sensors Article

All-Fiber Configuration Laser Self-Mixing Doppler Velocimeter Based on Distributed Feedback Fiber Laser Shuang Wu 1 , Dehui Wang 1 , Rong Xiang 1 , Junfeng Zhou 1 , Yangcheng Ma 1 , Huaqiao Gui 2 , Jianguo Liu 2 , Huanqin Wang 3 , Liang Lu 1, * and Benli Yu 1 1

2 3

*

Key Laboratory of Opto-Electronic Information Acquisition and Manipulation of Ministry of Education, Anhui University, Jiulong Road 111#, Hefei 230601, China; [email protected] (S.W.); [email protected] (D.W.); [email protected] (R.X.); [email protected] (J.Z.); [email protected] (Y.M.); [email protected] (B.Y.) Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; [email protected] (H.G.); [email protected] (J.L.) State Key Laboratory of Transducer Technology, Institute of Intelligent Machines, Chinese Academy of Sciences, 350 Shu Shang Hu Road, Hefei 230031, China; [email protected] Correspondence: [email protected]; Tel.: +86-551-6386-1760

Academic Editor: Vittorio M. N. Passaro Received: 30 May 2016; Accepted: 19 July 2016; Published: 27 July 2016

Abstract: In this paper, a novel velocimeter based on laser self-mixing Doppler technology has been developed for speed measurement. The laser employed in our experiment is a distributed feedback (DFB) fiber laser, which is an all-fiber structure using only one Fiber Bragg Grating to realize optical feedback and wavelength selection. Self-mixing interference for optical velocity sensing is experimentally investigated in this novel system, and the experimental results show that the Doppler frequency is linearly proportional to the velocity of a moving target, which agrees with the theoretical analysis commendably. In our experimental system, the velocity measurement can be achieved in the range of 3.58 mm/s–2216 mm/s with a relative error under one percent, demonstrating that our novel all-fiber configuration velocimeter can implement wide-range velocity measurements with high accuracy. Keywords: self-mixing effect; DFB fiber laser; Laser Doppler Velocimeter (LDV)

1. Introduction The traditional Laser Doppler Velocimeter (LDV) [1–3] based on two beam interference have been widely applied in optical sensor and industrial areas [4–7], on account of the advantages of anti-interference, fast dynamic response, and non-contact measurement. However, there still exist many restrictions in practical application, such as complex light path and high reference beam requirement. Laser self-mixing interference (SMI) technology is a novel coherent measurement technique which has been researched and developed in many sensing and measuring fields, such as absolute distance, displacement, velocity, and vibration measurement [8–11]. SMI technology applied in LDV [12,13] is called SM-LDV, which can replace traditional LDVs on many occasions because of its compact and simple structure, easy alignment, reliability, and low cost. In the common SM-LDV system, the laser source is usually semiconductor lasers [14,15], which have been broadly investigated as they have small size, long service life, and high optical feedback sensitivity resulting from short cavity length [16]. However, wide linewidth and multi-longitudinal mode characteristics of semiconductor lasers will lead to poor coherence and monochromaticity. Thus,

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more effective methods have to be developed for the purpose of obtaining preferable measurement results; for instance, employing a fiber laser as the laser source of a SM-LDV system. Recently, fiber lasers have developed rapidly, attracting considerable attention due to a variety of potential applications in fiber communication techniques and fiber sensing systems. It has been proven that fiber laser sensors show great superiority, including wide responsive bandwidth, remote optical pumping, immunity to electromagnetic interference, interrogation ability, and the capability of being a wavelength division multiplexed along a single fiber [17–21]. Compared to the semiconductor laser sensing technology, fiber laser sensing technology employed in SM-LDV is a preferable choice to realize a more flexible system and get better measurement results. Fiber ring lasers applied as the laser source in SM-LDV has been studied and experimented in detail [22,23], while the system measurement range and precision still have room to grow. This is because the dense longitudinal modes spacing resulting from long cavity length of the fiber ring laser would lead to multi-longitudinal modes oscillation and mode hopping in the resonant cavity, which seriously affect the stability of output laser [24]. Therefore, a shorter cavity used in the fiber laser is apparently a superior solution to solve the problem caused by the long cavity length of fiber ring lasers. The short cavity can enlarge the space of longitudinal modes and provide stable single longitudinal mode output. In addition, the laser sensitivity to optical feedback depends on the ratio of emission level lifetime and photon lifetime [25,26]; that is, shorter laser cavity length would lead to higher sensitivity to optical feedback. The above reasons have inspired many researchers, including us, to attempt to employ fiber lasers with a shorter cavity length, such as the distributed Bragg reflection (DBR) fiber laser as the laser source in the SM-LDV [27,28]. However, the cavity of the DBR fiber laser is formed by two Fiber Bragg Gratings (FBGs), and the laser cavity length is not short enough. Therefore, we employed the DFB fiber laser with much shorter cavity length as the laser source of the SM-LDV system. The distributed feedback (DFB) fiber laser is formed of all-fiber configuration with only one FBG to realize optical feedback and wavelength selection, which have same active region and feedback area. The cavity length of DFB fiber laser is only a few millimeters, which have high sensitivity to optical feedback. Compared to semiconductor lasers, DFB fiber lasers have further advantages, including good compatibility with optical fiber, stability of output power, a more pure optical spectrum, narrow linewidth, and inherent fiber laser advantages, which have been attractive devices for a range of applications in communications and sensing [29–31]. With the purpose of implementing a wider range velocity and higher accuracy measurement compared to traditional SM-LDV, the DFB fiber laser was employed as the laser source of SM-LDV in our experiment. In this paper, a novel all-fiber configuration laser self-mixing Doppler velocimeter with the DFB fiber laser as the laser source is presented, which is called all-fiber configuration DFB-SM-LDV. In the DFB-SM-LDV system, we use π-phase shifted DFB fiber laser as the laser source, expecting to acquire higher accuracy as well as a wider velocity measurement range compared to the common SM-LDV. The theory model of the all-fiber configuration DFB-SM-LDV was built up in this report, along with detailed theoretical analysis of velocity measurement. 2. Theoretical Simulation In this section, we proposed a basic theoretical model of DFB fiber laser based on the phase-shifted FBG. To prove the feasibility of the experiment and analyze the results of laser self-mixing output power, the theoretical model was established as shown in Figure 1. In Figure 1, the yellow part stands for the gain medium Er3+ -Yb3+ co-doped optical fiber (EYDF). The black bars stand for the fiber Bragg gratings (FBG), which are written directly into the active optical fiber. Figure 1 shows the theoretical model of the all-fiber structure DFB-SM-LDV, which is built based on the phase-shifted FBG and laser self-mixing effect. The DFB laser we employed in the experiment is a π-phase shifted DFB laser, which achieves single-wavelength operation and unidirectional output due to the extremely small length of the cavity [32–34]. From the phase-shift position, the original grating can be regarded as two grating sections, which can be considered as a pair of wavelength-matched

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Sensors 16, 1179section on the left side of the phase shift can be regarded as a mirror of 3 ofM 10 , and FBGs. The2016, grating 1 the grating section on the right side of the phase shift can be regarded as the output mirror of M2 . regarded as a mirror of M1, and the grating section on the right side of the phase shift can be In the phase-shifted FBG, the fields propagating to the left and to the right are constrained by the two regarded as the output mirror of M2. In the phase-shifted FBG, the fields propagating to the left and gratings, circulating short effective cavity, regarded within as the equivalent F-P cavity to theand rightthey are are constrained by within the twoagratings, and they are circulating a short effective of the DFB fiber laser [35,36]. cavity, regarded as the equivalent F-P cavity of the DFB fiber laser [35,36].

Figure 1. The theoreticalmodel model of of all-fiber all-fiber configuration self-mixing interference laser laser Doppler Figure 1. The theoretical configuration self-mixing interference Doppler 3+ 3+ velocimeter (SM-LDV) system based on the π-phase shifted DFB fiber laser. EYDF: Er 3+ velocimeter (SM-LDV) system based on the π-phase shifted DFB fiber laser. EYDF: Er -Yb3+-Yb co-doped co-doped optical fiber; FBG: fiber Bragg grating. optical fiber; FBG: fiber Bragg grating.

We analyze the laser self-mixing effect of the DFB fiber laser as shown in Figure 1. The pump We analyze theinto laser effect of the of DFB as shown in Figure 1. The pump light light is coupled theself-mixing effective resonant cavity thefiber DFB laser fiber laser, the output power is focused out, and Pseed on the object andeffective reflectedresonant or scattered by the moving In thethe Figure 1, the Pin, Pis is coupled into the cavity of the DFB target. fiber laser, output power focused on the represent the input theby output power, and the seed light power, respectively. object and reflected or power, scattered the moving target. In the Figure 1, the Pin , Pout , The andsubscripts Pseed represent p and s represent the pump and signal. In addition, the subscripts L and R represent that the laser the input power, the output power, and the seed light power, respectively. The subscripts p and s propagates to the left and right direction in the laser cavity, respectively. In the velocity represent the pump and signal. In addition, the subscripts L and R represent that the laser propagates measurement system, the scattered or reflected field is frequency-shifted by the Doppler principle to the left and right direction in the laser cavity, respectively. In the velocity measurement system, on the moving target. By combining the quasi-analytical method to solve the steady-state equations the scattered or condition reflectedinfield is frequency-shifted the Doppler principle on the equations, moving target. of the lasing the DFB fiber laser and theby calculation of Boundary condition By combining the quasi-analytical method to solve the steady-state equations of the lasing we could theoretically deduce the expression of output power, which can be written as [37,38]:condition in s

the DFB fiber laser and the calculation of Boundary condition equations, we could theoretically deduce P out  12 r122 [2 r22 PRout  (1  r22 ) Pseed ]exp  2 Leff  2Psabs /Pss  2Ppabs /Pss  the expressionR of output power, which can be written as [37,38]: s

 L1 ) tanh( L2 )     tanh(´  12 r122 [2 r22 PRout  (1  r22 ) Pseed ]exp  2    2Psabs /Pss  2Ppabs /Pss ¯ abs abs 2 2 2 out 2 2  2    “ ε1 r1 ε2 rε2 r2 PR ` p1 ´ r2qPseed sexp ´2αs Le f f ` 2Ps {Pss ` 2Pp {Pss

(1)

PRout

! ´ ¯ ) tanhpκL1 q tanhpκL2 q abs abs given outintroduced 2 qP as the total power of back-scattered light from a moving target, “ ε21Here, r21 ε2 rεP2seed r22 Pis ` p1 ´ r sexp ´2α ` ` 2P {P ` 2P {P s ss ss s p 2 seed R 2κ 2κ

(1)

as:

2 light from a moving target, given as: Here, Pseed is introduced as the total power of2back-scattered (2) Pseed   r2   (1  r2 ) 2 r3 cos  ext  PRout ” ı 2 2 “ powers r2 ` ηp1 r2 2 qabsorbed r3 cosϕext PRoutround trip and saturation, (2) where the indexes abs and Pss of´the in one seedare

respectively. Ppabs and Psabs are the variable values of the pump and signal light power, respectively.

where indexes abs and sspowers are powers of the absorbed one round trip and saturation, Pss the denotes the saturation of signal light. αs is theinsmall signal absorption coefficient.respectively. Leff is abs abs Pp the and Ps ofare variable values of the pump and signal respectively. Pss are denotes length thethe effective active doped fiber. The length of thelight left power, and right grating section L1 the  islight. saturation of signal αs is thecoefficient. small signal and L2, powers respectively. the coupling r1, r2absorption , and r3 are coefficient. the reflectionLcoefficient of the of the eff is the length M1, Mactive 2, and the target, respectively. η isofthe of thesection object toare theLcollimator. ε1 and effective doped fiber. The length thecoupling left andefficiency right grating 1 and L2 , respectively. ε 2 represent the total attenuation factors, including insertion loss. κ is the coupling coefficient. r1 , r2 , and r3 are the reflection coefficient of the M1 , M2 , and the target, Whenηthe external target efficiency moves far away the to laser, external phase canεberepresent expressed the as: total respectively. is the coupling of thefrom object thethe collimator. ε1 and 2 attenuation factors, including insertion loss. 4  L0  vtcos  (3)  extaway  from the laser, the external phase can be expressed When the external target moves far as:  ϕext “

4π pL0 ` vtcosθq λ

(3)

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Here, v is the velocity of a moving target and θ is the angle between the incident light direction SensorsHere, 2016, 16, 1179 4 of 10 v is the velocity of a moving target and θ is the angle between the incident light direction and the velocity direction. On the basis of the above equations, a simulation of laser output power and the velocity direction. On the basis of the above equations, a simulation of laser output power fluctuation byvelocity the speed an external carried The simulated self-mixing signals Here,caused v is the of aofmoving targettarget and θwas is the angleout. between the incident light direction fluctuation caused by the speed of an external target was carried out. The simulated self-mixing at and different velocities are shown in Figure theabove red solid line, black dotted line, and output blue dotted line the velocity direction. On the basis of2;the equations, a simulation of laser power signals at different velocities are shown in Figure 2; the red solid line, black dotted line, and blue causedsignal by thecorresponding speed of an external target was carried out.atThe simulated self-mixing arefluctuation the self-mixing to the external target speed 50 mm/s, 100 mm/s, and dotted line are the self-mixing signal corresponding to the external target speed at 50 mm/s, 100 atrespectively. different velocities are shown Figure 2; the red solid line,signal blackfringe dottednumber line, and blue 150signals mm/s, Figure 2,From weincan see that thecan self-mixing mm/s, and 150 mm/s,From respectively. Figure 2, we see that the self-mixing signal increases fringe dottedwith line increasing are the self-mixing signal velocity. corresponding to the external target speed at 50 mm/s, 100 linearly external target number increases linearly with increasing external target velocity. mm/s, and 150 mm/s, respectively. From Figure 2, we can see that the self-mixing signal fringe number increases linearly with increasing external target velocity.

Figure 2. The simulated self-mixing output signals at different velocities. Figure 2. The simulated self-mixing output signals at different velocities. Figure 2. TheTransform simulated self-mixing output signals at different velocities. Through a Fast Fourier (FFT) of the simulated output power at a certain speed, the Through a Fast Fourier Transform (FFT) of the simulated output power at a certain corresponding frequency can be obtained. In order to further explore the relationship of speed, externalthe Through a Fast Fourier Transform (FFT) of the simulated output power at a certain speed, the corresponding can be obtained. In order to further explore the of relationship of external target target speedfrequency and corresponding frequency, we simulated the speed the external target from corresponding frequency can be obtained. In order to further explore the relationship of external speed and corresponding we300 simulated speed of the external target from 300 mm/s to 300 mm/s to 3000 mm/s, frequency, with steps of mm/s at the θ = 60°. target speed and corresponding frequency,˝we simulated the speed of the external target from The simulated the simulated and corresponding frequency are plotted in 3000 mm/s, with stepsresults of 300of mm/s at θ = 60 velocity . 300 mm/s to 3000 mm/s, with steps of 300 mm/s at θ = 60°. Figure which areresults indicated and fitted by a redand line.corresponding From Figure 3, frequency we can observe that the in The 3, simulated of by thedots simulated velocity are plotted The simulated results of the simulated velocity and corresponding frequency are plotted in relationship the simulated andbycorresponding frequency with thethe Figure 3, whichbetween are indicated by dotsvelocity and fitted a red line. From Figureis3,in weaccordance can observe that Figure 3, which are indicated by dots and fitted by a red line. From Figure 3, we can observe that the Doppler principle, indicates velocity that it is and a considerable method to utilize self-mixing with signalthe relationship betweenwhich the simulated corresponding frequency is the in accordance relationship between the simulated velocity and corresponding frequency is in accordance with the frequency to measure theindicates velocity of a moving target. Doppler principle, which that it is a considerable method to utilize the self-mixing signal Doppler principle, which indicates that it is a considerable method to utilize the self-mixing signal frequency to measure the velocity of a moving target. frequency to measure the velocity of a moving target.

Figure 3. The simulated frequency of the external moving target at different velocities with θ = 60°. Figure 3. The simulated frequency of the external moving target at different velocities with θ = 60°. Figure 3. The simulated frequency of the external moving target at different velocities with θ = 60˝ .

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3. Schematic of the Experimental Set-up 3. Schematic of the Experimental Set-up For the the sake sake of of verifying verifying the the feasibility feasibility of of utilizing utilizing the the laser laser self-mixing self-mixing Doppler Doppler principle principle to to For measure velocity, experiments have been carried out. The experimental setup is shown measure velocity, experiments have been carried out. The experimental setup is shown schematically schematically 4. In our experimental system, the all-fiber configuration DFB-SM-LDV in Figure 4. In in ourFigure experimental system, the all-fiber configuration DFB-SM-LDV consists of a DFB consists of a DFB fiber laser, a target consisting of a rotating turntable with a rough reflective fiber laser, a target consisting of a rotating turntable with a rough reflective surface, and asurface, signal and a signal processing with a(PD). photo-diode (PD). As shown Figurelight 4, the pump light is processing circuit with a circuit photo-diode As shown in Figure 4, theinpump is coupled to the coupled to the effective cavity of the DFB fiber laser through wavelength division multiplex effective cavity of the DFB fiber laser through wavelength division multiplex (WDM1), and the signal (WDM1), the gain signal is amplified by the gain medium.byThe is scattered by the is amplifiedand by the medium. The output laser is scattered the output movinglaser turntable and is reflected moving andcavity is reflected backfiber into laser, the effective cavity the DFB laser, mixing with back intoturntable the effective of the DFB mixing with theofinitial laser,fiber modulating the output the initial laser, modulating the output power and spectrum. power and spectrum.

Figure set-up of our all-fiberall-fiber configuration SM-LDV SM-LDV based on the distributed Figure 4.4.The Theexperimental experimental set-up of novel our novel configuration based on the feedback (DFB) fiber laser. distributed feedback (DFB) fiber laser.

DFBfiber fiberlaser laseris is made of two 980 nm/1550 nm WDMs andmedium gain medium ofoptical active The DFB made up up of two 980 nm/1550 nm WDMs and gain of active optical fiber with phase-shifted FBG,iswhich is realize used tooptical realizefeedback optical feedback and wavelength fiber with phase-shifted FBG, which used to and wavelength selection. selection. lasing action thecan DFB can be as considered as signalbygeneration by the gain The lasingThe action in the DFB in laser belaser considered signal generation the gain medium and 3+-Yb3+ 3+ 3+ medium and feedback bygain the medium FBG. Theofgain medium thewe DFB fiber used is Eroptical feedback by the FBG. The the DFB fiber of laser used is Erlaser -Ybwe co-doped co-doped optical (EYDF), and the phase FBG had been written in reason it directly. The reason fiber (EYDF), andfiber the phase shifted FBG had shifted been written in it directly. The for employing for employing EYDF as the gain medium is that the DFB fiber laser requires high pump EYDF as the gain medium is that the DFB fiber laser requires high pump efficiency, owing toefficiency, the short owing length. to the short length. EYDF hasrange higher of pump lightas wavelength, as cavity EYDFcavity has higher gain, wider ofgain, pumpwider light range wavelength, as well higher pump 3+ doped fiber, which can satisfy the need well as higher pumptoefficiency compared to commonly efficiency compared commonly Er3+ doped fiber, whichEr can satisfy the need of high pump efficiency. of high pump efficiency. Thus, employing as the in theway DFBtofiber is an Thus, employing EYDF as the gain medium inEYDF the DFB fibergain lasermedium is an efficient solvelaser the issues efficient way efficiency. to solve the issues of low pump efficiency. of low pump As shown in Figure 4, the target is a rotating rotating turntable turntable with a rough reflective surface which is driven by bya aDCDC motor (Chongqing, China, Feiteng 41K2.5RGN-C direct motor). currentThe motor). The driven motor (Chongqing, China, Feiteng 41K2.5RGN-C direct current rotational rotational speed of the byspeed the motor’s speed controller, withspeed the revolving speed of the turntable is turntable controlledisbycontrolled the motor’s controller, with the revolving range of speedrotations range ofper 0–3.6 rotations laser output is through collimator fitted onto the 0–3.6 second. The per lasersecond. output The is through a collimator fitted aonto the three-dimensional three-dimensional adjustablewhich support brackets, to which employed adjust the (θ) light between adjustable support brackets, is employed adjustisthe angle (θ)tobetween theangle incident and the measured incident light and the measured velocity, as well as to regulate the collimator in vertical and velocity, as well as to regulate the collimator in vertical and horizontal shift directions to horizontal shift directions to ensure the velocity at a certain point of the turntable. Then, the ensure the velocity at a certain point of turntable. Then, the collimator receives the light reflected collimator receives reflected scatteredThe from the surfaceoutput of the power turntable. The modulated and scattered fromthe thelight surface of theand turntable. modulated is detected by the output power is detected by the PD connected at the end of the processing circuit, which consists of PD connected at the end of the processing circuit, which consists of an amplifying and a filtering an amplifying and a filtering circuit. The received signal is processed to realize signal amplifying

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and noise reductionsignal by the signal processing circuit. The processed signal is observed on a circuit. The received is processed to realize signal amplifying and noise reduction by the signal radio-frequency (RF) spectrum analyzer (Ohio, America, RSA-3408B time spectrum processing circuit. The processed signal is observed on a Tektronix radio-frequency (RF) real spectrum analyzer analyzer). (Ohio, America, Tektronix RSA-3408B real time spectrum analyzer). It can canbe beseen seenthat thatthe the laser incident upon a certain the turntable and the tangential It laser incident upon a certain pointpoint of theofturntable and the tangential speed speed direction of that point isinshown inwhich Figurecan 4, be which can be projected the light incident direction of that point is shown Figure 4, projected into the lightinto incident direction and direction and perpendicular the In incident light. In our value of the perpendicular to the directiontoofthe thedirection incident of light. our experiment, theexperiment, value of thethe angle between angle between incident light isand velocity isin60°. in turntable our experiment, the the incident lightthe and the velocity 60˝ .the Additionally, ourAdditionally, experiment, the rotates at a turntable rotates at a fixed direction, so the phase direction remains unchanged [39,40]. The fixed direction, so the phase direction remains unchanged [39,40]. The tangential velocity of a certain tangential of is a determined certain pointbyon turntable is of determined by and the rotating speed of the point on thevelocity turntable thethe rotating speed the turntable the distance between turntable that point and and the the distance turntablebetween center. that point and the turntable center. 4. ExperimentalResults Resultsand andDiscussion Discussion 4. Experimental In In the the experiment, experiment, by by adjusting adjusting the the rotating rotating speed speed of of the the turntable turntable and and changing changing the the incident incident position of the laser, we can continuously measure velocities ranging from 3.58 mm/s to 2216 mm/s. position of the laser, we can continuously measure velocities ranging from 3.58 mm/s to A spectrum analyzer (Tektronix time spectrum analyzer) is employed observe the 2216 mm/s. A spectrum analyzerRSA-3408B (Tektronixreal RSA-3408B real time spectrum analyzer) istoemployed to spectrum related to therelated measured velocity. Through observing theobserving spectrumthe analyzer, the analyzer, Doppler observe the spectrum to the measured velocity. Through spectrum frequency offrequency the certain of thepoint turntable be acquired. We give We typical signals the Doppler ofpoint the certain of thecan turntable can be acquired. giveDoppler typical Doppler displayed on the frequency spectrum analyzer in the small measurement range range and large signals displayed on the frequency spectrum analyzer in thevelocity small velocity measurement and velocity measurement range, which are shown in Figures 5 and 6. In Figure 5, we can observe the large velocity measurement range, which are shown in Figures 5 and 6. In Figure 5, we can observe ˝ experimental result of the all-fiber configuration DFB-SM-LDV under the the experimental result of the all-fiber configuration DFB-SM-LDV under thecondition conditionofofθθ==60 60° at at aa velocity mm/s,respectively. respectively. As As shown shown in Figure 5, the values of the Doppler velocity of of 3.585 3.585mm/s mm/s and 8.724 mm/s, frequency frequency peaks peaks caused caused by by the the measured measured velocities velocitiesare are2.3125 2.3125kHz kHzand and5.625 5.625kHz, kHz,respectively. respectively.

(a)

(b)

Figure 5. 5. Typical Doppler signal signal displayed displayed on on the the spectrum spectrum analyzer analyzer of of different different velocities velocities with with θθ == 60 60°. ˝. Figure Typical Doppler (a) v = 3.585 mm/s; (b) v = 8.724 mm/s. (a) v = 3.585 mm/s; (b) v = 8.724 mm/s.

Figure 6 shows the experimental results of the all-fiber configuration DFB-SM-LDV affected by Figure 6 shows the experimental results of the all-fiber configuration DFB-SM-LDV affected by the the turntable under the condition of θ = 60° at a velocity of 1814.88 mm/s and 2053.68 mm/s, turntable under the condition of θ = 60˝ at a velocity of 1814.88 mm/s and 2053.68 mm/s, respectively. respectively. From Figure 6, we can see that the values of the Doppler frequency peaks caused by the From Figure 6, we can see that the values of the Doppler frequency peaks caused by the measured measured velocities are 1170.3125 kHz and 1325.78125 kHz, respectively. velocities are 1170.3125 kHz and 1325.78125 kHz, respectively. From the data shown in Figures 5 and 6, there are some small extra peaks (which have been From the data shown in Figures 5 and 6, there are some small extra peaks (which have been remarked) corresponding to the frequencies of environmental vibration signal and electronic noise remarked) corresponding to the frequencies of environmental vibration signal and electronic noise signal. Meanwhile, it can be seen that the Doppler signals have certain broadening, which is derived signal. Meanwhile, it can be seen that the Doppler signals have certain broadening, which is derived from laser spectral broadening and non-uniform velocity distribution such as the inhomogeneity of from laser spectral broadening and non-uniform velocity distribution such as the inhomogeneity of angular speed, the inconformity of speed of each point in the irradiation light spot, the angular speed, the inconformity of speed of each point in the irradiation light spot, the determination determination of turntable center position, and the speckle effect. In our experimental system, we of turntable center position, and the speckle effect. In our experimental system, we adopt the peaking adopt the peaking searching method to collect the frequency peak value. Based on the frequency peak value, we could calculate the corresponding velocity according to the Doppler principle, which was clearly introduced in the theoretical simulation. This kind of peak searching method can mainly

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searching method to collect the frequency peak value. Based on the frequency peak value, we could calculate the corresponding velocity according to the Doppler principle, which was clearly Sensors 2016, 16, 1179 7 of 10 introduced in the theoretical simulation. This kind of peak searching method can mainly reduce the influence ofinfluence sideband of and broadening the Doppler but the uncertainty any peak position reduce the sideband and of broadening of signals, the Doppler signals, but theonuncertainty on any still depends on its width and the acquisition’s horizontal resolution (Resolution Bandwidth of the peak position still depends on its width and the acquisition’s horizontal resolution (Resolution Spectrum from 300 Hz tochanges 10 KHz from with different anddifferent vertical BandwidthAnalyzer of the changes Spectrum Analyzer 300 Hz frequency-scales) to 10 KHz with resolution (1 dB). and vertical resolution (1 dB). frequency-scales)

(a)

(b)

Figure 6. Doppler signal signal displayed displayed on on the the spectrum spectrum analyzer analyzer of of different different velocities velocities with with θ θ= = 60°. Figure 6. Typical Typical Doppler 60˝ . (a) v = 1814.88 mm/s; (b) v = 2053.68 mm/s. (a) v = 1814.88 mm/s; (b) v = 2053.68 mm/s.

The experimental results of the measured velocity of the external target are shown in Figure 7. The experimental results of the measured velocity of the external target are shown in Figure 7. As shown in Figure 7, black spots represent the measured velocities and the shadow bar represents As shown in Figure 7, black spots represent the measured velocities and the shadow bar represents the the relative error of the all-fiber DFB-SM-LDV system. The velocity measurement range is from relative error of the all-fiber DFB-SM-LDV system. The velocity measurement range is from 3.58 mm/s 3.58 mm/s to 2216 mm/s. The minimum measurement velocity in our experiment is 3.58 mm/s, to 2216 mm/s. The minimum measurement velocity in our experiment is 3.58 mm/s, which is lower which is lower than the minimum measurement result of SM-LDV with DBR fiber laser and ring than the minimum measurement result of SM-LDV with DBR fiber laser and ring laser in prior velocity laser in prior velocity measurement works [22,27], proving that our novel all-fiber configuration measurement works [22,27], proving that our novel all-fiber configuration DFB-SM-LDV has a much DFB-SM-LDV has a much wider measurement range compared to the SM-LDV with DBR fiber laser wider measurement range compared to the SM-LDV with DBR fiber laser and ring laser. For the and ring laser. For the moment, confined to mechanical conditions in the experiment, such as the moment, confined to mechanical conditions in the experiment, such as the minimum rotation speed minimum rotation speed and the dimension of the turntable, the velocity measurement range is and the dimension of the turntable, the velocity measurement range is limited. In order to realize a limited. In order to realize a much wider-range and higher-precision velocity measurement, the much wider-range and higher-precision velocity measurement, the experimental set-up should be experimental set-up should be improved and optimized repeatedly in further work. improved and optimized repeatedly in further work. From Figure 7, we can see that the relative error is less than one percent in the whole experimental range, which satisfies the requirement of high-accuracy measurement. The measured error may be introduced by the rotating turntable; the reason is that when the turntable rotates at a high speed, some vibration would be inevitable, which will cause the turntable rotational speed to be uneven and finally influence the measurement results. In the experiment, the measurement precision is increased by averaging the testing values of repeated measurements. In addition, we used the method of peak searching instead of the traditional fringe counting method to seek the corresponding Doppler frequency of the measured velocity, which can increase the measurement accuracy and avoid measurement error stemming from signal broadening. As shown in the above theoretical analysis and experimental results, it can be observed that the all-fiber configuration DFB-SM-LDV has many advantages as well as wide measurement range and high precision, which can solve the problems of small measurement range, complex structure, and low measurement accuracy caused by other LDVs.

Figure 7. The relative error of measured velocity and theoretical velocity.

laser in prior velocity measurement works [22,27], proving that our novel all-fiber configuration DFB-SM-LDV has a much wider measurement range compared to the SM-LDV with DBR fiber laser and ring laser. For the moment, confined to mechanical conditions in the experiment, such as the minimum rotation speed and the dimension of the turntable, the velocity measurement range is limited. In16,order the Sensors 2016, 1179 to realize a much wider-range and higher-precision velocity measurement, 8 of 10 experimental set-up should be improved and optimized repeatedly in further work.

Figure 7. The relative error of measured velocity and theoretical velocity. Figure 7. The relative error of measured velocity and theoretical velocity.

5. Conclusions In conclusion, this paper presents a particular description of theoretical and experimental studies of an all-fiber DFB fiber laser self-mixing Doppler velocity measurement system, which has been proposed for the first time. In the velocity measurement system, the scattered field is frequency-shifted by the Doppler principle on the moving target, and the Doppler frequency is linearly proportional to the value of velocity, which was theoretically analyzed and experimentally observed. In our experiment, the range of velocity measurement is between 3.58 mm/s and 2216 mm/s, and the relative error between the measured velocity and the actual velocity is under one percent. From the experimental results, it can be concluded that our novel all-fiber configuration DFB-SM-LDV system can achieve high-precision, wide-range velocity measurement, which has a great potential for a number of practical applications, such as high-speed measurement and velocity measurement in common room conditions without accurate environmental control. Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grant No. 61307098, 61275165), and the foundation of Key Laboratory of Environmental Optics and Technology of Chinese Academy of Sciences (Grant No. 2005DP173065-2013-2). Besides, the distributed feedback fiber laser was provided by Chun Gu of the University of Science and Technology of China. Author Contributions: Shuang Wu designed the experiments, carried out the experiment of velocity measurement and wrote this paper. Dehui Wang designed the simulated program and processed the simulated data. Rong Xiang participated in the experiment and prepared all figures and tables. Junfeng Zhou were responsible for the data acquisition and processing. Yangcheng Ma, Huaqiao Gui, Jianguo Liu, Huanqin Wang discussed the experimental results. Liang Lu developed the concept, revised the manuscript for content. Benli Yu supervised the entire project. All authors reviewed the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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All-Fiber Configuration Laser Self-Mixing Doppler Velocimeter Based on Distributed Feedback Fiber Laser.

In this paper, a novel velocimeter based on laser self-mixing Doppler technology has been developed for speed measurement. The laser employed in our e...
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