sensors Article High Accuracy Ultrasound Micro-Distance Measurements with PMUTs under Liquid Operation Iván Zamora , Eyglis Ledesma , Arantxa Uranga and Núria Barniol * Departament d’Enginyeria Electrònica, Universitat Autónoma de Barcelona, 08193 Bellaterra, Spain; ivan.zamora@uab.es (I.Z.); eyglis.ledesma@uab.es (E.L.); arantxa.uranga@uab.es (A.U.) * Correspondence: nuria.barniol@uab.es Abstract: Ultrasonic systems driven by multi-frequency continuous waves (MFCW) have been used for range distance measurement, offering high accuracy in long and medium range distance estimation. However, the use of continuous waves in very short-distance measurements causes large errors due to multipath reflections. This paper presents a new strategy to estimate very short relative distances with high accuracy based on the use of multi-frequency pulsed waves (MFPW). The proposed strategy allows to avoid the multipath reflections that appear when continuous waves are used, and it improves the achieved accuracy compared to the original MFCW method. To validate it, an 80 µm square AlScN piezoelectric micromachined ultrasonic transducer (PMUT) was chosen as a transmitter while a hydrophone was utilized as a target and receiver, immersed in fluorinert (FC-70) as a propagation medium. Three independent and consecutive tone-burst signals were transmitted successively. The selected frequencies are f1 = 2.3962 MHz, f2 = 2.327 MHz and f3 = 2.1195 MHz, giving first and second-order resolutions of 6.88 and 0.79 µm/◦ , respectively. Experimental results  show a ±6.2 µm measured range error in a range of 3.5 mm, and therefore it represents a good  candidate for ultrasound micro-profilometer applications under liquid operation. Citation: Zamora, I.; Ledesma, E.; Uranga, A.; Barniol, N. High Keywords: immersed distance measurement; multi-frequency continuous waves; phase measure- Accuracy Ultrasound Micro-Distance ment; PMUT; time-of-flight; ultrasound Measurements with PMUTs under Liquid Operation. Sensors 2021, 21, 4524. https://doi.org/10.3390/ s21134524 1. Introduction Academic Editor: Alberto Corigliano Time of flight (ToF) estimation has been a widely employed procedure to compute distances, using various forms of energy, such as ultrasound, radio frequency and light. Received: 9 June 2021 Several techniques have been utilized for ultrasonic distance measurement systems to Accepted: 29 June 2021 estimate the ToF. The simplest one is the delay estimation based on a short signal [1,2], Published: 1 July 2021 where an ultrasound pulse is transmitted to the surrounding medium, and the elapsed time between the outgoing signal and the detection of the reflected echo (ToF) is measured. Publisher’s Note: MDPI stays neutral The distance to the reflecting target (d) is directly proportional to the ToF and the speed of with regard to jurisdictional claims in the sound in the propagation medium (c), according to (1): published maps and institutional affil- c · ToF iations. d = (1) 2 Most of the systems based on the pulse-echo method employ the ToF estimation, based on cross-correlation techniques [3–6]. ToF estimation is obtained through the cross- Copyright: © 2021 by the authors. correlation function between the transmitted and received signals. This method although Licensee MDPI, Basel, Switzerland. is very robust against disturbances, it requires a high-level of signal processing. This article is an open access article An alternative method to the short signal delay estimation is the use of frequency mod- distributed under the terms and ulated continuous wave (FMCW) [7,8]. In these systems, the transmitter emits a frequency conditions of the Creative Commons modulated continuous wave (CW), which is reflected at the target and is collected by the Attribution (CC BY) license (https:// receiver. ToF is proportional to the difference in frequency between the transmitted and the creativecommons.org/licenses/by/ received signals [7,8]. To avoid multipath reflections, it is usual to shorten the continuous 4.0/). wave generating a Chirp signal, where the transmission frequency changes as a function of Sensors 2021, 21, 4524. https://doi.org/10.3390/s21134524 https://www.mdpi.com/journal/sensors Sensors Sensors 2021, 2021, 21, 452421, x FOR PEER REVIEW 2 of 11 2 of 11 continuous wave generating a Chirp signal, where the transmission frequency changes as time, and the transmission time is limited to a pulse with a Tsweep a function of time, and the transmission time is limited to a pulse duration [9–11]. Chirp with a Tsweep duration modulation [9–11]. Chirp and FMCW methods modulation and FMCW both achieve methods boththe samethe achieve range sameaccuracy, but the range accuracy, butuse of chirp the signals allows use of chirp to discriminate signals multi-target allows to discriminate echoes. echoes. multi-target However, both FMCW However, both FMCW and Chirp based andmethods Chirp based require a certain methods require bandwidth, which limits a certain bandwidth, the chosen which limits the transducer. chosen trans- Finally, the ToF can also be estimated using unmodulated CW signals. In this case, the ducer. ToF is estimated Finally, the based on the ToF can alsophase shift. The be estimated usingphase shift between unmodulated the continuous CW signals. electrical In this case, the ToF signal excitation is estimated and the based on the phase continuous shift.signal received The phase shift between is measured and itthe continuous is used to compute theelectrical distance. excitation signal and This technique is the continuous relatively receivedto insensitive signal is measured disturbances andphase since it is used data can to compute the distance. This technique is relatively insensitive be sampled for a significant number of wave periods and therefore, random noise tends to to disturbances since phase cancel dataThe [12]. canmain be sampled for a significant disadvantage number is of this method of the wave periods limited and therefore,range, measurement ran- due dom noise tends to cancel [12]. The main disadvantage of this method is the limited meas- to fact that phase shift can only be measured in the 0–360 degree interval and therefore, urement range, due to fact that phase shift can only be measured in the 0–360 degree in- the resulting distance range is limited to a wavelength. This drawback is solved by terval and therefore, the resulting distance range is limited to a wavelength. This draw- implementing back is solved two-frequency by implementing continuous wave (TFCW) two-frequency continuous [13]wave or multi-frequency (TFCW) [13] or multi-continuous wave (MFCW) [12,14] based algorithms, where the phase shift frequency continuous wave (MFCW) [12,14] based algorithms, where the phase shift of of two or more frequencies aretwo compared, allowing toare or more frequencies measure compared, distances allowing much greater to measure than one distances wavelength. much greater than Although one wavelength. CW based systems show a good performance in medium and large range, in shortAlthough distance CW measurements based systems (mm) show they suffer a good from multipath performance in medium reflections, and largethat can cause range, in short large rangedistance measurements (mm) they suffer from multipath reflections, that can errors [15]. cause largepaper In this range errors [15]. a new strategy that allows us to determine the relative we present position between a target andaanew In this paper we present strategypoint reference that allows us to for short determine range the relative (mm) measurements posi- with tion between a target and a reference point for short range measurements high accuracy. It is based on the determination of the ToF using three burst-tone (mm) with highsignals accuracy. It is based on the determination of the ToF using three burst-tone signals (each (each one composed of a fixed number of sinusoidal waves with a fixed frequency) that one composed of a fixed number of sinusoidal waves with a fixed frequency) that are sent are sent sequentially, see Figure 1. The measurement of the phase shift using zero crossing sequentially, see Figure 1. The measurement of the phase shift using zero crossing along along withwith a modified a modified algorithm algorithm allowsallows to discriminate to discriminate short distances, short distances, avoidingavoiding distance de- distance dependent distortion due to multipath pendent distortion due to multipath reflections. reflections. Figure Figure 1. 1.Excitation Excitation signals signals and andreceived receivedsignals. signals. AsAs a proofofofconcept, a proof concept, wewe implemented implementeda system a systemthat demonstrates that the functionality demonstrates the functionality of the proposed measurement strategy working in liquid for short distances measure- of the proposed measurement strategy working in liquid for short distances measurement. ment. The implemented system uses a piezoelectric micromachined ultrasonic transducer The implemented system uses a piezoelectric micromachined ultrasonic transducer (PMUT) (PMUT) that works as an actuator and a commercial hydrophone that works as the target. that works as an actuator and a commercial hydrophone that works as the target. The The hydrophone position is lifted up in fixed steps and the distance between the hydro- hydrophone phone and position is liftedpoint a fixed reference up in is fixed steps and the distance between the hydrophone measured. and a fixed reference point is measured. The paper is organized as follows. Section 2 details the proposed measurement strat- The egy. In paper Sectionis3 the organized as follows. experimental Section results for 2 details validation the proposed and comparison measurement with other ap- strategy. In are proaches Section 3 theand presented experimental results conclusions are givenfor in validation Section 4. and comparison with other approaches are presented and conclusions are given in Section 4. 2. Method The MFCW algorithm has been extensively applied in radio frequency distance mea- surement and in accurate air-coupled ultrasonic rangefinder [12]. It is based on the two Sensors 2021, 21, 4524 3 of 11 frequency continuous wave (TFCW) method [13] where a third frequency is included in order to increase the maximum range without sacrificing accuracy. The MFCW method consists of the generation of three different continuous ultrasound waves (f1, f2 and f3) that are transmitted sequentially from an ultrasound transducer. These three acoustic signals are produced by the application of the respective three electrical signals over the PMUT that works as a transducer. When the three ultrasound signals reach sequentially the target (in our case, the commercial hydrophone), three electrical signals are generated in response to the arrival of the ultrasound. The phase shifts (ϕ1 , ϕ2 and ϕ3 ) between the electrical received signal and the electri- cal excitation signal are measured, corresponding each one to each continuous wave (f1 , f2 and f3 ). The distance d between the transducer and the target is computed as Equation (2) [12,14]: ∆ϕ1,2 ∆f1,3 c ∆ϕ1,3 f c ϕ c d = Int[ · ]· + Int[ · 1 ]· + 1 · (2) 360 ∆f1,2 ∆f1,3 360 ∆f1,3 f1 360 f1 where Int [] is the integer operation, ∆ϕ1,2 and ∆ϕ1,3 are the phase differences (in degrees) between ϕ1 , ϕ2 and ϕ1 , ϕ3 , respectively, ∆f1,2 and ∆f1,3 are the frequency differences between f1 , f2 and f1 , f3 , respectively. The maximum allowed measured distance using the MFCW method is determined by c/∆f1,2 . According to Equation (2), the ranging distance d is computed in three steps. The first one defines the largest resolution scale (c/∆f1,3 )/360◦ , dividing the maximum range into ∆f1,3 /∆f1,2 divisions. In the second step, each division of the first step is subdivided into f1 /∆f1,3 divisions, giving a finer resolution. In the final step, the phase shift ϕ1 is used to yield the highest-level resolution, defined as (c/f1 )/360◦ . Considering this, the selection of the operation frequencies must achieve a trade-off between signal-to-noise ratio (SNR), resolution, and maximum measurable range. Therefore, f1 , f2 and f3 must be within −3 dB PMUT bandwidth to maximize the SNR, f1 must be high enough, and f3 must be as far away as possible from f1 to maximize both, the first and second order resolutions. On the other hand, f2 must be close to f1 in order to increase the maximum allowed measured distance. In our application, this algorithm shows some drawbacks. On the one hand and considering that the transducer will be relatively close to the target (hydrophone), the use of a continuous ultrasound wave causes the appearance of standing waves between the surface of the transducer and the target (multipath reflections). Multipath reflections of the acoustic waves produce an error in the phase shift measurements, leading to a non-linear distortion of the phase–distance relationship and therefore directly affecting the measurement results [15]. On the other hand, the use of the integer operation (Int []) in Equation (2) can generate errors of ±c/∆f1,3 (Equation (2) first term) and ±c/f1 (Equation (2) second term) in the distance estimation when ∆ϕ1,2 gets closer to multiples of (360 × ∆f1,2 /∆f1,3 ) and ∆ϕ1,3 gets closer to multiples of (360 × ∆f1,3 /f1 ), respectively. Taking into account the multipath reflections drawback, some solutions have been proposed in [15] to reduce the non-linear distortion of the phase–distance relationship, but at the expense of increasing the overall measurement time and the computational complexity. In this work, we propose the use of multi-frequency pulsed waves (MFPW), where the three continuous waves are replaced by three burst signals, each one composed of a fixed number of sinusoidal signals with a fixed frequency (f1, f2 and f3, respectively). The number of cycles is determined limiting the transmission time to be smaller than the arrival time of the echo signal (the echo is generated by the reflection of the ultrasound signal when it reaches the target), see Figure 1 where a brief schematic of the applied signals is shown. This signal goes back to the transducer where it reflects again and reaches the target. Therefore, the transmission time is determined by the position of the target along with the time for the transducer to reach its steady state. To enhance accuracy at points that generate ∆ϕ1,3 phase differences multiples of 360 × ∆f1,3 /f1 , which corresponds to distances multiples of λ1 (c/f1 ), we propose to apply on Equation (2) the round operation (Round []) on points located in the neighborhood of Sensors 2021, 21, x FOR PEER REVIEW 4 of 11 the target. Therefore, the transmission time is determined by the position of the target Sensors 2021, 21, 4524 along with the time for the transducer to reach its steady state. 4 of 11 To enhance accuracy at points that generate Δφ1,3 phase differences multiples of 360 × Δf1,3/f1, which corresponds to distances multiples of λ1 (c/f1), we propose to apply on Equation (2) the round operation (Round []) on points located in the neighborhood of in- integer multiplesofofλλ1,1and teger multiples , andtotoapply applythetheinteger integerInt Int[][] operation operation on the rest of the the points. points. To To identify identifythe theneighborhood neighborhoodof ofinteger integermultiples multiplesofofλλ1 ,1,the themeasured measuredphase phase(ϕ(φ11)) is is compared compared with± with 90◦ . The ±90°. The proposed proposed algorithm algorithmisisdescribed describedininFigure Figure2.2.IfIfdistances distanceslarger larger than c/∆f than c/∆f1,3 1,3 need to be measured, the same algorithm should be applied to the first need to be measured, the same algorithm should be applied to the first term of Equation term of Equation (2), using ∆ϕ1,3 (2), using ∆φinstead of ϕof1 as 1,3 instead φ1 aastest variable. a test variable. Figure 2. Figure 2. Algorithm Algorithm flowchart flowchart used used to to compute computethe thesecond secondterm termof ofEquation Equation(2). (2). 3. 3. Experimental Experimental Results Results and and Discussion Discussion To To validate validate the proposed MFPW the proposed MFPW algorithm algorithmfor forultrasound ultrasounddistance distancemeasurements measurements in in liquid, liquid, anan80 80 µmµm squared squared piezoelectric piezoelectric micromachined micromachined ultrasonic ultrasonic transducer transducer (PMUT), (PMUT), fab- fabricated ricated with with thethe MEMS-on-CMOS MEMS-on-CMOS process process from from Silterra Silterra waswas usedused [16,17]. [16,17]. In this In this casecase the the PMUT is composed of 1.2 µm AlScN (Aluminium Nitride doped PMUT is composed of 1.2 µm AlScN (Aluminium Nitride doped with 9.5 % Scandium) with 9.5 % Scandium) sandwiched sandwichedbetween betweenaluminum aluminumelectrodes electrodesandandcovered coveredbyby1.5 1.5µmµmSilicon SiliconNitride Nitrideasas elastic elas- layer [18]. The PMUT was wire bonded to a printed circuit board (PCB) tic layer [18]. The PMUT was wire bonded to a printed circuit board (PCB) and immersed and immersed in Fluorinert in Fluorinert(FC-70). A Signal (FC-70). Generator A Signal (Keysight Generator 81150A, (Keysight SantaSanta 81150A, Rosa,Rosa, CA, USA) was used CA, USA) was to drive the PMUT. The acoustic characterization of the PMUT in FC-70 used to drive the PMUT. The acoustic characterization of the PMUT in FC-70 (685 m/s) (685 m/s) gives a resonance frequency for the first flexural mode of 2.327 MHz, and a − gives a resonance frequency for the first flexural mode of 2.327 MHz, and a −3 dB band- 3 dB bandwidth of 740 widthkHz.of 740 kHz. Figure Figure 33 shows shows the theexperimental experimental set-up set-up used usedto toperform performthe thedistance distancemeasurement measurement experiments experiments along with an optical image of the PMUT. It is composed of thedesigned along with an optical image of the PMUT. It is composed of the designed PMUT (used as an actuator) and a commercial hydrophone (ONDA-HNC-1500, Sunnyvale, PMUT (used as an actuator) and a commercial hydrophone (ONDA-HNC-1500, CA, USA) that was used both as a receiver and as a target (to measure the distance between Sunnyvale, CA, USA) that was used both as a receiver and as a target (to measure the the hydrophone and a fixed reference point). The commercial hydrophone was placed distance between the hydrophone and a fixed reference point). The commercial hydro- in a xyz-micro-positioner stage and its position was changed vertically in steps of 20 µm phone was placed in a xyz-micro-positioner stage and its position was changed vertically with 1 µm resolution (see Figure 3). The micro-positioner was used to validate the relative in steps of 20 µm with 1 µm resolution (see Figure 3). The micro-positioner was used to measured distances. The phase shift angle between the excitation signal and the amplified validate the relative measured distances. The phase shift angle between the excitation sig- received signal was measured using the zero-crossing approach directly on the oscilloscope nal and the amplified received signal was measured using the zero-crossing approach di- (Keysight DSOX3054A, Santa Rosa, CA, USA). rectly on the oscilloscope (Keysight DSOX3054A, Santa Rosa, CA, USA). In order to achieve a trade-off between signal-to-noise ratio, maximum range and accu- racy, three frequencies were chosen: f1 = 2.3962 MHz, f2 = 2.327 MHz and f3 = 2.1195 MHz, resulting in a 6.88 µm/◦ coarse-resolution and 0.79 µm/◦ fine-resolution. Since we want to ensure that the echo-signals do not overlap in time with the measured signal, there is a minimum measurable range that can be computed using Equation (1), the sound velocity c = 685 m/s (previously calibrated) and the minimum unidirectional ToF. The minimum ToF is achieved when the f3 excitation signal and the start of the steady state of the received signal overlap in time, keeping in mind that this time has to be small enough to avoid the arrival of the first echo. Since our PMUT reaches its steady state at least after 4 cycles (4T, being T the period of the excitation signal), these two conditions Sensors 2021, 21, 4524 5 of 11 force that the minimum time needed for the ultrasound signal to reach the target should be larger than two cycles (2T). Therefore, a minimum transmission time of six signal cycles is Sensors 2021, 21, x FOR PEER REVIEW 5 of 11 obtained. According to Equation (1), the minimum distance that assures that overlapping does not occur is around 750 µm. (a) (b) (c) Figure 3. (a) Figure 3. (a) The The set-up set-up diagram; diagram; (b) (b) experimental set-up; (c) experimental set-up; (c) optical optical image image of of the the PMUT PMUT device. device. To order In demonstrate to achievethe advantages of our MFPW a trade-off between strategy we signal-to-noise performed ratio, maximum tworange different and experiments. accuracy, threeThe first one is were frequencies aimedchosen: at comparing the performance f1 = 2.3962 MHz, f2 = 2.327 of the MHzMFPWand fversus the 3 = 2.1195 MFCW MHz, (Continuous resulting Waves), in a 6.88 µm/° while the second experiment coarse-resolution and 0.79 µm/° analyzes the improvement in fine-resolution. termsSince of absolute we want error and standard to ensure that thedeviation echo-signalswhendothe notproposed overlap computation in time with algorithm the meas- is used with the MFPW method. ured signal, there is a minimum measurable range that can be computed using Equation (1), the sound velocity c = 685 m/s (previously calibrated) and the minimum unidirectional 3.1. Multi-Frequency ToF. The minimum ToF Continuous is achievedWaveswhen(MFCW) vs. Multi-Frequency the f3 excitation signal andPulsed Waves the start (MFPW) of the steady state Aoffirst experiment the received signalwasoverlap done toincompare the useinofmind time, keeping continuous that thiswaves versus time has to bepulsed small waves. The enough hydrophone to avoid the arrival wasoflocated the first2.5 mmSince echo. awayour from PMUTthe transducer. reaches its To corroborate steady state at the distance, least the PMUT after 4 cycles was driven (4T, being by fourof T the period sine thecycles at 2.327 excitation MHz these signal), with 22 two Vpp and the conditions ToF was roughly estimated using an oscilloscope, based on the force that the minimum time needed for the ultrasound signal to reach the target should time the ultrasound signal needs to reach the hydrophone and the ultrasound speed in fluorinert. be larger than two cycles (2T). Therefore, a minimum transmission time of six signal cycles After corroborating is obtained. According to the position Equation (1),ofthetheminimum hydrophone, distancethreethatexcitation assures signals, each that overlap- one with frequencies ping does not occur is around f 1 = 2.3962 MHz, 750 µm. 2 f = 2.327 MHz, and f3 = 2.1195 MHz, composed of a 16 period-long sine wave with an amplitude To demonstrate the advantages of our MFPW strategy we performed of 22 Vpp were applied consecutively. two different experiments. The first one is aimed at comparing the performance for The micro-positioner was moved away axially using a micro-meter 50 steps of the MFPW of versus 20 µm each one, giving a measurement range from 2.5 to 3.5 mm. the MFCW (Continuous Waves), while the second experiment analyzes the improvement The number of cycles was determined to assure the overlap of the excitation and the in terms of absolute error and standard deviation when the proposed computation algo- received signals, avoiding the overlap with multipath rithm is used with the MFPW method.reflection signals. Three phase shift angles ϕ1 , ϕ2 and ϕ3 between the electrical received signal and the electrical excitation signal 3.1. Multi-Frequency Continuous(one for Waveseach(MFCW) frequency) were measured Pulsed vs. Multi-Frequency at eachWaves distance point, (MFPW) and they were used as input data for the implemented algorithm. The number of cycles wereAincreased first experiment by one each wastime donetheto hydrophone compare the was use of continuous lifted one λ1 . waves versus pulsed waves. The hydrophone was located 2.5 Figure 4 shows the measured phase differences, ∆ϕ1,2 mm away from the transducer. (Figure 4a) To corroborate and ∆ϕ1,3 the distance, the PMUT was driven by four sine cycles (Figure 4b), when MFCW (red curves) and MFPW (blue curves) were used. The at 2.327 MHz with 22 Vpp and the measured ToF phase differences for the MFCW curves show a non-linear behavior with the distance,signal was roughly estimated using an oscilloscope, based on the time the ultrasound with needs to reach a periodic errorthe hydrophone around 140 and 160 andµmtheforultrasound ∆ϕ1,2 andspeed∆ϕ1,3in fluorinert. According to [15], , respectively. After corroborating this periodic componentthe position is given by ofthethe hydrophone, multipath three excitation reflections and it hassignals, each one a periodicity of with frequencies f1 = 2.3962 MHz, f2 = 2.327 MHz, and f3 = 2.1195 λavg /2 (where λavg = c/((f1 + f2 )/2) for ∆ϕ1,2 and λavg = c/((f1 + f3 )/2) for ∆ϕ1,3 ), whichMHz, composed of a 16 period-long is in agreement sinewith wavethe with an amplitude obtained values. of 22 blue The Vpp curves, were applied consecutively. corresponding to theTheMFPW mi- cro-positioner was moved away axially using a micro-meter method, show a great improvement of the linearity, where it can be seen that the periodic for 50 steps of 20 µm each one, giving a measurement range from 2.5 to 3.5 mm. The number of cycles was deter- mined to assure the overlap of the excitation and the received signals, avoiding the over- lap with multipath reflection signals. Three phase shift angles φ1, φ2 and φ3 between the electrical received signal and the electrical excitation signal (one for each frequency) were measured at each distance point, and they were used as input data for the implemented algorithm. The number of cycles Figure 4 shows Figure 4 shows the the measured measured phase phaseΔφ differences, differences, Δφ1,2 (Figure 4a) and Δφ1,3 (Figure 1,2 (Figure 4a) and Δφ1,3 (Figure 4b), when MFCW (red curves) and MFPW 4b), when MFCW (red curves) and MFPW (blue curves) were used. The (blue curves) were used. The measured measured phase phase differences for the MFCW curves show a non-linear behavior with the distance, withdistance, differences for the MFCW curves show a non-linear behavior with the a with a periodic error around 140 and 160 µm for Δφ 1,2 and Δφ1,3, respectively. According to [15], periodic error around 140 and 160 µm for Δφ1,2 and Δφ1,3, respectively. According to [15], this this periodicis component periodic component given by theis multipath given by the multipath reflections andreflections and it has of it has a periodicity a periodicity of Sensors 2021, 21, 4524 6 of 11 λavg/2 (where λλavg /2 (where λavg = c/((f1 + f2)/2) for Δφ1,2 and λavg = c/((f1 + f3)/2) for Δφ1,3), which is in avg = c/((f1 + f2)/2) for Δφ1,2 and λavg = c/((f1 + f3)/2) for Δφ1,3), which is in agreement withagreement with the the obtained obtained values. values. The blue The corresponding curves, blue curves, corresponding to the MFPWto the MFPW method, show a great improvement of the linearity, method, show a great improvement of the linearity, where it can be seen that where it canthebeperiodic seen that the periodic error was suppressed. error wasHowever, error was suppressed. suppressed. However, However, a residual a residual a residual distortion distortion distortion is still is still present,isbeing present, still present, being being mainly mainly caused mainly caused caused by by the the electronic electronic noise noise of of hydrophone’s hydrophone’s pre-amplifier, pre-amplifier, by the electronic noise of hydrophone’s pre-amplifier, which is explained later. which which is is explained explained later. later. (a) (a) (b) (b) Figure Figure Figure 4. Measured 4. Measured 4. phaseMeasured difference phase phase difference usingdifference using multi-frequency using multi-frequency multi-frequency continuous wavecontinuous continuous waveand wave (MFCW-red) (MFCW-red) (MFCW-red) and multi-frequency and multi-frequency multi-frequency pulsed pulsed pulsed wave (MFPW-blue): wave (a) wave (MFPW-blue): (MFPW-blue): (a) Δφ1,2; (b) Δφ1,3. 1,3. ∆ϕ1,2 ; (b) ∆ϕ1,3 . Δφ1,2; (b) Δφ(a) Figure 5 showsFigure 55 shows showsthe the received thereceived received signals by the signals signals byby thethe hydrophone hydrophone hydrophone when when it was when it3 was it was placed placed mm placed 3 mm3from mm from the the PMUT PMUT surface. surface. As it As can it be can seenbe seen the the first first echo echo arrives arrives after after the the phase from the PMUT surface. As it can be seen the first echo arrives after the phase shift meas- phase shift shift meas- measurement urement is done, urement is done, is done, avoiding avoiding avoiding the the non-linear the non-linear non-linear duedistortion distortion distortion due to duereflections. to multipath to multipath multipath reflections.reflections. Figure 5.results Figure 5. Measurement Measurement 3 mm fromresults PMUT3 mm from The surface. PMUT surface. redthe curves Thethe are redelectrical curves are the electrical excitation excitation Figure 5. Measurement results 3 mmand signals, fromthePMUT green surface. curves Thethe are redelectrical curves are electrical received signals excitation by the signals, hydrophone. and the green signals, curves are the andreceived electrical the greensignals curvesbyare the the electrical received signals by the hydrophone. hydrophone. 3.2. Relative Distance Measurement Our main goal is to prove that the proposed strategy allows us to implement a highly accurate relative distance measurement. For this purpose, we fixed the reference point 2.5 mm away from the transducer and we measured the ϕ1 _2.5 mm, ϕ2 _2.5 mm and ϕ3 _2.5 mm phase angles at that distance. Relative distances from this reference point were measured using the proposed new strategy. Again, the micro-positioner was moved away vertically for 50 steps of 20 µm 3.2. Relative Distance Measurement Our main goal is to prove that the proposed strategy allows us to implement a highly accurate relative distance measurement. For this purpose, we fixed the reference point 2.5 mm away from the transducer and we measured the φ1_2.5 mm, φ2_2.5 mm and φ3_2.5 Sensors 2021, 21, 4524 7 of 11 mm phase angles at that distance. Relative distances from this reference point were measured using the proposed new strategy. Again, the micro-positioner was moved away vertically for 50 steps of 20 µm each one, giving each one, giving aa measurement measurement range range from from 2.52.5 to to 3.5 3.5 mm mm that that corresponds corresponds to to aa relative relative movement of 1 mm from the reference reference point. point. To compute relative relativemeasurements, measurements,φϕ 1_2.5 mm, 1 _2.5 mm, φ2ϕ _2.5 mmmm 2 _2.5 andand φ3_2.5 mm mm ϕ3 _2.5 werewere sub- tracted fromfrom subtracted eacheach newnewphase angleangle phase measured measuredon each new point. on each FigureFigure new point. 6 shows a graph 6 shows a of the real graph relative of the distance real relative from the distance reference from point (obtained the reference according point (obtained to the micro- according to the positioner) versusversus micro-positioner) the computed measured the computed distance, measured whenwhen distance, Equation (2) is(2) Equation used withwith is used the new algorithm. the new In particular, algorithm. redred In particular, points correspond points correspond totothe theuse useofofthe theInt Int [] [] operator in Equation (2) while blue points are obtained using the the proposed proposed algorithm algorithm (Figure (Figure 2).2). Figure 6. Experimental computed relative distances vs. real relative distances from the reference reference (2) in point (2.5 mm) using Equation (2) in red red and and with with the the proposed proposed MFPW MFPW algorithm algorithm in in blue. blue. The use The use of ofEquation Equation(2) (2)(red (red points points in in Figure Figure 6) shows 6) shows thatthat higher higher errorserrors in theincom- the computed distance are obtained (around puted distance are obtained (around ±λ1) compared ± λ1 ) compared to the use of the new algorithm, to the use of the new algorithm, when when the measured the measured distances distances are veryare very close close to an to anofinteger integer λ1. Blueofdots λ1 . in Blue dots6 in Figure Figure 6 correspond correspond to the proposedto the proposed MFPW MFPW strategy. It isstrategy. proven thatIt is proven the jumpsthat the jumps around around integer integer multiples of multiples of λ are minimized thanks to the use of the proposed λ1 are minimized thanks to the use of the proposed algorithm, as it was expected. 1 algorithm, as it was expected. Figure 7 presents the obtained absolute distance errors computed as the difference Figure between the7average presentsofthe obtained absolute 5 measurements donedistance errorsand on each point computed the realas the difference distance. In par- between the average of 5 measurements done on each point ticular, a maximum error of ~291 µm is achieved using the Int [] operator while Sensors 2021, 21, x FOR PEER REVIEW and the real distance. the8maxi-In of 11 particular, a maximum error of ~291 µm is achieved mum error is reduced to ~6.2 µm with the new MFPW strategy. using the Int [] operator while the maximum error is reduced to ~6.2 µm with the new MFPW strategy. Figure 7. Figure Obtainedabsolute 7. Obtained absoluteerrors errorsusing usingEquation Equation(2)(2)inin red red and and thethe proposed proposed MFPW MFPW algorithm algorithm in blue. in blue. 3.3. Uncertainty Analysis To estimate the random errors, three uncertainty sources were identified: ultrasound velocity, oscillator stability and phase shift measurements at the zero crossing. Consider- ing that the propagation medium used in our experiment (fluorinert FC-70, Sigma-Al- drich, St. Louis, MO, USA) is thermally and chemically stable [19], we assumed that the Sensors 2021, 21, 4524 8 of 11 3.3. Uncertainty Analysis To estimate the random errors, three uncertainty sources were identified: ultrasound velocity, oscillator stability and phase shift measurements at the zero crossing. Considering that the propagation medium used in our experiment (fluorinert FC-70, Sigma-Aldrich, St. Louis, MO, USA) is thermally and chemically stable [19], we assumed that the uncertainty due to the ultrasound velocity is negligible. On the other hand, taking into account that the used signal source in our experiment is a high stable oscillator (Keysight 81150A Signal Generator), the distance error caused by oscillator error will not be a concern. Therefore, the dominant random error source is the phase error. From [20], the standard deviation of the phase angle (σϕ in radians) at zero crossing for a sinusoidal pulse is given by: 1 σϕ = √ (3) E/N0 where E is the pulse energy and N0 is the power noise spectral density. If we consider the root mean squared (rms) values of both signal and noise, Equation (3) can be rewritten as: 1 1 σϕ = = (4) Va,rms /σn SNR where Va,rms , σn are the rms values of both the signal and noise and SNR is the signal-to- noise ratio. Taking into account that the derivate of both, the integer and round functions are zero when their arguments belong to Real Domain, the standard deviation of the distance (σd ) according to Equation (2) can be calculated as: s 2 ∂d c 1 σd = ( σϕ1 ) = · (5) ∂ϕ1 2πf1 SNR Considering that the acoustic pressure distribution in far-field of the used PMUT presents an exponential dependence with the distance (2.66/z Papp ) [18], being z the axial distance, the rms voltage at the output of Hydrophone’s preamplifier (Va,rms ) is given by: 2.66 1 Va,rms (z) = M · · √ (6) z 2 2 where M is the reception sensitivity at the output of hydrophone’s preamplifier (11.22 µV/Pa) [21]. In our case, the measured amplitudes are inside a range from 4.2 (corresponding to the reference point located at 2.5 mm) to 3 mVrms (3.5 mm). Combining Equations (5) and (6), the standard deviation of the distance has a linear dependency with the distance, given by: cσn σd ( z ) = ·z (7) 10.53 · 10−6 · 2πf1 Considering the chosen frequencies, Equation (7) can only be used from the minimal measurable distance (750 µm) to the maximum range (c/∆f1 = 9.8 mm). Figure 8 shows the measured standard deviation for each distance point, and the theoretical standard deviation obtained from Equation (7), considering that the output-referred noise of the preamplifier (AH-2010 from Onda) is 160 µVrms in its 3-dB bandwidth (from 50 kHz to 25 MHz) [21]. tion obtained from Equation (7), considering that the output-referred noise of the pream- plifier (AH-2010 from Onda) is 160 µVrms in its 3-dB bandwidth (from 50 kHz to 25 MHz) [21]. Considering that a small number of measurements were performed (5 measure- ments), calculation of the confidence interval was done assuming that our measurements Sensors 2021, 21, 4524 9 of 11 have a Student’s t distribution. Taking into account the maximum value of the standard deviation (see Figure 8), the 70% confidence limit is ~1.95 µm. Figure 8. Experimental and theoretical relative distances from the reference point (2.5 mm). theoretical σσdd vs. relative Considering Table 1 compares that a the small number MFPW proposed of measurements algorithmwerewithperformed (5 measurements), other reported methods im- calculation of the confidence interval was done assuming that our plemented to measure distances using ultrasound. In order to compare the performance measurements have a Student’s t distribution. Taking into account the maximum value of the of the different methods, it is necessary to take into account the two main parameters thatstandard deviation (see Figurethe influence 8), accuracy: the 70% confidence the central limit is ~1.95 and frequency µm. the SNR (Equation (5)) although the Table 1 compares the proposed MFPW algorithm measurement distances can be completely different. Considering with other reported methods the final accuracy,imple- our mented to measure distances using ultrasound. In order to compare MFPW approach gives a range error of ±6.2 µm which is the smallest one reported. If we the performance of the different compare methods, it with other MHz it is necessary to take into systems operated alsoaccount the environment in a liquid two main parameters [4,5], the that pro- influence the accuracy: the central frequency and the SNR posed method is more accurate at the expense of a reduced measurement range. (Equation (5)) although the Conse- measurement distances can be completely different. Considering quently, the proposed MFPW provides an attractive alternative in liquid environment at the final accuracy, our MFPW approachfor high frequencies gives a range target error of ±6.2 with micro-positioning µm which is the smallest one reported. If fine steps. we compare it with other MHz systems operated also in a liquid environment [4,5], the proposed Table method comparison 1. Performance is more accurate at the expense of ultrasound of a reduced measurement distance.measurement range. Conse- quently, the proposed MFPW provides an attractive alternative in liquid environment at [13] [1] high frequencies [11] micro-positioning for target [4] with fine steps. [5] This Work (2012) (2015) (2021) (2015) (2019) Method TFCW Table 1.Pulse-echo Performance Chirp modulation comparison Cross-correlation/PSM of ultrasound Cross-correlation measurement distance. MFPW AlN Commercial Commercial AlScN Transducer N/A [13] [1] PZT [11] [4] [5] (2012) PMUT (2015) (2021) (Vico WK-21B) (2015) (Goworld (2019) 1P28) PMUT This Work Liquid Cross- Liquid Liquid Propagation Method medium Air TFCW Air Pulse-echo Air Chirp modulation Cross-correlation MFPW (distilled water) correlation/PSM (water) (FC-70) AlN Commercial Commercial AlScN Transducer N/A PZT PMUT (Vico WK-21B) (Goworld 1P28) PMUT Liquid Liquid Liquid Propagation medium Air Air Air (distilled water) (water) (FC-70) Frequency (kHz) 40/40.82 220 94–107 1000 1000 2392.6/2327/2119.5 33 2 at 25.26 3 at 25.5 at SNR (dB) N/A N/A N/A 500 mm 550 mm 3.5 mm 155.7 1 at 40 at 1.95 5 at Standard deviation (µm) N/A N/A N/A 200 mm 200 mm 3.5 mm ±136 at 410rms at 18,700 4 at ±202 at ±6.2 at Range error (µm) N/A 200 mm 500 mm 550 mm 25 mm 3.5 mm 1 Corresponds to the greater value of all reported. 2 Extracted from a SNR versus range graph. 3 Computed using the received power characterization in air of their transducer (−60 dBm) and the input-referred noise of the amplifier (12.2 µVrms). 4 Corresponds to the standard deviation of the absolute error. 5 Represents the 70% confidence limit considering that the measurements have a Student’s t distribution. 4. Conclusions This work presents a new strategy applied to an ultrasound system that allows the measurements of relative distances with high accuracy, using a PMUT with a modified multi-frequency phase shift with three transmission frequencies. The new approach, MFPW, improves the linear dependence between phase angles and target’s range avoiding the multipath reflections. It improves the accuracy in relation to the traditional MFCW al- Sensors 2021, 21, 4524 10 of 11 gorithm, decreasing considerably the error around integer multiples of the wavelength. The experimental verification was made using an 80 µm AlScN squared PMUT in liquid environment (FC-70), achieving a measured range error of ±6.2 µm in 3.5 mm, offering better performance than the described algorithm by Equation (2), under the same condi- tions. Integration of the presented AlScN PMUT over CMOS circuitry would derive SNR levels comparable with those reported here. Considering this, a very compact and low power ultrasound distance measurement system based on a single PMUT using the MFPW strategy will achieve very high accuracy for short distances in liquid environments. Author Contributions: Conceptualization, I.Z., A.U. and N.B.; methodology, I.Z.; acoustic experi- ments and validation, I.Z. and E.L.; writing—original draft preparation, I.Z.; writing—review and editing, E.L., A.U. and N.B.; supervision, A.U. and N.B.; project administration, N.B. All authors have read and agreed to the published version of the manuscript. Funding: This research was partially funded by the Spanish AEI with project PID2019-108270RB-I00. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: Special acknowledgments are made to SilTerra’s MEMS and SENSORS technol- ogy development team for supporting fabrication of the PMUT-on-CMOS wafers. 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