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A Vibrometer Based on Magnetorheological Optical Resonators

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A Vibrometer Based on Magnetorheological Optical Resonators vibration Article A Vibrometer Based on Magnetorheological Optical Resonators Edoardo Rubino 1,* and Tindaro Ioppolo 2 1 Mechanical and Industrial Engineering Department, University of Wisconsin Platteville, Platteville, WI 53818, USA 2 Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-(608)-342-6058 Received: 23 August 2018; Accepted: 9 October 2018; Published: 17 October 2018 Abstract: This paper addresses the feasibility of an optical vibrometer that is based on the shift of the optical modes, also known as whispering gallery modes (WGMs), of a magnetorheological optical resonator. The optical resonator that is used in this study is fabricated by mixing polyvinyl chloride plastisol with magnetically polarizable particles. When a permanent magnet that is located nearby the optical resonator is moved, it induces a perturbation of the morphology of the resonator, due to the magnetostrictive effect. This change in the morphology induces a shift in the optical modes of the resonator. The shift of the optical modes can be related to the displacement of the permanent magnet. The proposed sensor concept is based on monitoring the displacement of a tiny magnet that is attached to a moving surface. The optical quality factor of the resonator used in these studies was of the order of 106. The experimental results show a sensitivity of 0.32 pm/µm and a resolution that is less than 300 nm. Keywords: vibrometer; magnetorheological; optical resonator; composites; smart materials; whispering gallery modes 1. Introduction Several techniques have been developed so far, to detect and monitor the amplitude and the frequency of the displacement of vibrating systems. Laser vibrometers are interferometric instruments [1] that make use of the coherence properties of a laser beam [2]. A laser light is pointed toward the vibrating object, and the backscattered light is detected with a photodiode. By comparing the Doppler frequency between the source beam and the backscattered light [3], it is possible to determine the vibrating characteristics of the tested object. Laser vibrometers have been studied extensively [4], and they are employed in several fields such as structural health monitoring [5,6] and fruit textural changes [7,8]. Other studies reported that it is possible to obtain a resolution of the order of attometers with this technique [9]. Other optical methods have been developed to determine the displacement of vibrating objects. Light emission diodes (LED) were, for instance, used to measure the bending and torsional vibrations of pipes [10–12]: the pipe is located between a projector and a receiver to create a shaded area on the receiver. The vibration of the pipe can then be detected by measuring the amount of light that reaches the receiver. With this technique, a resolution of 60 nm can be obtained, and the sensor size is in the order of tens of centimeters. Optical digital techniques have been developed to detect the displacement of flexible bridges for structural analysis purposes [13]: the motion of a marked panel placed on the bridge was followed by a camera placed on a fixed point, and the recorded images were analyzed through digital image processing software. The resolution and Vibration 2018, 1, 239–249; doi:10.3390/vibration1020017 www.mdpi.com/journal/vibration Vibration 2018, 1 240 Vibration 2018, 2, x FOR PEER REVIEW 2 of 11 sensitivitysoftware. ofThe the resolution proposed and device sensitivity are a function of the of proposed the camera device and lensesare a used,function as well of the as thecamera distance and betweenlenses used, the cameraas well andas the the distance targeted between point. the camera and the targeted point. AnotherAnother opticaloptical systemsystem thatthat isis usedused toto developdevelop vibrometersvibrometers makesmakes useuse ofof anan opticaloptical fiberfiber thatthat pointspoints the the light light to to thethe surfacesurface ofof thethe vibratingvibrating objectobject andandof of aa photodiodephotodiodethat that measuresmeasuresthe the variationvariation ofof thethe intensityintensity ofof the reflectedreflected light [14,15]. [14,15]. With With this this method, method, a asensitivity sensitivity of of0.893 0.893 V/mm V/mm in the in thefrequency frequency range range between between 75 and 75 275 and Hz 275 was Hz obtained. was obtained. Also, this Also, technique this technique was used wasfor multipoint used for multipointmeasurements measurements [16], obtaining [16], a obtaining resolution a resolutionin the order in of the 1 orderμm. Another of 1 µm. study Another reported study the reported optical thedetection optical of detection the resonant of the frequency resonant of frequency a quartz crys of atal quartz resonator crystal [17]. resonator A resolution [17]. in A the resolution order of in10 theμm order has been of 10 reachedµm has in been developing reached a in displacement developing asensor displacement based on sensora Fabry-Perot based on device a Fabry-Perot [18], or of device142 μm [18 with], or a of vibrometer 142 µm with for a vibrometercryogenic applications for cryogenic ba applicationssed on fiber based Bragg on gratings fiber Bragg [19]. gratings In addition, [19]. Inrecent addition, studies recent have studies reported have reported that the that optical- the optical-knifeknife edge edge technique technique allows allows for for displacementdisplacement p measurementsmeasurements inin thethe rangerange betweenbetween 13 MHz andand 895 MHz, with with a a resolution resolution of of 455 455 fm/ fm/√HzHz [20]. [20 In]. Inthis this paper, paper, we we present present a a novel novel technique technique to to meas measureure the out-of-plane displacementdisplacement ofof aa vibratingvibrating objectobject oror surface.surface. TheThe sensingsensing conceptconcept isis basedbased onon thethe shiftshift ofof thethe morphology-dependentmorphology-dependent resonancesresonances (MDR),(MDR), also also known known as whisperingas whispering gallery gallery modes modes (WGM) (WGM) of a magnetorheological of a magnetorheological spherical resonator.spherical Theresonator. WGM phenomenonThe WGM phenomenon has been used has in been the pastused for in variousthe past applications, for various applications, due to the high due optical to the qualityhigh optical factor ofquality the optical factor modes. of the These optical micro-cavities modes. These have beenmicro-cavities used for the have development been used of devicesfor the fordevelopment telecommunication of devices (filtering, for telecommunication switches, multiplexing, (filtering, etc.)switches, [21–24 multiplexing,] as well as mechanical etc.) [21–24] [25 as– well32], thermalas mechanical [33–36 ],[25–32], and biological thermal [[33–36],37–42] sensing and biological applications. [37–42] sensing applications. 2.2. SensorSensor ConceptConcept TheThe proposed proposed sensing sensing modality modality exploits exploits the optical the op modestical ofmodes spherical of dielectricspherical opticaldielectric resonators. optical Theresonators. optical resonancesThe optical inresonances a spherical in resonatora spherical can resonator be described can be using described geometric using optics geometric as long optics as theas long wavelength as the wavelength of the light of that the is light used that to excite is used the to optical excite modesthe optical is much modes smaller is much than smaller the radius than ofthe the radius resonator. of the Usingresonator. this description,Using this description, an optical resonancean optical resonance is excited whenis excited the lengthwhen the of thelength path of ofthe the path light of traveling the light on traveling the internal on the surface internal of the surf resonatorace of the is resonator a multiple is integer a multiple of the integer wavelength, of the namelywavelength, when namely 2prn = whenll, where 2πrn r= islλ the, where radius r is of the the radius microsphere, of the microsphere,l is an integer, l is ann isinteger, the index n is the of refractionindex of refraction of the resonator of the resonator and l is theand wavelength λ is the wavelength of the light. of the Figure light.1 Figureshows 1 the shows coupling the coupling of the opticalof the optical fiber and fiber the and optical the optical resonator. resonator. From Laser To Photodiode FigureFigure 1.1. SchematicSchematic ofof thethe pathpath ofof thethe lightlight fromfrom thethe fiberfiber totothe theresonator resonator and and back back to to the the fiber. fiber. When excited, the optical resonances, also known as optical modes or Whispering Gallery When excited, the optical resonances, also known as optical modes or Whispering Gallery Modes Modes (WGMs), are seen as sharp dips in the transmission spectrum (see Figure 2). If the radius or (WGMs), are seen as sharp dips in the transmission spectrum (see Figure2). If the radius or the index the index of refraction (or both) of the resonator are perturbed by an external effect, a shift of the of refraction (or both) of the resonator are perturbed by an external effect, a shift of the optical modes optical modes (Δλ) can be written as follows: (Dl) can be written as follows: Dl Δ DrΔ DΔn = = + (1)(1) l r n TheThe variationvariation ofof thethe radiusradius andand thethe indexindex ofof refractionrefraction ofof thethe microspheremicrosphere representrepresent thethe strainstrain effecteffect andand stressstress effecteffect respectively.respectively.
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