APPLICATION OF TRANSMISSION BRAGG GRATING FOR VIBRATION MONITORING

Size: px

Start display at page:

Download "APPLICATION OF TRANSMISSION BRAGG GRATING FOR VIBRATION MONITORING"

Shon Nicholson
6 years ago
Views:

1 1 PACS 42.79Dj, 42.79Qx APPLICATION OF TRANSMISSION BRAGG GRATING FOR VIBRATION MONITORING Tikhoov E.A., Lyamets A.K. Istitute of Physics Natioal Academy Sci., Kiev, Ukraie, 1.INTRODUCTION I the moder scietific ad egieerig activity there are fields, which study, aalyse, supress or apply various type of vibratios /1/. The broad et of seismographs costatly traces global earthquakes ad a tsuami, also seismic sigals from uclear detoatios, pressure variatios for the ocea bottom called by waves etc. Costatly to be led the iteratioal cofereces o study of oise ad egieerig vibratios, solvig major problems o safety of fuctioig of various egieerig systems ad buildigs from bridges ad high-rise towers to the large vessels ad airplaes. Eve the short eumeratio of subjects icludes followig directios of the termed examiatios: a aero acoustics, measurig techique of vibratios, a oliear acoustics, railway dyamics, automobile ad airplae oise ad vibratios etc /1-3/. The diffractio optical structures belog to class the optical elemets, carryig out various a tasks of guidace ad the aalysis of radiatio due to the multibeam iterferece o their ow periodic structure. As typical represetative of similar elemets it is possible to cosider the volume periodic structure that has bee realized with holographic methods: holographic phase gratigs (HPG) /4,5,6/. Used i give work trasmissio HPG with the efficiet (up to 1%) Bragg diffractio are recorded i real time by argo laser o the self-developig photopolymer PPC-488 that has bee developed ad used i author s istitute /5/. Bragg character of diffractio of a trasmitted radiatio o such gratig is accompaied by 2-beam formatio o output - the zero ad first order of diffractio, besides diffractio process is efficiet i quite arrow gap of icidet agles cocerig a exact Bragg value: from tes of miutes to several degrees - depedig o third dimesio of a gratig - its thickess. 3D character of such gratigs makes its similar to a photo crystal ad simulteesly improves its spectral resolvig ability /6,8/. The first study of specific applicatio the trasmissio HPG for moitorig of small low frequecy vibratios was the purpose of the preset work. I the give cotributio the results cofirmig the possibility ad peculiarities of applicatio of the optical system o the basis HPG ad a laser for vibratio moitorig are preseted. 2. QUALITATIVE MODEL OF A GRATING VIBRATION SENSOR For the quatitative descriptio of light diffractio o HPG the theoretical model of the coupled waves was developed ad successfully applied. The quite successful model was based o approximatio 2-coupled wave iteractio (trasmitted ad diffracted) i periodic structure with the harmoious space idex modulatio /7/. The degree adequacy the give model to cosidered photopolymer gratigs is ot margial ad eeds demostratios which have bee

2 2 provided i our work /6/. Measurig of a space period of maufactured HPG is ot related to the specified theory ad grouded o margial usability of the Bragg coditio to moochromic light diffractio o the similar periodic structure. Cook-Klei's measure of referece of a light diffractio o the cosidered gratigs to multiwave or 2 wave is aother importat compoet for the theory /7/. Exact estimates behid this measure are possible at direct method of measuremet of a actual thickess T ad a spatial period of the gratig Λ or by aalysis o the basis of actual measurig of their agular selectivity formfactor. The short metioed presetatios ad the stored experiece of photopolymer HPG maufacture allows us to record the trasmissio Bragg gratigs with a agular selectivity from some degrees to some tes of miutes purposefully. A estimate of spectral resolvig ability ad applicatio a such HPG for measurig of optical wavelegths i a visible spectral bad was preseted i our work /8/. The essece of proposed applicatio of volume HPG for vibratio registratio is cojugated with presece of the sharp agular depedece diffractio efficiecy (DE) aroud Bragg agle for laser beams, i.e. beams with small divergece. Therefore agular diversios i system HPG - a wave vector of a icidet beam lead to a ati-phase amplitude modulatio of output radiatio powers for zero ad first diffractio order beams that ca be registered by correspodet electroics tools. Iitial estimates of expected sesitivity of a such system to agular detuig ca be gaied at kowledge of agular selectivity volume HPG ad a divergece of the laser beam. If agular selectivity of HPG is over the rage (2-6) agular miits ad used laser beam has typical divergece 1mrad, so it is possible to detect out agles of displacemet ot less tha the laser bream divergecy. For compariso let s give the threshold sesitivity of the moder stadard seismographs of type АРСС (desigs 29 year from istitute of Oceaographic techique of the Russia Academy of Scieces) o frequecy of vibratios 1Hz makes ( ) km/s. If the liear biases matchig to give sesitivity ca call the laser beam displacemet o (3-4) miutes the proposed system HPG+laser ca register the agular displacemet at use of the shoulder exceedig legth ( ) m / (1-4 rad) = (,1-1)mm that is simply carry out i costructio. Accordigly, the similar system o the basis of diode ijectio lasers ad the volume HPG ca be cosidered as a sesor of vibratios of the arbitrary ature callig agular detuig i dispersio plae of gratig. O the other had, the study ad determiatio of the requiremets settig best sesitivity of the volume HPG to vibratios ca be useful at solutio a iverse task of miimizatio of the termed sesitivity at makig o the basis of such gratigs the optical systems of other appoitmet: iterferometers, polychromators, adjustable atteuators of light, etc. 3. ELEMENTARY ANALYSIS OF HPG + LASER VIBRATION SENSOR The agular depedeces of diffractio efficiecy for s, p- liear polarized waves for cosidered HPG gaied i /7/ it is possible to preset as the followig expressios coveiet for the aalysis form /6/:

3 3 η = ν + δ θ / + δ θ s 2 2,5 2 si [(1 ( si(2 )) ] [(1 ( si(2 )) ] s 1 1 η = ν + δ θ / + δ θ p 2 2,5 2 si [(1 ( ta(2 )) ] [(1 ( ta(2 )) ] p 1 1 (1а) (1б) π 1 T ν s = λcosθ ν p, π 1 T cos(2 θ) = λ cosθ, (1с) here θ, λ - the iterior Bragg agle at the zero detuig ad diffractio wavelegth, δ = Θ Θ -agular detuig cocerig a exact Bragg agle, T - the thickess ad Λ - the space gratig period, ad 1 - refractive idex of photopolymer ad amplitude of its space modulatio resultig after a holographic gratig record. The give depedeces specify that DE=max is determied oly by gratig force ν, ad the formfactor of agular depedece is determied by sik-fuctio i square brackets. It allows to cotrol i ecessary limits the DE formfactor i a recorded gratig ad its depedece o a trasmitted light wavelegth. I fig.1. typical depedece of DE o a detuig cocerig a exact Bragg agle θ=41,25 for a s-polarisatio wave 632,8m He-Ne - laser is preseted. It is remarkably featured by first of the above-stated desig formulas (1а). This HPG has bee used at experimets with a agular diversio of a icidet beam uder artificial vibratios. By the way of illustratio rated depedece of DE of a HPG ad its derivative o a detuig agle δ= Θ Θ. is preseted also o fig.2a,b.,8 41,25,6 Absolute DE,4,2, agle of diffractio, degree Fig. 1. Measured DE of trasmissio HPG o a wavelegth 632,8m, s-orietatio of liear polarized light

4 4 1 f ( x) x d xd f ( x) x.1 Fig. 2а.b. Desig values of DE ad derivative of DE o a agular detuig (х - i radias) at phase shift («force of gratig»), equal π/2. It is possible to see that at a agular diversio i a plae of diffractio HPG of a laser beam with divergece a lot of smaller of gratig agular selectivity will occur a atiphase amplitude modulatio of power of trasitig ad diffracted beams. For the subsequet aalysis of modulatio of diffractig radiatio o a vibratig gratig we will spot a stadig of the characteristic operatig poit o curve DE ad its derivative o fig. 2 ad 3. These are fields of maximum DE=max ad a zero value of a derivative of DE o a detuig: ДЭ / δ = o fig. 2а,b accordigly. Operatig areas o fallig left ad right parts of depedece of DE coicide with a stadig of mai maximums of a derivative of DE o a detuig also are visible o specified fig. 2a,b f( x) b( x) x x Fig. 3а,b. Agular depedece of DE ad its derivative o a agular detuig at phase shift equal π (x - i radias). I case of phase progressio equal π, rated depedece of DE for a similar gratig is

5 5 preseted o fig. 3а. I this case DE has a zero value o exact frequecy of the Bragg ad a peak value i symmetrically arraged 2 maximums. Let's guess that the agular detuig betwee HPG ad beam (with divergece small i compariso with agular selectivity of the gratig defied by a stadig of the first ulls o depedece DE=f (δ)) occurs. Let variatios of a detuig cocerig a operatig poit θ submit to the harmoious approximatio δ(t) = δ si (Ωt). I the determied coditios it is possible to preset depedece of diffracted power by a Taylor series with values of derivatives o a diffractio agle θ i a operatig poit θ : ' ' dηθ ( ) Pout ( t) = Pηθ ( ± δsi( Ω t)) P[ ηθ ( ) ± δ si( Ω t)( ) θ ' ± dθ (2) d ηθ ( ) ( δ si( Ω t) ( ) ' ±...) 2 θ 2! dθ Depedig o a operatig poit select o a agle θ, DE(θ) ad its derivatives will have sigificat or zero values, ad it will effect o a relatio betwee frequecies of vibratios Ω o HFG iput ad o a exit after diffractio. For example, if at θ=θ, the detuig is abset, DE=max, the first derivative of DE o a agle is equal to zero, but secod oe accepts a peak value, providig a modificatio of goig out diffracted power o double frequecy 2 Ω. I case of a operatig poit select i a positio matchig to 2 symmetrical maximums of a derivative (fig. 2б), modulatio Р (t) happes o frequecy of vibratios forcig it. These ad other possibilities will be observatioally illustrated. Other possibilities origiate at similar agular scaig of a gratig (or iput beam) i case of HPG, phase shift for which is equal π (fig.3а). At a select of the operatig poit, satisfyig to the strict Bragg requiremet, the direct emissio compoet i a goig out diffracted power misses at all as DE(θ )=, while the alterative compoet shows emissio o the doubled sca frequecy for the same parets, as i the first featured case. The specified agle depedece of DE ca be used i systems of beam stabilizatio i space. 4. EXPERIMANTAL RESULTS The approbatio of a sesor of vibratios was carried out i the optical scheme costituted from HPG with differet magitudes of agular selectivity, He-Ne laser o 632,8m with beam divergece 1-2mrad ad s-orietatios of its polarizatio plae. The vibratig mirror was iterfaced to the electromechaical actuator operatig at a frequecy 16 Hz ad givig rise to agular sca i a gratig dispersio plae with amplitude to 3 mi. The gratig were set o a goiometric table for their smooth agular tur ad a select of a iitial agle of icidece - a iitial operatig poit cocerig which agular scaig by vibratios was carried out. The diffracted beam ad a beam of zero diffractio order directed o semicoductor detectors PhD- 24 workig i the photodiode regime which were switched o iputs of the 2-beam oscilloscope. At a operatig poit samplig o oe of 2 fallig braches cocerig a maximum DE scaig of a iput beam o frequecy Ω was accompaied by expected atiphase modulatio of the diffracted ad feed-through emissios o the same frequecy (fig. 4).

$The operatig poit is set i a maximum of a DE derivative o a diffractio agle. Fig. 5.$ The operatig poit coicides with a DE maximum ad a maximum of a secod DE derivative. The scaig frequecy is the former as o fig. 4.

The operatig poit coicides with a DE maximum ad a maximum of a secod DE derivative. The scaig frequecy is the former as o fig. 4.

6 6 Fig. 4. Atiphase modulatio of beam power o a gratig exit at agular scaig of a iput beam with amplitude some agular miutes. The operatig poit is set i a maximum of a DE derivative o a diffractio agle. Fig. 5. The operatig poit coicides with a DE maximum ad a maximum of a secod DE derivative. The scaig frequecy is the former as o fig. 4., but observed modulatio frequecy of output radiatio is doublig scah amplitude, mi ,5,6,7,8,9 1, voltage, v Fig. 6. Depedece of amplitude of the agular scaig of a beam from a applied voltage o the used actuator

7 7 At replacemet of the used gratig with agular selectivity 2,4 with oe at selectivity 5 (at other ivariable parameters) the modulatio depth decreased multiply. The peak amplitude of scaig i the give istaces did ot exceed oe degree ad matched to agular selectivity of the chose gratig ( fig. 1.). It was see that the amplitude of the modulated sigal multiply exceeded a oise level of registerig system at radiated power of the laser earby 1мВт. The miimum scaig agle registered by the tested sesor by supply voltage decrease to the vibratio actuator has bee measured. Results of measurig are preseted o fig. 6. Showed that at scaig amplitude close to agular beam divergece of the used laser the pickup sigal i the form of the modulated diffracted powerl dicreased to a zero value. 5. CONCLUSIONS It is show that proposed оptical-electroic system i compositio of the volume trasmissio gratig, a laser ad itermediate sesitive to vibratios mirror detects vibratios whe the agular scaig amplitude of a icidet beam exceeds agular divergece of a laser beam provided that iitial diffractio agle coicidig with a maximum of the first DE agular derivative of the used gratig. Sesitivity of sesory system to vibratios i agular miutes depeds o a operatig poit samplig o agular DE depedece ad takes max value for gratig with agular selectivity comparable with agular divergece of the max laser beam quality. Mathematical model of fuctioig of a sesor i the form of a Taylor series well featurig a sesitivity it ad effect of a respose frequecy doublig to relative frequecy of vibratio is preseted. 6. THE QUOTED LITERATURE /1/ M.D.Geki, Optical measuremet of vibratios, edited by Masiostroeie, (i Russia), Moskow, v.5. pp , (1981) /2/ G. Ausaio, A.C. Baroe, C. Hiso ad others, Mechaical vibratio sesor based o elastomagetic composite, Sesors ad Actuators A129, pp.25-28, (26), /3/ E. Ollier, P.Philippe, C.Chabrol, P.Mottier, Micro-opto-mechaical vibratio sesor itegrated o silico, Lightwave techology joural, 17, 26-29, (1999) /4/ D. Psaltis, Itroductio to volume holographic gratigs, Sciece v.298, pp (22), /5/ E.A.Tikhoov, Holographic volume gratig recorded o self-developig photopolymers: useized advatages i optical egieerig, Applicatio of Photoic techology, Photopic North 2, SPIE v.487, p.767, (2) /6/ E.A.Tikhoov, Aalysis ad measurig of parametres of holographic Bragg gratigs, (i Russia), Vestik Sait-Petersburg Akademy of Egieerig scie., 4, pp.57-78, (28), /7/ H. Kogelik, Coupled wave theory for thick hologram gratig, Bell Sys. Tech. J. v.48, #9, p.299, (1969) /8/ E. A. Tikhoov, A. A. Tyutyuik, "Measurig the wavelegth of light usig Bragg diffractio gratigs," J. Opt. Techol. 74, , (27)

SPECTROSCOPY and. spectrometers

SPECTROSCOPY and. spectrometers Observatioal Astroomy SPECTROSCOPY ad spectrometers Kitchi, pp. 310-370 Chromey, pp. 362-415 28 March 2018 1 Spectroscopic methods Differet purposes require differet istrumets Mai spectroscopic methods: