LASER VIBROMETER CALIBRATION AT HIGH FREQUENCIES USING.pdf

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XIX IMEKO World Congress

Fundamental and Applied Metrology

September 611, !!", #isbon, $ortugal

LASER VIBROMETER CALIBRATION AT HIGH FREQUENCIES USING

CONVENTIONAL CALIBRATION EQUIPMENT

Thomas Bruns, Fran% &lume, Angeli%a '(ubner1 $)ysi%alis*)+'e*)nis*)e &undesanstalt, ermany, t)omas-bruns.ptb-de

Abstract ')e *alibration o/ #aser 0ibrometer is anin*reasing demand in industry and resear*)- ')e euipment

suggested /or use in parti*ular /or )ig) /reuen*y*alibration, )o2e0er, is typi*ally o/ prototype stage and not

*ommer*ially a0ailable- ')is is due to t)e demand o/ t)e

employed )omodyne uadrature met)od /or a *ertain

minimum displa*ement, typi*ally a uarter o/ a 2a0elengt),o/ t)e 0ibrating ob3e*t- ')e aut)ors demonstrate t)at t)is is

not ne*essarily a *ompulsory *ondition- Wit) *on0entional,*ommer*ially a0ailable *omponents it is possible to set+up a

system /or #aser 0ibrometer *alibration up to "! %45- ')is*ould be a*)ie0ed by employing a distin*ti0e opti*al set+up

*ombined 2it) an unusual dual /reuen*y7 e8*itation andan impro0ed or e8tended signal pro*essing-

Keywors #aser 0ibrometer, *alibration, multisine

!" INTRO#UCTION

#aser 0ibrometer as non *onta*t measuring de0i*es2it)out inertia e//e*ts on t)e measured ob3e*t are ideal

instruments to measure )ig) /reuen*y me*)ani*al 0ibra9tions, e-g-, in t)e /ield o/ MEMS te*)nology- A**ordingly

t)e te*)ni*al spe*i/i*ation o/ *urrent *ommer*ial de0i*esstate a appli*able /reuen*y range /rom :C to se0eral M45-

In order to support su*) te*)ni*al spe*i/i*ation a *alibrationis ne*essary, 2)i*) in t)e optimal *ase is an o0erall mea9

surement on a system 2)i*) pro0ides a 2ell de/ined motionuantity li%e a**eleration, 0elo*ity or displa*ement-

4o2e0er, /or /reuen*ies beyond ! %45 it be*omesin*reasingly di//i*ult to pro0ide su*) a 2ell de/ined motion

2it) su//i*ient amplitude, due to limitations in t)e per/or9

man*e o/ t)e ele*trodynami* motion e8*iters- For t)eappli*ation o/ t)e so *alled ;ar*tan+met)od< in *ombination

2it) a )omodyne uadrature inter/erometer a displa*ement

amplitude o/ appro8imately 16! nm is reuired- At =! %45t)is is eui0alent to an a**eleration o/ appro8- 1=,> %m?s@

and at 1!! %45 an a**eleration o/ appro8- 6 %m?s@ 2ouldbe ne*essary- ')is is not /easible 2it) any *ommer*ial

ele*trodynami* e8*iter- ')e reason /or t)e displa*ementreuirement is t)e need /or at least one /ull inter/eren*e

/ringe in*luded in t)e signal to apply t)e non+linearity*orre*tion B1, -

In /a*t t)is reuirement is essential /or t)e e0aluation o/

t)e inter/eren*e signal B, )o2e0er, it is not essential to/ul/il it at t)e nominal, )ig) /reuen*y- Starting /rom t)isobser0ation t)e aut)ors de0eloped a #aser 0ibrometer

*alibration set+up, 2)ere t)e e8*itation 2as pro0ided 2it) adual /reuen*y signal, in*luding a lo2 /reuen*y *omponent

pro0iding t)e ne*essary displa*ement and a )ig) /reuen*y*omponent used as nominal *alibration /reuen*y-

In order to *ope 2it) t)is type o/ signal in t)e dataanalysis t)e usually applied sine+appro8imation met)od 2as

e8tended-

$" THE TECHNICAL SET%UP

2.1. The optical arrangement

')e opti*al set+up ma%es use o/ a %ind o/ beam

re*y*ling, i- e- t)e #aser beam o/ t)e de0i*e under test:D'7, a *ommer*ial )eterodyne #aser 0ibrometer $olyte*-

OF =!7, is re+used as t)e #aser sour*e /or a modi/iedMi*)elson inter/erometer MMI7, 2)i*) is t)e re/eren*e-

')e general s*)eme is depi*ted in /ig- 1- ')e lig)t emitted/rom t)e :D' is *ir*ular polari5ed ;*ir*-< in Fig- 17- In

order to ad3ust t)e polari5ation in t)e beam line o/ t)e MMIt)e uarter 2a0eplate #? is in*luded in t)e re/eren*e beam-

It 2as t)e e8perien*e o/ t)e aut)ors t)at t)e rotational

position o/ #? needs to be ad3usted indi0idually in order toget ma8imum uadrature in t)e I and G signal-

Fig- 1H Opti*al arrangement /or t)e #aser 0ibrometer *alibration

*ombining a )eterodyne and a )omodyne+uadrature set+up usingt)e :D' as t)e single #aser sour*e-

2.2. The vibration excitation part

')e 0ibration e8*iter used, 2as a &rel J K3r type>!", 2)i*) )as a membrane borne armature o/ 6! g-

Mounted on top o/ t)e armature 2as a solid pie*e o/ steel o/a mass o/ 1! g, 2it) a polis)ed sur/a*e a*ting as t)e

0ibrating mirror M in Fig- 1, $)otograp) in Fig- 7-

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Fig- H Commer*ial 0ibration e8*iter 2it) mounted steel re/le*tor

')e ele*trodynami* e8*iter 2as dri0en 0ia a &EAK&A =!! po2er ampli/ier, 2)i*) in turn 2as *onne*ted to an

arbitrary 2a0e/orm generator AW, Agilent !A7- ')eabo0e mentioned dual /reuen*y signal 2as stored in t)e

user memory o/ t)e AW be/ore measurement- Fig- s)o2s typi*al 2a0e/orms /or a /reuen*y ratio o/ 1H1! and

an amplitude ratio o/ 1H in 0oltage-

Fig- Cal*ulated signals o/ displa*ement and a**eleration /rom t)e

dual /reuen*y e8*itation /or t)e ratios mentioned in t)e te8t-

Considering t)at t)e /or*e and t)ere/ore t)e a**elerationis roug)ly proportional to t)e applied 0oltage t)e gi0en

ratios result in a displa*ement ratio o/ =H1- ')us in*ombination 2it) t)e te*)ni*ally reuired 16! nm lo2

/reuen*y displa*ement amplitude a )ig) /reuen*yamplitude o/ 6, nm *ould be reali5ed-

2.3. The Data acquisition

Four data *)annels 2ere syn*)ronously a*uired /or t)e

measurement, t)e I and G signals o/ t)e MMI as re/eren*e,generated by t)e p)oto diodes $:I and $:G, respe*ti0ely,

t)e /reuen*y modulated output FM7 o/ t)e :D' and t)e0elo*ity proportional analogue output E#7 o/ t)e :D'-

Lote, t)at t)e FM is a modi/i*ation o/ t)e *ommer*ially

a0ailable de0i*e, pro0ided /or t)e spe*i/i* use at $'&- All

*)annels 2ere sampled 2it) =! MS?s at 1 &it resolution-Syn*)roni5ation is a*)ie0ed by employing a *ommon

*lo*% line running at 1! M45 2)i*) is *onne*ted to all*omponents but t)e transient re*order- ')e A:C *ards used

)ere *ould only be dri0en by a ! M45 *lo*%- ')ere/ore it2as ne*essary to pro0ide t)is *lo*% rate 2it) t)e )elp o/ a

supplementary /reuen*y generator 7 2)i*) 2as in turnsyn*)roni5ed 2it) t)e *ommon 1! M45 *lo*% signal- ')e

*ommon *lo*% signal 2as retrie0ed /rom t)e internal *lo*%o/ generator 1-

Fig- :iagram o/ t)e data a*uisition and 0ibration e8*itation set+

up in*luding t)e syn*)roni5ation-

Lote t)at t)e /reuen*y *ounter FC 2as syn*)roni5ed,too, in order to )a0e t)e measurement o/ t)e *arrier

/reuen*y o/ t)e :D', i-e- t)e *arrier /reuen*y o/ FM, ont)e same time s*ale-

3.2. The data processing

')e digital demodulation o/ I+G+data /rom MMI set+ups)as been des*ribed e8tensi0ely in literature and s)ould notbe dis*ussed in detail )ere- 4o2e0er, it is 2ort) to mention,

t)at t)e non+linearities 2ere treated 2it) t)e 4eydeman+*orre*tion B1-

')e demodulation o/ t)e FM is done by /irst do2nmi8ing t)e pro0ided ! M45 *arrier /reuen*y o/ t)e signal

to 1 M45- Wit) t)is *on0enient *arrier /reuen*y t)e signalis sampled and subseuently synt)eti* I and G signals are

generated by digital mi8ing 2it) sine and *osine time series-')e met)od is des*ribed in some more detail in B

A/ter t)e respe*ti0e demodulation t)e t2o *)annels o/t)e MMI resulted in a displa*ement timeseries as did t)e

single FM *)annel o/ t)e :D'- ')is t2o deri0ed displa*e9ment signals 2ere subseuently di//erentiated in order to

deri0e 0elo*ity- ')is 2as done 2it) t)e intention to diminis)t)e in/luen*e o/ lo2 /reuen*y disturban*es- A se*ond

di//erentiation 2ould )a0e in*reased t)e amplitude o/ t)e

)ig) /reuen*y part, )o2e0er it 2ould in*rease t)edisturban*es due to noise as 2ell- ')ere/ore, t)e e0aluation

as 0elo*ity as in *ontrast to displa*ement or a**eleration7

turned out to be best suited in an o0erall sense-')e 0elo*ity signal, E# did not need any pro*essing in

terms o/ demodulation- For t)is output, 2)i*) is typi*allyused in industrial appli*ations, t)e demodulation is done

internally in t)e :D' and a 0elo*ity proportional 0oltage

output is supplied- Lote, )o2e0er, t)at t)is paper /o*uses ont)e *omparison o/ t)e MMI and t)e FM- ')e pro*essing o/

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t)e E# *)annel 2ould be straig)t /or2ard and almost

identi*al- For t)e internal use at $'&, )o2e0er, it is o/ little

*on*ern-

3.2. The data analysis

')e establis)ed met)od to analyse *alibration data based

on sinusoidal e8*itation is t)e ;sine+appro8imation met)od! %457-

Fig- =H $lot o/ t)e digiti5ed and pro*essed 0elo*ity data o/ t)e FM*)annel *ir*les7 toget)er 2it) t)e appro8imated lo2 /reuen*y

and )ig) /reuen*y 0ibration /un*tions-

A/ter /itting t)e t2o di//erent data *)annels MMI and FM7

t)e results 2ere *ompared in terms o/ relati0e magnitude

de0iation to t)e re/eren*e MMI7 and absolute p)asede0iation to t)e re/eren*e- ')e preliminary uantitati0e

results are gi0en in t)e ne8t se*tion-

&" PRELIMINAR' RESULTS

As des*ribed abo0e, t)e results 2ere ta%en as*omparison 0alues o/ t)e :D' FM output7 0s- t)e MMI as

re/eren*e- ')e magnitude de0iation bet2een MMI and MMIand :D' is gi0en as a relati0e root mean suared de0iation

MS: 2it)

RMSD=

k

xFM xMMI

k

xMMI,

2)ile t)e p)ase de0iation is gi0en in absolute termsin degree and as t)e standard de0iation o/ repeated

measurements- Freuen*ies *ombined in one measurement,I.e. in one dual /reuen*y e8*itation, are reported in sub9seuent lines o/ table 1-

table 1H preliminary results o/ t)e #aser 0ibrometer *alibration2it) dual /reuen*y e8*itation

Low()*+)

,re-.e/cy

*/ 0H1

Ma+/"

x:D'

*/ /2

Ma+/" #e3"

RMS#

*/ 4

P)ase e3"

*/ 5

St" #e3"

*/ 5

1! 1="," !,!N ,=!1 !,!!

=! , !,N 1,! !,N

1! ==,= !,!1 ,6=> !,!!6

>! >, !,6 1"," !,=

1! 1"," !,! ,66! !,!1

"! ,1 1,6 ,1 ,

6" OUTLOOK

')e *ombination o/ t2o inter/erometri* set+ups 2it) one*ommon *o)erent lig)t sour*e poses some *ompli*ations

due to t)ree 2a0e inter/eren*e e//e*ts, 2)i*) generate some*rosstal% bet2een t)e distin*ti0e inter/erometers and mig)t

e0en disturb t)e laser emission- ')is 2as parti*ularly

en*ountered 2it) t)e ort)ogonally aligned set+up depi*ted inFig- 1- A small intentional misalignment, 2)i*) redu*ed t)e

retro+re/le*tion o/ t)e re/eren*e beam into t)e :D', redu*ed

t)e e//e*t to an e8tent 2)i*) enabled t)e reported measure9ment results- In order to eliminate t)ese problems, t)e set+up

2as re*ently modi/ied as depi*ted in Fig- 6- ')is modi/i9*ation guides t)e re/eren*e beam in an opti*al loop su*),

t)at it does not pass &S a se*ond time a/ter re/le*tion atM- ')us, t)ere is no re+introdu*tion o/ t)e re/eren*e beam

into t)e :D'- First measurements at standard /reuen*iese8)ibited an impro0ement in t)e signal to noise ratio o/ t)e

MMI *)annels o/ a /a*tor o/ t)ree- ')is substantial impro0e9ment ma%e us *on/ident, t)at e0en )ig)er /reuen*ies t)an

"! %457, i-e- lo2er amplitudes *an be measured and e0al9uated 2it) t)is ne2 arrangement-

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Anot)er optimi5ation 2)i*) is in preparation is

*on*erned 2it) t)e 0ibration generation- :ue to its ele*tro+

me*)ani*al properties t)e amplitude o/ t)e utilised *om9mer*ial e8*iter *on0erges rapidly to 5ero /or t)e )ig)

/reuen*y *omponent- 4o2e0er, t)e t2o+/reuen*y e8*ita9tion *an as 2ell be generated 2it) t2o distin*t e8*iters

2)i*) are eit)er me*)ani*ally *oupled or subseuentlyintrodu*ed into t)e measurement beam- ')e latter *ould be

a**omplis)ed by a /olding o/ t)e beam-

Fig- 6H Optimi5ed set up o/ t)e MMI 2)i*) a0oids spuriousre/le*tions o/ t)e re/eren*e beam MMI into t)e :D' by guiding

t)e beam in a loop -

An e8*iter 2)i*) is, a**ording to preliminary in0esti9

gations 2ell suited to pro0ide t)e ne*essary displa*ement is

an ele*trostati* spea%er as it is used /or ultra sound genera9tion- ')is de0i*es are a0ailable 2it) a mass o/ about ! g,

2)i*) ma%es t)em suitable /or mounting on t)e armature o/t)e &JK e8*iter 2)i*) 2as utilised so /ar- In preliminary

measurements using a #aser+:oppler+0ibrometer su*) ade0i*e produ*ed a displa*ement amplitude o/ 6! nm at

1!! %45, 2)i*) is 0ery promising-

7" CONCLUSION

')e des*ribed met)od employing a dual /reuen*ye8*itation /or #aser 0ibrometer *alibration using a MMI as

re/eren*e proo/ed its 0alidity- Dsing t)is met)od a #aser0ibrometer *an be *alibrated up to "! %45 probably e0en

beyond7 2it) *on0entional euipment- ')e parti*ular inter9/erometri* set+up 2it) ;beam re*y*ling< greatly redu*es t)e

e//ort usually ne*essary /or proper opti*al alignment, in

addition it remo0es t)e disturban*es /rom relati0e motion*ompletely- Wit) a modi/i*ation o/ t)e Mi*)elsoninter/erometer re/eren*e 2)i*) a0oids re+introdu*tion o/ t)e

re/eren*e beam into t)e :D' an additional signi/i*ant

per/orman*e gain is possible-

REFERENCES

B1 4eydemann $ # M, :etermination and *orre*tion o/

uadrature /ringe measurement error in inter/erometers,Appl- Opt- ! >, 1">17

B Wu C+M, Su C+S and $eng +S, Corre*tion o/ non+linearity

in one+/reuen*y opti*al inter/erometry, Meas- S*i- 'e*)nol-,N, =!, 1""67

B Sun G, Wabins%i W, &runs ', In0estigation o/ primary

0ibration *alibration at )ig) /reuen*ies using t)e )omodyneuadrature sine+appro8imation met)odH problems and

solutions, Meas- S*i- 'e*)nol-, 1N, 1"N!=, !!67B &runs ', Kobus*) M, :ata *iition and $ro*essing /or $'&Ps

Impa*t For*e Standard Ma*)ine, IMEKO 1"t) Con/eren*e

on For*e, Mass and 'orue Measurement, Cairo, Egypt,!!=

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LASER VIBROMETER CALIBRATION AT HIGH FREQUENCIES USING.pdf