Physics Procedia 73 ( 2015 ) 198 – 204

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1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)doi: 10.1016/j.phpro.2015.09.157

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© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)

V.I. Busurin et al. / Physics Procedia 73 ( 2015 ) 198 – 204 199

Itranpara

2. G

Pduemedthe

G(PT(refextetranof th(198modas: a

Tof thgapvelois ab

Tof tR[d

Fdefi

wresp

I

In this paper: nsducers, consameters of the

Generalized s

Proposed MOe to the fact thdium not onlywavelength o

Generalized stT), photodetecfractive index ernal factors nsducers of anhe SE. Separa80), Busurin dulated surfacarcsin(n2/n1)

The magnitudhe optical rad

p d0, by the maocity or accelebsorbed, and iTransfer functthe measured d( )] of interfaFor non-polarined as [Born

[ (R d

whereR [d( )pectively, undIn this situatio

it is carryingstructed by meese transducer

structure of M

OEM transducehat the electr

y by mean of dorder on the mtructure of tractor (PD) and– n1) and sen( ) (includin

ngular velocitiation medium and Nosov (

ce is the condi arcsin(n

de of gap d betdiation and it sanufacture, aseration. Whileit leads to dection MOEM trmagnitude oface "prism - airized optical and Wolf (19

1)] [2

R

)], R [d( )] - der the influenon for output

g out investigaean of using “rs and errors e

MOEM trans

ers use boundromagnetic wadirect mechan

medium. ansducers based processing nsing elementng angular ves and accelerbetween the p

(1990)]. The ition of total i3/n1).

Fig. 1. Generali

tween the basshould be arous well as the de decreasing thcrease the outpransducers rep

f SE. Transferir - SE" to thewave reflecti

980), Busurin

( )] [d R

reflectivity once of external

optical power

ation of the c“total internalstimation gen

ducers based

dary modulatioave, which pr

nical contact o

ed on OTE counit (PU) (F

t with thin layvelocity and rations are theprisms and SEcriterion for nternal reflect

ized structure of M

se of the prismund hundreds

deflections SEhe magnitudeput signal of thpresents the our function is ge gap d( ), locivity in structet al. (2012)]:

( )]d ,

of mediumsbl factor . r PD( ) can b

characteristics l reflection of nerated due to

d on OTE

on of radiationropagating in

on the medium

onsists of optiFig. 1). PT ryer (refractiveacceleration).e difference oE may be air m

selection of tion at optical

MOEM-transduc

m and the SE m of nanometer

E ym( ) which e of gap d, mohe photodetecutput voltage

generally detercated betweenture with one

boundaries fo

be written as:

of MOEM af prism – SE” their variation

n produced bya medium is

m, but also by

ical radiation represents as e index – n3), . In this casf structural so

medium (refrathe incident

l contact with

ers based on OTE

must not excers. The magniare proportio

ost of the penector. Uout = F ( ) ormined by dep

n the base of the reflection fr

or perpendicul

PD( )=POS·R

ngular velocitsystem, deter

ns.

y OTE. Optic affected impmean of appro

source (OS), total internawhich is und

e, the differeolutions and opctive index – nangle of oa prism, whic

E.

eed the magnititude of the gaonal to externaetrated optical

of PU that deppendence of mhe prism and trom the modu

lar and parall

R[d( )]·k, wh

ity and accelermination of d

cal tunneling opact from the oaching distan

primary transal deflection der the influenences betweeperational prinn2) [Born and

optical wave ich can be desc

itude of wavelap is fixed as al factors -an energy into t

pends on the immedium reflecthe SE. ulated bound

lel polarized

here, k – coeff

eration design

occurs other

nce of

sducer prism

nce of en the nciple

d Wolf in the cribed

length initial ngular he SE

mpact ctivity

ary is

(1)

wave,

ficient

200 V.I. Busurin et al. / Physics Procedia 73 ( 2015 ) 198 – 204

of opPU U– sen

3. M

TbasetransMOE

Uallowpossconslargethe iaxis x – cdf – excitsizestwo

Wvariathe sincidas wcont

wA

defin

ptical losses; Uout( ) can bensitivity of ph

Model of MOE

Theschematicsed on the piezsferring the anEM angular v

Under the influws to measuresible to mounsidered that, te additional minfluence of thwill be a func

coordinate of piezomodule

tation voltages and materialorders of mag

While investigability of gap source of radident rays. In th

well as the deftact Aopt:

max .md

where r, – cuAt fixed designed as the inte

POS – power e represented hotodetector; R

EM angular v

s diagram of tzo material, wngular velocit

velocity transd

uence of mease angular vel

nt additional mthe effective mmass is mountehe angular vection of manySE ends along

e with feedbae, that causes ls, mounting agnitude greategating the chafor different oiation creates his situation eflection of SE

in 0 md y

urrent polar cogn parametersegral relations

of OS. By usias: Uout( )=(I

RI-U – resistan

velocity trans

the MOEM anwhich is operty of SE to theducer is used w

Fig. 2. MOE

sured angularocity Z. To

mass m, situatmeasuring raned and the op

elocity Z ampy parameters [Bg axis; pi

ack piezo effea longitudina

additional maser than the casaracteristics ooptical radiatia circular op

extreme magn’s end m

*, tak

m( , ,m Z l h

oordinates (rads extreme maship within fr

ing an op-ampID+SPD·POS·k·Rce in feedback

sducer

ngular velocitrating at AC e movement [with two chann

EM angular veloci

r velocities, smincrease the

ted, for examnge is reducederating capaciplitude deflecBusurin et al. ezo– density of

ect; lm, hm, bmal vibration alss about m=5e without the

of MOEM anion contact potical spot withitude of gap d

king into acco

m m, , ,h b m U

dius and angleagnitude of oames of the e

p based transdR[d( )])·RI-U,wk loop of op-a

ty transducer iexcitation vo

[Sharapov et anels, reading

ities transducer b

mall deflectionsensitivity of

mple, at the twd and the lineity of transdu

ction of SE w (2015)]:ym=ff piezocerami

m– length, thilong the axis 5gwill provide

additional mangular velocityoints on the mth a radius ropdmax,min dependount the variat

exct piezo, ,U

e) of optical eoutput optical elliptical area

ducer "currentwhere ID – daramp based tran

includes SE inoltage Uexct anal. (2006)].Toout output opt

ased on OTE.

ns of SE occuf MOEM tranwo ends of SEearity of the tcer may be faith the additio

f( z,x,lm,hm,bmic; Epiez – Youckness and wOX with freq

e the maximumass m. y transducer,

modulated bounpt on the planeds on initial gation of the gap

piezo f, , ,E d

lliptical area Apower, that

of optical con

t-to-voltage", rk current of nsducer "curre

n the form ofnd using the C improve the tical signals (F

ur due to Corinsducer of angE. In this situaransducer is d

ailure in criticaonal mass m wm,m,Uexct, , piung’s modulu

width of SE reuency .Not

m deflection o

it is necessarndary of the pe, which is peap d0, fixed byp along ellipti

, , )r ,

Aopt. achieving the

ntact Aopt, taki

the output vophotodetectorent-to-voltage

f vibration eleCoriolis effectransfer efficiFig. 2).

iollis effect, wgular velocityation, it shoudeteriorated, wal situation. Uwith respect tiezo,Epiezo,df), w

us of piezocerarespectively; Ute that at the

of 1.4 μm, whi

ry to consideprism. Assumeerpendicular ty manufactureical area of op

(

e photodetectoing into accou

oltage r; SPD e" .

ement ct for iency

which y it is ld be when

Under to OY where amic; Uexct–same ich is

er the e that to the e, and ptical

(2)

or, is unt of

V.I. Busurin et al. / Physics Procedia 73 ( 2015 ) 198 – 204 201

the

DhighSE gapindepowchanCha

Tfuncsyst

4. M

Tconerroconthe withacceacceMOaccetranwhe

variation of g

PD maxP

During the inh sensitivity awere selected

p d0 = 0.41 mex ofSE n3 =

wers PPDm=Pnnel transducanging rotation

Fig. 3. Depend

The investigatction within thtem.

Model of MO

To provide tnfigured as canor, SE of transnsider restrictio

influence of lhout additionelerations witeleration tran

OEM accelerateleration SE i

nsducer with ere az – appli

gap dmax.min(r,

x,min ( )

nvestigationtheand work in md: length lm = m; power sourc= 1.46; refractPPD1max( z)-PPer of angular nal direction l

dence of extreme

ted angular vhe measured r

EM accelera

the possibilityntilever, beamsducer can beons on sizes alateral acceler

nal mass doeth high sensitisducer is usedtion transduces deflected aloadditional ma

ied acceleratio

, z):

OS2

optcP

r

e parameterswmeasured rang

10 mm; thickce PSO = 1 mWtive index of PD1min( z) andvelocity by uleads to chang

a

values of output

velocity transdrange of sever

tion transduc

y of acceleram or multibeae made up of and minimal iration a four bes not providivity in the sed a body wither consists of ong OZ axis, aass mc(az) ison along axis

opt

osA

k

were determinge (± 4 rad/s). kness hm = 60W; optical losf the separatind amplitudes sing the desig

ge the output p

optical power de

ducer based oral radians per

cer based on

ations measuram elements. fused quartz. influence of labeam SE was de therequiredelected measuh additional mprism, base, Sand displacems a function o

OZ; m0 – ma

t

max,min[R d

ned, which arFor the transd

0 μm; width bsses coefficienng medium n

of output vgned parametephase of signa

eviation (a), and a

on OTE with tr second, whi

OTE

rement, SE, In this situatiWhile constr

ateral acceleraused, which h

dmagnitude ouring range ±mass madd, fixSE, air gap, ad

ment magnitudof parameters

mass of fused q

n ( , , )r

re providing oducer the follobm = 1 mm; thnt k = 0.5; refr

2 1. dependevoltage Uout.m(ers, described al in .

amplitude of outp

two channel sch provides it

described inion, for achieructing the acations (along has been fixedof the SE de10g. Therefored in the cendditional masde of central ps set [Ryder quartz four b

opt] .dA

operation of Mowing geomethe incident angractiveindex nncies of extre( z)=[ID+ PPabove,were d

b

put voltage (b) to

sensing has qts effective us

generalized ving low addceleration tranthe axis OY ad at the ends. eflections, reqre, in the schentral part of ths (Fig. 4).Undart of SE of M(1969)]:ymc=feam SE, madd

MOEM transdtrical dimensiogle = 49 °; n1 = 1.46; refreme output o

PDm( z)]·RI-Uodetermined (F

angular velocity.

quasi-linear trase in mobile c

structure maditional tempensducer, we sand OX). To r

The use of thquired to meematics diagrthe SE. Diagrder the influen

MOEM accelef(az,madd,m0,l4,d – additional

(3)

ducer, ons of initial active

optical f two ig. 3).

.

ansfer ontrol

ay be erature should reduce his SE easure am of am of nce of

eration ,J,Eq), mass;

202 V.I. Busurin et al. / Physics Procedia 73 ( 2015 ) 198 – 204

l4,h4You

Ttakinpart mass

Tsuchwere0.28

1);

,b4 – length, ung’s modulus

The magnitudeng into accounof a SE and ths madd at the c

The transfer fuh form: Uout(aze determined mm, the refrathe incident a

thickness ans of fused quar

e of the gap d(nt the initial ghe prism is coentre of the SE

unction of accz)=[ID+SPD·PPat the follow

active index ofangle = 49 °

Fig. 5. D

d width of fortz.

Fig. 4. MO

(az) depends ogap d0:d(az) =onstant along tE.

celerations tranPD(R[d(az)])]·Rwing selected

f the prism n1 (Fig. 5).

a

ependence of out

our beam SE

OEM acceleration

on the displac= d0 ym(az). Athe modulatio

nsducer is theRI-U. Dependenparameters: i = 1.46; the re

tput optical powe

E respectively

n transducer base

cement of the Assume that t

on boundary o

e dependence nces of outpuinitial gap d0 efractive inde

er (a), and output

;J=b4·h43/12 –

ed on OTE.

central part othe magnitudef prism by mo

of output voltt power and o= 0.45 μm,

x of SEn3 = 1

voltage (b) to acc

– inertial mom

f the SE,and ie of the gap bounting undefo

tage to acceleroutput voltagelength l4= 4m.46; separatio

b

celeration.

ment of SE;

it is determinebetween the ceformable addit

ration, which e to acceleratimm thickness on medium - a

Eq –

ed by entral tional

have on az h4 =

air (n2

V.I. Busurin et al. / Physics Procedia 73 ( 2015 ) 198 – 204 203

Awhitranwith

5. E

Odispalonalso

Aareasmainci

Dtranthe of i

Tinac

of rvelo

Terro

According to ich provides qnsfer function h respect to th

Error analysi

One of the fuplacement senng the gap: S(o varies due to

Fig. 6

Analysis of pra of high sensall deviations ident angle 49During the mnsducer some models from initial gap d0 aThe movemenccuracy while

PDP

The gap magrelative error ocities (±4 radThe simulationor composes o

the graph, thquasi-linear coutput optica

he central part

s of MOEM t

undamental pansitivity, caus(d)= R/ d. Noo design param

6. Dependence of

rovided depensitivity. While

it is determi9°), where senmeasurement kinds of errothe calculatedand the incident of initial g manufacturin

PD 0

PD

(P dP

gnitude of tranof optical ou

d/s) and accelen showed that

of 1.6% for an

he investigatedharacteristics

al signals withof the SE, can

transducers

arameters of sed by externaote that the semeters (includ

f MOEM transduc

ndences showse changing aninedthe rangesitivity is not process of p

rs are arised, d values, affecent angle . gap d0 betweeng and assemb

PD 0

D 0

) (( )d P d

d

nsducers mustutput power eration (±10g)t the deviation

ngular velocity

d model of Mwithin measutwo readout c

n be arranged

the performanal factors, whensitivity of trding gap d and

cers’ sensitivity t

s that decreasingular velocitis of acceptabreduced morephysical quanand the cause

cting the optic

n SE and pribling the trans

) 100% .

t be within theon varying th) are determinn of magnitudy transducer an

MOEM acceleuring range ±channels by u

d.

nces of MOEhich is defineransducers is nd incident angl

to magnitude of g

ing of the inciies and acceleble values of e than3 times. antities using es of these errcal tunnelling

ism within thesducer and lea

e defined acche value of i

ned (Fig. 7, a).de of the initiand 2.4% for th

eration transdu±10g. In orderusing additiona

EM transducered as the partnot constant ile of radiation

gap with various v

idence angle erations to prothe gap, for

MOEM angrors are the d. Particularlly

e area of opads to relative

eptable value initial gap d. al gap d0 in thhe acceleration

ucer possessesr to improve al prism, mou

rs based on Otial derivativein the range on ) (Fig. 6).

value of incident

of radiation ovide the requexample, 0.04

gular velocityeviation of dethese may in

tical contact merror of ouput

of sensitivityd0at maximum

he range of ± n transducer.

s transfer funthe linearity

unted symmetr

OTE is nano-e of the reflecof measuremen

angle .

leads to expanuired sensitivi

04...0.73 μm (

y and acceleesign parametnclude the dev

may be causeut optical powe

y. The dependm value of an

16 nm, the re

nction, of the rically

-range ctivity nt and

nd the ity for (while

eration ters of viation

ed the er:

(4)

dences ngular

elative

204 V.I. Busurin et al. / Physics Procedia 73 ( 2015 ) 198 – 204

Fig. 7

Ainstafrom3.6%com

6. C

Intransprovbe u

Fdepe

Texamangutrans

Ack

T

Refe

Born L

BusurBusurBusur

VFradeKostsRyderShara

7. Relative errors

Axial displacealling OS. The

m which it foll% at the dev

mpensated duri

onclusion

n the course sducer based ovide quasi-linesed in control

For providing ends on value The deviationamined. It is shular velocity tsducer with th

knowledgemen

This work was

erences

M., Wolf E., 198Ltd. rin V. I., Nosov Yrin V. I., Gorshkorin V. I., KazaryVestnik MAI.1, 2en J., 2004.Handbsov E.G., 2009.Sor G. H., 1969.Stre

apov V.M., Musie

s of optical output

ement of incide dependencelows that the iation of incing the proces

of work a gon OTE wereear characterisl system of mowith high-senof incident an

al influence ofhown that thetransducer, anhe relative erro

nt

s supported by

80. Principle of o

Yu. R., 1990.Voloov B. G., Korobkyan A. V., Pham29-37. book of modern sostayanie i perspeength of materialenko M.P., Shara

a

t power of angulath

dent angle of of output optrelative error ident angle s of calibratio

generalized bl developed. Tstics within thobile objects. nsitivity MOEngle, is determf the initial ga

e deviation of nd 7 nm and 0or less than 1%

y grant 13-08-

optics: Electroma

okonno-opticheskkov V. V.,2012. Vm Anh Tuan.,201

sensors.Physics deecktivy mikro- i nls.3rd edition, Thapova E.V., 2006.

ar velocity PD (he deviation of inc

f radiation ontical power refor angular v

0.2°. Idon.

ock diagram The transfer fuhe calculated

EM transducermined. ap and the angthe gap and

0.06° for accel%.

00493-a from

agnetic Theory of

kiedatchiki: fizichVolokonno-optich15. Research of

esigns and applicnanoelecktromeche Macmillan pres. Piezoeletrichesk

z) and acceleraticident angle (

n the base of elative error ovelocity transddentified erro

of MOEM aunctions for mregion of me

rs based OTE

gle of incidenthe angle of ileration transd

m Russian Foun

f Propagation, Int

heskieosnovy, voheskie i nformatiothe characteristic

cations,3rd editionhaniki, Avtometrss ltd. kiye datchiki / Ed

on PD (a), transd(b).

the prism ocon incident anducer is 1% anors of transdu

angular velocmeasuring angu

asurement an

E the range of

nce on the chaincidence muducer, respect

ndation for Ba

terference and D

oprosy rascheta i ponno-izmeritelniycs microelectrom

n, Springer-Verlariya. 3, 3-52.

d. by V. M. Sharap

b

ducers at the mov

ccurs due to igle is detend for accelerucers must b

ity transducerular velocitiesd such types

acceptable va

aracteristics ofst not exceed ively to achie

asic Research

iffraction of Ligh

primeneniya .- Mye systemy. - M .:mechanical angul

ag, New York.

pov, -M .: Techno

vement of gap d

inaccuracies wermined (Fig. ration transducbe considered

r and accelers and acceleraof transducer

alue of gap, w

f the transducd 9nm and 0.2eve a measure

(RFBR).

ht, 6th edition, El

M .: Energoatomiz: MAI. lar velocity trans

nosphere.

d0(a) at

when 7,b),

cer is d and

ration ations s can

which

ers is 2° for ement

lsevire

zdat.

sducer,