain, the error in the hundreds mm large range displacement measurement is decreased to 0.4μm. At the same time the speed of the interferometer in the large scale displacement measurement is improved to nearly 100mm/s theoretically.
ACKNOWLEDGEMENTS
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This work was supported by the National Natural Science Foundation of China (Grant Nos. 91123015, 61178044), Jiangsu province prospective joint research project (Grant Nos.SBY2012005), thanks to them!
REFERENCES
[1]M. Wang, and G. Lai. Self-mixing microscopic interferometer for the measurement of microprofile. Opt. Comm. 2004, 238:237-244. [2] M. Norgia, S. Donati A displacement-measuring instrument utilizing self-mixing interferometry. IEEE Trans. Instrum. Meas. 2003, 52:1765-1770. [3] Wang Ming, Nie Shouping, Li Dacheng. Optical feedback interference and its sensing applications of the Laser Diode. Chinese Journal of Lasers, 2002, A29 :1122-1126. [4] PA Roos, M.Stephens, and CEWieman. Laser vibrometer based on optical-feedback-induced frequency modulation of a single-mode laser diode. Appl. Opt., 1996,35 (34) :6754-6761. [5] T. Suzuki, T. Yazawa and O. Sasaki Two-wavelength laser diode interferometer with time-sharing sinusoidal phase modulation . Appl. Opt . 2002, 41:1972-1976 [6] T. Suzuki, X. Zhao and O. Sasaki Phase-locked phase-shifting laser diode interferometer with photothermal modulation. Appl.Opt. 2001, 40:2126-2131
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[7] Guo Dongmei, Tan Suqing, Wang Ming Micro displacement measurement accuracy analysis for a sinusoidal phase-shifting self-mixing interferometer [J] Acta Optica Sinica, 2006,26 (6): 845 ~ 850. [8] Huali Lu, Ming Wang etal. All-Fiber Self-Mixing Interferometer Based on DFB Laser and Phase Modulating Technique, IEEE PHOTONICS TECHNOLOGY LETTERS,2011,23(4):221-223 [9] W. Wang, W. J. O. Boyle, K. T. W. Grattan etal. Self-mixing Interference in a diode laserfor optical sensing applications, IEEE J.Lightwave Technol. 12, 1577-1587 (1992). [10] Yang Ying,Li Xingfei,Li Hongyu,Wang Cuo,Kou Ke. Acceleration Sensor Based on Laser Self-Mixing Interference[J]. Acta Optica Sinica, 2013, 33(2): 0228003. [11] Wei Xia, Zhenyu Yang, Qiang Liu, and Ming Wang.Development of a sinusoidal phase-shifting self-mixing interferometer for realtime displacement measurement with nanometer accuracy.Measurement Science and Technology. 2013, 24 (5): 1 ~ 9. [12] Zhang Zhaoyun, Gao Yang, Zhao Xinghai etal. The theoretical study of measurement speed limit of the diode laser's self-mixing effect. Chinese Journal of Lasers, 2010,37 (1) :211-214.
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S0030-4026(15)00951-1 http://dx.doi.org/doi:10.1016/j.ijleo.2015.08.184 IJLEO 56108
To appear in: Received date: Accepted date:
1-9-2014 25-8-2015
Please cite this article as: Q. Liu, M. Wang, Implementation of the reflection phase-shift laser self-mixing interferometer for large-scale displacement measurement, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.08.184 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Implementation of the reflection phase-shift laser self-mixing interferometer for large-scale displacement measurement Ming Wang*
(Tel:(086)02583598685; Mobile:15850525102;
Email:[email protected])
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Qiang Liu
Abstract
cr
(Key Laboratory of Optoelectronic Technology of Jiangsu Province, College of Physics Science and Technology, Nanjing Normal University, Nanjing, Jiangsu , China, 210023)
Begining with introducing / 2 phase-shift on the laser self-mixing
Ac ce p
te
d
M
an
us
front output signal reflected by the metal-dielectric film , the new measurement technique of laser self-mixing interferometer is studied. Through the glass substrate coated by metal film attenuating the laser intensity while introducing / 2 phase-shift on the reflection self-mixing interference front signal in the electronic domain, it is easy to make the laser self-mixing interferometer system work under weak feedback conditions and to produce two orthogonal interference signals which are used to measure the displacement. The simulation result indicates high measurement accuracy. In order to improve the measurement accuracy and resolution of interferometer in hundred mm level displacement, the collected self-mixing interference signal is dealt with electronics subdivision in the digital domain, improving the noise performance and measurement reliability. Calibration experiments with high precision guide shows that 0.4μm resolution in 100mm displacement measurement process is achieved. As the self-mixing interference signals are acquired directly, the system measurement speed can be high. But subject to sampling rate of the data collection and processing system, the speed can reach close to 100mm/s in hundred mm range displacement measurement theoretically.
Keywords: self-mixing interference, reflection phase-shift, electronics division 1. Introduction
With the development of VLSI technology, ultra-precision machining industry, and bio-medical technology, the displacement measurement technique with hundred mm range and the nm positioning accuracy is needed and the successful implementation of such instruments will have great significance. The laser self-mixing interference (SMI) [1-4] is a novel large-scale high-precision displacement measurement technology different from the conventional two-beam interference, which refers to the output of the laser light is reflected or scattered by an external object where the portion of the light fed back to the laser cavity which carries information of the object and is mixed with light in the cavity, thus modulating output power and frequency of the laser. The laser self-mixing interferometer has the same phase sensitivity as traditional interferometers, and has a great advantage in high-precision displacement measurement owing to its simple
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M
an
us
cr
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structure, compact and easy collimation features. With the study on laser self-mixing interference, sinusoidal phase-shifting [5][6] was introduced into it, and various demodulation algorithms have also been proposed accordingly, such as the time domain carrier phase shifting technique, fast Fourier transform (FFT)[7]. They have greater advantages in the field of micro and nano diaplacement measurement and nanoscale precision can be achieved [8]. However, if these modulation and demodulation techniques is used to measure hundred mm level displacement , as the high speed is required in the measurement process , which will cause a large increase in the bandwidth of the modulated self-mixing interference signal. If some of the existing demodulation methods are adopted, the amount of data collected will be very large, demanding the cost of the system hardware and difficult to achieve real-time displacement measurement. This paper presents a phase-shift laser self-mixing interferometer based on reflection by the metal film. The metal-dielectric film is placed in the external laser cavity, which is used not only as an attenuator but also as a reflection mirror. The laser self-mixing interference system can work under weak feedback condition, and front self-mixing interference output signal can obtain / 2 phase-shift relative to the rear output. As phase-shift is sensitive to the direction of external object’s movement, two orthogonal interference signals are obtained for the real-time displacement precision measurement. PC and data acquisition card are used to acquire two orthogonal laser self-mixing interference signals. Electronics subdivision in the digital domain and fringe counting are dealt, so the external cavity’s phase is demodulated and the displacement is recovered simultaneously. The results of the displacement measurement are consistent with precision guide’s movement parameters. Factors affecting the speed in real-time displacement measurement were analyzed. Speed test is also conducted, so the speed limit of the interferometer is derived from theory. The experiment results show that the interferometer in the absence of sinusoidal phase-shifting can obtain 0.4μm error in the 100mm level displacement measurement process, ensuring the measure speed and real-time .
2. Principles
2.1 Optical System
Fig.1 Optical system of the reflection phase-shift laser self-mixing interferometer
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The overall system we have constructed is described as Fig.1, the He-Ne laser tube, the sloping metal-dielectric film (ND), photodetector1 (PD1), photodetector2 (PD2) and other components. The angle of ND is adjusted to make the laser selfmixing interference system works under weak feedback conditions; PD1 will detect this standard cosine wave.From the literature[9], the laser self-mixing interference front and rear output signals are in phase opposition and we observe the inverted laser self-mixing interference signals from PD1 and PD2 in experiments. However, we integrated a phase shifter (PS) in PD2, and thus will be able to detect two orthogonal laser self-mixing signals sensitive to the direction of motion in PD1 and PD2. 2.2 Laser self-mixing effect under weak feedback condition and displacement measurement principles According to the theory of laser self -mixing interference’s three-mirror FP cavity model, the interference wave function is determined by its feedback factor C, when
C<<1, ignoring multiple feedback of external cavity, F (ext ) is the cosine function[10]
an
and the laser output power meets equation (1):
P P0 [1 mF ( ext )] P0 (1 m cos ext )
(1)
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Where P0 is the optical power without feedback , m is the modulation factor, approximately equals 10 3 .
d
ext 4Lext / 4 ( L0 d (t )) /
(2)
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L0 is the initial cavity length of the external cavity, d (t ) is the object’s real motion.
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Assume that the speed of external object is in uniform motion V , the phase change caused by it is: (t ) 2 ( 2V / ) t
(3)
The rear output of the laser self-mixing interference signal can be expressed as:
y1 cos( (t ))
(4)
The front output signal is expressed as:
y2 cos( (t ))
(5)
Obviously, they are in phase opposition, which is meaningless for the displacement measurement. But, if y2 signal is / 2 phase-shifted by electronic circuits, we can get two orthogonal signals, which are important to measure the displacement. The reasons are as follow: i) When the movement direction of the object is positive, V is positive, then
(t ) is positive, the signal y1 remains unchanged,
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y1 cos( (t ))
(6)
but the signal y2 changes to be y2 cos( (t ) / 2) sin( (t ))
(7)
y1 cos( (t )) cos( (t ))
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is negative, because cos function is an even function, the y1 signal
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ii)When the movement direction of the object is negative, V is negative, then (t )
(8)
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still remains unchanged, but y2 signal changes to be
(9)
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y2 cos( (t ) / 2) sin( (t ))
From the above analysis, it can be concluded that: when the y2 signal is phase
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shifted by / 2 , y1 and y2 are quadrature, and the y2 signal is sensitive to the
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d
direction of the movement object, which is very useful for measuring displacement. We can take advantage of the two signals for displacement precision measurement, similar to optical grating for the displacement measurement. In order to verify the above idea, the rail is controlled in uniform motion, and the self-mixing interferometer system works in weak feedback level. The waveforms of self-mixing interference’s front and rear output signals detected by PD1 (yellow line) and PD2 (red line) are observed when the external object is in positive and negative uniform movement, as shown in Fig.2 & Fig.3,which can be seen that phase-shift is sensitive to the motion direction of the object. Two orthogonal signals allow real-time displacement measurement,because they contain the speed and displacement’s direction and magnitude information.
Fig. 2
Two orthogonal signals detected when in positive motion
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Fig. 3
Two orthogonal signals detected when in negative motion
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2.3 Electronics subdivision: In actual signal processing, in order to improve the measurement accuracy and resolution, the electronics subdivision in the digital domain is adopted. Known from the above theory, a sine wave stripe corresponds to / 2 displacement, and it will be changed to a square wave signal by the zero-crossing comparator, then by n subdivision and counting the number of the square wave, obtaining the actual displacement of the external object. After this processing, the resolution / 2n can be obtained. Shown in Fig.4, in period of a sine wave (the red line), through its zero-crossing comparator, square wave signal is obtained (the green line), wave after five subdivision (as blue line), so it can improve the resolution by counting method. In addition, the interference signal were plastic before subdivision, significantly enhancing the anti-jamming capability to the Gaussian noise superimposed on the self-mixing interference signal, and the measurement result will be more stable and reliable.
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Fig.4
Schematic diagram of five electronics subdivision
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Subdivision in the digital domain is performed as follows (Fig.5): the square-wave signal obtained above is rewritten into binary codes (1111100000), and is right shifted nine times. The odd-shift and even-shift results will be dealt with XOR gate, thus obtaining five subdivision signals (1010101010) and its complementary signal (0101010101), realizing five subdivisions to the original self-mixing interference signal. The above method is simulated; the results are shown in Fig.6 below. First assume that an object moves 1 mm, as Fig.6-a shows, two orthogonal self-mixing interference signals as a result of the movements are obtained as Fig.6-b, subdivision results as Fig.6-c, reconstructed displacement as Fig.6-d. It can be found that the method can accurately recover the movement displacement of the object. (b, c is lateral magnification in 0.5s position)
Fig.5
Scheme of five subdivision in digital domain
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Fig.6
Simulation of the displacement reconstruction
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3. Experimental setup
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The PD1 and PD2 detect two weak quadrate signals which will be converted into a voltage signal after current-voltage (IV) transformation, and the DC offset will also be derived by the high-pass circuits. After being processed by the amplifier circuit, the two SMI signals will be acquired by the NI’s data acquisition card USB-6251, preparing for subdivision and counting by LabVIEW program on PC. Since the phase of two SMI signals differs 90°, it can reconstruct and display the displacement of external object real-time after electronics subdivision in the digital domain and counting backwards. The signal processing process is shown as Fig.8.
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Fig.7 Flow diagram of the signal processing for laser self-mixing interference
Fig.8
Diagram of real-time displacement recovery
4. Experimental results
4.1 Calibration experiments 4.1.1 Experimental method: The M-521.DD precision guide is adopted. Its unidirectional repeatability of positioning resolution: 0.1μm, straightness parameters: 1μm/100mm, maximum operating speed: 50mm/s, range: 200mm. The M-521.DD drives the cat mirror target, and the movement range is set to 100mm, each uniform step: 10mm, the movement speed: 10mm/s, 10 times, each step displacement showing as a standard; this process is finished automatically, and the
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self-mixing interferometer measures and records each step displacement , giving the real-time error automatically. The experiment is repeated dozens of groups, and the data is saved. Four experiments data are chosen to analyze , which NO.1, NO.2 NO.3 are carried out in the same environmental conditions (optical vibration isolation units, thermostat:20℃ 1℃, humidity :50% 3% ,the laser preheating for two hours , laser wavelength :632.8334nm) , and the NO.4 results are obtained in other test field. 4.1.2 Data analysis: The result of the four experimental groups (NO.1, NO.2, NO.3, and NO.4) is shown as the following Fig.9: 4
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4
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m u/ t n e m e c al p si D d er u s a e M
NO.1 NO.2 NO.3 NO.4
2
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0 0
Fig.9
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3
4 5 6 PI Displacement/um
7
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10 4
x 10
Diagram of comparison between the measured and PI’s displacement
Experimental results show that the interferometer’s maximum standard deviation compared with the precision guide is 0.3μm, the maximum error is 0.4μm, and the worst linear fit parameter is 0.9999. Measurement results of the laser self-mixing interferometer is consistent with the guide’s setting parameters, indicating that affected by the measurement environment and circuit noise restrictions, the interferometer has the ability of measuring hundred mm large-scale displacement with 0.4μm error real time and has good repeatability .
5. Analysis of error and speed limit 5.1 wavelength stability: In this interferometer, the laser is part of the measurement optical path and not a separate wavelength stabilized light source, whose stability has a great influence on measurement accuracy. The center wavelength of the He-Ne laser is 632.8334nm, and the short-term frequency stability is 1.5ppm [11].Therefore, in the
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absence of feedback, the laser wavelength stability is 0
v 0.9492 10 6 μm, v
showing a good performance. When the laser is used for self-mixing interference measurement, the frequency equation can be described as equation (10): ( 0 ) C sin( arctan( ))
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(10)
d
Fig.10 The frequency fluctuation of the laser self-mixing interference signal changes along with the feedback coefficient C
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Fig.10 shows that: when the feedback coefficient C is very low, the frequency fluctuation is also small. The metal-dielectric film in the optical path can be adjusted to make the feedback level be very low, making the value of C very small, increasing the frequency stability. Theoretical calculations show that when the external cavity length is in one hundred mm, the measurement accuracy of wavelength stability can achieve 10 8 .
5.2 The analysis of speed limits [12]: A. Response bandwidth of PD: PD’s response bandwidth is consistent with the upper frequency of the laser self-mixing interference. The self-mixing interference signal is very weak, to increase the signal to noise ratio and facilitate the subsequent signal processing, so an external resistor should be selected to amplify the signal’s amplitude. PD’s response bandwidth depends on the external resistor and junction capacitance, as formula (11) shows, RLOAD is the load resistance of the PD, C j is
the junction capacitance of the PD. f BW
1 2 R LOAD C j
(11)
B. The sampling rate of data acquisition and processing system: Due to maximum sampling rate of the data acquisition card is 1.25M/s, and dual-channel simultaneous acquisition is required, so each channel sampling rate is 625K/s. According to the
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Nyquist sampling theory, it can meet the acquisition of the dual quadrate signals containing motion phase information. From the formula (3), the real-time measurement speed of self-mixing interferometer can reach close to 100mm / s. C. The actual noise level in the circuit: Due to the laser intensity fluctuations and environmental factors, noise level will become sensitive to the increased speed, affecting the measurement accuracy greatly. It is necessary to rationalize the circuit design system and adopt high-performance PD and high-precision data acquisition and processing system to reduce noise in the interferometer.
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6. Conclusion
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This paper presents reflection phase-shift laser self-mixing interferometer which has a more simple, compact and easy collimation structure. By introducing / 2 phase-shift to the self-mixing interference front output signal reflected by the metal film, and two orthogonal laser self-mixing interference signals are obtained for the real-time displacement measurement directly, which greatly reduces the cost and enhances the reliability of the measurement system, owing to no modulation and demodulation. Through the subdivision method in the digital domain, the error in the hundreds mm large range displacement measurement is decreased to 0.4μm. At the same time the speed of the interferometer in the large scale displacement measurement is improved to nearly 100mm/s theoretically.
ACKNOWLEDGEMENTS
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This work was supported by the National Natural Science Foundation of China (Grant Nos. 91123015, 61178044), Jiangsu province prospective joint research project (Grant Nos.SBY2012005), thanks to them!
REFERENCES
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[7] Guo Dongmei, Tan Suqing, Wang Ming Micro displacement measurement accuracy analysis for a sinusoidal phase-shifting self-mixing interferometer [J] Acta Optica Sinica, 2006,26 (6): 845 ~ 850. [8] Huali Lu, Ming Wang etal. All-Fiber Self-Mixing Interferometer Based on DFB Laser and Phase Modulating Technique, IEEE PHOTONICS TECHNOLOGY LETTERS,2011,23(4):221-223 [9] W. Wang, W. J. O. Boyle, K. T. W. Grattan etal. Self-mixing Interference in a diode laserfor optical sensing applications, IEEE J.Lightwave Technol. 12, 1577-1587 (1992). [10] Yang Ying,Li Xingfei,Li Hongyu,Wang Cuo,Kou Ke. Acceleration Sensor Based on Laser Self-Mixing Interference[J]. Acta Optica Sinica, 2013, 33(2): 0228003. [11] Wei Xia, Zhenyu Yang, Qiang Liu, and Ming Wang.Development of a sinusoidal phase-shifting self-mixing interferometer for realtime displacement measurement with nanometer accuracy.Measurement Science and Technology. 2013, 24 (5): 1 ~ 9. [12] Zhang Zhaoyun, Gao Yang, Zhao Xinghai etal. The theoretical study of measurement speed limit of the diode laser's self-mixing effect. Chinese Journal of Lasers, 2010,37 (1) :211-214.
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