sensors

Letter Development of a High-Resolution All-Fiber Homodyne Doppler Vibrometer

Jianhua Shang 1,*, Yan He 2, Qi Wang 1, Yilun Li 1 and Lihong Ren 1

1 Shanghai Collaborative Innovation Center for High Performance Fiber Composites, School of Information Science and Technology, Donghua University, Shanghai 201620, China; [email protected] (Q.W.); [email protected] (Y.L.); [email protected] (L.R.) 2 Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China; [email protected] * Correspondence: [email protected]

 Received: 17 September 2020; Accepted: 12 October 2020; Published: 14 October 2020 

Abstract: Based on the homodyne detection, a compact and cost-effective all-fiber laser Doppler vibrometer (LDV) with high resolution is presented. For the signal processing, the discrimination algorithm combined with the nonorthogonal correction is applied. The algorithm corrects the quadrature imbalance and other nonlinearity. In the calibration experiment, with the glass pasted on a piezoceramic transducer (PZT), the velocity resolution of 62 nm/s at 4 kHz and displacement resolution of 2.468 pm are achieved. For the LDV-based acousto-optic communication, the minimum detectable sound pressure level (SPL) reached 0.12 Pa under the hydrostatic air-water surface. The results demonstrate that the designed homodyne LDV has a low system background noise and can offer high precision in the vibration measurement.

Keywords: LDV; homodyne; velocity resolution; minimum detectable SPL

1. Introduction The laser Doppler vibrometer (LDV) is adopted primarily to measure the vibration characteristics in an optical nonintrusive and remote way. The principle of the LDV relies on the coherent detection concerning the Doppler frequency shift of the reflected or scattered laser beam from a moving target [1,2]. Hitherto, its development has received great attention, and it is also widely applied to various fields ranging from the acousto-optic detection for the underwater sound [3], the remote voice acquirement [4], the health monitoring for the composite materials [5–8], the biomedical assessments [9–12], the trace explosive detection [13,14], and the vibration analysis of the component motions and the civil structures [15,16]. Compared with the contact sensors, such as the piezoelectric , the LDV is good at performing the noncontact vibration measurement of the rotating structures. Abbas et al. [17] obtained the underwater vibration response of the blades of rotating propellers by means of the LDV and compared this response with that obtained with the wireless contact piezoelectric . Concerning whether the intermediate frequency (IF) equals zero or not, the LDV can be classified into the homodyne detection and heterodyne detection. Pursuing a higher phase-sensitive detection, some consideration of the signal to noise ratio (SNR) related to the optical homodyne and heterodyne detection has been discussed previously [18]. The relative intensity noise (RIN) and phase noise of laser and other optical phase variations caused by the internal factors of the LDV and surrounding noises will restrict its minimum detectable capability. Compared with the homodyne detection, the heterodyne detection can provide a good performance in the frequency band less than 1 kHz at the expense of a much more complicated optical implementation and the extra signal demodulation processing for

Sensors 2020, 20, 5801; doi:10.3390/s20205801 www.mdpi.com/journal/sensors Sensors 2020, 20, 5801 2 of 11 the IF signal. However, the serious IF crosstalk signal will impair the heterodyne LDV performance, and substituting the fiber circulator with a polarization prism can eliminate this crosstalk to a certain extent [19]. In recent years, the growing maturity of the LDV makes various types of LDVs commercially available. Several types of multi-channel and multipoint LDVs have been well established; besides, the continuous scanning LDV is investigated to measure the out-of-plane vibration of a structure surface [20]. However, the frequency bandwidth should be taken into account when realizing the LDV-based underwater acousto-optic communication. Under the hydrodynamic air–water interface, the tiny vibration caused by the underwater sound source is amplitude modulated by the water surface wave motion, and the movement of the water surface is at the level of cm/s or above. In order to obtain the transmitted frequency of the underwater sound source, the water fluctuation must be detected without any missing [21]. Besides, for the nondestructive testing (NDT) with the scanning LDV, it is time-consuming and easy to lose focus during the scanning situation [22,23]. Whatever the single-point LDV, the multi-point LDV or the scanning LDV, the performance of this small-amplitude vibration measurement requires that the spatial resolution or detection sensitivity be as sensitive as possible. Reducing the noise floor level of the LDV is an effective way to improve the performance of the LDV. In order to promote the detection sensitivity, many analyses related to the measurement noise have been done [24]. The influence of the internal parasitic reflections of the LDV is analyzed in Ref [25]. When measuring the rotational angular displacement with dual LDVs, Ref [26] improves the measurement accuracy to 0.0088◦ after analyzing the influence of the light intensity non-uniformity error, the systematic defect error, the synchronization error, and the sampling frequency-caused error. Besides the analysis of SNR of the LDV,diverse optical configurations and signal processing methods have been reported in the scientific literature and by commercial manufacturers. With the birefringent dual-frequency LDV and a new signal-processing scheme based on a digital signal processor lock-in amplifier and a low-frequency demodulation algorithm, the average velocity resolution of this dual-frequency LDV is improved from 0.31 to 0.028 mm/s due to the characteristics of good directionality, low speckle noise, and good coherence [27]. By using the 1550 nm all-fiber pulsed LDV and a new digital range gated signal processing method, the cochannel interference can be eliminated, and the SNR of the demodulated signal is improved consequently [28]. As the spectrum leakage and fence effect decrease the measurement precision of the LDV significantly, the trispectral interpolation of the Nuttall window is proposed for the LDV signal processing [29]. For the four-channel heterodyne LDV developed in Ref [30,31], a new calibration method based on the Bessel function of the first kind is introduced to improve the measurement resolution. The minimum detectable displacement of this LDV is up to 0.7 nm (RMS) at a bandwidth of 90 kHz and the vibration velocity can reach 3.8 m/s. Recently, Ref. [32] employs the phase multiplication to enhance the LDV measurement resolution, and the minimum detectable displacement of 72 nm with an error range of 14 nm is achieved through direct counting of interference fringes. ± In view of our previous research, it was observed that the match and the balance between the local oscillator (LO) laser beam and the transmitted laser beam is a fundamental and critical guarantee for achieving the highly sensitive experiment results. Insufficient control may produce associated noise and measurement error. In addition, referring to the acousto-optic detection for the underwater sound, the infrared radiation laser is more advantageous than other . Besides, the in-air platforms give a real demand that the LDV should be able to present a non-contact and fast response with a high performance as well as a simple and easy-implementable structure. In this letter, a compact cost-effective eye-safe wide-band high-sensitivity homodyne LDV with a self-correction ability of nonorthogonality and nonlinearity is designed. With a piece of thin glass pasted on the ring-shaped piezoceramic transducer (PZT), the minimum resolvable velocity resolution and the frequency response of this self-made homodyne LDV are investigated. With the compensation of the optical path on the LO laser arm, the system background noise is able to be kept at the same level with an increase in the detection distance. Compared with the results obtained with the air-water Sensors 2020, 20, 5801 3 of 11 interface under the hydrostatic water surface in the anechoic tank, the detection capabilities acquired with theSensors. vibrating 2020, 20, x glass FOR PEER are REVIEW discussed. 3 of 12

2. Homodynethe air-water LDV interface Instrument under and the Principle hydrostatic water surface in the anechoic tank, the detection capabilities acquired with the vibrating glass are discussed. Due to the rapid progress in the compact solid-state and fiber laser technology, the laser sources get an2. excellent Homodyne opportunity, LDV Instrument and components and Principle operating at eye-safe wavelength range are commercially available. In this case, it is possible to build more compact LDVs with small power consumption Due to the rapid progress in the compact solid-state and technology, the laser sources and low-cost fiber optical components. The schematic layout of the LDV based on the homodyne get an excellent opportunity, and components operating at eye-safe wavelength range are detectioncommercially is shown available. in Figure In1. this The case, laser it operatingis possible atto abuild wavelength more compactλ of 1550LDVs nm with is thesmall single-mode power continuous-waveconsumption linearlyand low- polarizingcost fiber optical semiconductor components. laser The with schematic an output layout power of the of LDV 5 mW based and on a spectralthe line widthhomodyne of 1 kHz.detection After is shown the single-mode in Figure 1. The polarizing laser operating fiber optical at a wavelength isolator (PFOI),λ of 1550 the nm laser is the beam was splitsingle into-mode two continuous parts by a-wave 1 2 linearly single-mode polarizing polarizing semiconductor fiber optical lasersplitter with an (PFOS). output To power be specific, of × the first5 mW part and acts a as spectral the LO line laser width beam of while 1 kHz. the After second the part single plays-mode the polarizing role of the fiber transmitted optical isolator laser beam. Through(PFOI), a single-mode the laser beam polarizing was split into fiber two optical parts by circulator a 1 × 2 single (PFOC)-mode andpolarizing a telescope fiber optical consisting splitter of an aspherical(PFOS). lens To with be specific, the aperture the first of part 50 acts mm as and the the LO focallaser lengthbeam while of 200 the mm, second the part transmitted plays the laserrole of beam the transmitted laser beam. Through a single-mode polarizing fiber optical circulator (PFOC) and a was directed normally and focuses on the vibration surface. Meanwhile, the returned optical signal telescope consisting of an aspherical lens with the aperture of 50 mm and the focal length of 200 mm, was collected with the same telescope and mixed with the LO laser beam in the single-mode polarizing the transmitted laser beam was directed normally and focuses on the vibration surface. Meanwhile, optical 2 4 90 hybrid. Instead of the traditional electrical method realizing the phase difference of the returned× ◦ optical signal was collected with the same telescope and mixed with the LO laser beam 90 , the optical 2 4 90 hybrid here can eliminate the random phase drift caused by the heat from the ◦ in the single×-mode ◦polarizing optical 2 × 4 90° hybrid. Instead of the traditional electrical method chipsrealizing and guarantee the phase a stabledifference phase of 90°, diff theerence. optical Then, 2 × 4 90° the hybrid mixed here optical can eliminate signals werethe random detected phase by the balanceddrift photoreceivercaused by the heat 1 (BP1) from and the balancedchips and photoreceiverguarantee a stable 2 (BP2) phase in difference. order to reduceThen, the the mixed influence of theoptical common signals noise were as detected much as by possible. the balanced The outputsphotoreceiver of BP1 1 (BP1) and BP2and werebalanced frequency photoreceiver modulated 2 signals(BP2) and in the order modulation to reduce frequencythe influence was of the the common Doppler noise shift as frequency much as possible. caused byThe the outputs vibration of BP1 of the detectedand surface.BP2 were Subsequently, frequency modulated the two signals output and signals the modulation were sampled frequency by a dual-channelwas the Doppler high-speed shift frequency caused by the vibration of the detected surface. Subsequently, the two output signals were data acquisition card (DAC), and then undertook signal processing in the computer. In order to make sampled by a dual-channel high-speed data acquisition card (DAC), and then undertook signal the system set-up and the alignment more flexible and reliable, the fiber optical components were processing in the computer. In order to make the system set-up and the alignment more flexible and used.reliable, In addition the fiber to that, optical as thecomponents phase changing were used. comes In addition from the to opticalthat, as signalthe phase propagation changing comes difference betweenfrom two the armsoptical of signal this homodynepropagation LDV,difference an easy between and two promising arms of this implement homodyne idea LDV, is toan addeasy aand certain lengthpromising fiber onto implement the LO laser idea beamis to add arm. a ce Therefore,rtain length the fiber local onto noise the LO of thislaser LDV beam can arm. be Therefore, kept at the the same level evenlocal noise if the of detection this LDV distancecan be kept increases. at the same level even if the detection distance increases.

FigureFigure 1. 1.Schematic Schematic layout layout of the homodyne homodyne LDV. LDV.

Theoretically,Theoretically, the phase the phase difference difference between between the outputs the outputs of BP1 of and BP1 BP2 and was BP2 90was◦. Whereas 90°. Whereas suffering the minorsuffering phase the imbalanceminor phase of imbalance the two of beams, the two imperfect beams, imperfect phase bias phase off biasset offset of the of optical the optical 90◦ 90°hybrid, and otherhybrid, factors and other in practice,factors in therepractice, are there the are quadrature the quadrature imbalance imbalance and and other other nonlinearity nonlinearity that can decreasecan decrease the phase the measuringphase measuring accuracy accuracy to a to great a great extent. extent. Therefore,Therefore, signal signal processing processing falls falls into into two steps.two steps. In the In the first first step, step, the the nonorthogonal nonorthogonal correction correction was was to carry to carry out outthe correction the correction algorithm algorithm to modify the quadrature phase shift error and other systematic phase imbalance errors; in the second to modify the quadrature phase shift error and other systematic phase imbalance errors; in the step, the discrimination algorithm tended to obtain the interested vibration parameters of the second step, the discrimination algorithm tended to obtain the interested vibration parameters of the vibrating surface. vibrating surface.

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The outputs of BP1 and BP2 are described as the in-phase signal i(t) and the quadrature signal q(t), shown in Equations (1)–(3). Due to the mismatch of quadrature and other nonlinearity under the actual operating condition, there was some error on the 90◦ phase difference between i(t) and q(t). Consequently,Sensors. 2020, i(t)20, xand FOR PEERq(t) constitute REVIEW one ellipse depicted in Equation (4). 4 of 12 The outputs of BP1 and BP2 arep described as the in-phase signal i(t) and the quadrature signal i(t) = R P P cos(∆ϕ) = I + I cos(∆ϕ) (1) q(t), shown in Equations (1) to (3). Due Sto· theLO mismatch of 1quadrature2 and other nonlinearity under the actual operating condition,p there was some error on the 90° phase difference between i(t) and q(t). q(t) = R P P sin(∆ϕ + δ) = Q + Q cos(∆ϕ + δ π/2) (2) Consequently, i(t) and q(t) constituteS· LO one ellipse depicted1 in Equation2 (4). − = ( ) 푖(푡) = 푅√푃푆 ∙∆푃퐿푂ϕ 푐표푠2⁡(π∆휑fd) =t t퐼1 + 퐼2푐표푠⁡(∆휑) (1) (3) 2 2 [i(t)푞(푡I)1=] 푅√푃[q푆 (∙t푃)퐿푂 푠푖푛Q1(]∆휑 +2훿[i)(t=) 푄1I+1][푄q2(푐표푠t) ⁡(∆Q휑1+]sinδ −δ π⁄2) (2) − + − − − = cos2δ (4) 2 2 I Q − I2 Q2 2 2 ∆휑 = 2휋푓푑(푡)푡 · (3) [ ( ) ]2 [ ( ) ]2 [ ( ) ][ ( ) ] where R is the BPs’ responsivity;푖 푡 − 퐼1 δ refers푞 푡 − to푄1 the random2 푖 푡 − 퐼 phase1 푞 푡 di−ff푄erence1 푠푖푛훿 caused2 by the LO laser beam, 2 + 2 − = 푐표푠 훿 (4) the transmitted laser beam,퐼2 and other non-ideal푄2 factors; P퐼2S∙and푄2 PLO represent the average powers of the returned optical signal and the LO laser beam at the input of the optical 2 4 90 hybrid, and f (t) where R is the BPs’ responsivity; δ refers to the random phase difference caused by× the LO◦ laser beam, d denotesthe thetransmitted laser Doppler laser beam frequency, and other shift non introduced-ideal factors; by P theS and moving PLO represent vibration the surface.average powers of Withthe returned the analog-to-digital optical signal and conversion, the LO laser a beam series at ofthe discrete input of in-phasethe optical/quadrature 2 × 4 90° hybrid, signals andi(m) fd(t) /q(m) weredenotes obtained the correspondingly, laser Doppler frequency and fit shift an elliptical introduced equation. by the moving Based onvibration the method surface. of the least-squares estimatorWith [33], the by analog employing-to-digital the conversion, coefficients a series of this of ellipticaldiscrete in equation,-phase/quadrature the initial signalsi(t) andi(m)/q(t)q(m)were expressed.were obtained Following correspondingly, the least squares and estimator, fit an elliptical an algorithm equation. of Based circle fittingon the [ method34] was of applied the least in- order to makesquares the estimator in-phase [ and33], by quadrature employing signalsthe coefficients orthogonal of this completely. elliptical equation, In Figure the initial2, the i(t) in-phase and q(t) and were expressed. Following the least squares estimator, an algorithm of circle fitting [34] was applied quadrature signals before and after the correction for nonorthogonality and nonlinearity are depicted. in order to make the in-phase and quadrature signals orthogonal completely. In Figure 2, the in-phase The originaland quadrature outputs signals of BP1 before and BP2 and are after displayed the correction in Figure for nonorthogonality2a and are close and to the nonlinearity quadrature are with eachdepicted. other. By The means original of the outputs correction of BP1 algorithm and BP2 of are the displayed least-squares in Figure estimator 2a and and are theclose circle to the fitting, the finalquadrature in-phase with and each quadrature other. By signalsmeans ofi1 (t)theand correctionq1(t) are algorithm shown inof Figurethe least2b,-squares and they estimator are orthogonal and and constitutethe circle fitting, a perfect the final unit i circlen-phase whose and q coordinatesuadrature signals are (0, i1(t) 0). and q1(t) are shown in Figure 2b, and they are orthogonal and constitute a perfect unit circle whose coordinates are (0, 0). i1(t) = cos(∆ϕ) = cos[2π fd(t)t] (5) 푖1(푡) = 푐표푠(∆휑) = 푐표푠[2π푓푑(푡)푡] (5) ( ) ( ) q1푞(1t)푡==sin푠푖푛(∆∆ϕ휑) = 푠푖푛sin[[2π2π푓푑fd(푡()t푡)]t ] (6) (6)

(a) (b)

FigureFigure 2. ( a2.) ( Thea) The original original set set ofof in-phasein-phase signal signal i(t)i(t) andand quadrature quadrature signal signal q(t) fromq(t) BP1from and BP1 BP2; and (b) BP2; the corrected signals i1(t) and q1(t) after the nonorthogonal correction algorithm. (b) the corrected signals i1(t) and q1(t) after the nonorthogonal correction algorithm.

After the correction mentioned above, with i1(t) and q1(t), the discrimination algorithm abstracting the laser Doppler frequency was carried out. The final output uOUT(t) of the signal processing is shown as Equation (7).

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After the correction mentioned above, with i1(t) and q1(t), the discrimination algorithm abstracting the laser Doppler frequency was carried out. The final output uOUT(t) of the signal processing is shown Sensors. 2020, 20, x FOR PEER REVIEW 5 of 12 as Equation (7). d[q1(t)] d[i1(t)] 푑[푞 (푡)] [i1(t)] 푑[푖 (푡)][q1(t)] u (t) = 1 dt ∙·[푖 (푡)] − dt1 · ∙ [푞 (푡)]= 2π f (t) (7) OUT 푑푡 1 2 푑푡 2 1 d (7) 푢푂푈푇(푡) = [i1(t)]2 + [q1(t)]2 = 2π푓푑(푡) [푖1(푡)] + [푞1(푡)] Therefore, the minimum resolvable velocity or velocity resolution vmin(t) of the vibration surface Therefore, the minimum resolvable velocity or velocity resolution vmin(t) of the vibration surface in thein direction the direction of the of the incident incident laser laser beam beam correspondscorresponds to to the the minimum minimum resolvable resolvable Doppler Doppler frequency frequency shift f (t) and( ) is denoted as Equation (8). Thus, with the help of f ( )(t), the minimum resolvable shiftdmin 푓푑푚푖푛 푡 and is denoted as Equation (8). Thus, with the help of⁡푓푑푚푖푛dmin푡 , the minimum resolvable velocityvelocityvmin v(t)mincan(t) can be be achieved. achieved. λ ( ) = λ ( ) vmin t fdmin t (8) 푣푚푖푛(푡) = 2푓푑 (푡) (8) 2 푚푖푛 3. Calibration Experiments and Results 3. Calibration Experiments and Results 3.1. Calibration Tests of Detection Capability with Glass and PZT 3.1. Calibration Tests of Detection Capability with Glass and PZT In order to verify the detection capabilities of the designed homodyne LDV and compare the test In order to verify the detection capabilities of the designed homodyne LDV and compare the test results with the theoretical vibration values of the detected surface, the calibration tests were conducted results with the theoretical vibration values of the detected surface, the calibration tests were under room temperature and normal conditions with the setup shown in Figure3. The detected conducted under room temperature and normal conditions with the setup shown in Figure 3. The vibratingdetected target vibrating included target a ring-shaped included a ring PZT-shaped (the yellow PZT (the part) yellow and part) a piece and of a same-sizepiece of same thin-size transparent thin glasstransparent (the white part)glass (the stuck white on its part) surface. stuck Theon its glass surface. and The the glass PZT and were the mounted PZT were at mounted a fixed distance at a fixed of 3 m awaydistance from the of homodyne 3 m away from LDV the and homodyne exhibit a vibrationLDV and totallyexhibit dependinga vibration ontotally PZT depending response toon its PZT driving signalresponse output to from its driving the signal signal generator. output from Here, the the signal driving generator signal. Here, was a the repeated driving pulse-modulated signal was a sine functionrepeated with pulse- themodulated sine function sine function frequency with of the 4 kHz, sine the function pulse frequency modulation of 4period kHz, ofthe 1 pul s, andse the dutymodulation cycle of 50:50, period respectively. of 1 s, and the Correspondingly, duty cycle of 50:50, the respectively. vibration ofCorrespondingly, the glass and thethe vibration PZT is a of simple harmonicthe glass vibration, and the andPZT theis a theoreticalsimple harmonic vibration vibration, displacement and the theoreticals(t) and vibration velocity v(t)displacementcan be expressed s(t) and velocity v(t) can be expressed as Equations (9) and (10). as Equations (9) and (10). s(푠t()푡)==σ휎퐴푠푖푛Asin(22ππ푓ft t)) (9) (9)

v푣(t()푡)==22ππ 푓휎퐴푐표푠f σAcos(2π2π푓ft t)) (10) (10) where σ is the strain coefficient of the PZT, and it is 5 nm/V; A and f are the amplitude and frequency where σ is the strain coefficient of the PZT, and it is 5 nm/V; A and f are the amplitude and frequency of of the sine function part belonging to the driving signal which were equal to 0.5 mV and 4 kHz, the sinerespectively. function partIn this belonging case, the totheoretical the driving maximum signal which vibration were velocity equal toof 0.5the mVglass and and 4 kHz,the PZT respectively. was In this62.8 case, nm/s. the theoretical maximum vibration velocity of the glass and the PZT was 62.8 nm/s.

FigureFigure 3. The3. The calibration calibration test test setupsetup for the the detection detection capabilities capabilities of the of theLDV LDV..

FigureFigure4 is a4 time-frequencyis a time-frequency diagram diagram of of the the homodyne homodyne LDV LDV output. output. The The 4 kHz 4 kHz signal signal represents represents the vibrationthe vibration frequency frequency of of the the glass glass and andthe the PZT,PZT, while its its lasting lasting time time is consistent is consistent with with that thatof the of the drivingdriving signal signal which which is is 0.5 0.5 s. s. ForFor a a selected selected small small segment segment (0 to (0 2.6 to ms) 2.6 of ms) the ofsignal the in signal Figure in 4, Figurethe 4, the correspondingcorresponding timetime-domain-domain waveform waveform is is displayed displayed in Figurein Figure 5, 5 and, and its its longitudinal longitudinal coordinate coordinate denotesdenotes the normalized the normalized Doppler Doppler frequency frequency shift. shift. Consequently, Consequently, the minimum the minimum distinguishable distinguishable Doppler Doppler frequency shift of the homodyne LDV is about 0.08 Hz and its corresponding minimum frequency shift of the homodyne LDV is about 0.08 Hz and its corresponding minimum detectable detectable velocity vmin reaches 62 nm/s according to Equation (8). Compared with the theoretical velocityvibrationvmin reachesvelocity of 62 62.8 nm n/sm/s, according the measuring to Equation uncertainty (8). is Compared about 1.28%. with The thevelocity theoretical resolution vibration of velocitythe designed of 62.8 nm LDV/s, theis inherently measuring frequency uncertainty sensitive, is about and depends 1.28%. The both velocity on the accuracy resolution of the of Doppler the designed LDV is inherently frequency sensitive, and depends both on the accuracy of the Doppler frequency shift

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Sensors. 2020, 20, x FOR PEER REVIEW 6 of 12 Sensors. 2020, 20, x FOR PEER REVIEW 6 of 12 measurement and the noise and/or drift during this measurement. Therefore, not only the background noisefrequency or SNR ofshift the measurement LDV but also and the the noise surrounding and/or drift around during this the measurement. LDV influences Therefore, the measurement not only frequencythe background shift measurement noise or SNR and of the noiseLDV butand /oralso drift the duringsurrounding this measurement. around the LDVTherefore, influence not sonly the accuracy. In order to further improve the measurement accuracy and other detection performance of themeasurement background accuracy noise or. In SNR order of tothe further LDV but improve also the the surr measurementounding around accuracy the andLDV other influence detections the this LDV,measurementperformance it is necessary of accuracy this LDV, to. In place itorder is thenecessary to LDVfurther onto improve place the vibration-isolating the the LDV measurement on the vibration accuracy platform-isolating and and other platform reduce detection the and e ffect of airperformancereduce turbulence the effect of as this much of LDV, air asturbulence it possible is necessary as besides much to place as optimizing possible the LDV besides on the the structure optimizingvibration and-isolating the the structure parameters platform and and the of the LDV.reduceparameters Furthermore, the effectof the it of canLDV. air be turbulenceFurthermore, observed as that it much can there be as observed are possible frequency thatbesides there disturbances optimizing are frequency the of structure 1disturbances kHz and and 500 of the 1 Hz in FigureparameterskHz4, and and the 500 of time-domain Hz the in LDV. Figure Furthermore, 4, waveform and the timeit is can fluctuating-domain be observed waveform a little that withthereis fluctuating theare timefrequency a in little Figure disturbances with5, the which time of mostly in 1 resultskHzFigure from and 5, the which500 following Hz mostly in Figure tworesults 4, major and from the aspects,the time following-domain namely two waveform the major surrounding aspects, is fluctuating namely noises, thea little disturbances,surrounding with the time noises, and in other Figure 5, which mostly results from the following two major aspects, namely the surrounding noises, unexpecteddisturbances vibration, and other except unexpected for the undergoingvibration except detected for the vibration,undergoing and detected the amplitudevibration, and instability the disturbances, and other unexpected vibration except for the undergoing detected vibration, and the fromamplitude the homodyne instability LDV, from such the as homodyne the drift ofLDV, laser such intensity as the drift and of the laser voltage intensity amplitude and the voltage fluctuation amplitude fluctuationinstability from of photoreceivers. the homodyne LDV, such as the drift of laser intensity and the voltage of photoreceivers.amplitude fluctuation of photoreceivers.

FigureFigure 4. Time–frequency4. Time–frequency analysis analysis of the homodyne homodyne LDV LDV output. output. Figure 4. Time–frequency analysis of the homodyne LDV output.

FigureFigure 5. Time-domain 5. Time-domain waveform waveform ofof the homodyne LDV LDV output output at 4 at kHz. 4 kHz. Figure 5. Time-domain waveform of the homodyne LDV output at 4 kHz. The LDVThe LDVis a vibration is a vibration or velocity-sensitive or velocity-sensitive system. system. Each Eachcorrupt corrupt that can that be can eff ectively be effectively converted The LDV is a vibration or velocity-sensitive system. Each corrupt that can be effectively to theconverted velocity toor thevibration velocity will or cause vibration frequency will cause interference frequency to interference the final output to the correspondingly. final output converted to the velocity or vibration will cause frequency interference to the final output Thus,correspondingly. besides the phase Thus, control besides by using the phase the correction control by algorithms using the correction mentioned algorithms before, it mentioned is also critical correspondingly.before, it is also Thus,critical besi to des address the phase the issue control of keeping by using good the correction amplitude algorithms stability for mentioned the high to address the issue of keeping good amplitude stability for the high sensitivity. before,sensitivity. it is also critical to address the issue of keeping good amplitude stability for the high When the working frequencies of the calibrated PZT are far away from its resonance frequency, sensitivity.When the working frequencies of the calibrated PZT are far away from its resonance frequency, basedbased on EquationsWhen on Equations the working (9) and(9) and frequencies (10), (10), it isit is obvious ofobvious the calibrated thatthat the PZTPZT arevibration vibration far away displacement displacement from its reson is directlyance is directly frequency, linear linear to to the voltagebasedthe voltage on of Equations the of given the given (9) driving and driving (10), signal, it signal, is obvious and and has thathas no relationshiptheno relationshipPZT vibration with with displacement the the frequency frequency is ofdirectly of the the driving linear driving to signal. However,thesignal. voltage the However, vibration of the thegiven velocity vibration driving of veloc thesignal, PZTity and ofwas the has PZTnot no onlyrelationshipwas not affected only with byaffected the frequency voltage by the voltage but of alsothe butdriving influenced also by thesignal.influenced frequency However, by of the the the frequency drivingvibration of signal. veloc the drivingity Therefore, of the signal. PZT Therefore, onwasthe not critical only on the affected state critical of by state the the vibrationvoltage of the vibration but detection, also influenced by the frequency of the driving signal. Therefore, on the critical state of the vibration the minimumdetection, detectablethe minimum capabilities detectable ofcapabilities this designed of this homodynedesigned homodyne LDV were LDV obtained. were obtained. Its minimum Its detection, the minimum detectable capabilities of this designed homodyne LDV were obtained. Its detectableminimum displacement detectable candisplacement be up to 2.468 can be pm up at to 4 kHz.2.468 Meanwhile,pm at 4 kHz. when Meanwhile, the driving when signalthe driving frequency minimumsignal frequency detectable is lower displacement than the resonance can be up point to 2.468 of the pm PZT, at 4 the kHz. minimum Meanwhile, detectable when velocity the driving will is lowersignal than frequency the resonance is lower than point the of resonance the PZT, point the minimumof the PZT, the detectable minimum velocity detectable will velocity scale withwill the scale with the frequencies of the driving signals. Depending on the minimum detectable velocity vmin frequencies of the driving signals. Depending on the minimum detectable velocity v at 4 kHz, scaleat 4 kHz, with the the velocity frequencies resolutions of the driving at other signals. frequency Depending bands can on bethe calculated minimum one detectable by one. velocity min vmin the velocity resolutions at other frequency bands can be calculated one by one. at 4 kHz,With the the velocity help of resolutions the glass andat other the frequency PZT, it was bands meaningful can be calculated to evaluate one the by homodyneone. LDV WithperformancesWith the helpthe (frequency help of the of the glass response, glass and and local the the PZT, noise, PZT, it itminimum waswas meaningful detectable to tocapabilities evaluate evaluate the, and the homodyne others) homodyne for LDV the LDV performancesperformancesremote voice (frequency acquirement (frequency response, response, and thelocal NDT local noise,of noise, composite minimumminimum materials. detectable detectable Considering capabilities capabilities, these, and two and others) applicat others) forions, the for the remoteremotethe voice LDV voice acquirement spectrum acquirement range and andwas the thestudied NDT NDT of of from composite composite 0 to 10 materials. materials. kHz. When Considering Considering the system these minimum these two twoapplicat detectable applications,ions, the LDVthe spectrumLDV spectrum range range was studiedwas studied from from 0 to 10 0 to kHz. 10 kHz. When When the system the system minimum minimum detectable detectable velocity v min reaches 62 nm/s, by using its corresponding amplitude spectrum (Figure6), there was an obvious peak that can be observed at 4 kHz, and the SNR was approximately 17 dB. Sensors. 2020, 20, x FOR PEER REVIEW 7 of 12

Sensorsvelocity2020, 20, v 5801min reaches 62 nm/s, by using its corresponding amplitude spectrum (Figure 6), there was7 of 11 an obvious peak that can be observed at 4 kHz, and the SNR was approximately 17 dB.

FigureFigure 6. Amplitude 6. Amplitude spectrum spectrum of of the the homodyne homodyne LDV output output with with the the vibrating vibrating glass glass and andPZT. PZT.

In contrastIn contrast with with the heterodynethe heterodyne LDV LDV [35 [],35 it], isit meaningfulis meaningful that that the the homodyne homodyne LDV has has removed removed the disturbancethe disturbance in the frequency in the frequency of 4 and of 8 kHz 4 and significantly 8 kHz significantly resulting resulting from the from in-phase the in and-phase quadrature and demodulationquadrature circuit demodulation centering circuit at thecentering frequency at the offrequency 55 MHz. of 55 In MHz. terms In of terms the frequencyof the frequency response, the homodyneresponse, the LDV homodyne was consistent LDV was with consistent that of thewith driving that of the signal driving to the signal PZT. to Its the frequency PZT. Its frequency error was no error was no more than ±1 Hz. In addition, the homodyne detection mode achieved the same more than 1 Hz. In addition, the homodyne detection mode achieved the same background noise level background± noise level after 3 kHz as that of the heterodyne detection mode with a reliable, simple, after 3and kHz cost as-effective that of the structure. heterodyne detection mode with a reliable, simple, and cost-effective structure.

3.2. Calibration3.2. Calibration Tests T ofests Detection of Detection Capability Capability with with the the Hydrostatic Hydrostatic Air-WaterAir-Water S Surfaceurface under under the the Anechoic Anechoic Tank OneTank profound application of the LDV is the acousto-optic communication which is capable of receiving theOne acoustic profound signal application without of anythe LDV mechanical is the aco contact.usto-optic As communication for the acousto-optic which is communication capable of underreceiving the actual the water acoustic situation, signal without the minimum any mechanical detectable contact. sound As for pressure the acousto level-optic (SPL) communication of the LDV is the criticalunder factor the that actual determines water situation, the fundamental the minimum detection detectable limit sound of the pressure whole level LDV-based (SPL) of sensingthe LDV system. is Forthe specifying critical factor the that minimum determines detectable the fundamental SPL of the detection designed limit homodyne of the whole LDV, LDV the- minimumbased detectablesensing SPL system. calibration tests were performed under the anechoic tank at the National Defense For specifying the minimum detectable SPL of the designed homodyne LDV, the minimum Underwater Acoustics Calibration Laboratory. The experiment setup was similar to that mentioned in detectable SPL calibration tests were performed under the anechoic tank at the National Defense the previousUnderwater report Acoustics [28]. TheCalibration homodyne Laboratory. LDV wasThe experiment located on setup the in-air was similar platform, to that and mentioned the distance betweenin the the previous transmitted report telescope [28]. The ofhomodyne the LDV LDV and thewas water located surface on the was in-air 3 mplatform, (Figure and7). Thethe distance underwater acousticbetween transmitter the transmitted was just directly telescope below of the the LDV detection and the point water of the surface LDV, was and 3 it m was (Figure 1.5 m 7). away The from the waterunderwater surface. acoustic Using transmitter one function was generator, just directly the below underwater the detection acoustic point transmitter of the LDV, was and set it towas emit a 2 ms acoustic1.5 m away pulse from of the sinusoidal water surface. signals Using repeating one function every generator, 0.5 s. During the underwater the test, the acoustic underwater transmitter acoustic signalwas was set observed to emit a 2 using ms acoustic a ceramic-based pulse of sinusoidal reference signals hydrophone repeating every TC4019, 0.5 s. 1.23During m the away test, from the the underwater acoustic signal was observed using a ceramic-based reference hydrophone TC4019, 1.23 acoustic transmitter. The output voltage uOC of the reference hydrophone TC4019 was the calibrating signal,m andaway it from demonstrated the acoustic the transmitte minimumr. Th detectablee output voltage capability uOC of of the the reference LDV. For hydrophone the tested TC4019 sinusoidal was the calibrating signal, and it demonstrated the minimum detectable capability of the LDV. For signal, the frequencies were chosen from 6 to 200 kHz. In this way, not only can the surrounding the tested sinusoidal signal, the frequencies were chosen from 6 to 200 kHz. In this way, not only can disturbancethe surrounding distributing disturbance in thelow-frequency distributing in the band low be-frequency prevented band eff beectively, prevented but effectively, it can also but meet it the TC4019can frequency also meet the bandwidth TC4019 frequency limitation bandwidth of 200 kHz. limitation of 200 kHz. ThroughThrough a series a series of calibrationof calibration tests, tests the, thedemodulated demodulated output output signals signals were were obtained obtained with with the the help ofhelp the of homodyne the homodyne LDV. LDV. As As the the amplitudes amplitudes of of thethe functionfunction generator generator reduce reduced,d, the theoutput output signal signal amplitudesamplitudes of the of the LDV LDV decreased decreased at at thethe same time. time. When When the theoutput output signal signal of the ofLDV the bec LDVame just became just indistinguishableindistinguishable from from the the background background noise, noise, the the minimum minimum detectable detectable SPL SPL and and the the amplitude amplitude spectrum could be acquired based on the TC4019 output voltage uOC. Under the hydrostatic surfaces, spectrum could be acquired based on the TC4019 output voltage uOC. Under the hydrostatic surfaces, the correspondingthe corresponding minimum minimum detectable detectable SPLs SPLs of theof the homodyne homodyne LDV LDV at at di ffdiffereerentnt frequency frequency bands bands were were compared. After that, when the transmitted acoustic pulse of the sinusoidal signal was at 10 compared. After that, when the transmitted acoustic pulse of the sinusoidal signal was at 10 kHz, kHz, the LDV reached its detection limit that the minimum detectable SPL was as low as 0.12 Pa. At the LDV reached its detection limit that the minimum detectable SPL was as low as 0.12 Pa. At this time, this time, the uOC was about 20 mV measured by an oscilloscope. Figure 8 shows the Fourier the uOCtransformswas about of the 20 LDV mV measuredoutput when by the an detected oscilloscope. acoustic Figure pulse8 wasshows at 10 the kHz. Fourier It was transforms clear that the of the LDV outputSNR was when almost the 21 detected dB when acoustic the LDV pulse reache wasd the at level 10 kHz. of the It wasminimum clear thatdetectable the SNR SPL was which almost was a 21 dB when the LDV reached the level of the minimum detectable SPL which was a preferable frequency band for the realization of the acousto-optic communication. In view of the FM communication, the designed homodyne LDV was still featured with good extendibility because the LDV had a wide frequency bandwidth and a large dynamic range. Sensors. 2020,, 20,, xx FORFOR PEERPEER REVIEWREVIEW 8 of 12

preferable frequency band for the realization of the acousto-optic communication. In view of the FM Sensorscommunication,2020, 20, 5801 the designed homodyne LDV was still featured with good extendibility because the8 of 11 LDV had a wide frequency bandwidth and a large dynamic range.

FigureFi 7.gureThe 7. setupThe setup of calibration of calibration tests tests of of detection detection capabilitycapability with with the the air air–water–water surface surface under under the the anechoicanechoic tank. tank..

FigureFigure 8. Amplitude 8. Amplitude spectrum spectrum of of the the homodyne homodyne LDV output output with with the the air air–water–water surface. surface.

4. Differences4. Differences between between Background Background Noise Noise of the of the LDV LDV with with Glass Glass and and that that with with the the Air–Water Air–Water Surface Surface Only with different kinds of detected surfaces, the glass and the air–water surface, were there some differencesOnly with in thedifferent same kinds homodyne of detected LDV surfaces, response the performances. glass and the air–water surface, were there Whensome differences the detected in the surface same homodyne was the LDV glass response whose performances. vibration was caused by the PZT and its correspondingWhen driving the detected signals, surface the noisewas the distribution glass whose shown vibration in Figurewas caused6 was by in linethe PZT with and the its same corresponding driving signals, the noise distribution shown in Figure 6 was in line with the same conclusion from Figure4, and it mainly occupied the frequency range under 1.5 kHz. Subjected to the conclusion from Figure 4, and it mainly occupied the frequency range under 1.5 kHz. Subjected to characteristicthe characteristic of the photoreceivers of the photoreceivers and the inevitable and the inevitable and undesirable and undesirable vibrations vibrations in the measurement in the environment,measurement this environment, spectral distribution this spectral in thisdistribution frequency in this range frequency was mainly range was aff ectedmainly by affected the 1/ fbynoise. However,the 1/ thef nois locale. However, noise spectral the local distribution noise spectral above distributi 3 kHzon was above flat 3 and kHz was was maintained flat and was atmaintain –96 dBed which is an eatff ective–96 dB guaranteewhich is an foreffective small-amplitude guarantee for vibration small-amplitude testing vibration in this frequency testing in this range. frequency In this range. case, it is a goodIn choice this case, for it the is a NDT good ofchoice composite for the NDT materials. of composite In addition, materials. as for In theaddition, remote as voicefor the acquirement, remote voice it is necessaryacquirement to suppress, it is ornecessary remove to the suppress fixed disturbance or remove the of fixed 500Hz disturbance and 1 kHz of within500 Hz theand audio1 kHz rangewithinso as not tothe aff ectaudio the range voice so signal as not measurement. to affect the voice In the signal caseof measurement. the acousto-optic In the communication, case of the acousto the-optic detected communication, the detected hydrostatic air-water surface remarkably leads to performance hydrostaticcommunication, air-water surfacethe detected remarkably hydrostatic leads air to-water performance surface deteriorationremarkably leads in the to background performance noise deterioration in the background noise of the LDV. The local noise spectral distribution appears at −84 of the LDV. The local noise spectral distribution appears at 84 dB from 2 to 200 kHz, and besides, dB from 2 to 200 kHz, and besides, the noise below 2 kHz− badly affects the detection of the the noiseunderwater below 2sound kHz badlyin the low affects-frequency the detection band. of the underwater sound in the low-frequency band. In theIn calibration the calibration experiments, experiments, the the minimum minimum detectabledetectable capabilities capabilities were were both both obtained obtained when when the outputthe output signals signals of the of the LDV LDV were were indistinguishable indistinguishable fromfrom the the background background noise. noise. When When the LDV the LDV reachedreache itsd detection its detection limits limits with with the the detected detected vibrating vibrating surface of of the the glass glass and and the the PZT, PZT, the thedriving driving signalsignal to PZT to PZT was was 0.5 mV.0.5 mV. At thisAt this time, time, the the background background noisenoise of of the the LDV LDV is is−96 96dB dBand and the theSNR SNR was was − 17 dB.17 Therefore, dB. Therefore, the signal the signal was 79was dB. −79 For dB. the For LDV-based the LDV-based acousto-optic acousto-optic communication, communication, the detected the − vibrating surface was the hydrostatic air–water interface, and the output voltage uOC of the TC4019 was the calibrating signal demonstrating the minimum detectable capability of the LDV. When the LDV reached its detection limits, the uOC was 20 mV. Meanwhile, the background noise of the LDV was 84 dB, and the SNR is 21 dB. Therefore, the signal was 63 dB. For the same LDV and nearly the same − − experimental conditions (such as the detection distance, the reflection coefficients of the glass and the water surface, the lab environment, and so on), the different levels of background noise of this designed homodyne LDV were mainly affected by the structural features of these two kinds of detected vibrating Sensors 2020, 20, 5801 9 of 11 surfaces, and the total difference can be equivalently expressed as 16 dB in the power spectrum. Due to the mismatch of the acoustic impedance between the air and the water, the air–water interface is the underwater sound pressure releasing surface, and vibrates at the same frequency as the incident acoustic fields when the sound wave travels to the water surface. However, the air–water interface’s vibration response to the sound was less than that of the glass. In addition, the hydrostatic air–water surface is the structure of liquid whose rigidity is weak and, therefore, induces much more speckle noise than that of glass. Consequently, the vibration response performance to the acoustic signal in the LDV-based acousto-optic communication with the detected air–water surface differs from that in LDV-based voice signal detection with the detected glass or the similar solid media. The SPL of the underwater sound source needs to be stronger in order to compensate the worsened background noise caused by the hydrostatic air-water interface. The amplitude relationship between the driving signal to the PZT and the output voltage uOC of the TC4019 consists with the variation of the background noise of these two kinds of vibrating surfaces. Furthermore, it is obvious that the SNR of the LDV-based sensing system will rapidly deteriorate under the real water surface conditions suffering from the water motion and the wind disturbance. In respect to the frequency response range, whatever the glass or the air–water surface, the homodyne LDV was capable of providing a wide frequency bandwidth and has a good consistency with that of the incident soundwave. The frequency error is no more than 1 Hz, and the time ± delay is about 49 ns under the ideal condition. In addition, assuming the sampling frequency of DAC is 2.56 times the detected laser Doppler frequency shift fd(t) based on the traditional sampling theory-Nyquist sampling theorem, the detectable maximum vibration velocity of the designed LDV can be up to 7.57 m/s. Therefore, this homodyne LDV can satisfy the requirement for vibration measurement in most cases.

5. Conclusions Aiming for the acousto-optic sensing, the voice signal detection and the future NDT for the composite material, an all-fiber homodyne LDV is demonstrated. Referring to the least-squares method, with the signal processing involving the correction of the quadrature imbalance and other nonlinearity, the orthogonal state between the in-phase and quadrature signals can be realized. In the calibration experiment, with the laser power of 5 mW, the telescope aperture of 50 mm, the detection distance of 3 m, and a piece of thin glass pasted on the ring-shaped PZT whose driving signal is 0.5 mV at 4 kHz, the designed homodyne LDV shows good performance with extreme accuracy and sensitivity. The measured vibration velocity and vibration displacement can reach 62 nm/s and 2.468 pm respectively. Thus, the vibration values of the glass and the PZT obtained from the experiments differ from the theoretically calculated ones within 1.28%. Compared with the heterodyne detection mode, there was no disturbance at the frequency of 4 and 8 kHz, and the background noise and the SNR from 3 to 10 kHz are able to be at the same level as that of heterodyne LDV. For the NDT of composite material, it is necessary to develop the multi-point LDV to meet the engineering requirements in terms of efficiency, real-time, and rapidness. There is no doubt that the performance of the multi-point LDV relies on the single point LDV. The detection sensitivity of the single point LDV is overarching consideration to build one practical multi-point LDV so that the weak signal can be picked up from the surroundings. For the detection or communication with the underwater sound source, the requirements are more specific and demanding than those of the normal industrial applications, and the minimum detectable SPL is also the fundamental factor. Besides, the tiny vibration caused by the underwater sound is mixed with the obvious fluctuation of the water surface (up to the level of m/s) which means the high-speed data acquisition must be applied. For the purpose of these, the proposed LDV is both with a good minimum detectable SPL of 0.12 Pa and a large frequency response bandwidth of 25 MS/s per channel. However, when the LDV is used for the acousto-optic communication under the hydrostatic air-water interface, the background noise of the same LDV is approximately 16 dB worse than that obtained Sensors 2020, 20, 5801 10 of 11 with the transparent glass and the PZT, which is mainly caused by the characteristics of the detected air–water interface. To summarize, for the unidirectional vibration measurements, such as the LDV-based voice signal detection and LDV-based NDT of composite materials, this homodyne LDV has more promising potential to offer a good choice when concerning pointing a low-power laser beam at the remote target and obtaining the vibration information in a cost-effective, compact, precise, and high-sensitivity way. In our following research, the control of the amplitude stability or the approach to eliminating its influence will be further studied. Meanwhile, a series of associated acousto-optic practical applications and the diagnostics for the composite material relying on this homodyne LDV will be drawn.

Author Contributions: Conceptualization and methodology, Y.H. and J.S.; data curation, J.S. and Q.W.; formal analysis, L.R. and Y.L.; project administration, Y.H.; validation, J.S., Q.W., L.R., and Y.H.; writing—original draft, J.S.; writing—review & editing, Y.H. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, Donghua University, grant number LK1113. Acknowledgments: The authors acknowledge researchers from the National Defense Underwater Acoustics Calibration Laboratory for their technical assistance with the calibration test facility and experimentation. Conflicts of Interest: The authors declare no conflict of interest.

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