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19880014584 

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G3/35 0148171 

FINAL REPORT 

"Fiber Waveguide Sensors for Intelligent Materials" 

NASA Grant NAG-1-780 

June 1988 

Prepared for: Dr. Robert S. Rogowski 

MS 231 

NASA Langley Research Center 

Hampton, VA 23665 

Prepared by: A. R. Flax 

R. O. Claus 
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TABLE OF CONTENTS 

SUMMARY 

DISCUSSION 

REFERENCES 

APPENDIX A - Thesis Abstracts 

AI. B. D. Duncan, M.S.E.E., "Modal 

Interference Techniques for strain 

Detection in Few-Mode Optical Fibers," 

April 1988. 

A2. A. R. Flax, "Micro-Optical Fiber Devices 

Used With Modal Domain Sensing," 

June 1988. 

APPENDIX B - Embedded Optical Fiber Sensor Engineering 

B1. "A Rugged Optical Fiber Interferometer 

for strain Measurements Inside A Composite 

Laminate," ASTM, Journal of Composites 

Technology, vol. 10, no. 1, Spring 1988, 

(K.A. Murphy and J.C. Duke, Jr.). 

APPENDIX C - Modal Domain sensing, Related M.S. Thesis I 

C1. "Modal Interefernce Techniques for strain 

Detection in Few-Mode Optical Fibers," 

M.S. Thesis, Electrical Engineering Department, 

Virginia Tech, April 1988, (B.D. Duncan). 

APPENDIX 0 - Modal Domain Sensing, Related M.S. Thesis II 

01. "Micro-Optical Fiber Devices Used with Modal 

Domain Sens~ng," M.S. Thesis, Electrical 

Engineering Department, Virginia Tech, To Be 

Defended - Ju~e 1988 (A.R. Flax). 

i 

1 

2 

6 
......... 

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APPENDIX E - Paper Abstracts from Smart Structures Workshop 

(Blacksburg, VA) - April 1988 

APPENDIX F - Abstracts from Papers To Be Presented at the SPIE 

Conference (Boston, MA) - September 1988 

APPENDIX G - Invited Lectures 

APPENDIX H - Papers To Be Presented 

ii 
• 42; FCA¥t tP 2 2S 12 P £ lif ... ..., 2 '.4 ( 

SUMMARY 

This report, an addendum to the six month report submitted 

to NASA Langley Resesearch center in Dececember 1987, will cover 

the research performed by the Fiber and Electro-Qptics Research 

center (~ORC) at virginia Tech for the NASA Langley Research 

Center Grant NAG-1-780, for the period from December 1987 - June 

1988. This final report will discuss the research performed in 

the following four areas that are mentioned in the proposal: 

Fabrication of Sensor Fibers optimized for Embedding in Advanced 

Composites, Fabrication of Sensor Fiber with In-Line splices and 

Evaluation via OTDR Methods, Modal Domain Optical Fiber Sensor 

Analysis, and Acoustic Fiber waveguide Implementation. 

. . 

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DISCUSSION 

This section will discuss the four research areas mentioned 

in the NASA Langley Grant, NAG-1-780. The four research areas 

which will be discusssed are the following: Fabrication of 

Sensor Fibers optimized for Embedding in Advanced Composite 

Materials, Fabrication of Sensor Fiber with In-Line Splices and 

Evaluation via OTDR Methods, Modal Domain Optical Fiber Sensor 

Analysis, and Acoustic Fiber Implementation. 

1. Fabrication of Sensor Fibers Optimized for Embedding in 

Advanced composite Materials 

Optical fibers embedded in materials, i.e. composites, can 

sense position, strain, temperature, structural vibrations, and 

impact [2]. Several embedded optical fiber sensors have been 

investigated in the past six months. A Mach-Zehnder 

interferometer was used to sense tensile and composite strains in 

a composite material laminate [1]. Acoustic emission in 

symmetric cross-ply composite laminates due to axial loading 

was interroqated with embedded optical fibers. This data was , 

successfully compared to a piezoelectric transducer adhered to 

the composite where the transducer monitored acoustic emissions 

due to axial loading [3]. Fibers attached to an aluminum plate 

were used to assess impact damage. The various signals could be 

correlated to an impact height. Also, methods were used to 

! 

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determine ~ct location [4]. The integrity of the composite 

due to embedded optical fibers has been examined by Moire 

interferometry techniques [5,11]. There has been a movement 

toward creating an 'intelligent structure.' An intelligent material 

consists of embedded actuators and sensors. Fiber optic sensors 

used to create intelligent aerospace structures have been examined 

[16]. Several papers review what smart structures are [6,7,13, 

17]. Problems associated with smart structures have been 

identified [8]. 

In the past six months there has been no progress in 

developing specialty fibers for improving specimen integretiy 

because the draw tower is not fully operational. 

2. Fabrication of Sensor Fiber with In-Line Splices and 

EValuation V1a OTDR Methods 

Detecting localized strain with in-line air-gap splices in 

an optical fiber in conjunction with an Optical Time Domain 

Reflectometer (OTDR) was reviewed at the Smart structures 

Workshop [9]. This experiment using the high resolution OTDR, 

has been delayed due to a defective OTDR. Due to this delay, 

another graduate student working on this project, Sanjay Sudeora, 

will send a report to NASA as soon this difficulty is overcome. 

3. Modal Domain Sensor Analysis 

In the past six months the research in modal domain sensing 

has been directed towards analytically describing the movement 

of few-moded speckle patterns as perturbations are applied to an 

optical fiber [10,15,18], pursuing micro-optical fiber devices 

3 

j 

. 

, . 

. -
==--------------------~~ 

~ 

which can be used with modal domain sensing systems [19] and 

real time signal processing of modal domain signals [14]. 

FEORC has analytically described the movement of two fewmoded speckle patterns as perturbations are applied to the 

optical fiber: a three-lobed rotational speckle pattern and a 

two-lobed speckle pattern where the two lobes exchange power as 

the optical fiber is perturbed. The system sensitivity for both 

of these modal patterns has been described. FEORC has concluded 

that the two-lobed pattern is the optimum modal pattern 

[10,15,18]. 

In conjunction with modal domain sensing two in-line microoptical devices can make a modal domain sensing system compact 

and packageable. An in-line laterally offset few-moded optical 

fiber splice can monitor one lobe of the two-lobed speckle 

pattern, thus performing in-line signal processing. The splice 

loss of two laterally offset few-moded optical fibers has been 

derived, because existing single mode and multimode optical fiber 

splice loss formulas can not be applied to few-moded optical 

fiber splices. The other device is a modal conversion coupler, 

which converts the input modes of the modal conversion coupler, 

a fused biconical taper coupler, to another set of modes. The 

amplitude coefficients associated with the modes propagating in a 

modal domain sensor are unknown. The modal conversion coupler 

may be a method of creat~1g a mode with a known modal amplitude 

and superimposing several modes to create a totally 

characterizable modal domain sensor [19]. 

4 
~~~,~~ ~.~~_ ~.~ __ ~ ••• ~G __ ~"~ __ -~ ______ ~_-__ -----~ ____________ .'_._': _________ P ___ '_5 ___________ q_~ 

A detector array can be used to process modal domain output 

patterns. This array is linked to an IBM-PC to analyze the data 

in real time [14]. 

Finally, the modal domain demonstration unit was delivered 

to NASA Langley in April 1988. This unit uses modal domain 

sensing techniques to detect quiscent strain, AC strain, 

structural vibrations, and acoustic emission in a graphite-epoxy 

composite. 

4. Acoustic Fiber Waveguide Implementation 

Acoustic waveguide sensors were reveiwed at the Smart 

structures Workshop [11]. In the second six months of this 

contract, there has been no significant progress in the area of 

acoustic waveguides. FEORC is waiting for the arrival of some 

ultrasonics equipment and the draw tower to become fully 

operational. 

5 

, 
---- .--

REFERENCES 

JOURNAL PAPERS 

[1] "A Ruqqed optical Fiber Interferometer for strain 

Measurements Inside a Composite Material Laminate," 

ASTM,Journal of Composites Technology ! Research, 

Sprinq 1988, Vol. 10, No. 10 pp 11-15 (K. Murphy 

and J.C. Duke, Jr.). 

SMART STRUCTURES WORKSHOP PAPERS (Blacksburq, VA) - April 1988 

[2] "Fiber Optic Methods for Structure Monitorinq," 

(K.D. Bennett and R.O. Claus). 

[3] "Acoustic Emission Detection in Smart Materials," 

(K.D. Bennett and K.D. Zehner). 

[4] "Fiber Optic Assessment of Impact Damaqe in Smart 

Materials," (M.R. Dumais and K.D. Bennett). 

[5] "Experimental Analysis of Smart Structure Materials 

by FUll-Field Optical Techniques," (R. Czarnek). 

[6] "Introduction Issues for Smart Structures," 

(R.O. Claus). 

:: 

[7] "Material Issues for Smart Structures," (G.L. Wilkes). 

[8] "Control and Siqnal Processinq Desiqn Issues in Smart 

Structures," (J.c. McKeeman and D.K. Lindner). 

[9] "Applications of OTDR Methods for Structural Analysis," 

(R.G. May, Jr.). 

[10] "Modal Interference Techniques for strain Detection in 

Few-Mode Optical Fibers," (B.D. Duncan). 

[11] "Acoustic Fiber Methods for Structural Monitorinq," 

(A. Safaai-Jazi). 

SPIE CONFERENCE (Boston, MA) - SEPTEMBER 1988 

[12] "Interferometric Meeasurements of strain concentrations 

Induced By An optical Fiber Embedded in Fiber 

Reinforced composites," (R. Czarnek, Y.F. Guo, K.D. 

Bennett and R.O. Claus). 

7J;~ ! 

I 

! 

6 
... "" ---- -. - - - . - . --ra;:, -------- ---.. , 

[13] "Demonstration of A Smart Structure With Embeedded 

Actuators and sensors," (C.A. Rogers, K.D. Bennett, 

B.B. Robertshaw and J .C. McKeeman). 

[14] "Full Field Analysis of Modal Domain Sensor Signals for 

Structural Control," (K.D. Bennett, J.C. McKeeman and 

R.G. May). 

[15] "Intensity Pattern Modulation in Optical Fiber Modal 

Domain Sensor Systems: Experimental Results," 

(B.D. Duncan and B.W. Brennan). 

[16] "Smart Structures Proqram at Virqinia Tech," (R.O. 

Claus and K.D. Bennett). 

[17] "Fiber optic Sensor Systems for Smart Aerospace 

Structures," (W.J. Rowe, R.O. Claus, D.A. Martin and 

D. Trites). 

M.S. THESES 

[18] "Mode Interference Techniques for Strain Detection in 

Few-Mode Optical Fibers," M.S. Thesis, Electrical 

Engineering Department, virqinia Tech, April 1988 

(B.D. Duncan). 

[19] "Micro-optical Fiber Devices Used with Modal Domain 

Sensing," M.S. Thesis, Electrical Engineering 

Department, Virginia Tech, To Be Defended - June 1988 

(A.R. Flax). 

7 
, __ ~v_:_~_·-_._~ __ ~_-_-_-__ -_--__ " ____________________________________ . ___________ ~{~ 

t • 

APPENDIX A - Thesis Abstracts 

, 

: 
-------------------

Modal Interference Techniques for Strain Detection in Few-Mode Optical 

Fibers 

by 

Bradley Dean Duncan 

Richard O. Claus. Chairman 

Electrical Engineenng 

(ABSTRACT) 

Interference between the modes of an optical fiber results in speCific intensity 

patterns which can be modulated as a function of disturbances In the optical 

fiber system. These modulation effects are a direct result of the difference In 

propagation constants of the constituent modes. In this presentation It IS 

shown how the modyiateu intenSity patterns created by the interference of 

speci6jc mode groups in few-mode optical fibers (V < 5.0) can be used to 

detect strain. A detailed discussion of the modal phenomena responsible for 

the observed strain induced pattern modulation is given and it IS shown that 

strain detection sensitivities on the order of 10-9 can be expected Data taken 

during the evaluatIOn of an actual expenmental strain detection system based 

on the developed theory is also presented. 
;\hcro-Optl'::ll Fiber D('\icc'\ l \t'd With :\IOtbI Domam Sensmg 

R. O. Cl.!us. Cha!IT.la'1 

Elccmc.ll Engll1c.::rn:g 

(ABSTRACT) 

In order to ~':::\clop more compact optical fiber s.!nsmg systems, modal ftltenng can be 

perforrr.cd rn-ime b} u~ing IlUcro-optlcal de\!ccs Two such devices are a laterally offset 

fc;\·-n:ode..:! Op~lC:J.! fiber n:echani:<ll spbce :!n~ J r.:odal conyerslon opucal fiber coupler . 

.-\ thIrd de\I:':. ti!e air-gJP sphc~ l.!sed \\lth rr.ultur.cde fibers. can examme the modal 

CC:ltent of an o;':Jcal fiber A bastc th.::orct.':1! understanding on how these devIces 

c;>erai.::: IS rC\'lcn .-:d. A splIce lC5<; caIcul:!~:~" fer :cw-modcd optical fibers IS presented. 

ApplIc~tlOns of ,he as) mrnctncJ.I fe'.\"-mo~cd ;r • .::d:aruca.l opt:.:al fiber spllce, the modal 

cor,.\e:Slon coupler, and the arr-gap splice .:re clst.ussed. 

·,. ~ l' ~..., 

, 

f 

• 
-------------------------------------, 

APPENDIX B - Embedded optical Fiber Sensor Engineering 

t • 

-" 
APPENDIX C - Modal Domain Sensing 

Related M.S. Thesis I 

.. 

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APPENDIX D - Modal Domain Sensing 

Related M.S. Thesis II " 

"' ~ 

--

, 

1 
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___ ~---~-. --'---c, 

:\lkro-Opttc;<1 fIber DI.'\ices l;,ed \\ilh l\lod:lI Domain Sensmg 

by 

Am~ rl.l\ 

TheSIS subnutted to the Faculty of the 

\'Irprua Pol~te~nmc Institute and State l!nherslty 

In rartlal fulfillment of the rcqurrcments for the degree of 

\Iaster of SCience 

In 

Electncal Englneenng 

APPRO\'ED, 

R, 0, Gaus, Chrurman 

A Safaal-Jazl J. C. McKeeman 

June 1988 

mack.sburg, VrrglIlla 

! 

, 
Micro-Optical rlber De\ices Used With Modal Domain Sensing 

by 

Ao-::.' Fla"<. 

R O. Claus, Chairman 

Electncal EnglOecring 

(ABSTRACT) 

••• 

In order to develop more compact optical fiber sensmg systems, modal flitering can be 

performed m-Ime by USlOg nucro-optical devices. T\\o such devices are a laterally offset 

few-moded opucal fiber mechamcal splIce and a modal com'erSlon optical fiber coupler. 

A third de\1Ce, the aIr-gap splIce used \\1th multimode fibers, can examine the modal 

content of an optIcal fiber A bas!c theoretical understandu.g on how these devices 

operate IS re\ie\\ed. A srhce loss calculatIon for few-moded opucal fibers is presented. 

ApplIcations of the as~ r :.-netncal fe\\ -modcd mecharucal opucal fiber splice, the modal 

com ersion coupler, and the aIr-gap splIce are dIscussed. 
!i we 2 "Ii; Q.-S;: : 'I.V' .~...... -, . • _ t' 

---- ---------- --- -----

2 ; j £ $ L sa £ 3 C & 2 a 22 2 ( i a 4 _ ( 5 

Acknolvledgelnents 

I would hke to express my apprecIation to my ad\'lSOr, Dr. R.O. Claus, for lus guidance 

and encouragement I \\ ould hke to t~ank Dr. Safaal·Jazi for }us paUence and 

aSslstance. 

I would, also, hke to thank all the FEORC employees and graduate students for their 

consultation and companionship 

I would hke to thank my t\\0 dear fnends, Amy Matthews and Paul Werntz. for their 

support. encouragement, and understandmg. Fmally, I would hke to espeClally thank. 

Paul for helpmg me focus 

iii 

-
Table of Contents 

1.0 Introduction •......•••...••....••••..••••••••••••.•••••••••••.••••••• 1 

2.0 Optic:ll Fiber Theory ...•• • .• . .•..•.....•.•.••.•••••••••.••.••••••••• 3 

2 I Basle Paramcters Go\CmIDg Optical Flbers .. . . . .. ........ .......... . ... 3 

2 2 Optical Fiber Mode Thear., . .............•.........•.... ........ 6 

3.0 :\lodal Dom:lin Sensing ••••.•.••••.••.••••••••••.•••••.•••••••••••••••• 13 

3.1 Phase Modulatlon .. ,.... . . . . . . . . . . • . . . . . . . . . . . . . • . . . . . . . . • . • . .. 14 

32 Ihlferential Phase :'otodulation . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18 

3 3 The Optimum ~todal Pattern ................... '" ......... 20 

3.3.1 Intensity ofthc LPo1 and LPu Modes ............................... 22 

3 3 2 Intensity :-'1odulatlOD ...... .......•...•..........................• 24 

4.0 Principles of Operation of :\licro-Optic:2l fiber DC'ices •••••••••.••••••••••••••• 32 

4.1 :-.todal COQ\'ef'Sion Coupler .. . ............•.•....•.•.•...•• , 32 

4.2 An Asymmetrical Optlcal Flber Spllcc . ........•........ . .... ..,. . ... 36 

4.2.1 Analysis of Laterally Offset Optical Fiber Sphces .......................... 38 

Table or ContCDlS iv 
4.2.2 Lalerally Offset Spbccs for :\lu1wnoJe Opttcal rlben 

4.2.3 Laterally Offset Sp~ces for Singlcmode Optical rlben 

424 Laterally Off~t Sphces for rC\\-\loded Optical Flben 

4 2.5 lmplementauon of the Latcrall) OfT~t Sphce .... 

4 3 The Alr-Gap Sphce 

38 

41 

43 

. ......• S8 

............. 62 

5.0 Future \York and Arp:ications •......•...••••••••••..•••.•.•..••••••••••• 69 

6.0 Conclusions •••••••••.••.••.•.•• ...•••••....•.•.....•.•.•.•••••••••• 72 

Appendix A: Amp Fortr:an listing .....•••..•••.......••..•...••.•••••.•••••• 74 

Append., B: Int Fortran Usl1ng .•....•....• • .••..•...•.••••••••••••••••••• 79 

Ref erenc:es ••••••••••••••••••.••.••••••••••••••••••••••••••••• • • • • • • • •• 83 

Vita .•.•.•••••..•.••..•..•..••••••••..••••.•..••••••••.•••••••••••••• 8S 

Table or Contents y 
.. ------------.................... ~====~~~.m ............ &a~.~'·~ .............. ~a 

List of Illustrations 

Figure 1. An Optlcal Fiber (4] . 

FIgure 2. b \5. V-number (5] .. 

. .................................. 4 

Figure 3. A :\tod;!l Domain Sensmg Expcnrnental Set-Up .................. l_ 

FIgure .t. Interference Pattem: LPolI and LP1I :\fodes .................... 21 

Figure 5. Intensltj of the LPOl ~fode (11] .•........••..•..•..........• 25 

FIgure 6. In~er.~lty of tile LPII ~tcJe (lIJ ................•••. 26 

Figure 7. The Cross Term at a :\Iaximurn (II] .. .. . ................... 27 

Figure 8 One Labe Is A ~faximu~ Wrole The Other Is A ~linimu.m [11] •..... ~Q 

FIgure 9. A :\Iodal Con\ersion Coupler ....................... . 

FIgure 10. A Modal FIlter (l.t] ........ . ............................. 35 

Figure I l. An Asymmetrical Splice for Modal DomaIn Sensing .............. 37 

Figure 12. Two IdentIcal Fibers Laterally Offset .......................... 39 

Figure 13. The Futering Fiber's Core InSIde The Sensing Fiber's Core ......... 40 

Figure 14. Cross-Sectlon of the Asymmetrical Spbce \lith Identical FIbers ...... 44 

Figure IS. Relatlonship Bet\\cen t.:npruncd and Primed Coordmates .......... . 50 

Figure ,16. Cross·Sectlon of the Asymmetrical Splice ...................... 54 

FIgure 17. The Air-Gap Splice (3) ••••••.••••••••.••.••••••••••.•••••• 63 

Figure 18. OrDR Set.L"p With Arr-Gap Splices to Detect Localized Strain [3] ... 64 

Figure 19. :\Iodal Dispersion Due to Launching Conditions [3) ....••.•••.•••• 66 

L~ oIlDustratioas 

, 
.... • t, .-_ ... , ... _ .... -rc:--• ...., ... -~'''''P •• -.'''( .. P---.---,po 

,\- 4f11r-",__ --

- --------

A " ¢.- IC 

Figure 20. ~todal Dispersion Due 1'0 Apphed Stram (3) .•.....•.•..•• .... 68 

tnt of IUustr:"'iollS ~ii 

"' 
------------------------~----------------------~----~~ 

1.0 IntrGduction 

FIber optIC sensing s) stems rna) be used to detect temperature. pressure, acoustic waves, 

stram, and a \\lde range of phYSical obsenables The clasSIcal method for detecting 

these parameters \\ith m:uunum sensltl\ It) uses smgle mode fiber OptIC interferometers, 

\\ hlch requlle two optical fibers. The reference fiber m such an interferometer must hn 

maintamed in a controlled emllonment for optImum detection. To eliminate this . 

of two Optical fibers m a sensmg system, the modal changes in one multimode optical 

fiber due to perturbations of the optical fiber can be exploited. This type of fiber optic 

sensmg is called modal domam sensing. 

Modal domain sensing is most effectl\ e when used \\ith a few-moded optIcal fibers. So 

far the few-moded optical fibers used \\lth modal domain sensing support 2 to 10 modes 

(1,2) The optimum far field mterference pattern of the fiber modes, the speckle patter.1, 

is a modal fieII! interference pattern t.'1at can be characterized by simple rotations or . SImple intensity changes m the far field intensity pattern due to modal changes from 

perturbations to the optIc::.l fiber (2) But the question now IS what to do With the OptIcal 

information at the output of the sensor fiber (how to glean the relevant information 

1.0 I.troduc:tioo 
"..... :pqO. ~; - .................. ---____ --__ ----M----.t~e-\-.-::-:::-:'~~~~1 

from the modal domain sensor). In-line micro-optical fiber devices would eliminate 

cumbersome non-opu~al spatial filters, realignment problems, and additional electrical 

cIrcultry which mak.e far field pattern processing difficulL ~icro-optical fiber devlces 

create and enable compact, packageble modal domain sensing systems. 

Two such rrucro-optlcal fiber devices used \\ith modal domain sensing systems are an 

optical fiber asynunetncal sphce and an optical fiber modal conversion coupler. The 

"pucal fiber asymmetncal splice conslsts of a few-moded optical fiber spbced to a 

laterally offset few-moded optical fiber or to a single mode optical fiber for m-Ime spatIal 

filtering. The optical fiber modal converter is an optical fiber coupler which generates a 

set of output modes from a given set of Input modes. 

Another lmportant ffilcro-opucal fiber device lS the alr-gap splJce used \\1th multimode 

optical fibers to detect local stram changes \1a Fresnel backscattered-based OptIcal Time 

Domain Reflectometry (OTDR) [3]. The arr-gap spllce causes pulse delay effects 

depending on the modes which are propagating in the multimode optical fiber. 

The prmclples of operauon of the two de\ices used with modal domain sensing, the 

a~'mmetrical optical fiber splice and the optical fiber modal converter coupler and the 

princlple of operation of the air-gap splice \\111 be e~pIained in Chapter 4 of thts thesis. 

Finally. future applications of these micro-opucal devices will be discussed In Chapte 

5. 

I 0 Introductioa 1 

~ 

f 

~. 
-r""'":~~~, _~ "_"_ -:. ~" ~_~_-,-.-__ _ . . .. - -

2.0 Optical Fiber Theory 

The basIc parameters that c!eternune the nature of the electromagnetic fields which may 

propagate In optical fibers. and the bastc mode theery which describes those fields need 

to be re\ le\\cd 1:1 order to understand the operation of the micro-optlCal fiber deVlces 

intended for sensor signal processing 

2.1 Basic Paramete,'s Go)'erning Optical Fibers 

An optical fiber tYPically IS a cylindrical \\"3.veguide fabricated from a dte!ectnc, silica, 

as shown in Figure 1 [4}. The center of the optical fiber, the core, has an index of 

refraction of n._ The core has a radiUS, a Surroundm~ the core is the claddmg wht~ 

has an mde.'t of refraction. fZt, which is sbghtly smaller than n, . 

The optical fiber wavegwde \\;ll onl) support a dtscrete number of modes, having a 

uruque propagation constant, /1. The propagation constants of the modes supported by 

2.0 Optical Fiber Th~r1 3 
,-., . ...,.... , .... ' 

• 

. , 

• 

F'rpre I. An 0phcaI Fiber I~I 

2.0 Optical F~r Tbecry 
the optical fiber must fall between the \\ave number of the core and the wave number 

of the claddmg, Equation :?1-1. 

(2.1 - I) 

where 

/...J = w .. J /Jo o£', , fru space WaH!Ilumber, 

The amount of lIght that can be accepted by the optical fiber is determined by the 

numerical ,perture (SA). The numencal aperture defmes the acceptance cone for the 

light that will propagate m the core. The numencal aperture is defmed in terms of the 

mdlces of refraction of the core and claddmg as 

(2.1- 2) 

where 8 is the cone of acceptance angle as shoVti1 in Figure 1. 

The Y - number of an optical fiber determines how many propagating modes the optlcal 

fiber will support The V - number is defined m terms of the numencal aperture (NA), 

the optIcal fi~r's core radius (a) and mput source's wavelength of operation (l) \is 

mdicated.in (2.1-3). 

Y = 2:-ra (2 2)lfl 

-;- "l - "2 (2.1- 3) 

2.0 Optical Fiber Theory s 
By knowmg the V - number for a few-moded optical fiber, the number of propagating 

modes can be detemuned anal) lIc.llly The results of the anal} sis are shown graplucally 

In Figure:! (5J. ~o\\'. the propagation constant for each mode can be determined from 

the nomlaJ.led propagation constant. b, \\here 

b= , and (2.1 - 4) 

(2.1 - 5) 

2.2 Optical Fibe,. ll10de Theory 

After reHewing the parameters that go\em the operatIon of an optICal fiber. are' 

of basic mode theory IS essential in understanding the pnnciples of operation 01 

rrucro-optlcal fiber uences. The electromagnetIc field solutions in optical fibers are 

solutIOns to the wave equation for cylIndrical wavegUIdes, i.e. 

(2.2 - 1) 

In Equation 22-1, k. IS the free space wavenumber and n is the index of refraction ( . 

= core, n1 = claddtng) Equatlor: ~.2-1 can be separated into six scalar equations 1 ~ 

components e. , e" e, , h •• h,. and Jz.. The Laplacian operator, V2. can be separated into 

a Laplacian operator trans'erse to the dIrection of propagatIon, V,1, and a Laplacian 

operator in the direction of propagation, V, l, i.e. 

2.0 optical Fiber Theory 6 , 

-
-... 

c:' 

, 

0.8 

~ 0.6 

--

-.... 

~ 

I 

Figure 2.. b YS.. "-number IS) 

2 0 Optical Fiber T~r} 

t' 

7 
• 'q" j Ji ISChiav' ;;.!..~¥!¥JIS..s a JL. 5 i aiL w a $ Q 

(22- :2) 

If the electromagnet\l; field solutions are solved for the z -component of the 

electromagnettc field, the rand () components of the electromagnetic field can be found 

from the knO\\ll z-components These relatIOnships \\111 be defined la.er, after the field 

solutions for z -components are establtshed. 

The follo\\1ng anal~sls IS for the scalar field component, e. or Ir.. which wIll be redefined 

as 't', I e 

(2.2 - 3) 

\\ here j3 IS the propagation constant 

't' can be descnbed as a function of Rand <1>, \\here R and <I> can be separated. as sho',"1 

10 the follo';\1ng equations. 

\\here, 

d2R 1 

2 + r dr 

't' = R(r)<I>(41). 

2 k 2 2 fJl q = 0 n - . 

The soluuon to Equauon 2 2-5 can be one of the folloning 

2 0 Optical Fihcr Theory 

(22- 4) 

(2.2 - 5) 

(22- \.. 

(2.2 -7) 

8 

:: ::!jif 
AI sm \'~ 

<1J = {BI (.05 \'c,? }, (22 - 8) 

AI Sm vc,? + BI cos \.t/J 

and the solution to Equation 2 2·6 mSlde the core IS a Bessel function of the first k.md, 

1 e. 

R = i.(q,'), q2 > 0 (I e.n = nl)' (2.2 - 9) 

The solution to Equation ~.2·6 outside the core IS a modified Bessel function of the 

second kind, 1 e. 

2 R = BK.(q,,), q < 0 (I e n = n2)' (2.2 - 10) 

So, for the scalar electnc field In the z,clre.:tlon inside the core (, < a), the solution f 

a mode IS Equauon 2.2·11. Sinuliar equations hold true for h., i.e. 

ez = J.( ~' )( Bl cos vt/J ) (2.2 - 11) 

A 1 sin vC:> + Bl cos v¢ 

where 

(2.2 - 12) 

For the scalar electric field In the z-directlon in the cladding region (, < a), the solution 

IS given in Equation 2 2·13 Smular equations hold true for h.. i.e. 

2.0 Optical Fiber Theory 9 

.... 
l :~~~~: " : __ ' _~ ~ __ ii_ .... _~ -_.~I!I_~t", ........... -----~-=-.. -4:; ::::':-"'"*_ -_':W:_ ,_~_::::'::'-=_t:::...~::,::::::-: :;;::::::::;=;::,::::&=;I.~,q,"~~~~ 

81 cos \'0 ) (2.2 - 13) 

where 

(2.2 - 14) 

It IS lIDportant to note that the V -llumber can be also defmed in tenns of U and 

(Equation 2 2-t 5), 

(2.2 - 15) 

Since the field solutions for the z-components of the electromagnetic fields can be 

detennmed, the rand 4> components of the electromagnetic fields can be found :n 

Equations 2.2-16 thru 2.2-19. 

2.0 Optical Fiber ThCOf~ 

e , = 

h = _ - - - -- and J (11 olrz WE: oez ) , l!l r ... .J..' q Cir 0.., 

(2.2 - 16) 

(2.2 - Ii' 

(2.2 - 18) 

(2.2 - :9) 

10 

i 

\ 

. 

.I 
.-----~.-.------~------~------~~---- -----------------------~--.-~~------.~;~'-~ --- -_ - -l+ 

L sually the modes of the optical fiber are defined In terms of H E_ and EH .... \I, here \I 

IS the order of the Bessel function and In IS the root of the \I order Bessel function. A 

~rc"lahzcd classificatIOn of these modes are the lInearly polanzed ( LP) modes. These 

are the moues that \\lll be specified In conjunction \\1th the nucro-optlcal fiber del .ces. 

Lmearly polanzed modes are electromagnetic fields that are linearly polanzed. LP 

modes need to propagate m fibers that are weakl~ guidmg. Weak guidance is dermed 

by EquatIon 2.2-20. 

~= (2.2 -10) 

The linear polanzation causes degeneracIes among the EH_ and liE.. modes (6}. The 

LP, .. can be defmed In terms of llE. .. and Ell ... by the following relatlonsbps' 

(= \I + 1. 

jort ~ 2. LP~," = HEw+I/'I' OT EH..-I/'I' 

_The solution for the LP modes in the core )ields the following: 

2.0 Optical Fiber Theory 

Jt<L',/a) (COS t¢) E = ~ J~ul smt~ and 

(2.2 - 21) 

(2.2 - 22) 

(2.2 - 23) 

(2.2 - ~. 

(2.2 - 25) 

(2.2 - 26) 

II 
----~--.-... -~.i--(j~---_~'-.~_4-4_~~_~i~_~~--.----:-=~:~r(ir+~ 

, 

where 

l' - J£o"l 

I - PO' (2.2 - 27) 

The solution for the LP modes m the claddmg sinularly }lelds the following: 

E)( = K,(Wr/a) (COS (,p) 

Kt< W) sin (,p aJld (2.2 - 28) 

(2.2 - 29) 

where 

(2.2 - 30) 

The LP modes can be decomposed further into even modes denoted by LPt... and odd 

modes denoted by LPt_. The odd modes are defmed by the electric field componen" 

\\1th the cos«(</» term, and the e\en modes are defined by the electric field compone •. 

Wlth the sin«(</» term. 

The basic parameters of optical fibers, the mode theory, and the understanding of LP 

modes v.ill aid in understanding the prinicple of operation of micro-optical fiber de\ ices 

for fiber sensor applications. 

2.0 optical Fiber Theory 12 

I 

. 

. -

•• 

. -
9 Y • 

.- _ :~. >F : ~ = :p.:~i .. ::::-:, ~ 

3.0 ~Iodal Domain Sensing 

The no\e! idea of U!'!f'g a smgle oFttcal fiber's modes mstead of an optical fiber 

mterferometer for dctectmg pcrturbauons (i.e, strain. \ibrauons. etc.) was discovered 

b) layton [i) and Kingsle::- IS). C sing the modes of an optical fiber to glean information 

about the opucal fiber s surroundmgs will be r-ferred to as modal domain sensing. 

Durmg the last few years at Vtrgmla Tech a better understandmg of the mechcmisms 

behind modal domam sensing and practical implementations of modal domain sensing 

has been accomplished by Bennett (9), Ehrcnfeuchter (ll. Srinivas [10), 

Shankaranar3.)anan [2], and Duncan [11). The primary mechanism behind modal 

uomain sensing is the change in the modes" propagation constants due to penurbatiom 

to the optical fiber. These changes in the propagation constants cause changes in the 

modal interference pattern which can be related to the applied perturbations to the 

optical (:,cr. ~ome apphcations of modal domain sensing thus hr are the use of 

embedded o;>tical fibers 10 composites to detect acoustic emission [9). optical fibers to 

detect structural Vibrations (1.11), and optical fibers to detect axial strain (2,10,11]. 

J.O \1oda1 Domaia ScasiDt 13 
A basic experimantal set-up of a modal domam sensing system is seen in Figure 3. The 

laser, the lens, and the opucal fiber aligner can be considered to -the mput optics· for 

the optIcal fiber. The optical fiber is the sensing region. At the end of the perturbed 

optical fiber is the signal proccssmg (the filter) which may be implemented using an 

out-of-hne spatial filter (no optical fibers are used) or an in-hne optical fiber as a spaual 

fllter. Chapter 4 \\ll1look at some spatIal filtering techniques which may be unplemented 

, .. ith an optical fiber. After the spatial flltering section is the detection scheme, a 

photodiode detector feeds an oscilloscope m order to monitor the signal from the modal 

domain sensor. Then, a computer can be used 10 conjunction WIth this system for 

frequency analysIs of the signal 

This chapter \\ill examme the phase modulatlOn 10 an optical fiber introduced by 

perturbations to the opucal fiber; then, the opumum modal 10terference pattern for 

modal domam sensing will be reVIewed [II]. 

3.1 PI,ase ~/odlliation 

To understand the phase modulation of the an optical fiber due to perturbations, the 

phase modulation in one mode will be presented first (i.e. the change in the mode's 

propagation constant) [12.131. 

The trans\erse electric field solution is def10ed in Equ:l.tion 3.1-1. 

(3.1- I) 

3.0 :\lodaI Domain Semin& 14 

.-
!.-.:;. 

::::!.-

:,..1 

--.,------_.-

~ I 

<'-5>i 

:.gure. ~. 3 \ . "'0113.1 .. Domain Sensing Experimental Set-l'p 

ORlGlN"ATI PAGE IS 

OF POOR QUAUTY 

3.0 :\1odal Domain Sensing IS 
----.l(tJ 

The phase ofa mode is defined b} Equauon 3.1-2. 

~ = pz + t/I. (3.1-2) 

Here, Z IS defmed as the distance along the dS the length of the opucal fiber, L. The 

phase modulation due to a pcrturbauon IS represented m Equation 3.1-3. 

6.~ = P& + z6.p (3.1 - 3) 

Equation 3.1-3 b valid for &l.ual stram (E. ) or small acoustic waves (small vibrations ). 

6.z can be expressed m terms of axial strain and the length of the optical fiber, Equation 

31-t 

6.z = E~, for axial stram (3.1 - 4) 

P6.z can be expressed In terms of an isotropic stress due to hydrostatic pressure, P, 

POisson's Tatio, p., and Young's modulus, E, as indicated in Equation 3.1-5. 

P(l - 2!.t)LP 

E (31- S) 

The 6.p term depends on a photoelastic effect and a dimensional effect, Equation 3.1-6 

[12,13). 

-

6P = ( dn )6.n + ( !! )w (3.1- 6) 

where, 

3.0 ;\todal Domain SeesiDI 16 
-----------

n = refractive lIIdex 

fJ = longltudznal propagation constant 

D = diameter of lire core. 

Equation 3 1-6 can be decomposed further by expanding the lln term. Equation 3.1-7 

[12,13]. 

(3.1- 7) 

"here, 

f.z = aXial stram 

Jl = POlssons rauo 

PIl , Pll = photoelaslic constants. 

It is important to note that for small changes in the index of refraction. i.e. the difference 

bet\\ een the core and the claddtng indIces of refraction is slight, an effective index of 

refraction, neJT. can be considered to be equal to n. and to n1 (Equation 3.1-8). 

(3.1- 8) 

So dn can be approximated as indIcated in Equation 3.1-9. 

(3.1- 9) 

r • 

3.0 \lodaI Domain Smsin& 17 
-----u 

For the second term 10 Equation 3.1-6 changes 10 phase Jue to changes 10 the diameter, 

~D, can be e'ltpanded mto the follo\\;ng 

2P ~ Also. the term dD 1:J.I1 be rewntten as Equation .).1-11 

cp 

dD 

(3 1 - 10) 

(3.1-11) 

Howe\ er, the change m phase due to changes m the dtarnetcr 1S negligible compared to 

cp 

dn &1,0;0 the second term 10 Equatlon 3.1-6 can be negkcted. 

Fmally. LlO due to changes m thc propagat1on constant from external perturbations 

app\1ed to the opt1cal fiber can be rc\\ntten as Equation 3.1-12 [12.13). 

(3.1- 12) 

3.2 Differential Phase illodillation 

For the few-moded ('ptical fibers and the micro-optical fiber devices that are used Wlth 

m~dal domam sensmg an understan~tng of th" dlfferenual phase modulauon between 

the propagatmg modes when eAternal perturbations are apphcd to tlY! optical fiber is 

essential. Smce the cptlcal fibers used 10 the e'(.penments for modal domain sensing 

support 1\\ 0 modes, dlffercntial phase modulat.lon for two modes will be considered. The 

3.0 \lodal Domain Stnsi"l .1 
&9 !4( E( - dW?G?SM'_l_d_' __ ,!~J •• _tlllll __ a(ll";. & a -0 sa a 2 i! i 52! ( 3d i 

reason why a mode combination of two modes IS used with modal domain sensing \\;11 

be explained in Section 3 J. 

The dlfference in phase under static conditions can be defmed as rPll (Equation 3.2-1), 

\\ here 1 is for the first mode and where 2 IS for the second mode. 

4>12 = rPl - ~2 (3.2 - 1) 

For applied perturbations to the few-moded optical fibers Equation 32-1 becomes 

Equation 3 2-~. 

(3.2 - 2) 

The dlfferentlal phase modulation IS descnbed by Equation 3 2-3. 

(32- 3) 

Equation 3 1-12 can be restated for dUferentIal phase modulation between two modes, 

and Equation 3.2-2 can be written in the form of Equatlon 3.1-12. 

(3.2 - 4) 

where, 

(3.2 - 5) 

J.O \loda1 o-ia Sensing 19 
...... IB~!lI!!!~~~~!~za!!t~~.~A4~~S~$~W~4!!S~s~~~~eA.$~.a~&~p~~S-~A$.C~_~".S" •• ~£$"S"~"_"42"4~ ..... a.SIl"'SQ~2!:" 

ThIS IS the differential phase modulatIOn betneen two modes. This differential phase 

modulation IS Important for the amphtude modulation of the electnc field Intensity. The 

mtenslty \\111 be c"<plamcd for the optimum modal pattern In the follo\\1ng section 

3.3 Tile Optit1ZlIlIl l\;/odal Patte,on 

Recently, there has been a great deal of research to detenrune an easily characterizeable 

modal mtt"-ferc:lce pattern This modal Interference pattern needs to be easy to 

generate. Cnanges 10 the modal mterference pattern need to be correlated with external 

perturbatIOns applted to the optIcal fiber. 

It has been proven b} Duncan (11) that the modes that produce the opumum 

mterference pattern IS the x- polanzed even LPol and LPu modes, Figure 4 (11). This 

modal interference pattern meets the two requirements mentioned earlier. fhis pattern 

is qUite easy to generate, and as this pattern IS perturbed the two lobes exchange power. 

This exchange in power between the two lobes can be correlated to external 

perturbations bemg applted to the opucal fiber. A sensing system using this modal 

interference pattern can achieve a system sensitiVity for strain of 10--' [Ill Changes in 

intenSIty for a modal domain sensing system using the LP,• and LPn modal interfcrence 

pattern need to be revie\\ ed. 

3 0 \Social Domain SmsinC 20 

-
!.J 

: .25 1 

I 

I 

I 

I 

:.53 j 

4.::0 

Fi,urc 4. latcnemlce Pattern: LP •• and LPII \lodes [11] 

3.0 \todaJ Domain ~nsin& 21 

... 
"'_U_ ... :_:.;,:t;;El!S4::,4,;.;;a::_=.;J<;'-W_=_U_ • .;;Z!!_ ... !_=:U __ -_'_'_r--__ =_ __ c : .P : eu 

3.3.1 Intensity of the LPol and LPII Modes 

The fields m the core of the optical fiber, the LPol and LP.. modes, are defined 

respectIvely in Equations 3 3 I-I and 3.3.1-2. 

(3.3.1-1) 

(3.3.1 - 2) 

The fields for the LPcI and LPH modes m the claddmg are defmed respectIvely by 

Equatlons 3.3.1-3 and 3.3 1-4. 

(3.3.1 - 3) 

(~.3.1 - 4) 

No\\, the total fields m the core can be descnbed by Equation 3.3.1-5. 

(3.3.1 - 5) 

J.O ;\lodaI Domain SensiaJ 
1/101 and "'II are random phase terms 

I t IS important to note at this POlllt that the amphtudes of the fields AI and Al , are 

undetemuned. At this pomt the amphtudes to the LPo, and LPII can not be detemuned 

from the launchtng conditIOns. The work based on these amphtudes wIll be relauve to 

the modes, because the modal amphtudes cannot be detennined exphCltly. 

Intensity for the electromagnetic fields IS found in Equation 3.3.1-6. 

(3.3.1 - 6) 

B) substltutmg Equation 3.3.1-5 mto Equation 3.3.1-6, Equation 3.3.1-7 is obtamed. 

where, 

I = lo{AI 2102(c.:or/a) + .42 :11 2(U)r/a)[ cos !/Ii + 

AIA210U:or/a)Jl(Ulr;a)cos(L!Pz - l1",)cos¢} 

l1P = POI - PII , 

J.t/I = 1/101 - "" 

(3.3.1 -7) 

B~ examining Equation 31.1-7 the fust term of tlus int';'1sity equation is the intensity 

of the LPo- mode, Figure 5 (111. The second term in the mtensity equation is the 

mtenslty of tbe LPu mode, Figure 6 (II}. The tlurd term in the mtensity equation is the 

interference of the LPcl and the LPII modes The third term is defmed as the -cross 

J f) 'todal Domain Sensing 

J 
--....., , ' 4< ..... _ .... ,~ ... _~...2._- . » ... " »!7'4 iP ...... , SO 

term.· The cross teml IS a cosme functIOn as seen m Figure 7 when this term IS a 

maximum [11]. 

Equation 3.3 1-7 can bc rc\\ntten as Equation 3.3.1-8 as a senes of functions dependent 

on T, ~, and =, Ie. 

(3.3.1 - 8) 

The mtenslty of the LPol and LPu modes when I] = 0 IS displayed in Figure 4. 

The assumption for the rest of thIs paper IS that Al = 2A,. This ass-.:mptlon v:ill 

enhance the changes in Intensity due to applied perturbations. If ~: is less than I then 

the LPo, term will donunate, and a stOgie bnght spot will be present at the output. If 

~: IS much greater than one, httlc po\\cr 'Hll eXIst m the LPo, mode, and nunimal 

interference between the two modes \\ill occur as perturbations are applIed to the optical 

fiber [11). 

3.3.2 Intensity ~lodulation 

In modal domain sensing the main focus IS the beha\ior of Equation 3.3 1-7 as 

perturbations are applied to the opucal fiber. The tlurd term of Equation 3.3.1-7 is 

affected by the perturbatIons to the optical fiber. When I) = 0, the LP" and the LEu 

mtenslty are as displayed, respecuvely m Figurcs 5 and 6. As the OPL~ fiber is 

perturbed to the pomt where I] is a maXimum, there is an exchange of power between 

the two lobes as shO\\ll m Figure 8 (11) In Figure 8 one lobe is a maximum \\hUe the 

other lobe IS a minimum. 

3.0 'todaJ Domam ~n5lnl 24 

..... 

. 
---------~ 

----.--~ - -- -- ......... .........- -_ ....... ---.. -----

-----

z 

: ~-

... ::-

: .. ;; -

\ 

\ 

,. 

3 0 'tOllal Domain SC1I!-in, 
? 

1.': -

F""ure 6. Intensity of. LPII ;\tocle 1111 

3.0 \lodaJ Doawn SmsUtc 

O'RIGrn>x P~GE IS 

OF pOOR QtruII"ii 

26 
-, 

, , i j 

3 

5 

3 

C 

CROSS TERM 

I 

/ 

:2 

: 5 

/ 

: 

o a 

o 5 

RADIUS 

l 

C 

Figur: 7. The Cross Term at • ~IL"mum III) 

3.0 :\lodal Domaia Smsiaa 

l 

5 

1 

5 

, 

o 

, 

5 

27 

--

.... 

.. 
-... --.... - - . 

TOTAL. ~.Q.----------------------------r--------------------------- , .. ,; 

'.1' 1 ,! 

, • i '- '5, r 1 •• 

L '.31 r '.2- - ,.t; 

\I) ~ ;; ~ 2 e! 

.c.. 2 " U1 2.S1 ~ l.51 

r- 2 '3 

2 l"l 2.2 

- Z., 

2 : 1 

-1 ~':j 

.( ; ;~ r 1.5-

Fo Ul1, 1.1 

1.0 

O.S 

o • 

0.' 

o 11 c.sl 

0.' 1 0.'] ___ 

g ~, 

O~~~~==~~~~~~==~==~==r=~~==r=~~====== , , 5 Q 

3 l 

Q S 

Fi&ure 8. ODe Lobe Is A \luimum While The 0tIIcr Is A :\hrumam IIII 

3.0 ~lodal DomaiII ~iJtl 21 
---. ----=-=~--. 

The cross term intensity, IJ(;, t/J, z), causes a sinsusoidal oscIllatIon bemeen the two 

lobes as the optIcal fiber IS perturbed. ThIs change m mtenslty can be related to an 

applIed stram fer an applied aXial stram or for small amplItude sinUSOidal stram. 

In the IJ(r, q" =) term the dlfferentlon phase modulation betv.een two modes from 

Section 3.2 can be applIed to the ~p term. The intensity equation, Equation 3.3.1-8, can 

be rewntten as Equ<:.tlon 3.3.2-2 by a,lpi)mg the followmg tngonometnc identity: 

I + cos 2." = 2[ cos x]2, (3 3.2 - 1) 

(3.3.2 - 2) 

{ ( ~pz - ~'" )} I = 10 '" cos 2 2. 

I:' consists of I. , 11(;) and 11(;, ¢) from Equation 3.3.1-8, and I:" = 21:'. 

The phase modulation between two modes from Se;;tion 3.2, Differential Phase 

~1odulation, can be applied to the ~pz term. & can be defmed as a functton of strain 

"here 

& = t.zZ, where (33.2 - 3) 

z = LI , the length of the oplIcaljiber, c~d 

t.z = axial strain in the z - dlrecllon 

Equation 3.3.2-2 can be nplamed as a function of strain, i e. 

3.0 \loc1a1 D-a. Scnsmg 29 

.. 
, or. . _-0 _______ + 

I = I'" COS [ ( 

~P(:c)r.zLf - ~'" )J2 o 2 ' (3.3.2 -~) 

\\ here x IS optical fi~er parameters related to the phase modulation, I.e. indices of 

refractlon. photoelastlc constants, POIsscn's ratio. 

A change m mtenslty, ~/, can be dlCectly related to a change m an applied aXial strain 

(Equauon 3.3 ~-5). Assume that ~'" = ~ [ll). 

For a'<lal stram' 

(3.3.2 - 5) 

For srr.all amphtude smsusoldal axial stram: 

1 II' 

~/(&z petlk.,) = T (:c~fJLf)~£zpHk cos OJI. (3.3.2 - 6) 

&.,- is the peak of the sinusoidal stram and w is the frequency of the smusoldal strait,. 

Equation 3.3.2-6 means that there are smusoidal vanations in intensity , .. hen the bendmg 

of a \ibrat ng structure IS quite small. 

Theorcticall~. Duncan has shown that the mirumum detectable axail stram, & .. is 

o 3xlo-' by a Pl~ dIode and IS 2xlO-u by an Avalanche PI~ diode (APD), which is the 

shot noise litrut of the detector. 

3.0 \lodaI DomaiD Smsiol 30 

~ 
Two of the rrucro-opuca\ fiber devIces pre~ented 111 this rJpcr "111 be discussed In 

conjunction "1th the Ide:!.~ presented m tim chapter. moJa\ domain sensing 

J.O \loda.1 Dllmam SCtI$Ut.; JI 
4.0 Principles of Operation of l\Iicro-Optical Fiber 

De\ices 

Three nucro-opucal fibcr d.:\!ces \\111 be cC:lSlccred' the :nodal con'wcrSlon coupler. the 

as~mmetncal spbce and an air-gap splIce. Two of these devIces. the modal COO'werSlon 

coupler and the as) mmetncal splice can be used for signal processmg in conjunction 

WIth modal doIIUUl sensmg The third m.cro-opucal fiber de\ice. the air-gap sphce. 

detects modal effects m multlffiode step-mde~ optical fibers. The air-gap splice IS us~ 

with Optical Time Domain Reflectometry (OTI1R) techniques to detect locahzed 

chan£cs 10 stram. 

4.1 Alodal COlu'ers;on Couplel" 

A f:1odal con\'~on coup'er IS a fused b!c~:l1cal tarer coupler that is not made to spIlt 

pc\\cr m a 50 - SO ratio. b~lt uses the t.J.rer and the coupler region to generate new 

.a.O PrlDClplts of 0tflatton cf \llcre-Oplical Fiber ~lCts 32 

- _ ..t) 
¥¥4, e 5-'I- i .... :=:J'i.iO:-~.ro.- .. - •• ';--.-_ ...... F' .. ~5Ii&~ .....,..sc-.-.,---- ~ ..-..A::::",", ",. 

. . 

• 

r 

, 

, 

l 

~ 

I 

i 

I 

..Ie 

modes at the one of the c.:'urler's outpe- arms. The modal conversion coupler that \\as 

fabricated 10 the Fiber .me Elcctro-OpticS Lab by Kent ~furph} IS shown III Figure 9 . 

A sinuliar de\ice. a modal filter. has been fabricated by Sorm. Kim. and Shaw (I~)_ TIus 

de\ice is shown 10 Figure 10. ThIS dc\ice IS an optical fiber coupler fabncated from a 

dual core optical fiber and a slOgle mode Optical fiber Tills de\1ce uses an applied 

acoustic 11,1\ e to couple between the LPo, and the LPu modes. This system can then 

generate the LPn mode fror.l the LPo, modc. Ho\\'c\er, this system IS not entirely optical 

like the modal com-erslon cO.Jpler and requires external perturbations to induce modal 

conversion. 

The all opucal modal com :::mon oup!er was fabncated from a 9pm core optical fiber, 

which is single mode at 13("),:m The modal conversion optical fiber coupler was excited 

at 633nm usmg a Hclium - ~con (lk~e) laser At 633nm the V - numbtT for tills optical 

fiber is .t~7. At tlus V - number this optical fiber supports the following modes: 

HEt •• H~, HEll' ElIu , anc llEz, (5). This optical fiber also supports the dege:leracies 

of these modes, the x- and y- polarizations of the these modes and the TE and TM 

modes. The modes that are launchecl into the optical fiber depend on the launcbillg 

conditions. 

As seen in Figure 9, the EHu and H~, modes plus minor amounts of some other modes 

are launchoo into Arm I [15). Arm 1-3 is one optical fiber. and Arm 2-4 is the other 

"ptical fiber, the coupled optical fiber. In Ann 3 another mode combmatio:l is 

generat.ed. This optical fiber has w:: liEu mode and probably some of the HEll mode 

[15}. These two modes were deduced to be pres.!nt c.'tperimentalIy by observing the 

concentricty of the far field pattern. Arm 4 has another mode combination, but the 

Signal in this arm is about 10 dB dO\\n in power from that in Arm 3. Therefore, tlus 

4.0 PrinciplEs of O~r.~ 01 \licro-Opttcal Fiber ~ica 3J 

.+., ~ - -\: 
•• 

•• 

• 

Arm 1 

Arm 2 

Fipre 9. A \lodaJ Comersion Coupler 

4.0 PrWciplcs of O~.hon of \licro-OpticaJ Fiber Dc_ices 

Arm 3 

Arm 4 

--.... -. -- ---- W 

.0 

•• 

I 
. -'.~.~~', " 

",----- --- ... , 

r.1oee POI;!',~ .. =, StrlP"~· Con:rc ~. 

____ ~~ 

~ __ <L'~, ____ ----..... ~ _ S -~ C" :~~ F c~r _,roc L:: .. 

_/ 

/" C_IpUI 

./.. 'ne LP11 ------ L!od.:;' Filter '-------------'--r.Ode 

LF: • 

Cc .. p,~r Dcuble U"ded Fltler 

r-Igure 10. A \locIal Filtcr 1141 

( ;:J.;!llel :abc.s 

" :I dl"i'c' o-al coup c: ) 

4.0 PrincIples of Operatic;a of \hero-Optical Fiber Oc\iccs 

s,-pp ... rt5 :~2 

LPOI and LP11 

moC:C's I 

--.- r.. 

! 

3S 
..... , ---.- -..--- - - ---- r - --- - ------~ 

coupler converts modes I:': the tnput arm, Ann I, to other modes 10 the output arm, Arm 

3 

How thiS coupler comerts modes IS quahtatl\ely descn~. In the coupler region, the 

,. - number becomes q Ultc large. and new modes arc g.enerated 10 thiS regIOn. At both 

ends of the coupler IS a taper regIOn In thiS taper region hIgher modes are lost due to 

the decrease 10 the V - number. Due to the combinatIon of new modes bemg generated 

10 the coupler region and modes bemg lost 10 the taper regIOns, some new modal 

combinatlons, which are cWTcrent than the Input modal combinatIons, can propagate ill 

the 9p.m optIcal fiber Tbs modal comCrsIon coupler :s a method of creatmg other 

modes from a g1\ en set of mput conditions 

4.2 An ASYlnlllet,.ical Optical Fibe,· Splice 

This micro-optIcal de .. ice is us:d for SIgnal processmg in I:lodal domain sensmg syste:ns 

This splIce is designed to work 10 conjunction WIth the LPo, and LPu x-polarized e .. en 

modal combmatlons. As strain is apphed to the cptical fiber, the two lobes exchange 

power. The asymmetncal splIce is designed to collect the change in intensity of one lobe 

of the speckle pattern as ShO\\l1 In Figure II. The intenSity changes m the filtering 

optical fiber em be correlated to perturbations applied to the seI'~ing optical fiber. 

One \\ay tills asynm1etncal srhce can be fabncatcd IS shc'Xll 10 Figure 12. The filtenng 

fiber IS identical to the ser.smg fiber, but the flltcnng fiber is laterally offset With respect 

4.0 PrmClplrs of OpcratJoa or \hcr;rOptlcal F~r D~Yicrs 36 
, 

I 

As~rr,.,eIlIC'::: 

S;;lce 

, 

• 

Tnt!' :~T:CO I i'fS 

c~tt :=~ 'r=M "-<l-

~c ... s-: ':;;:~r 

Fipre II. An As~II'.·:triaI Splitt ror ;\lodal Domain Sensing 

4.0 Principles or O~r.tion or'ticro-Optical Fiber De'icn 

~ ~ 

.... ---

37 

--

-
~ ..... -- - '-, 

.~--------- -

to the sensing fiber. The ofT<;et filter fiber can detect the IIltensi!: changes of one lobe 

of the LPol and LPII medal pattern due to perturbations applied to the sensing fiber 

Another method ofacrue\mg this same effect IS to ha\e the filtenng fiber's core dIameter 

be: one half of the sensmg fiber's core diameter ~s 10 Figure 13. The filtenng fiber's core 

then wIll sit inside of the sensing fiber's core. 

4.2.1 Anal~-sis of Laterally Offset Optical Fiber Splices 

To anal)zc tlus as}nunctncal spbce t>roblem for few-moded optiCal fibers, one may want 

to apply the standardized splice loss fonnulas for mulumode optical fibers which are 

rC\le'.\cd 10 Se-.:tlon'; :! 2 .-\ltematl\ci~. one may want to apply standardized splIce loss 

formulas for single mode optlcal fibers which are reVIewed 1fi Section 4.2.3. This splice 

problem is nather in the smgle mode nor the Olulttmode regime. A method for 

e\ aluating lateral splice losses for few-modes optical fibers IS developed in SectIon 4.2.4. 

4.2.2 Laterally Offset Splices fer lVluItimode Optical Fibers 

For muluOlode optical fibers (V> 10) the a:1aylsis of the laterally offset splice is based 

upon the fact that many modes preplgate in the sensing fiber and t!1e fIltering fiber. 

The numbc:- of modes that propa~.lte In a multimode Optical fiber can be approximated 

by Equatioll 4~3-1 [5} 

.\f = (4.22- 1) 

40 Princlpln or {);la_lIOn or \llcro-OpllCaI F~r Devices 33 
Sensing Fiber 

Sensing fiber's core radius 

is as 

Figure 12- Two Identical Fibers Laterally Offset 

4.0 Princip&es of OperatIOn of 'tiero-Optlcal Fiber ~iccs 

Filtering Fiber 

Filtering fiber's core radius 

is a, 

39 
ySensing FIber 

Sensing fiber's core 

radius is as 

Filtering Fiber 

Filtering fiber's core 

radius is a, 

as is at least 2 times 

greater than a, 

Fipre 13. The Fi!tmng ~r's Core Inside The Seasinc Fiber's Core 

.. .0 PritIcipb or Operation or 'hcro-Optica.I Fiber l)e,icn 40 
__ #-tl 

Lateral displacement bet\\ cen t\\ 0 Optical fibers can be appro\lmateJ as Equation 

-l 2 2-2 (5J 

-:=-cos 2 - ( - - d ) '" 2a (42.2-2) 

where, 

a = .:ore radius, 

d = lateral offset, 

.1:0 ,"", = common core !lr~'a Ot!t.~ em ;lte sensing cr.d lhefilurlllgfiber 

This formula can also be appltcd to 1'.0 fibers of slightly dUTerent sizes except 

A ...... = ::a1 2 , where al is the cere radiUS of the ftitering fiber. For the asymmetrical 

splice fer the LP:1 and LPn modes, these formulas cannot be applied. The few-moded 

optical fiber is not operJting to the true -multimode regime-. The V - number that 

supports the propagation of only the LPcl ttd LPu modes falls between 2.405 and 3 9 . 

.... 2.3 Laterally Cffset Splices for Singlemode Optical Fibers 

For singlemcde optlc:lI fibers (" < 2.4!05) t1:e propag-lting electromagnetic \Va\ e can be 

modeled as a Gaussian beam. The splIce losses can be defmed in terms of the beam 

40 Pnncipln or O~ration or \ticro-OpllUl Fiber ~icn 41 
., 

waist, w. The loss in a slJ\J,;le mode srlice due to a trans\er~e oflfset can be defined by 

Equation 4.2 3-1 [16). 

" = 4_3~( ~ ) (dB), (4.2.3 - I) 

where, 

d = Iransurse offset dlStallce beu"een thefilteringfiber and the sensingfiber, and 

w = \~alst of the Gaussian beam. 

If two different Optical fibers \1.C. different core radii ) are used for the asymmetrical 

splice, mode field radIUS nusmatch r.eeds to be conSidered. The mode field radtus is 

dermed as ••. z beam \\iJth of the G:lUh;ltl CeJ.m [16]_ ThIS splice loss IS dermed m 

EquatIOn 4.2.3-~. 

(4.2.3 - 2) 

where, 

Wr = ,,,·aisl of lhe Gaussian beam of IhL filtering fiber. and 

WR = waUl of the Gaussian beam oflhe recenmgfiber. 

For the asymmetncal spl1ce that supports the LP~I and LPu modes cannot be modeled 

as a Ga'lssian beam These modes do not fall in the single mode regtme of operatlon 

(V < 2.405). Another method needs to be developed for fcw-moded optical fibers. This 

method will be rresented in the follo\\"Ulg sectIOn. 

4.0 Principln of Operation of 'Iicro-Optical ~r Dc~itts 41 
-1.2.4 Laterally Offset Splices for Fen-l\Ioded Optical fibers 

Ilus problem needs to be sohcJ h} \\orkmg \\Ith the mdlVlJual modes. Thc mcthods 

for spbce loss c\aluatlon Jc\c1opcd for smgle mode or multlmode fibers cannot be 

applied to fe\\·moded fibers .\nothcr nlLthoJ for c'.aluatlOn IS presented m this scctIO.l. 

For the few·modcd sensmg fiber. it IS assumed that the LPo• and the LPu modes are 

propagating tIl :hO! ~orc 

(.t24-1) 

The fields th;lt are prcF<!gatmg In he sensmg fibcr's claddmg are defmcd by Equauon 

4.~.4-2. 

(42.4 - 2) 

The mterflce of the splice IS shown m Figure 14. Both fibers are identical in this 

configuration. At tlus pomt each fiber will be referred to ItS own coordinate systcm. 

The sensing fiber will be defmed in terms of unprimed coordmates: '. 9. z. The flltering 

fiber will be defined in terms of primed coordInates: ". (J'. z' . 

A method of determining the amount of power which is received by the filtering fi:,er is 

to determine the modes proPJgating in the flltering fiber from the sensing fiber. and then 

an l:ltenslt) in the fUtenns fiber can be deterrruned. A ratio of intensity bet\\een the 

fUtenns fiber and the sensin·g fiber can be e'\pressed as Equation ·t2.4·3. 

'1 = IJ: 'mngf..'u 

IwuJ''::.pu • 

4.0 rnnClples of Opnatioa of '\ficro-Optlcal fiber Dc.KCS 

(42.4 - 3) 

43 
~-- --

r ,0 

r',c>' - sensing fiber 

- filtering fiber 

F'rgure 14. Cross-Section of the As}mmctrical Splice "lth Identical Fibtts 

01.0 Principln of <>pttatlon or \Iicro-Opucal Fiber Dc'ic:n 

'" , 
- -- ------

TI1JS ratio IS the efficlcnc) of the o;phce. 

Another loss across the mterface IS reflectIOn losses. I e. loss due thc to mdex of 

refraction nusmatch Smce n1 ;;:;; n1 , the transnuc;slon across the interface \\111 be 

appro,(lmatcd as I . 

Since weak gUidance IS assumed because the LP modes are dependent on the weak 

gUidance condition, the modal amplitudes 10 the second fiber can be lf~termined from the 

propagating modes In the sensmg fiber (I II 

If tr.tr) COS(s¢))tk(r') cos(f9')r'dr'd4J' 

I I~i.r') CQS(:9JI 2r'dr'cf¢' 1 

where, 

{ 

A.,ls(U?/a), r < a} 

fr<r) = , 

BrKs{H'j/a), r> a 

{

J/(Lir'/a), r<a} 1;- = ,and 

Ai(lfjr'/a), r>a 

S = Ihe surface area 10 be mtegrated. 

(4.2.4 - 4) 

In Equation 4.2.4-4J.{r) cos(s9) are tre modes propagating In the sensing fiber. A. and ~ 

B. arc the amplitude cc:fficlents associated \\lth the modes in' the ~ensing fiber. 

fl..T') cosif¢') are the modes propagatmg in the filtering fiber. A, is the resultant modal 

amplitude aSSOC1J.ted \\lth thenr') cos((¢') mode. The denonunator of Equation 4.2.4-4 

4.0 Pnociples or Opnation or \Ilcro-Optical Fiber De>ices 45 

.... 

, 
-- ---- . - -

IS a normalization factor or the fIr') cost}"") mode Tne area which IS to be mtegrated 

o\er IS the filtenng fiber or the pnmcd coordmates Thc unprlmed coordmatcs nced to 

be convcrtcJ ~o pnmcd coordmates In order to perfJrm this mtegratlon 1111s opcration 

\\111 be performed later 

:\s secn m Figure 14, there are thrce dlstmct are;lS of mtegratlon' 

the scnsmg core - the filtenng core mterface, 

2 the sensmg c1addmg - the filtenng core mtcrface, and 

3 the sensmg claddmg - the filtenng cladJm£ mterface. 

I t IS Important to note that each of these three Illtegratloas needs to be performed tv.ice. 

Smce the LP,;, and the LPII mcdes are propagating m the sensmg fiber, some of these 

modes \"ill be coupled mto the LPc, and the LPu modes in the filtering fiber. So a moCal 

amplItude mtegration needs to be performed for the LPo, and LPu modes 10 each ofthcse 

three areas. These mtesratlons are defined as fodows: 

The sensing core - filtenng core mterface 

{L[A.rtJJO(L·~~Jla)lo(L('/la) ~ ~ 

Arllll ( U1s'ia) cos t/>lc{L'o/ /a)}'dr' d4>'} 

L' lJ( u·o/ fa) I"r' dr' d4>' 

4.0 Pnoclples or OperatIOn of'tu:ro-OpticaJ Fiber De'lces 

(4.2.4-~ 
{t [..fuI Jo(lios'/a)JI, t"1.t"'/a) cos ¢' + 

ASI til ( UIs'/a)J1( £':I/,'/a) cos 4> cos q,']r drd¢'} 

t IJ,(U,/Ia) cos ¢'1 2r'dr'dq,' 

2. The senSl·lg claddmg - filtenng core mterface 

{t [8 11 Kc,(Wcs'ia)Jo(Uo//a) + 

B'-II :1 (H"s,/a)J~( Uo/ fa) cos 4>'Jr' dr' d¢'} 

t I Jo( Vol" / a) 1

2

1" dr' d¢' 

{t [BJOI Ko( Wosr/a)JI( UIj,'/a) cos t/>' + 

(41.4 - 6) 

(4.2.4 -1) 

AJ1I = BSIIKI(JJ"ISr!a)JI(UIj,'/a) cos ¢ cos 4>']r'dr'd4>'} (~.2.4 - 8) 

J IJI ( UlJ,'/a) cos ¢'1 2r'dr'dt/>' 

J 

3. The sensing cladding - filtenng claddmg interface 

B;11 K1( Wlsria)K~i WoJ"'/a) cos 4> Jr' dr' d¢'} 

t I Ko( WOll"' fa) 1

2

1" dr' dq,' 

•• 0 Principles or Operation or \hero-Optlcal Fibct' DeYicn 

(42.4 - 9) 

47 
If [BsQ\ hO( WOr-/a)KI( WlJl"/a) cos I)' ~ l S 

Bj1\ = Rrll K\ (1VIrr/a)K\ (il'/) cos <P cos <p']r' dr' d4>'} (4 2.4 - 10) 

J I KI ( ""-f'/a) cos <p' 1

2

r'dr'd<p' 

S 

From these three regions, only the scnsmg core - ftltenng core interface and the sensing 

ctadd~lg - filtenng cere mtcrface contnbute to the filtenng cere's fields. 

In order to sohe thiS prcbkm the unpruned functions need to be converted to primed 

coordmates A rr.'!thod of comerung the unpnmcd coordmates to the pruned 

coordInates IS to appl~ the Summation Theorem for Bessel functions [18). The 

summation theorem 15 th~ follo\\ mg 

'r.1 "'" 

;"';'Z.(mr) = L lJr.(md)Z. + k(mr')e{Jk(-: - 91 (4.2.4 - 11) 

k=-oo 

where, 

Z 1 Y H (I) H m y = ., yt y • or 'I' 

\\here, 

1. IS a Bessel Funclion oflheJirsl kmd. 

Y.;s a Bessel Funcllon of the second kmd. 

oS 0 Pnnclples of Operation of 'tlcro-Optlcal Fiber De'Kes 48 

-~ 
H. (II is ,: Hankel FUllc/lon ollMJirsl kmd. 

II. OI,S a Hankel FUIICllon oflhe second kind. 

I. IS a modified Bessel FUIICllOn of lire firsl AIItti.. 

K IS a modified Bessel FunClIOn oflhe second lcind. 

In IS arbitrary. 

The relatlOnslup between the primed and 'he unprimcd cooordinates is shown in Figure 

15. d IS the distance that the scns:ng fiber's COR: is offset from the flltenng fiber. The 

angles rclate to one another from Hmple georr.cuy. 

./1 + (J = ¢' (4.2.4 - 12) 

t/I = (J' - q, (42.4 - 13) 

Equation 4.2 4-11 can be rewritten in terms of primed and unprimed coordinates. 

C) 

e'Y{~'-¢) = I Jknd)Z" + j.rv')e'k.(ft - ~1 (42.4 -14) 

1"" -<>0 

To convert Jo(UaTla) mto the pnmed coordinate s:stem via Equation 4.24-14, the 

[ollc.\\mg relationships are true. 

v=o 

Z" = Jo 

4.0 Pranciples or O~ratJoD of'tacro-OpbcaJ Fiber Dnic:es 49 
t ~::-------:: 

-

- . 

• 

o· 

o d o· 

Figure IS. Relationship Bero.-ren L.uned and Primed Coordlllates 

./ 

,s.O PrInciples cr O~rahon of \hcro-OpIica.I Fiber Dcnccs 

" 
, ...... 

In order to ~\Tlte Equation -l 2 -l-I-l 10 a more compact form. the followmg rccurrence 

rc1atlonsillP \\111 be c1l\okcd. 

(42.4 - 15) 

~ow. J:( l:.ria) can be \\Tltten 10 tcrms of the pnmed coordinates. 

Jo(L'odja)Jo(Uo,'fa) + 00 

Jc( Ce,/a) = 2 I ( _1)k J.JL·cdia)Jk(to" fa) cos(J..</J') (424-16) 

k=1 

To convert JI( lIlr/a) COS" mto pnmed coordmates can be re\\Tltten as Equation 

42--l-17. 

(4.24- 17) 

J,\l./l,/a) cos ¢ 10 terms of the primed coordmates can be expressed as Equauon 

4 2.-l-1 S 

Jo(Uld/a)JI(UI,' la) cos 4>' + 

lJUI,/a) cos </J = t~lk(Uldla)( -ll[Jk+l(lil ,'/a) cos[(k + 1)<p'] 

-Jk_I(UI"la)cos[(~ - 1)¢']J} 

(4.2.4 - 18) 

Kd. w ~/a) needs to be expressed 10 tem1S of the primed coordinates. It IS important to 

note the followlOg relauonshlps. 

4.0 Principia of Operation of 'liero-Optical Fiber D~icn 51 

• 
t'- .... • --------- -

(.J 2.J - 19) 

So Equation 4 2.4-14 can be re..mttcn In terms ofthc Hankcl of the first lund. 

(4.2.4 - 20) 

\\here 

By appl)1ng the relationshIps of Equauon ... 2.4-19 to [quatlOn 4.2.4-20, Ko{ Wo,ja) can 

be wntten m terms of the primed coordmates. 

<>0 

Ko(Wo,/a) = 2 L( -lllk(H'cd/a)Kk(Wo,'/a)cos(k¢') (4.2.4 -""21) 

k=1 

Finall}, KI(WIT/a) cos ¢ nceds to be expressed in terms of the primed coordma~es. 

loC Wld,'c:)KI( WIT' fa) cos ¢' + 

KI(WI,/a) cos tP = L~/l(JVldla)[Kk+ l(W\r'/a) cos[(k + 1)¢'] + 

Kk _ IUS-iT"/a) cos[(A: - l)cP']]} 

(.J.2.4 - 22) 

Now all of the unprimed coordmates are c'\pressed in terms of the primed coordmates. 

The integratIons discussed earlier can be performed. However, it is important to point 

4.0 Priaciples or Operation or'licro-Op6caI Fibn D~m 52 

• 
out that this integration I" "till dlm~-ult to perform. lbe geometf} of tillS problem as 

shown In Figure 14 does not lend itself to a readily doable IntcgralJon III polar 

coordmates. The s) mmetf} IS lost. ThIs problem could be modified, so the sphce loss 

due to a lateral offset could be evaluated. Instead of offsettmg the two IdentIcal fibers, 

the filtenng fiber could be a fiber tl>..at has a core dlamenter half of the sensmg fib;:r's 

core, as shown In I 19ure 16. ThIS filtering ~ber's core would Sit In the core of the sensmg 

fiber. This configuration wuuld stil pick-Up one lobe of the LPo, and LPn modal 

pattern. Ho\\ever, the fUtenng fiber 'Iilil onl~ support the LPo, mode because due to the 

decrease In the filtenng fiber's core s:ze, the V - number -1.11 be halved The mtegratlons 

presented earller \nil onl) deal WIth L;e LP~. amplitude coefficient. Finally, it \nll be 

assumed that t~e PO\\ er contnbutlon to the flltering fiber score \\1.11 be due to the 

sensmg fiber's core 

~ote. The filtenng fiber s core Inset in the sensing fiber's core WIll be considered an 

approxunation for the case where two ider.tlcal fibers are laterally offset. 

The modified IOtegratlon can be wotten as EqUltion 4.2.4-23. 

A)OI = 

{L AJ'OJo( c.:o/2/a)[Jo«-·oflJa)Jc(l,'os"!a) + 

2 f~ (-I)1r.JIt,(L'o,ala)J;.(Uos"!a) CC;(Ic~')J + 

j: .. 1 

ASllJc(Uo/~/a)[JiJ( Uo,aJa)}I(Ulr'ja) cos~' + 00 

LJk.tUlflla}( -1)~[J.t+I(Uts"'la) cos[(lc + l)~'] 

J1r._I(~'Is"la) cos[(A. - l)~']J} L I Jo(Uo/2!a) 1

2

r'dr'd¢' 

4.0 Principles of Opcr:ltlOn of \llcro-Opticai Filler Devices 

(42.4 - ~1) 

53 

• 
,.. .. ....;.~ -------, - ------

• 

r , ¢ sensing fiber 

r', Q' - filtering fiber 

Figure 16. Cr055-5ec:tiOll or,he Asyametrical Splice: The Filtering Fi~ Is H:slfThe Core DIameter 

of the Senstng Fiber 

4.0 PriDciples or Operation or \tlcro-OptJCaI ~ Devices 
This equation can be slmrhfieJ hecause the limits of integration for 4>' are 0 to 2n. Any 

cos(,,4» IOtegrated from 0 to 2;r, "here n IS an integer, IS zero 

(42.4 - 24) 

This can be further slmphfied to Equation 4.2.4-25. 

(4.24- 25) 

The integration In Equallon 4.2.4-2_ can be earned out after knOlling the dimenSions 

of the filtering and sensing fibers. This \\111 be done in Section 4.2.5, Implementation 

of the Asymmetncal Sphce. After the IOtcgration is performed, Equation 4.2.4-25 will 

take the form of Equation 4 2.4-26, 

(42.4-26) 

where X is a number. 

The field propagating Ir~ the filtering core is defmed by Equation 4.2.4-27. 

(4.2.4- 27) 

4.0 Principles or Operation or 'hero-Optical fiber Dniccs S5 

.." ....... 
.-----. . ---- -

The efficiency of this splice can be expres~ed In terms of the intensities of the modes 

propagating in the senslOg fiber, and the intensity of the LPol mode propagatmg 10 the 

filtcnng fiber. The mtenSlt~ of the field propagatmg m the filtenng core IS 

~l rl - - • Y1 2 2 2 , 

-.,- IE. E I = TAjOJ X 10 (UoJ' 2/a). (4.2.4 - 28) 

The intensity of the LPc1 mode 10 the scnsmg fiber IS 

IsO I (424 - 29) 

The mtenslty of the LPn mc.!e 10 the sensmg fiber IS 

(4.2.4 - 30) 

In deterrrurung the efficlcncy of the spltce, Equation 4 2 4-34, the intensity funCtiOns, 

1/01,1.010 and I'll need to be mtegrated over therr respectl\e fiber core areas. The ftltering 

fiber's intensity funCtion, ~'OI' is mtegrated o\er the primed coordinates as mdlcated in 

Equation 4.2.4-31. The sensing fiber's intensity functions./.e1 and 1,11' are integrated Oi"er 

the unpriroed coordmates as indicated in Equauons 4.2.4-32 and 4.24-33. 

(4.2.4 - 31) 

(42.4 - 3~) 

4.0 Principles or Oprratlon or \tacro-Optical Fiber Dellca 

\.;0,-j 

.... 
The efficiency of thIs splice, '7. IS descnbed 10 Equation ~ 2.4·31. 

'1 = Anll '701 + Asll'7l1 

AsOl + AslI 

(4.2.4 - 33) 

(4.2.4 - 31) 

/"1 where JfOI = -I -. couplmg cOiClency of the LPc, mode m the sensmg fiber to the s'JI' I I 

LPol m the fUtermg fiber, 11.1 = i"'l.l , coupling efficiency of the LPn mode in the 1'1~. 

sensmg fiber the LPo, 10 the filtermg fiber, and A,a and A'II are weighting factors. As 

seen 10 Equauon 4 2.4·25, the only mode which contributes to the fIltering fiber is the 

LPc, mode Equauon 4 2.4·26 can be rewntten as 

(4.2.4 - 35) 

where 

XII = O. 

The couplIng efficIency of the LPn mode in the sensing fiber to LPo) mode m the fIltering 

fiber. Jfn. is zero. EquatIOn 4.2.4-34 simphfies to 

(4.2.4 - 36) 

This sphce loss calculation can be used to approximate the case where two identical 

fibers are laterally offset. as " -ll as the case where the fiitering fiber's core sits inside of 

4.0 Principia of Operation of \Iicro-Optic:al Filla Dewices 51 
the sensing fiber's core 10 log of the efficIency, Equatton 4 2.4-36, wdl YIeld the spltcc 

1055. However, the spbce 1055 can not be exphcJtly evaluated because A.a, and A,II are 

unknown. 

4.2.5 Implementation of the Laterally Offset Splice 

ThIS sectIon \\111 examine a system which uses a few-moded laterally offset spltce for 

tn-lme sIgnal processmg \\lth a modal domatn sensing s}stem. ThIs splIce could be 

fabricated \\lth two Identical fibers laterally offset, but the slmpWied verston of this 

sphce WIll be consIdered tn thiS section. The sphce \\ill consist of a ftltering fiber which 

IS half the core diameter of thc scnsmg fiber. Thus, the mam tnterest will be the 

core-core transfer of power. 

Parameters of the sensmg fiber arc' 

a = 4Sp.m 

SA = 0.1 

ft .... 1.458 

~ = 145~3 

1.,..,.._" .. 780nm 

v = 3.62~9 

4.0 Principles or Oprration or \1lcro-Optical Fiber Deyices 58 
.-------- ------- ----

L'. = 1.9571182 

VIJ = 3.02101~S 

). .... "' .... _ = 1300nm 

Parameters of the filtenng fiber are: 

a = 2p.m 

NA = 0.1 

nl = 1458 

J.., __ = 780nm 

v == 1.611073 

L'v = 1.57061 

) ... __ = 633nm 

The filtering fiber could have been singlemode at 780nm. but the core diameter is Sp.1n. 

111at is more than half of the sensing fiber's radIus. This optical fiber will ruter more 

than one lobe of the speckle pattern. So it ~ more feasible to we an optical fiber 

which is shghtly less than half of the sensing fiber's diameter. This filtering fiber has a 

diameter of 4p.m. 

4.0 PriDcipln or Operatioa or \ticro-Optical Fibtr DcYica 

"" 

.. 
------ .-

Equauon 4.2.4-25 can be re\\ ntten with the parameters of the optical fiber. 

(4.2.5 - I) 

where 

d = 2 Op.Jn 102 5p.m, 

at = 2wn. 

a, = -l5p.m, 

L'CIt = 19571182. and 

UC/ = 1 57061. 

After integrating Equation 4.2 5-1. AJIlI can be expressed as EquaLon 4.2.5-2, 

(4.25 - 2) 

where X IS calculated from the program. Amp Fortr.:lO. which is found in the AppendIX 

A. Then 'It .. Equa~on 4 2.5-3. can be calculated. after mtegrattng ~1f!1 and 1.01 These 

calculations are performed by usmg the fortran program, Int Fortran wluch IS found m 

AppendiX 8 . 

.. 0 rrinclples or Operatton or 'Ilcro-Optlca.l .. iber DuicC$ 60 

, 
__ L.....J)..:;:r:y=-;;:a;:::.;.:.,1-.:"Y"x:.-. _ _ _ _ _ ______ _ -----·--r 

"01 = 

I /01,1 

IsQl,l 

= .. ') 2 2 1

2 fa, 1.' 

T AOI 10 (Uor/as),drd~ 

o 0 

(4.2.5 - 3) 

Fmally, the effiCiency of the sphce can be determined from Equation 4.2.4-36. The 

assumption which was made 10 Chapter 3, that A'II == 2A.o1, will be used to crudely 

exanune the sphce effiCiency Equation 4.24-36 can be rewntten as Equation 4.2.5-4, 

71 = 

7101 

3 (4.2.5 - 4) 

The follo\\ing \alues for X, 7101' and L, the splice loss, were calculated for various lateral 

offsets, d: 

d = 2.50pm: X = 0.8847932, "a = 0.2118394, L = 11.51 dB 

d = 2.25~m: X = 0.944511, ". = 0.2413998, L = 10.94 dB 

d - 2.00pm: X = 09994462, If. = 0.2676080, L = 10.496 dB. 

The fIlterir.g fiber will detect more of the sensing fiber's LPo1 mode, as the fIltering fiber 

is brought closer to the center of the sensing fiber ( d goes to 2pm). This is due to the 

fact that LPII mode IS a Gau!)sian beam. The optunum plaN:ment of the fIltering fiber 

fer power considerations is a lateral offset of d = 2.01U'L Now, the propagating field in 

the filtering fiber s core for d = 2sun can be \\TItten as Equation 4.2.5-3. 

4.1 Priociples 0( Operation 0( ;\Iacro-Optical Fibn-Devices 61 

, 
(4 2.S - S) 

In order to perform the splice calculation exactly, the amplitude coefficients an Equation 

'u.s need to be determ.ned. This splice \\11\ enable in-hne Signal processing of the 

perturbations appbed to the sensing fiber. 

4.3 Tire Abo-Gap Splice 

A third nucro-opucal fiber de\ ICC that IS presented 15 the air-gap splice as shown in 

Figure 17 (3). Vnltke the last two de\lCeS, the modal conversion coupler and the 

as)m.mctrical splice, the ai!-gap splice is not used in conjunction with modal domam 

~nsmg. The air-gap spltce is used with an OTDR system to monitor locahzed strain 

effects, Figure 18 (3) The fiber which is used with the air-gap splice has a 100"," core 

cEameter an1140pn: claddmg diameter; this fiber has a step-index proftle. 

Tnere is a Fresnel reflection at each of this air-gap splices, a pulse (4'l.reflected power) 

can be seen on the OTDR due to the ;ur-gap splice. Due to the change in the medium 

at the air-gap splice (from glass to air ), some of the higher order modes will be lost as 

light propagates in t.l}e air regime. The light will diverge, and the modes which tra\el 

closest to the core-cladding interface, the hig}7er order modes will be lost a~ cladding 

modes. 

61 

• 
---.. ------- -- - -------- -- - ----

ALllaN MEJIlT ~L££Ve. 

l.2.rnm 

.$mm 

f.- I.q em ---I 

Firure 17. ~ Air-Gap Splitt 13) 

4.0 Principla,J( Operatioll or'licrcMlpticaJ Fiber Dcric:a 

FilteR. COAT'NCa 

63 
; 

EXPErm.1EtJTS 

System Description 

------------ , 

, I 

'--

of 

I 

r--- ,,,-, ' es --1 '<: 

I \ 

DEie. 

l...--.J 

-:. iOI\ ~ 1-

I 

!-i r--J 

OrDR " , y 

I 

\. :"S:::R ,/ 

, ' I : I 

I ~ I \ ,I 

I~ .-'. ~l 

I 

I 

o :) 0: 

o 00 C 

ooc 

I SAM. "~It:A 10 Q I: I 

I I. I 

L ____ --1 . ________ ---1 

Tektronix 7854 

/ -\ 

L: I 

! I 

0 n y I 

I I 

'rl r / 

~ 

L03d Frame 

rlKure IS. OTOR Sct-Cp \\ith Air-w, Sptic:cs to Ikt~ct Localized StraiD 131 

4 .. Pnnci.,lcs or OperatioD or '\liao-OptiaU"ibcr OC'ns 

I 

I 

I 

j~ -- , I '--' ~ 

I 

I 

I 

I 

I 

I 

I 

--J-'-' 

~ ..... I_-
-----~-

The air-gap splice \\111 magntfy modal effects such as the modal content of the optical 

fiber and modal dispersIOn \Iodal effects due to modal disperSion are shown In Figure 

)9 [31. :\lo.!.11 disperSion can be expressed as EquatIOn 4.3-1 (5) 

(4.3 - 1) 

where 

T rno4 = modal disperSIon In tmle , 

T rna = ;alh oJllre hlblzesl order mc1o!, 

Trr,n = r",.llh oJtho! lo~~est order ,.,ode, 

n, = Index oJ reJractlon, core, 

~= 

L = ler.glh oJlhefiber, and 

c = 3 x loa mIs, 

T _ is depe:;.dent upon the launching conditions, as shown in Figure 19 (3), If mainly 

lower order modes are jaunchcd as in a of Figure 19, the pulse is not as .. cry board. If 

bIgher order modes are launched mto the optical fiber as m b of Figure 19, the pulse 

tends to be more boarden than tJlt case where mainly lower order modes are launched 

into the optical fiber. This is true due to the later arrh'al times of the higher order 

a:.odes . 

.u Principles or OpHation or '1icro-Optic.aJ Fiber Dniccs 

-" 

• 
OR!GtNf..r; Pf:2G"'!', rs 

:OE ;:.OO?- Q~:fcLITY. 

ttgUfe 19.. \Iodal m .. persion Due to uUftching Conditions 13~ :1) Lower Order ~lodes b) Higher 

Order \todes 

.~.o Principles or Operation or :\2icro-Optieal Fiber De~ices 66 
As the fiber IS strained, the pulses become boardencd and elongated as In Figure 20 [3J. 

This IS due to modal disperSIOn As the modes travel dO\\ll the fiber as the fiber IS 

elongateJ (strained), the rulses \\111 boarden. This effect is demonstrated In Equation 

0.1 3-2 

(4.3 - 2) 

\\here, 

~L = change In l.:nglh oflhe 0Pllcalfiber due 10 an applied axial slra;n 

The same effect can be ~een \\ith a fiber \\ hlch has several air-gap sphces. The further 

away from I he begmmng of the fiber each air-gap spbce IS located, the more boardened 

the pulse becomes. This boardemng is due to modal disperSIOn. This is related to L in 

the numerator of Equation 4 3-1. The longer the light propagates the more dispersed it 

becol"~es. 

4.0 Principles of OperatlOD or \licr~Fiber Dc\1CU 67 

---

• II 
Figure 20. Mod&1 Dispersion Due To Applied StraillfJl 

.. 4.0 Princip!~1 or Operation or :\ticro-Optica.l Fiber Devi«s 68 

--

.. 

-
5.0 Future Work and Applications 

These three micro-optIcal fiber devIces, the modal coo\ersion coupler, the asymmetrical 

splice and the air-gap splice, can help further research in fiber optIC sensing and 

commumcations. 

In conjuncuon wIth modal domam sensing, the modal conversion coupler is a method 

of generating new modes from a gIven set of input conditIons. The modal conversion 

coupler needs to be mathematically descnbed. The mechanisms behind the modal 

conversIons in the taper regions a1'ld the coupler region needs to be modeled. Once a 

mcx!el is esublished for the modal conversion coupler, a repeatable method for 

fabricating these couplers needs to be established. This method must be consistent to 

generate the same output modes from a gi\'en set of input modes. 

An applict.tion of this device is that a modal conversion coupler could generate the 

LPn mode. The LPn mode amplitUde could be measured from '.he output of the modal 

comiersioI~ coupler. This field could be supenmposed with a knO\\'ll LP. field. With the 

correct modal amphtudes these two superimposed modes could generate the two-lobed 

5.0 Fllhlrc wort ud Applications 69 

I 

. 

r- . ..t\! 
speckle pattern used for modal dom:un sensing. ThIS would solve the present problem 

of unknown modal amplitudes due to variahlc launchtng conditions. 

Another application of this device is a multiplexer 10 a communications system. This 

de\lCe would use the method of modal multlplexmg. Certam modal combmatlons ,ould 

carry a -channel of data - The coupler could be used lor generatmg the modal 

combmatlon to be multiplexed onto a fiber. All of these modal channels would need to 

be surenmposed onto the data cart'}ing optical fiber. An analogous device would need 

to be fabncated to demultiplex the modal channels. This modal conversion coupler 

could mcrease the mformatlon carrying capacity of a I.lultimode optical fiber. 

Also, 10 conJunction \\1th modal domam sensmg, the asymmetrical splIce is a means of 

perfomung m-lme Signal processmg In order for this sphce to be completely effective, 

a function correlatmg the mtensity changes 10 the filtenng fiber due to apphed 

perturbations to the sensmg fiber need to be denved. ThiS function "111 be nonlinear, 

since the intensity is a point function. wluch IS a linear function. Tlus asymmetrical 

splice \\ill allow for a compact and packageable modal domain sensing system. This 

splIce \\ill be in the near field as opposed to the far field, so more power can be coupled 

into this splice as opposed to fiber placed in the far field. In terms of the loss 

calculations associated with the asymmetrical splice. the modal amplitudes for the 

sensing fields in the core need to be determmed, so this calculation can be complete As 

mentioned earlier. to soh·e the problem of unknown modal amplitUdes. the modal 

conversion coupler could be applied for a completely characterizable modal domam 

sensing system. Once the modal amplItudes are known. the theoretical results can be 

compared to an experimental asymmetrical splice wtth the ftltering fiber·s core inside the 

sensing fiber"s core as in Figure 16. Then. the theoretical approxim:ltion of the filtering 

5.0 futule W..rk and Applicatioas 70 
fiber's core insIde the serlSms fiber's core can then be compared to the expC'nmentaJ 

as}mmetrical splice with two Identical fibers laterally offset as m Figure IS. 

Fmally, the aIr-gap sphce exhibits modal effects evident m multtmode optical fibers. For 

appltcatlons where modal dispersIon effects are undesireable, the aIr-gap sphce could be 

fabncated \\lth single mode optical fibers, However, the aIr-gap splice could be used to 

momtor modal dispers.on '!ffects as a fiber is stramed, or morutor dlsperson along the 

length of the optIcal fiber. The air-gap sphce could be used to analyze the modal content 

which IS launched mto the optical fiber. ThIs coald be a method of determinmg whether 

lower, rugher, or evenl} dIstributed modes are propagatmg in the optical fiber, 

S.O FIIhIrc Work aDd Applications 71 

- .. -~ -_._----

I 

-

C! 
-

6.0 Conclusions 

Three ffilcro-optlcal fiber dc\ Ices, a modal conversion coupler, an asymmetncal splice, 

and an air-gap splice, \\ere presented. Two of these devIces can be used in conJuncuon 

WIth modal domam sensmg, the modal com crSlOn coupler and the asymmetrical splice. 

The modal conversion converSIon coupler can be a method of descnbmg launchmg 

conditions. ~todal amphtudes m conjunction With modal domain sensing are unknown 

at this time. The modal con\ erslon coupler can gerlerate a mode from a given set of 

input condItions. The modal amplitude from the output of the coupler can be 

determined, and then superimposed With other known modal amplitudes. This is a 

po!osible solution to unknown launching conditions. 

The asymmetncal splice IS a method of performing in-line signal processm~ The 

asymmetrical sphce allows a modal domain sensing system to be a compact and 

packageable system. Intensit) ch:>'lges Ul the flltering fiber can be correlated to 

perturbations in the sensing fiber. Finally, sphce loss calculation! for laterally offset 

multimode and single mode fibers is not applicable to few-moded fibers. A new method 

72 

..... 
for evaluatmg splice loss for few-modcd fibers has been developed In order to detcrnune 

the sphce loss expbcltl:., amphtude coefficients for the modes propagating 10 the filtenng 

fiber need to be detemuned from the modes propagatmg 10 the senslOg fiber. 

The air-gar splices e\hlblt modal effects when used with multlmode fibers. The air-gap 

sphce IS a method of \ le\\1ng modal dispersion, whether modal dlspefSlon IS dependent 

upon the modal content launch.:d mto the optical fiber or IS due to ler gth elongation 

due to aXial stram <t?phed to the optical fiber 

6.0 COCIdllSions 

\ 

( 

\ 

73 

/ 

-
-

Appendix A: Amp Fortran Listing 

Appendix A: Amp Fortran ListinC 74 
• 

eeeeeeeeeceeeceeeeeccccecceceeeeecccecceecceeeeeeeeeeeeceeceeeeeeeeeee 

c c 

C AMP FORTRAN C 

C C 

C e 

C e 

C WRITTEN BY AMY FLAX C 

C C 

ecccccecccccccccccccceccccccccccccccccccecccccccccccccccccceeeeeeececc 

eeeeececeeccccccceccccccceccccceccccccecccccccceeeeeeccceeeceeccceecc 

c e 

c THIS PROGRAM IS DESIGNED TO AID IN CALCULATING AFOl IN e 

c c 

c EQUATION 4 2.5-1, WHERE AFOI = ASOl X. THIS PROGRAM CALCULATES C 

e c 

c X. THE MAIN PROGRAM USES AN IMSl ROUTINE, DCADRE, TO DO THE C 

C C 

C ItHEGRATIOtIS. DCADRE USES THE FOLLOWING PARAMETERS. e 

c e 

c F=FUNCTION TO BE INTEGRATED. WHICH IS CALLED EXTERNALLY e 

c A=LOIlER LIMIT OF INTEGRATION C 

C B=UPPER LIMIT OF INTEGRATION e 

c AERR=I1IPUT ERROR C 

C RERR=RETURN ERROR C 

e ERROR=ERROR MESSAGES e 

c C=INTEGRATED At~SHER C 

C C 

ecccececccccccccceecccccccccccceeccccccccccccecccccccccececeeeceeeccc 

ceccccccc~cccccceccccccccccccccccccccccccccccecccccccccccceceeeeeeecc 

c e 

c DeADRE IS USED THIeE. c 

e c 

c 1) TO ItITEGRATE THE NUMERATOR OF EQUATION 4.2.5-1. C 

C THE EXTERNAL FUt~CTlOtl TO BE INTEGRATED IS 'F'. C 

C THE RESULT IS "C". C 

c e 

c 2) TO INTEGRATE THE DENOMINATOR OF EQUATION 4.2.5-1. e 

c THE EXTERNAL FUNCTION TO BE I1H~GRATED IS "FX". C 

C THE RESULT IS "D". C 

C e 

ccccecceccccccececcccccccccccccccccccccccccceecccececeeccecceeeeccccc 

INTEGER IER 

REAL DCADRE.F.A,8, AERR, RERR. ERROR,C,D,FX,J,DI.UF,AF EXTERNAL F,FX A=O.O 

B=2.0 

• 

AppaIdix A: Amp Fortran Listinc c - d,... 75 
RERR=O. 

AERR= 1.0E-5 

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeecceccccecceeeeceeccceeeeeceeeeeee 

e e 

e DCADRE IS CALLED TO INTEGRATE F AND FX, WHICH ARE FOUND IN C 

C C 

C SUBROUTINES AT THE BOTTOH OF THE PROGRAM. C 

e c 

ceeccceeceeecececeeeeceeeeeeeeeeeeeceeeecceeeeeeeceeeeeeeeeceeeeeec 

e = DCADRE CF.A.B.AERR.RERR.ERROR,IER ) D = DCADRE (FX.A,B,AERR,RERR,ERROR,IER) 

eeceeeeeeeeeeeeeeeeeeeeeeeecccccccceccccecccccccccccccccecccecccccc 

c c 

c THIS SECTION CALCULATES JO( UOS DI/AS) OF EQUATION 4.2.5-1. C 

e c 

e THIS TERM ACCOUNTS FOR THE LATERAL OFFSET OF THE FILTERING C 

e c 

e FIBER. c 

e c 

c US = UOS/AS. FIBER PARAMETER CALCULATED C 

e c 

e DI = DISTANCE CENTER OF FILTERING FIBER OFFSET FROM C 

e CENTER OF SENSING FIBER C 

C C 

C J = JOS (US 01 ). BES5EL FUNCTION OF THE FIRST KIND C 

C APPRoxnlATED BY A ?Ol yt~OHIAl. THE APPROXlHATlor~ C 

e OF THIS FunCTION IS FOUND In REFERENCE c 

c C 

ccececccccerceccecccccccccccccccccceccceecceeceecccecceecceeeceeeee 

01=2.00 

US=O.434915159 

J=(I- 2.2499997- C(USKDI/3.0).-2 ) + 1.265620aKCCUS-DI/3.0)-.4) 

c - O.3163166-CCUS-DI/3 0)--6) + 0.0444479_((USKDI/3.0) •• ') - eO.0039444-CCUS-DI/3.0)--10) - 0.0002100-((US-DI/3.0)-.12» 

eccccceeecceececcecccecceecececeeeccceeeeccecceeeecceeeecceeeceeccece 

e c 

c X OF EQUATION 4.2.5-1 IS CALCULATED. HHERE AF = X. C 

C C 

C X IS PRINTED OUT ON THE TERMWAl SCREEN. C 

C C 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

• 

----- - -- . 

76 
r 

AF=J*C/D 

WRITE C ••• ) AF 

STOP 

END 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

C C 

C THIS IS A SUB ROUTInE TO CALCULATE THE FUNCTION IN THE C 

C C 

C NUMERATOR OF EQUATION 4.~-5.CJO CUOS X / AS » CJO CUOF X /AF».C 

C C 

C I) US = UOs/AS C 

C 2) UF = UOF/AF C 

C 3) THE BESSELS FUNCTIon ARE APPROXIMATED BY A POLYNOMIAL C 

C 4) S = JO (US X) C 

C S) FF= JO CUF X) C 

C 6) F=S.FF.X. WHICH IS THE FUNCTION TO BE INTEGRATED C 

C C ccccccccccccccccccccccccccccccccccccccccccccccccccccccCCCCCCCCCCCCCCC 

REAL FUt4CTIOtl F(X) REAL X.UF.US.S.FF 

UF=O.7a53052 

US=O.434915159 

FF=CI- 2 2499997* CCUF.X/3.0) •• 2 ) + 1.265620a.CCUF.X/3.0) •• 4) 

c - 0.3163866.(CUF.X/3.0) •• 6) + O.0444479*CCUF*X/3.0) •• 8) - CO.0039444.CCUF.x/3.0) •• lO) - O.0002100.CCUF.x/3.0).*12» 

S=CI- 2.2499997. CCUS.X/3 0) •• 2 ) + 1.26S6208*CCUS*X/3.0) •• 4) C-0.3163866*«US*X/3.0) •• 6) + 0.0444479.CCUS_X/3.0)*.8) - CO.0039444*CCUS.x/3.0) •• lO) - O.0002100*(CUS.x/3.0) •• 12» 

F=S.Ff*X 

RETURN 

EtlD 

cccccccccccccccccccccccccccccccccccccccccccccccccccccccCCCCCCCCCCCCC 

C C 

C THIS SUBROUTINE CALCULATES THE FUtlCTION W THE DENOMINATOR C 

C C 

C IN EQUATION 4.2.5-1. THE METHOD IS THE SAME AS IN THE OTHER C 

C C 

C SUBROUTINE. EXCEPT THESE MODIFICATIONS: C 

C C 

C I) FF. UF ARE THE SAME AS IN THE OTHER SUBROUTINE C 

C 2) THE FUNCTION TO BE INTEGRATED IS FX C 

C 3) FX = CABS CFF» •• 2 x c 

C C cccccccccccccccccccccccccccccccccccccccccccccccccccccccccCCCCCCCCCCC 

• 

77 

I 
• 

REAL FUIICTIOIl FXeX) REAL X.UF.FF 

UF=O.7IIS30S2 

FF=Cl- 2.2499997_ CCUF_X/3.0) __ 2 ) + 1.265620a.CCUF.x/3.0) •• 4) 

C - O.3163866-CCUF-X/3.0) •• 6) + O.0444479-CCUF-x/3.0) •• S) - CO.0039444-CCUF-X/3.0).-lO) - O.OOOZlOO-C(UF-X/3.0) •• lZ» 

FX= C( ABS CFF) )--2 ).x RETURN 

EIlD 

•• 

I 

. 

( 
• \ . 

Appendix B: lot Fortran Listing 

AppeDdix B: lilt FortraD LisUr. .. '79 

f 
c 

... 

r 

, 

t 

~ t 

t 

f· 

t. 

~-

-------------.,. -----

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeccccceceeeceeeeeccecceee 

e c 

e ltH FORTRAN e 

C e 

c e 

e c 

e WRITTEt~ BY AMY flAX e 

e c 

eeeeeeceeeeeeeeeceeeeceeeceeeeeeeeeeceeeceeeeceeeeeeeeeeeeeeeeeeeeeeee 

eeeeeeeeeeeeeeeececeeeccecceeceeeececceceeeeeceeceeeeeeeceeceeeeeeeee 

e e 

e THIS PROGRAM IS DESIGnED TO AID IN CALCULATING NOI IN e 

e e 

e EQUATIOn 4.2.4-31. THIS PROGRAM CALCULATES e 

e e 

r: NOI. T~E HAIN PROGRAM USES An IMSL ROUTIt~E. DeADRE. TO DO THE e ~ e 

e INTEGRATIOns DeADRE USES THE FOLLOHInG PARAMETERS: e 

e e 

e F=FuneTIOt~ TO BE WTEGRATED. WHICH IS CAllED EXTERNAllY e 

e A=LOWER LIMIT OF InTEGRATIOn e 

e B=UPPER LIMIT OF INTEGRATIOn e 

e AERR=It~PUT ERROR e 

e RERR=RETURN ERROR e 

c ERROR=ERROR MESSAGES C 

C C=WTEGRATED AI~SI~ER e 

e e 

eeeeeeeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeececeeeeeeeeeeeceeeececee 

eteeeeeeeeeceeeeeececeecceececeeceeeecccceeececceeececcceeccecceeeecc 

e e 

e DeADRE IS USED THleE. e 

e e 

e 1) TO INTEGRATE THE NUMERATOR OF EQUATION 4.2.4-31. C 

e THE EXTERNAL FunCTION TO BE INTEGRATED IS 'F'. e 

c THE RESULT IS 'C' WHICH IS I"TEGRATED FROM 0 TO 2. C 

C e 

c 2) TO INTEGRATE THE DENOMInATOR OF EQUATION 4.2.4-3. e 

c THE EXTERNAL FUNCTION TO BE INTEGRATED IS 'FX'. C 

C THE RESULT IS '0' HHIeH IS INTEGRATED FROM 0 TO 4.5. e 

e e 

ceeeecceececccceeecccccececececeeccccceccccccccccccccccccccccccceeccc 

INTEGER IER 

REAL DCADRE.F.A.B. AERR. RERR. ERROR.C.D.FX.E.Xl.A2.B2 

EXTERnAL F.FX 

A=O.O 

B=2.0 

• 

AppeDdut B: hat Fortraa Listing aD 
RERR=O. 

AERR= 1. OE-5 

A2 =0.0 

B2= 4.5 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

C C 

C DCADRE IS CAllED TO ItHEGRATE F AND FX. WHICH ARE FOUtlD W C 

C C 

C SUBROUTINES AT THE BOTTOM OF THE PROGRAM. C 

C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC~CCCCCCCCCCCCCCCCCcCCCCCCCCCCCCC 

C = DCADRE CF.A.B.AERR.RERR.ERROR.IER ) D = DCADRE (FX.A2.B2.AERR.RERR.ERROR.IER) 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

C C 

C X=X1. CALCULATED FROM THE M1P f'JRTRAN PROGRAM IS ENTERED HERE. C 

C C 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

Xl = 0.994462 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC:ccccccccccccccc 

C C 

C N01 OF EQUATION 4.2.4-31 IS CALCULATED. WHERE N01 = IF01/ISOI C 

C C 

C E = N01 C 

C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC~CCCC 

E=(XI •• 2 ) • C /D 

WRITE C ••• ) E 

STOP 

END 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

C C 

C THIS IS A SUBROUTWE TO CALCULATE THE FUNCTION IN THE C 

C C 

C NUMERATOR OF EQUATION 4.2.4-31. JO C UOF X /AF). C 

C C 

C 1> UF = UOF/AF C 

C 2) THE BESSELS FUNCTION ARE APPROXIMATED BY A POLYNOMIAL (19) C 

C 3) FF= JO (UF X) C 

C 4) F=CCFF)--2).X. WHICH IS THE FUNCTION TO BE INTEGRATED C 

C C 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

AppeadVt B: lilt Fortru Listin& II 
.. 

, 

-

.. 

, 

t 

, 

r 

l 

r -

.. 

---_ ... _-- • - ._-----"11 

REAL FUNCTION F(X) REAL X.UF.FF 

UF=0.7aS30S2 

FF=(l- 2.2499997. «UF.X/3.0) •• 2 ) + 1.26S6208.«UF.X/3.0)._4) C - 0.3163866-«UF-X/3.0)--6) + 0.0444479.«UF.X/3.0)._8) - CO 0039444-«UF.X/3.0) •• 10) + 0.0002100.«UF.x/3.0) •• 12» 

F= (CFF)"2 ).X 

RETURN 

Elm 

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccCCCCCCCCCC 

C C 

C THIS SUBROUTINE CALCULATES THE FUNCTION Ifl THE DENOMINATOR C 

C C 

C IN EQUATION 4.2.4-31. THE METHOD IS THE SAME AS IN THE OTHER C 

C C 

C SUBROUTINE. EXCEPT THESE MODIFICATIONS: C 

C C 

C I) S AND US. tlHERE US = UOS/AS. REPLACE FF AND UF C 

C 2) THE FUNCTION TO BE INTEGRATED IS FX C 

C 3) FX = (S)"2 - X C 

C C 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

REAL FUNCTION FX(X) REAL X.US.S 

US=0.4349151S9 

S=(I- 2.2499997- «US.X/3.0).-Z ) + 1.26S6208.«US-x/3.0) •• 4) C - 0.3163866-«US.X/3.0) •• 6) + 0.0444479-«US.x/3.0) •• 8) CO.0039444.«US.X/3.0) •• 10) + 0.0002100.«US.x/3.0) •• 12» 

FX= ( (S)"2 ).X RETURN 

END 

Appmdix B: lat Fortru ListiDc 12 
.... _ MIC ))1 

.. 

References 

1. PA. Ehrenfcuchter, -~{odal Domain Sensing of VIbration in Beams,- M.S. 

Thesis, Virginia Tech, December 19S6. 

2. :--';.K Shankaranarayanan, -:\lode-Mode Interference in Optical Fibers: 

AnalySlS and Experiment: :'of-So ThesIs, Virginia Tech, April 1987. 

3. B.D. Zimmermann, -High Resolution Optical Time Domain Reflectometry and 

Its Appbcations; M.S. Thesis, Virginia Tech, January 1988. 

4. D".:igners Guide lO Fiber Oplics, AMP Inc. 1982. 

5. G. Keiser, Oplical Fiber Communications, McGraw-Hill, New York. 1983. 

6. A. Yariv, Oplical Electronics, Holt, Rinehart and 'Vmston, ~ew York. 1985. 

7. M.R. Layton and JA. Bucaro, -Optical Fiber Acoustic Sensor Utilizing 

:'olode-Mode Interference,- Applied OptiCS, vol IS, no. 5, p. 666, ~Iarch 1979_ 

8. S.A. Kingsley and J.A. Bucaro, -Multimode Optical Fibre Phase Modulation 

and Discrimination I & 11,- Eleclronics Leiters, vol. 14, no. 11, p.322/33S, May 

1978. 

9. K D. Bennett, -Fiber Optic Methods for Remote Sensing,- M.S. Thesis, 

Virginia Tech, August 1985 . 

10. K.T. Srinivas, • Alia! Strain Effects on Optical Fiber Mode Patterns,- M.5. 

Thesis, Virginia Tech. January 1987. 

II. B.D. Duncan, -Modal Interference Techmques for Strain Detection in 

Few-Mode Optical Fibers; M.S. Thesis, Virgirua Tech, April 1988. 

Rd'craca Il 
.. 

12. G.B. Hocker. -FIber OptiC Sensing of Pressure and Temperature; Applied 

Optics, vol. 18. no. 9, p.I~45. I ~..Iy 1979. 

13. CD. Butter and G B. Hocker. -Fiber OptiC Stram Gauge,- Applied OptICS, vol. 

17, no. 18, p.2S67, IS September 1978 

14. W.V. Sorin. B.Y. Kim and HJ. Shaw, -Highly Selective Evanescent ~odal 

Futer for Two·:\foded Optical Flbers,- OptiCS Lemrs, vo1.ll, no. 9, p.581, 

September 1986. 

IS. !\.S. Kapany and JJ. Butke. OpllCaJ Waveguides, Academic Press, l'ew York, 

1972. 

16. C~1. Muler, Optical Fiber Splices and Conneclors' Theory and Methods, :\farcel 

Dekker Inc., ~ew York, 1986. 

17. A.W. Snyder and J.D. lo\c. 0pllcal Waveguide Theory, Chapman and Hall, 

~ew York, 1983. 

18. I.S. Gradshteyn and I.W. RYZl:"', Tat'e of Integrals. Series and Products, 

Academic Press, ~ew York, 1965 

19. ~. Abramkositz and I. Stegum. ed .• Handbook of .\{alhemalicaJ Functions, 

DovCf PublIcations, Inc., ~e\\ York. 1972 . 

• 

, 
Vita 

Amy Flax was com on August 26, 1964 in Framingham, ~assachusetts. She graduated 

from Virgirua Tech in Junc. 1986 with a Bachelor of Science m Electrical Engineering. 

Amy decided to pursue g:aduate studies in electrical engineering at Virginia Tech, 

specializing in fiber optics. Durm: her stay at Virgirua Tech, she worked under Dr. R.O. 

Claus at the Fiber and Elec:ro-Optlcs Research Center. Amy enjoys theatre, travelling, 

aerobics, and Bruce Springsteen. Amy is going to be a world traveller this swruner as 

sbe crosses the Atlantic to e'\plore older civilizations and the night life in Paris. Then, 

after many yean ofbcing a student Amy will be gainfully employed with AT&T in New 

Jersey. 

• 

\£.J 
/ 

• 

Modal Interference Techniques for Sb':1ln Detection In Few-Mode Optical 

Fibers 

by 

Brac"ley Dean Duncan 

Thesis submitted to the Faculty of the 

Virginia Polytechnic Institute and State University 

In partial fulfillment of the requirements for the degree of 

Master of Science 

in 

Electrical Engineering 

APPROVED: 

Richard 0 Claus, Chairman 

Ahtnad Safaai:J'azi 

April 1988 

Blacksburg, Virginia 
....... \ ~-- .. --~'"t"--

• 

Modal Interference Techniques for Strain Detection in Few-Made Optical 

Fibers 

by 

Bradley Dean Duncan 

Richard 0 Claus. Chairman 

Electrical Engineering 

(ABSTRACT) 

Interference between the modes of an optical fiber results In specific intensity 

patterns which can be modulated as a function of disturbances In the optical 

fiber system These modulation effects are a direct result of the difference j •• 

propagation constants of the constituent modes. In this presentation It is 

shown how the modulated Intensity pattern:; created by the interference of 

specific mode groups In few-mode opt' ~I fibers (V < 5.0) can be used to 

detect strain. A detailed discussion of the modal phenomena responsible for 

the observed strain induced pattern mJdulatlOn is given and It is shown that 

strain detection sensitivities on the order vf 10- 9 can be expected. Data taken 

dUring the evaluation of an actual experimental strain detection system based 

on the developed theory IS also presented. 

• 
I 

~. 

~ Acknowledgements 

I would like to express my sincere gratitude to Or R.O. Claus. my graduate 

advisor. for his gUidance. assistance and patience. Special thanks goes to Or. 

A Safaal-Jazi for his encouragement and help In understanding the many 

subtle concepts of modal analysIs. Thanks also goes to Dr. R. Pieper for 

serving on my graduate Committee. 

I wish also to gratefully acknowledge Brian Brennan, Bill Spillman, Jeff Lord 

and the other members of the Advanced Development Organization of 

Simmonds Precision, Vergennes. VT, for providing me with the resources with 

which to carry out the experimental tests of the modal domain sensing 

.. concepts developed in this thesis and for making my brief stay In Vermont a . very pleasant one. 

Acknowledgements ill 
~-'-' ---------- \ 

Many thanks to my fellow graduate students at the Fiber & Electro-Optics 

Research Ce.,ter, Virginia Tech, for their advice, consultation and lasting 

friendship Thanks also to Robin Rogers for her assistance in prepanng the 

figures. And finally, sincere thanks to my parents and to my very dear fnend 

LUCie Pelletier for their unending support and encouragement. 

This work has been sponsored In part by Simmonds Precision ISO, Panton 

Road, Vergennes. VT 

Acknowledgements IV 
r 

Table of Contents 

1.0 INTRODUCTION •.• .• 

2 0 REVIEW OF BASIC FIBER OPTICS 

2 1 Optical Fiber Classification 

2 2 Lmearly Polanzed Modes 

2 3 Photodetectors 

2.4 The Photcelashc Errect 

3.0 MODAL DOMAIN SENSING 

3.1 The MOS/9-633 Sensor 

3 2 The MOS/9-850 Senso:-

. .. ........... .... . ....... 1 

4 

5 

6 

14 

20 

..•....••..........•...•••..•....•..• 34 

36 

49 

4.0 MDS19-633 SENSC~ EVALUATION •••••••••••.••••••••••••••••••••••.•••• 71 

4 1 Reslsbve Strain Gage Evaluation 

4 2 Dynamic Strain Measurements 

Table of Contents 

75 

78 

y 

ft-
~~- -, f -----~--~---

____ -_ --I 

4 3 Extraneous DynamiC Modulation 85 

44 Stallc Strain Measurements (First Attempt) 87 

.s 5 Static Strain Measurements (Second Attempt) 92 

5.0 CONCLUSION •..•..... ••.•.• ••••••.•.•••.•.••••••••••••••••.•••• 11cJ 

APPENDIX A: Strain Characteristics of Loaded Cantilever Beams 121 

A 1 Average Stram Induced In an Optical Fiber 123 

APPENDIX B: The Resistive Strain Gage 129 

B 1 Stram Gage Calibration 131 

B 2 The Use or Wheatstone Sndges to Measure ~R 134 

APPENDIX C: Bessel Function Numerical Expansions •..•••.•.••••••••••••••••• 141 

APPENDIX D: FORTRAN Programs •••••••..••.•.••• ••.••••••••••••••••••• 143 

References •.•.••••••••••.••••••••.••.•...•••••.••.•••••••••••••••••. 147 

Vita •..•.....•••...••••••.••.•••.. . .•..... ~ •••.•••••.••••.•.••...• 149 

.. 

Table of Contents vt 
~ ..... " .. " -

.. 

• 

, List of Illustrations 

, 

Figure Optical fiber geometry summary ... . . . . • ....... oo ... 25 

i Figure 2 Numencal aperture (NA) of an optical fiber [16] .......... . ... 26 

1 Figure 3. Bessel's function of the first kind for the first three orders [9) 27 

Figure 4. The normalized b versus V curves [9) ................... 28 

Figure 5 Intensity distribution of the LPg, mode . . ............ 29 

Figure 6. Intensity dlstnbullon of the LPn mode .......... .. .. .. .. .. .. .. .. .... .. 30 

Figure 7. Intensity distnbution of the LPn mode ......... .. ............... 31 

Figure 8. Intensity dlstnbution of the LP ~ mode ........... . ................. 32 

Figure 9. A simple photod""tector and its equivalent circuit [9] " 33 

Figure 10. A slmplist:: look at modal Interference ....... . ........ 58 

Figure 11. FOA-2000 fiber optic analyzer data .................... 59 

Figure 12. The MOS/9-633 background intenSity term ............... 60 

Figure 13. The MOS/9-633 strain modulated intensity term ........... 61 

Figure 14. The total MOS/9-633 output intensity dlstnbution .......... 62 

Figure 15. Axial view of the MOS/9-633 intenSity distribution ......... 63 

Figure 16 The LP., mode intenSity distribution of the MOS/9-850 sensor 64 

Ust of illustrations vii 
.. 

.. 

.. " 

, 

t 

l 

i 

L 

.. 

Figure 17. The LP" mode intensity distribution of the MOS/9-850 sensor 65 

Figure 18. The LPff mode intensity pattern ..... .............. 66 

Figure 19. MDS/9-850 intensity vanation of It(r) + Iz(r.«p). at quadrature 67 

Figure 20. IntenSity vanat,on of the MDS/9-850 cross term h(r.O.z}. at a 

maximum. . .................................... 68 

Figure 21. Total intenSity pattern of the MDS/9-850 output when h{r.";.z) is 

maximum... . ................................. 69 

Figure 22. The MDS/9-8S0 intensity dlstnbution at quadrature (3-D) .... 70 

Figure 23. experimental MDS/9-633 system 96 

Figure 24. First static strain control device ....................... 97 

Figure 25. Loading schemes of the experimental MOS/9-633 sensor system 98 

Figure 26. ReSistive stram gage calibration/evaluation data ...... 99 

Figure 27. Cantilever beam natural frequency of vibration .......... 100 

Figure 28. Highly aligned MDS/9-633 sensor output (see text for details) 101 

Figure 29. MDS/9-633 dynamiC strain measurement data (trial 1) 102 

Figure 30. MDS/9-633 dynamiC strain measurement data (tnal 2) 103 

Figure 31. MOS/9-633 and resistive strain gage outputs for small 

excitation ... .,. . .............. ...... ..... .. 104 

Figure 32. MDS/9-633 and resistive strain gage outputs for large 

excitation ....................................•... '05 

Figure 33. Input signal of the vibrat'on exciter .................. ' 106 

Figure 34. Noise floors of the MDS/9-633 and resistive strain gage 

sensors ......................................... 107 

Figure 35. MDS/9-633 dynamIC strain measurement data (lnaI3) ..... 108 

Ust of illustrations 

I 

-

r: 
FIgure 36. Extraneous dynamIc modulatIon 109 

Figure 37. ~raneous modulation sIgnals for large and moderate 

excitations .. . . . . . . . . . . . . . . . . . . . . . . . • . . . . . .. 110 

Figure 38. Extraneous dynamIc modulation signals for small beam 

excitation ........ .. ..... ...................... 111 

Figure 39 Extraneous dynamIc modulation nOIse floors ......... .. 112 

Figure 40. MDS/9-633 static strain measurements (first attempt: tnal 1) 113 

Figure 41 MDS/9-633 static strain measurements (first attempt. trial 2) 114 

Figure 42. RedeSIgned static strain control deVIce '" '" 115 

Figure 43. MDS/9-633 static strain measurements (second attempt; trial 1) 116 

Figure 44. MDS/9-633 static strain measurements (second attempt: trial 2) 117 

Figure 45 CantIlever beam geometry . . 127 

Figure 46 Optical fiber and resIstive strain gage placement parameters 128 

Figure 47. A resistive strain gage .. , ......................... 139 

Figure 48. A Wheatstone bridge circuit wIth amplifier .............. 140 

,. 

Ust of IlIustratJo ... ix 

t 
1.0 INTRODUCTION 

The past several years have given nse to many optical fiber sensing 

techniques which may be employed In systems to detect such physical 

observables as temperature. pressure, displacement and strain [1). As 

sensing devices, optical fibers are attractive In part due to their small size. 

flexibility, ruggedness and Intnns'c dielectric nature. In addition, their 

proclivity to be highly sensitive to external perturbations is quickly making 

optical fibers the sensing devices of choice for many passive non-intrusive 

sensor applications. 

Simply put. optical fiber sensors exploit tha effects of perturbations and 

• 

external factors on the light In the fiber. Si)tlCifically. the intensity. phase and 

polarization are among those properties of light which are available for 

alteration and the detection of these changes is the basis of most fiber optic 

, 0 INTRODucnON 

- --- ( 

, 

J 
a:L. '.~ V'--~ --- --" -------

" . ---- -------- - - --- -----

---~~---

sensors. Unparalleled in sensItivIty are the phase modulated sensors. a 

classic example of whIch IS the dual-fiber Mach-Zehnder interferometer [2]. 

Because It IS based on an absolute phase modulation scheme, however, such 

a sensor tends to be qUIte complex. with the reference phase and quadrature 

pomt often need 109 to be actively controlled. 

By comparison. sensor systems utilizing single-ftber modal interference 

schemes, such as those to be dIscussed in this thesis. essentaally have the two 

arms of the interferometer wlthm the same environment. This provides for a 

high common mode rejection capacity while affording the system the further 

advantages of SImpliCIty and Increased ruggedness. with no need for couplers. 

Though remaming highly senSitive, as Will be shown. some sensitivity Will be 

sacrificed 10 a Single-fiber interferometer, or modal domain sensor, due to the 

fact that the sensor mechanism Will now be based on differential phase 

modulation. 

PrevIous work with modal domain sensors has involved the detection of such 

observables as quasi-static stram [3,4], vibration [5], and acoustic emiSSion [6]. 

Often, though, this work was done without the prior benefit of a rigorous 

• theoretical basis for interpreting the sensor output. Also, no.effort as yet has 

been made to theoretically predict and experimentally verify the ultimate 

senSitivities achieveable with given modal domain sensor systems. Finally, 

1 0 INTRODUCTION 2 
~:.'~~ V~H ___ W .. ~.-

-=------------------

DC • , 

~---;.---.¥-.-------*~;". __ ~._.e~;~_~~_"_~ __ -_~ __ .. j¥~_.~~~~_ ' 

no attempt has yet been made to use anythmg but large discrete optical 

components in a modal domain sensor system design. This last pOint will, of 

course. limit the practicality of single-fiber modal Interference based systems. 

The obJectives of this thesIs are therefore several. First the theoretical 

considerations of the behaVior of the intensity patterns caused by the 

interference of speCific mode groups in few-mode optical fibers (V < 5 0) Will 

be thoroughly discussed and it Will be shown how these mtenslty patterns, 

when modulated as a function of strain, can be used as a sensor mechanism. 

Secondly. the ultimate sensitiVities achieveable with modal domain sensor 

systems Will be investigated both theoretacally and experimentally. And 

finally, a disCUSSion of how modal Interference techniques can be used in 

simple, practical sensor systems which avoid the use of large discrete optics 

will be presented. To begin. however. a bnef review o! several topiCS relevant 

to the understanding of fiber optics Will be presented. 

1.0INTRODUCllON 

. 

j 
JLLiN' sa p, '''z au c 0 a 

Q p ........ ; ~ --~ -- " 

j 

2.0 REVIEW OF BASIC FIBER OPTICS 

This chapter pnmarily consists of a senes of discussions of tOPICS relevant to 

the understandmg of basIc fiber OptiCS and IS meant as a review More 

detailed considerations of all topics may be obtamed from their respective 

references. Subjects te be add.-essed include linearly polarized (LP) modes 

in weakly guiding fibers. photodetectors and their associated noise factors and 

the photoelastic effect in optacal fibers under strain. We will begin. however. 

wIth a brief review of optical fiber classificatIon . 

• • 

2.0 REVIEW OF BASIC Fl8ER OPT1CS 
4U¥> eo a • ttC # S ")QAt:t jQ 

.~il ~~ ...... $§ WE'. Iii, 

±l"~~~~."' ________ _ C j 2.-'1 

2.1 Optical Fiber Classification 

Fibers used for optical communications and sensing are waveguides made of 

transparent dielectncs whose fundion IS to gUide visible and infrared light. A 

typical optical fiber consists of an Inner cylinder of glass, called the core, 

surrounded by a cyllndncal shell of slightly lower index of refraction called the 

cladding. Optical fibers may be classified In terms of the refractive index 

profile of the core and whether one mode (single-mode) or many modes 

(multimode) are allowed to propagate in the waveguIde. If the core has a 

Uniform Index of refraction n, II is called a step-index fiber. If the core has a 

nonuniform index of refrachon that gradually decreases from the center 

toward the core-cladding Interface the fiber is called a graded-index fiber. The 

cladding surrounding the core typically is of a uniform index of refraction nz, 

where 

(2.1.2) 

in a step-index fiber. This relation IS also approximately true for graded-index 

fibers where n, would then represent the index of refradion at the ce'1ler of the IS 

core. The parameter 6" is called the core-cladding mdex difference and 

nominally 6 $ 0 01. Figure 1 shows typical dimensions of commonly used 

optical fibers. And finally, as the chapters to follow will be dedicated to 

2.Q REVIEW OF BASIC FIBER OPT1CS 5 

/ 
0',,2 £ *ZOZ,) ".4& 04 

describing modal Interference as a sensor mechanism In step-index optical 

fibers we note here that a tYPical value of the core index In a step-index fiber 

IS nt :: 1.458 [7]. We now tum our attention to the gUided modes allowed to 

propagate In step-index optical fibers. 

2.2 Linearly Polarized A10des 

Put simply. a mode In an optical fiber waveguide (or any other waveguide) is 

an allowable field configuration. for a gIVen waveguide geometry, that satisfies 

Maxwell's equations {or the derived wave equations) and all the boundary 

conditions of the problem [7]. In an optical fiber a gUIded mode IS one in 

which electromagnetic energy JS earned al~ng the fiber axis only and whose 

transverse field components decay to zero in an approximately exponential 

manner at distances far from the core. For these modes the integral 

p - J IEI2 dx d" 

z=const 

(2.2.1) 

which is a mpasure of the power flow, is fimte. Also, at any given operatmg • 

frequency the number of guided mo~es IS finite wIth each mode being 

associated with a cutoff frequen.:y That is, for a guided mode to be allowed 

2.0 REVIEW OF BASIC FIBER OPTlCS 
*#~ a '.2.. e" US 3; ~! 1&( 4. a $ S_, 2 a 2D . I. t£ 4 & i '!IE 

!o exist. its cutoff must be less than the frequency of operation. It can further 

be shown that a mode Will remam gUided as long as its propagation constant 

fJ satisfies the condition 

(222) 

where In the case of the step-index fiber. as presently under consIderation, nf 

and nz are the Indicles of refraction of the core and cladding. respectively. and 

where ko = 2rr.1 ).0. with J.o being the free space source wavelength. Note, 

though, that in order for a guided mode to carry power along the fiber It must 

be excited by an external source. Indeed. smce modes are simply analytical 

solutions to the wave equations In a waveguide and represent allowed field 

configurations It is qUite posslb. ~ to have mode solutions of a fiber (or other 

waveguide) which do not carry power due to their not being externally excited 

[8]. A detailed discussion of selective mode excitation will not be given here, 

but it Will be seen later that the excitation of speCific mode groups In an optical 

fiber Will give nse to some very interesting sensor mechantsms. Recall, 

however, that for light entenng a fiber to excite a guided mode it must in 

general satiSfy the condition that It enters the core through an acceptance 

cone defined by the numencal -aperture, or NA, of the fiber. A physical 

Interpretation of a fiber NA is given in Figure 2 with the analytical value of NA 

given as 

2 0 REVIEW OF BASIC FIBER OPTlCS 7 
J 

i 

, 

t 

i-

• 

rIo 

I 

I 

NA (2.2.3) 

in a step-index optical fiber. This result IS derived from considering that light 

gUided In a fiber must satisfy the total internal reflection requirements at the 

core-cladding Interface according to Snell's law of refraction [9]. 

In practical optical fibers the refractive indices of the core and cladding are 

nearly equal With nf ~ nz an::i ~« 1 O. The condition ~« 1 0 is called 

the weak guidance conditIOn. and the corresponding optical fibers are called 

weakly gUiding fibers. The concept of weak gUidance is better appreciated if 

one notes that for .l = 0 the infinite clad optical fiber reduces to a 

homogeneous medium With no guidance properties. For ~« 1.0 but 

~ ~ 0 the guidance of energy is considered weak. However. this does not 

imply loose confinement of power to the core; at very high frequencies the 

energy can be tightly bound to the core, even in a weakly guiding fiber. 

Furthermore, the condition ~« 1.0 is mandated In both single-mode and 

multJmode fibers. In multi mode fibers tl« 1.0 is required for low 

inter-modal dispersion since the delay time between the lowest order and 

highest order modes is proportIonal to 6. In a SIngle mode fiber d « 1.0 Is 

necessary in order to have manageable core sizes. In addition, the weak 

• guidance condition leads to greatly Simplified modal expressicl's which are 

quite valid for short lengths of fiber, as is the case with typical fiber sensors. 

2.0 REVIEW OF BASIC FIBER OPT1CS 8 
, · ..... --

In a step-index. lossless and non-magnetic optical fiber that IS translatlonally 

invariant along the aXial dIrection. the gUided mode solutions can be 

summarized In phasor form as follows' 

e(rq» 

rcos({Q)l rall') 

= A J~(Urla)'l > 't , J\ sln(t9d lay r<a (22.4) 

h(r.C» _. - Y,(e(r, ¢) x .1z) 

and 

elrol 

r>a. 12 2 5) 

where there IS an implied multiplicative factor of e-t!Pl-wl. which represents ttphase of the mode and where t = 0.1 2 ... with r. 6. and z being the 

cylindrical coordinates representatIve of the fIber geometry Also. J/(x) IS the 

Bessel function of the first kind. order t, and Ki(x) IS the modified Bessel 

function of the second kind, order t JAx) is plotted for orders 0.1 and 2 in 

Figure 3 The a.nplitude coefficIent A is determined by the source input 

condItions and is assumed to absorb any signs (plus or ",-ninus) at present, 

• whIle y, and Y2 are the charactenstic admIttances of the core and claddmg, 

respectively. In addition. the parameters U and Ware given by 

2.0 REVIEW OF BASIC FIBER OPTICS 9 
(2 2 6) 

(2.2.7) 

where ~a' IS the fiber core radius and ~ = fJlka, with J1 beJng the modal 

propagation constant [8) 

Notice in equatIOns (22.4) and (22.5) that the electric fields are either x or y 

directed Since polarization IS defined by the direction of the electnc field, the 

modes desCribed by equations (22 4) and (2 2.5) are linearly polarized and are 

thus called linearly polarized or LP modes The bracketed quantities In 

equations (2 2.4) and (2 2.5) ma:' be taken as multiplicative factors In any 

combinatIOn with the only stipulation being that the magnetic field vectors be 

orthogonally Oriented with respect to the electric field vectors. Modes 

containing the cos(l ¢) multiplicative factor are called even modes while 

modes containmg the sin\t ci» multiplicative factor are called odd modes. For 

all cases except when t = 0 the modes have a degeneracy of four (Le .. even, 

x-polarized; even, y-polarized; odd, x-polarized and odd, y-polarized). When 

t = 0 it is obvious that LP modes are independent of cP and therefore t'lave 

., 

a degeneracy of two (I e., x-polanzed and y-polarized) [8]. 

2.0 REVIEW OF BASIC FIBER OPTICS 10 
__ 4. ___ ~ _____ _ 

The propagation constants Jl for LP modes are found by solving the following 

characteristic equation. the solutions of which are plotted In Figure 4 [9.10] 

JAU) KAW} ------ + --'--- = o. t = 0.12, ... UJc'_I(U) WKI _ 1lW) (2.2.8) 

Note that the solutions to this characteristic equation actually appear as 

functions of P vs C:J. where co IS related to the source wavelength i.o by 

wi.o = 2:rc. with c being the speed of light In free space. The solutions are. 

however. plotted In Figure 4 In the normalized form of b versus V where b IS 

the normalized propagation constant given by 

l2.2 9) 

The normalized frequency V is given in terms of the source wavelength and 

fiber parameters by 

(2.2.10) 

Note also that there are multiple solutions to the characteristic equation for 

each value of t. Therefore, specific LP modes are typically labeled LPI~' where 

the propagatIon constant for the LPIM mode IS the mIll solution for P. at a given 

frequency (or source wavelength). when the prinCipal mode number l takes a 

particular value. For example. the LPu mode is the mode whose propagation 

2.0 REVIEW OF BASIC FIBER opncs 
~ -'-~ - -----------

.. 

, 

-

.. " 

r 

f 

! -

constant P IS found fr~m the third solution to the characteristic equation when 

{ = 2 [8] . 

GUided mode cutoff occurs when b = 0 and as can be seen In Figure 4, a fiber 

IS operated In a single-mode regime when V ~ 2 405. As V increases (by 

decreasing the source wavelength ;'0 or by Increasing the core radius a) more 

and more modes are allowed to propagate In a fiber until the fiber enters the 

mUlti mode operating regime Stnctly speaking a fiber is a multi mode fiber If 

more than one mode is allowed to propagate. PractIcally, though. multi mode 

fibers are taken as those fibers with extremely high V values, typically in 

excess ot V = 50 To achieve these high V values the core radII are usually 

made very large In multlmode fibers. thus makmg the fiber multlmode for a 

wide range of source wavelengths. By comparison. single-mode fibers 

typically have very small core radii. For example. a fiber intended for single 

mode operation at a nominal source wavelength of 1300 nm Will have a core 

radius of approximately 4.5 J,lm (see again Figure 1). Using these values in 

equation (2.2.10). with n, = 1 458. we can solve for 1:\ to find ~::::: 0 003. It is 

therefore obvious that. as mentioned earlier. 0 must be much less than unity 

for slngle-moae fibers to have manageaoie core sizes . 

.. 

Of Interest m the study of modal domain sensing techniques are those fibers 

which allow the propagation of only a few modes. Such fibers Will often be 

2.0 REVIEW OF BASIC FIBER OPTICS 12 
- . -----------

called few-mode fIbers. typically with V < 5. and are of interest since It is much 

simpler to study and characterize the interference of a few modes than It IS the 

many modes In a true multimode optical fiber. Recall that modal domain 

sensors are essentially self-referenced interferometers which exploit modal 

Interference as the baSIS for a sensor mechanism. Few-mode fibers are also 

attractive for use In modal domain sensors since. as in all fiber optic sensors. 

the sensor data Will be collected by mOnltonng the modulated intenSity 

dlstnbution at the fiber/sensor output. These intenSity distributions (or 

patterns) at the output of modal domain sensors are created due to the 

interference of the gUided modes in the fibpr and are modulated as a function 

of the environmental disturbances bemg detected. For modal domain sensors 

uSing few-mode fibers these output intensity patterns are often q~alitatively 

Simple and well behaved as a function of disturbance and therefore give rise 

to Simple sensor systems. 

One can cause a fiber to be few-moded by Simply injecting into a single-mode 

fiber light of a shorter wavelength than that typically injected for single mode 

operation. For example. It will later be shown that a 45 p.m core radius fiber. 

usually intended for Single-mode operation at ;'0 = 1300 nm. will have 

V = 4.616 when the source wavelength is reduced to ).0 = 633 nm. as With 

" He-Ne gas laser inJection. We can thus see from Figure 4 that cdy the LPo •• 

LPn. LPzf and LPoz modes and their degeneracies will be allowed to 

2 0 REVIEW OF BASIC FIBER OPTlCS 13 
~ '~-=~------- ---- -- ------------ -------

propagate. Such a fiber is easily seen to be few-moded. Plots of the intensity 

distributions of the LPo., LP", LP2f and LPoz modes can be found in Figures 

5-8, respectively. These and other similar plots to be addressed later were 

created using the numerical expansions for Jo(x) and J.(x) given in Appendix C 

and the FORTRAN programs given in Appendix D. It should be mentioned that 

the x and y values of Figures 5-8 are given In microns and that these figures 

are valid only for r = " X2 ..... y2 ~ 4 5 um, as these plots were created 

consldenng only the modal solutions In the core for the case of 633 nm hght 

injection into a 4.5 urn radius fiber, as discussed above. The intenSity beyond 

r = 4 5 pm decays approximately exponentially Finally, it should also be 

mentioned that in Figures 5-8 no Interference has been considered and that 

the amplitudes of the modal Intensity distributions are quite arbitrary with only 

the general pattern shape being of any importance-at present. 

2.3 Photodetectors 

Oata is collected from a fiber optic sensor by monitoring the modulated 

intensity distnbution at the sensor output. Typically this monitOring is 

achieved through the use of a photodetection circuit. Such a photodetection 

CircUit is shown in Figure 9 with its equivalent CirCUIt. It is seen that the 

2.0 REVIEW OF BASIC FlBER OPTICS 14 
=., . ------

photodiode IS modeled by a series bulk resistance Rs and a total capacitance 

C~ consisting of junction and packaging capacitances. A bias (or load) 

resistance IS given by RL and the amplifier following the photodiode has an 

input capacitance C. and a shunt resistance R.. In a practical CircUit, however, 

Rs IS much smaller than R~ and can be neglected. Also, C~ is usually small and 

only affects the high frequency response (rise time) of the photodetectlon 

circuit Thus. for low frequency input signals, such as those created at the 

output of the modal domain sensors to be discussed later, the capacitance Cit 

is seen essentially as an open circuIt. Furthermore. for the present discussion 

It will be assumed that the amplifier is used as a high Impedence buffer with 

unity gain. as would be the case at the mput to an oscilloscope, for instance. 

For low frequency or DC Signals the photodetection circuit is therefore seen to 

reduce q.Jite simply to a photo diode in parallel wlth-a load resistance [9]. 

Optical power incident on the photodlode is converted into a photocurrent 

when the excess electron-hole pairs created by the Incident light are swept out 

of the photodiode depletion region by the fields created by the high reverse 

bias voltage ( - 10 V for pin photodiodes). The photocurrent is related to the 

incident optical power Po by the relation .. 

(2.3.1) 

2 0 REVIEW OF BASIC FIBER OPTICS 15 
where ~ is called the responslvlty of the photodlode and has the Units of amps 

per watt. &l is given In turn by the expression 

(2.3.2) 

where hll IS the energy of the incident photon, q is the electrOniC charge and 

71 is the photodlode quantum effiCiency which relates the number of 

electron-hole pairs created to the number of incident photons. For Silicon 

photodiodes a nominal value of responslVlty IS .-i=O.5 AlW for common 

detection wavelengths [9] The photocurrent thus created causes a voltage 

across the load resistor given by 

(2.3.3) 

ThiS is the quantity tYPically recorded when using ~iillple photodetectlOn 

Circuits and the measured quantity Vo is easily converted to a measure of 

incident optical power If the load ieslstance RL and the responsivily ;i at the 

detection wavelength are known If we now consider that the incident optical 

power Po consists of an average or quadrature pOint component Po and a 

signal component 6P such that Po = Po + 6P we see that the electncal signal 

power c.-eated by the sIgnal component of the incIdent optical power is given 

by 

20 REVIEW OF BASIC F1BE~ OPTICS 11 
:......w .~'~~', -- -" - .... -.. - ;F..'-__ _ _ __ --- ~-- - -~:-:r. 

- -- --- - ~ 

(2.3.4) 

The pnnclpal nOIses associated wIth photodetectors are quantum or shot 

nOise. dark-current noise generated in the bulk matenal of the photodiode, and 

the surface leakage current nOIse. For small and well packaged photodiodes. 

however. the surface leakage current nOIse is small and can be neglected. The 

shot nOise anses from the statistical nature of the production and collection 

of photoelectrons when an optical signal is mCldent on a photodetector and 

sets a fundamental lower limit on receiver sensItivity when all other 

conditions are optimum The RMS shot nOIse power IS given as 

(2.3.5) 

where B is the detection bandwidth and 10 is the average photocurrent given 

as 10 = !lPo where Po can be measured with no signal applied. 

The photodiode dark current IS the current that continues to flow when no light 

IS mCldent on the photodlode. This IS in general a combmation of bulk and 

surface currents. However. the bulk dark current is usually dominant and 

arises from the electron-hole pairs which are thermally generated in the pn 

junction of the photodlode. The RMS bulk d~rk current noise is given as . 

(2.3.6) 

2 0 REVIEW OF BASIC FIBER OPTICS 17 
· . 

where I:> is the primary detector bulk dark current and can be found for 

specific photodlodes In various vendor catalogs [9]. 

In addition to the detector noise factors just discussed the photodetector load 

resistor contributes an :1MS thermal (Johnson) nOise power given as 

Pj = 4ksTB • (2.3.7) 

where k, IS Soltzman's constant and T is the absolute temperature. This noise 

can be reduced by cooling the detection circUit [9]. 

The power slgnal-to-nolse ratIo SIN at the output of an optical receiver IS now 

eaSily seen to be 

P SIN = ES 

PSN + Poe + Pr . (2.3 C 

or 

(.2~)2 

SIN = 4k

s

TB 

2qB(~Po + 10 ) + R 

L 

(2.3.9) 

Of special interest is the case when SIN goes to UOlty. At this point the signal 

power just equals the nOise power and enables one to determine the minimum 

2.0 REVIEW OF BASIC FlBER OPTICS 18 
detectable optical signal j,P 'fun. When only photodelector and load resistor 

noise factors are accounted for. we find that 

1 l aka TB )'12 j,pmln = ;:A \ 4qB(SlPQ + 10 ) + RL (2.3.10) 

and in the shot noise limited case we find that 

(2.3.11) 

where a factor of 2 has been included In the noise power terms of equations 

(23.10) and (23 11) due to the fact that at the operatmg point the incident 

optical power is uncertain to within ± (shot nOise and/or thermal nOIse). 

Note that this analysIs has been for pin photodiodes only and that the shot 

noise limit of detection is practically unrealizable. In addition. if one must 

operate a photodetection circuit at elevated temperatures or if It is impractical 

to use a large load resistor. which would reduce the thermal nOIse component 

of equation (2.3.1 r\, one may have to resort to the use of an avalanche 

photodiode (or APe). An APe will also give a sharper system rise time for 

detection of high frequency signals but should not be used unless thermal 

noise is excessive This IS due to the generation of excess shot noise during 

• 

the avalanche process in APe's. At reasonable temperatures and for • 

reasonable values of R:. the signal-to-noise raho will be reduced by using an 

2 0 REVIEW OF BASIC FIBER OPTICS 19 

[ . 
APD. Finally, It should be mentioned that It has been assumed 10 the prevIous 

discussIons that noise factors ansing from sources other than the photodlOde 

or its load resIstor are negligIble. ThIs IS reasonable only in a laboratory or 

other situation where environmental factors can be controlled We now tum 

our attentIon to a diSCUSSIon of the photoelastlc effect in optical fibers under 

strain 

2.4 The Photoelastic Effect 

Recall that the phase of a mode is glven by ¢ = pz - '" where r/I is a random 

phase term. Since the modal domain sensors to be discussed in the next 

chapter will derive their output from a differential modal phase modulation 

(i e., modal Interference) as a function of stram, It is important to dIscuss how 

the phase of a mode changes as a function of fiber strain. 

As a fiber is strained three principal factors act to change the modal phase. 

First. the fiber length changes. Second. the index of refraction changes due 

• a 

to the photoelastic effect and finally, the fiber dIameter reduces. The change 

in phase due to these effects IS thus 

z.o rtEVIEW OF BASIC FIBER OPT1CS 20 
l~r·, 

= -' .lz CZ 

(2.4.1) 

where the effect of the change In fiber diameter IS considered negligible and 

where cjJ/cn, = Pin, [1] Also from [1], for low order modes. we have 

(2.42) 

where t: is the aXial strain \ IS POisson s ratio. n, is the Index of the core and 

p" and P'2 are the photoelastlc constants. Reasonable values of these unlUess 

constants are given for silica as follows [4]' 

\' = 017 

P11 = 0.12 

PI2 = 0.27 

n1 = lA58 

By substituting eql'3tion (2 LI 2) Into equation (2.4 1) and rearranging terms we 

find that 

2 0 REVIEW Of BASIC FIBER OPTlCS 21 

.. 
• .. 

.. 

, 

, 

.. 

~ 

.. 

L 

~I;> = P 6z {:x} • (2.4 3) 

where the relation z x t~ = ~ has been used. Using the constants given 

above we see that a = 0.78. Although this IS a reasonable value of ~. the true 

value may change from fiber to fiber Expenmentally determined values have 

been found as large as :x = 0.92. as will be seen later. In any case. though. 

it is clear that due to the photoelastlc effect a fiber under strain will see a 

Significant reduction of the core Index of refraction and therefore a Significant 

reduction In the effective optical pathlength of the modes In the fiber. Th._ 

results in a change in modal phase In a fiber under stram which is less than 

that expected If the fiber Simply undergoes pure-elongatIOn 

When a fiber supports more than cne mode It IS also important to Investigate 

how the differential phase of the modes is influenced by stram. Consider two 

modes With phases ¢, = p,Z - 1/1, and (!)% = P::z - 1/2' respectively. The 

differential phase is given as 

(2.4.4) 

We may now consider that tP12 = cPo + tlifJ12. where ~o IS the mitial differential 

phase of the modes In a no strain situation and where tlcP12 is the differential 

phase change induced as the fiber is strained. In an exactly analogous . manner that was used to prove the result of equation (2.4.3) we cail show that 

2.Q REVIEW OF BASIC FIBER OPTICS 22 

t_:' ___ "'--.. -' _ -

.. 
-

4 

,. 

.. 

-- -------~ ----" 

(245) 

so that 

(246) 

where £)., =..lz and L, is the gage length of. say. a fiber optiC sensor. Note 

also that «po = -uti. As will be eVident In the next chapter the relationshlD 

given In equation (246) IS extremely Important In the study of fiber optiC straIn 

sensors. 

One last comment should be made before concluding this discussion That is. 

note that In the prevIous analyses It has been assumed that the amplitudes of 

the modes in a fiber under strain remain constant and that only the modal 

phase is Influenced as strain IS varied. This is not exactly the case since the 

amplitude of a mode IS a function of U = koa,J n; - /32 • in the core region. and 

both n, and Ii are functions of stram. However. only very large amounts of 

stram vary n, or jj appreciably so that U Will essentially remam constant With 

stram. For instance. 

(2.4.7) 

.. usmg the prevIous calculation for .M in equation (2.~ 2) It IS thus seen that for 

strains even on the order of one percent (which is near the breaking point of 

2.0 REVIEW OF BASIC FIBER OPTICS 23 

-
.J:_-

most fibers) n, remains nearly constant. A Similar result can be obtained for 

~ as a functton of strain. making the assumption of constant field amplitudes 

qUite valid. 

» 

2.0 REVIEW OF BASIC FIBER OPTICS 24 

.. 
, 

t: 

• 

INDEX 

p~L-e LONCltTllDlt-JAL 5EC.TtON 

1 T 

'<'b 2.0 

1 1 

-t..J 

MULllMODc STEP INDE.X 

hI 

lSI 1 

I - ~ 

MUL.TlMODE. ClAAD~D INDe.X. 

i 

.tb 

SINGLE MODE; S-rE.P INDEX 

Figure 1. Optlul nb4r geometry summary 

2.0 REVIEW OF BASIC FIBER OPTICS 

DIMENSIONS 

• 

;t a = ,C'X:J.uZb :- ,qO..v--

~o = SO,.u..("Z'5jA-) 

;tb : 12.5,.u.. 

~o· 9~('500rwn) 

Zb :: 1~5"v25 
,- -- ... 

• 

FIgure 2. Numerical aperture (HA) of an optical fib., (16) 

2 0 REVIEW OF BASIC FIBER OPT1CS 26 

, 
-"---' - \: 

0.6 

0.4 

~ 0.1 .. ~ 

0 

-0.2 

-04 

-0.6 

.. 

FIgure 3. ae_r. functIon of the first kind for the first three orden [9J 

2.0 REVIEW OF BASIC FlBER OPnCS 21 

I 

-. 
• 

-0.6 

FIgure 3. BeaRr, function of the rltst kind for the first three orden [91 

2.0 REVIEW OF BASIC FIBER OPTICS 27 

.. 

4 
f ~ --- -·--~t~ 

1.0----.....----...,...---.-----....------...,...-----

-... 

I:." 

l 

0.8 

~ 0.6 ~ 

-.... 

c: 

I 

2 .. 

• 

FI!iure~. The normalized b versus V cun •• (9) 

2.0 REVIEW OF BASIC FIBER OPTlCS 

6 

V 

8 

28 
~ _ ..c. ... -. ~-

..,.-.--- - -- -

Z 

I 

\ •• ..J_ 

R9"" s. 'ntenSItY distributIOn of the LP .., ",ode 

2.0 REVlEW Of BASle fl8ER OP1lCS 
4 

.. 

• 

• 

-- -~ 

z 

I.: ~ 

ORIGINAL PAGE IS 

OF POOR QUALITY; 

FIgure S. IntenSity dlstrlbutlon of the LP" modo 

2.0 REVIEW OF BASIC FIBER OPTICS 

• 

30 

-. 
.. 

z 

1. S -

I 1 .. 0 .. 

2 _ 

T 

Figure 7. Intensity dlstnbutlon 0' the U' n mode 

2.Q REVIEW OF BASIC FIBER OPTICS 

x 

-1. s: 

i:: -oj. 50 

-II._C 

---- ~~. 

31 
. 

""""-'- .'~-:--:-;: -- ----~-- ------

• 

-.. ": ... 

• 

ORIGINAI.; PAGE IS 

OE P.OOR QU"ALlTY 

FIgure S. Intensity distribution or the LPOI mode 

2.0 REVIEW CF BASIC FlBER OPTICS 32 
.' 

.... 

81A5 VOL.TA<::aE 

nv PwoTODIOOe. 

-. 

(a) 

• 

Figure 9. A simple photod~t.ctor .nd It!! equ,ulent cJrcUlt (9] 

2.0 REVIEW OF BASIC FIBER omcs 

-. 

33 
3.0 MODAL DOMAIN SENSiNG 

Modal domain sensing IS a fiber optiC sensing technique ~ased on the 

differential phase modulation occurlng as a function of disturbance between 

the Interfering gUided modes of an optical fiber As we know, specific mode 

groups will propagate In a fiber and interfere to cause characteristic intensity 

distributions, or patterns, at the fiber output. as is shown in a very simple 

fashion In Figure 10. When the fiber IS subjected to a disturbance. these 

intensity patlerns are modulated as a direct function of the external 

disturbance and by mOnltorrng this pattern modulation, often by uSing simple 

spatial filters, one can obtain Information about the disturbance. 

. . Strlctly spealung, any sensor based on the Intt:rlere,lce of modes In an ooheal. 

fiber can be called a "modal domain sensor. ~ However, of special interest are 

those sensors based on modal Interference In few-mode optical fibers with 

J.O MODAL OOIl.\JN SENSING J4 

.. 
v < 5 O. Such sensors are qualitatively simple in that since only a few modes 

are allowed to propagate It IS possible to obtain Simple. closed form solutions 

for the modulated output patterns which may manifest themselves. This IS 

obviously an advantage when one wishes to design a predictable sensor. As 

a result. only modal domain sensors utrllzing few-mode fibers Will be 

discussed In the remainder of this chapter 

Specifically. this chapter Will be dedicated to descnbmg the electromagnetic 

basIs of the observed Intensity pattern modulation, as a function of aXial strain, 

of modal domain sensors uSing gum core diameter fiber at source 

wavelengths of 633 nm and 850 nm For SimpliCity we Will use the notation 

MDS/9-633 and MDS/9-850 to describe these modal domain sensors at the 

source wavelengths of 633 nm and 850 nm, respectively. Also, note that 

although only axial strain considerations Will be described here, modal 

domain sensors are not limited to measuring only aXial strain. AXial strain IS 

simply one of the most fundamental disturbances to which a fiber can be 

subjected and a detailed analysIs of how aXial strain affects an optical fiber 

sensor will proVide the basis for designing sensors to measure other 

disturbances. For instance, if a senSing length of fiber is embedded in a 

material with known thermal expansion characteristics, a thermal sensor 

based on modal Interference could be deSigned since the thermal expansion 

• of the material c::Jn be related to Induced axial strain in the embedded fiber 3 

3.0 MODAL DOMAIN SENSING 33 
sensor Sensors designed to detect many other environmental Influences are 

also possible We now proceed to a deta.led d.scuss.on of the MDS/9-633 

sensor. 

3.1 The MDS19-633 Sensor 

It has been observed that when 633 nm light from a He-Ne gas laser is Injected 

Into a 9 .urn core d.ameter fiber a symmetric three lobe pattern can be created 

at the output which exhibits pure rotation when the f.ber IS subJected to aXial 

stram Using a Photon Kinetics FOA-2000 f.ber optic analyzer, the second 

mode cutoff for the above mentioned fiber, which is designed for single-mode 

operation at 1300 nm, has been determined to be 1215 nm (i.e., V = 2.405 at 

;.0 = 1215 nm). Also. th.s fiber has a measured numerical aperture of NA = 0.1 

(refer to F.gure 11 for plots of the data generated by the FOA-2000 Unit) At a 

source wavelength of 633 nm thiS fiber IS eas.ly seen to have a normalized 

frequency of 

v = 2.405 1215 nm _ 4.616 

.633 nm 

ThiS allows the propagat.on of the LP01, LPn, LPz, and LPoz modes and their 

degeneracies, as discussed in section 22. However. as the three lobe pattern 

3 0 MODAL DC~IN SENSING 36 

- -- ~ .. -, -~_ .. ~ ... - _ .. ""- -

f 
under discussion exhibits a central null. It IS eVident from Figures 5 and 8 that 

the LPOf and LP02 must not be excited In the fiber for the three lob..! pattern to 

be created. If we further require that our source emits polanzed light. say 

x-polanzed. we are left With only four modes which may interfere to cause the 

rotatrng three lobe pattern of Interest. Specifically. these modes are the 

x-polan zed odd LP". even LP ... odd LPzI and even LPZf me-des and it can be 

shown that with a proper choice of amplitude coeffiCients. determined in reality 

by the launch conditions of the fiber. that these modes do interfere to cause 

the observed three lobe pattern and Its well defined rotational behaVior [11]. 

From equation l2 2 4} we see that the electnc fields in the ("ore of the above 

mentioned modes are given as 

E'r, = A~J,(Ullr/a)COs¢e-J(PI1Z-v~')ax 

Efl = Af J ,(Ullr/a)sm<;> e-I(P"Z-'''~') air 

E'~, = A; J2( U21 r! a) cos20 e -lIP: Z - V~') ax 

Eg, = A~ J~lU21r/a) sm2¢> e-J1P:.z - '''~') ax 

(3 1 1) 

Since the sensor behavior can be completely descnbed by investigating only 

the interference of the mode solutions in the core. no further considerataon Will 

be given to the modal solutions for r ~ a. 

The intensity pattern present at the fiber output IS found from 

3 0 MOD ".L DOMAIN SENSING 37 

~--"'- ~-- - --

f 
- - -- - - -, --. ---.. 

1 - 2 

= "2 y,IExl . (3.12) 

where 

(3.1.3) 

and Y, IS the characteristic admIttance of the core region 

We now assume that the amplitude coefficients are real and that 

A~ = Af = A, and A~ = Af = A2 wIth the further assumption that the odd 

terms of equation \3 1 11 are 9C" out of phase wIth relation to their respective 

even terms. so that 

.0 . ~ 

+ 900 1/1 11 ~ 900 

t;I'1 = 1,1,1 = 

and 

0 f!,~, 900 - 900 

t:l21 = - = v21 

Adding the even and odd terms of the LP" mode. it is easy to see that 

,. 

or 

30 MODAL DOMAIN SENSING 3. 

I 

'""::---~-- ,,- -- -
I 

• 

(Ee E~ ) A J ( U"r) -jIPIIZ - VII - ¢\ 11 + 11 = 1 1 a (; . (3 1 4) 

Similarly. adding the even and odd terms of the LPlf mode it IS seen that 

(Ee EO ) J ( u2,r) -111121 - 1~21 + 2¢) 21 + 21 = .... 2 2 -a- e (3 1 5) 

With these last two results In mind we now find the output intensity distnbutlon 

usmg equations (3.12, and (3 1 3). The result is 

(3.1.6' 

where ~p = PIt - P21 , tll/l = V" - 1/1 21 and 10 = Y.j2. 

It should be eVident that the intens'ty distributIOn of equation (3.1.6) results In 

a pattern consisting of three equal lobes displaced azimuthally by 1200. It 

should also be evident that this pattern rotates as the modes propagate 

through the fiber. The first two terms of equation (3.1 6) are Simply 

background intenSity terms and are constant. The sum of these two terms is 

plotted in Figure 12. where It is assumEd that At=Az=1.0 and ';'Ihere the x 

and y values are ,::"'ven in microns The third term of equation (3.1.6) is the 

3.0 MODAL DOMAIN SEN:ilNG 39 

.. - -.-... • 
- -----------.-....... 

term which gives rrse to the pattern shape and rotational behavIor as the 

modes advance In the z-dlrectlon and IS plotted In FIgure 13. The entIre 

intensIty distnbutlon of equatron (3 1.6) IS plotted in Figure 14. As wIth Figure 

12. Figures 13 and 14 are plotted assumIng At=A2=1.0, wIth the x and y 

values being given In mIcrons. The choIce of A, and A2 was made after 

evaluating several plots of equation (3 1 6), with the amplitude coeffIcIents 

taken as parameters For A, =::: Az It was seen that there were approximate 

radial intensity nulls In the calculated intenSity distrubution, displaced by 120°, 

whIch agree very closely with expenmental observations. In additIon, the 

plots In Figures 12-14 ar~ valid only for the core region of the fIber (I.e., the 

plots are valid only for r = " x~ ..... y. :S 4 5 pm) and were plotted uSing the 

Bessel function mumerical expansions given In Appendix C and the FORTRAN 

programs of Appendix D. Notrce also that for At = AJ. the amplitudes ot [. 

plots of Figures 13 and 14 are approximately equal in the radial regIon where 

the plotted functions are maximum. indicating that for this region In equation 

(3.1.6) 

(3.1.7) 

USing thIS result we can sImplify equation (3.l.6) at the radIal position where 

the function goes through a maximum to find 

3 0 MODAL DOMAIN SENSING 40 

• 
· -- ---,-~ 

I = l'o~l + cos(.lpz - ilv - 3c,.J,J 

I 2(/ Mlz - .11/1 - 3(."> ) = p cos 2 ' , (3.1.8) 

where 1'0 has Incorporated Into It the terms of equatIon (3 1.7) after they are 

factored from equation (3.1 6) In addItion to obtain the result of equation 

(3 1 8), the trigonometric Identity 1 .... cos(2x) = 2 cos:(x) has !Jeen used, wIth 

the peak lobe intensity I" taken as I" = 21'0 Now let us discuss how this 

rotating three lobe pattern can be used to detect axial strain. 

If we observe the three lobe pattern as It emerges from the end face of the 

fiber. we will see an intensity distribution similar to that shown in Figure 15(a). 

If we then Increase the optical path length of the fiber by inducing an axial· 

strain, we wIll observe a pattern rotation. Due to the cosine squared nature 

of this pattern alopg the cIrcular path whIch contains the lobe peaks. as given 

In equation (3 1.8) and as shown In FIgures 15(a) and 15(b). It is seen that the 

most sensitive and linear poslhon for mOnitoring the pattern rotation for the 

detection of axial strain is along thIs path at a poslflon where the intensify is 

half that of the intensity of a lobe peak. as shown in Figure 15(b). In other 

words, If in a no strain situation we choose a fixed quadrature point in -$pace 

to mOnitor Or'! the three lobe pattern that both has an intensity of exactly half 

that of the peak intensIty and is located on the circular path that contains the 

3.0 MODAL DOMAIN SENSIN':; 

I 

(+ 

.. -
• __ ~.!. r ~,.. - ~ -- .... -

lobe peaks. then for small mcreases m stram the mtenslty at this pomt Will 

mcrease or decrease. as the patterns rotates, in direct proportion to the 

mcrease In stram. 

If we define the aZimuthal coord mate v to take on the value ¢ = 0 at our 

quadrature pomt. then equation (3 1 8) becomes 

= I" ccs:!( ~Ilz - ~0 ) 

\ 2 (3 1 9) 

By now noticmg that tre ~/Jz - ~t!J term m equation (3 1 9) represents an 

ensemble differential phase of the maces contrlbutmg to the rotatmg three 

lobe pattern. we can use ar~uments analogous to those used to prove the 

result of equation (2.4 6) so that the phctoelastlc effects may be tncluded In 

equation (3.1 9). as the fiber IS strained. to give 

(3 1 10) 

where t z is the axial stram. L, is the gage length of the fiber sensor, :l is a 

constant less than unity that arises due to photoelastic effects and <Po is the " 

ensemble differential phase of the modes 10 a no strain situation. If we now 

choose the quadrature pomt. or Q-pomt. such that the intenSity at this pOint 

3.0 MODAL DOMAIN SENSING 42 
- -. - -~ 

Increases with stram from an unstramed value of 1=1.:/2. we must requir~ 

that tPo = - ::/2 so thQt at the O-pomt 

_ .2!..) 4 . (31.11) 

In practice however. once the quadrature pomt has been set It will often be 

of more use to measure the change In mtenslty from the O-pomt as a function 

of strain. This IS found simply to be 

(3 1 12) 

where 10 = I~/2. Note that this result was obtamed from an assumed no stram 

initial condition: however, It IS stili valid If the quadrature point is set with the 

fiber mltlally under stram. This is useful m a practical situation so that :: ilt~ 

can be detected. Also note that this result IS valid only for small changes in 

aXial strain and that for small I ~tz I, the function ..\I(~l:z) is Imear 

Some other observations should be made at this POint. First of all. since the 

response ill(~cz) is linear. we can use the same sensor arrangem'ent to 

measure static sh~un or small amplitude smusoldal strain. where ; 

(3.1 13) 

3 0 MODAL DOMAIN SENSING 43 

t 
---- --~ --- ---.,' - .... --1 ~ 

If 

: 

I 

If .lE::I!"_ is the amplitude of the sinusoidal aXial strain. ThiS result \~ III also hold 

for small amplitude vibrational strain such as would be caused If a fiber was 

bonded to a vibrating structure. -Small amplitude vibrational strain' IS meant 

to Indicate that the peak deflection of the vibrating structure is such that the 

fiber is tensIOned without being appreciably bent. Second, since for small 

amplitude sinusoidal perturbations In the fiber the resulting change In intensity 

IS also sinusoidal at the same frequency, the sensor has obVIOUS uses as a 

vibration sensor. And finally. It should be noted that in an actual sensor 

arrangement. a detection CirCUit will be used to convert intensity to voltage. 

If a small spatially filtering pinhole IS placed between the fiber end face and 

the photcdetector to monrtor the intensity pattern at the O-POlnt thiS voltage 

,YIII be directly related to the area of the spatial filter. the responslvlty of the 

photodetector and the load resistance of the detection cirCUit such that 

or 

(31.14) 

for the case of static strain In the fibPr and ., 

l.O MODAL DOMAIN SENSING 

..I 

, .-
kW , .. - --~. __ _ 

or 

---.--... -------~~--.------ ~..:- ""!'---~~- ..... .,.I~ 

~Vpeak COS(wt) 

VQ (tlP Lf a) (3 1.15) 

for the case of small amplitude tJ.-,e harmonrc strain and small peak 

displacement vibrational strain. Note thal in equations (3.1.14) and (3.1.15) the 

notation ..li, has been used to indicate the average measured aXial strain In the 

fiber This has been done since strain IS a localized quantity and fiber opt,'" 

strain sensors are only able to detect strain as averaged along their gage 

length. See Appendix A for further details of stra:n averaging In addition. the 

results of equations (3.1.14) and \3.1 15} Will likely be of most use In an actual 

system With Va measured at quadrature and ~V;~ •• and w measured, say. uSing 

a spectrum analyzer. 

Before discussing sensitivity let us diSCUSS c;ome of the practical aspects of the 

MOS/9-633 sensor. First. It should be noted that the interest in studying the 

rotating three lobe pattern of the MDS/9-633 sensor arose due to Its ability to 

be created using Simple optical components. Also, once created, thIS pattern 

IS easy to work with due to ItS well defined rotational behavior and due to the 

fact that 633 nm light IS VISible and requires no special V1ewing equipment. !I 

Creating the rotating three lobe pattern. however. is not at all an easy task. 

Indeed, it often seems that obtaining thiS pattern requires a fair amount of luck 

3 Q MODAL DOMAIN SENSING 
____ .... 'k=5Y''''''-_=>~,__=''''C'_ _ _ _ ___________ _ 

Once created. though the modal content of the pattern IS unique and can be 

studied, as has been done In the past few pages. leading to the sImple strain 

measurement results of equatIons (3 1.14) and (3.1.15). These equations state 

very SImply how small changes In stram can be measured in the optical fIber 

of a MDSi9-633 sensor once the quadrature pOint has been properly set. 

Setting the O-pomt of the MDS/9-633 sensor. however. IS another dIfficult task 

to accomplish TYPIcally. 10 order to poslhon a small spatial filter at the proper 

quadrature pomt. one must apply a small signal sinusoIdal disturbance to the 

sensor vIa a pIezoelectric deVice and use Imear posltioners to move the 

spatial filter until one locates the posItion of the pattern that gIves the largest 

amplitude and least distorted sinusoIdal sIgnal at the output of the 

photodetection circuit. as dIsplayed on. say, an oscilloscope. Note that the 

spatial filter must be placed between the output end of the fiber sensor and the 

photodetector and must be small so that any intensIty variation. which is a 

pomt function. can be accurately Simulated and monitored. One may also set 

the quadra~ure point by aligning the spatial filter at the peak of a lobe and by 

then causing a static strain in the fIber, via some static strain control device, 

so that the pattern rotates untIl the quadrature paint is properly alig"ed with 

the spatial filter The use of both of these techniques for setting the Q-point 

WIll be discussed in chapter 4. 

3_0 MODAL DOMAIN SENSING 

I 

• c. 
__ ~... ~ .... ,. __ "111---

It should be obvIOUS now that the MDS/9-633 sensor has practical limitations. 

In addition, due to the expected ease of use of the MDS/9-850 sensor to be 

discussed In the next section, no analysIs has been given for the Inlection 

conditions necessary for the rotating tllree lobe pattern to exist in a MDS/9-633 

sensor Therefore. from this POint on it Will be assumed that If one wishes to 

use a MDS/9-633 sensor that a rotating three lobe pattern can be obtained and 

that there IS available equipment which allows the quadrature pomt to be set. 

The results of equations (3.1 14) and (3.1.15) can then be used With thiS In 

mind the sensitivity of the MDSi9-633 sensor can now be addressed 

Although in a tYPical measurement situatIOn one ..... ould measure ul, as a 

function of the change In voltage at the output of a photodetectlon CirCUit with 

respect to Its O-pomt value. we may shll relate .ll, to the change In optical 

power through the spatial filter with respect to Its O-pOlnt value This is done 

simply by diViding the numerator and denommator of equation t3 1.14), say. 

by ~RL' where £I is the responslvlty of the photodlode and RL IS the load 

resistance of the detection CircUit ThiS Yields 

(3.1.16) 

.. By refenng to Figur~ 4 we can see that bll = 0 55 and bZI = 0 22 . USing 

equations (2 2.9) and (2.2.10) and Figure 4 we can therefore find that ~fl for the 

3 0 MODAL DOMAIN SENSING 47 
Sf , • ..... 9 ...... __ • -- __ -oo.~ 

MDS/9-633 sei,sor IS ~jJ = 1 2xl0: m I when V = 4 616, n, = 1 458, a = 4 5 J.l.m 

and 1.0 = 633 nm In additIOn W6 will reasonably assume for our detection 

Circuit that for pin diode detection the fiber gage length L, IS 05 m , the bulk 

dark current I~ of the photodlode IS approximately 1 nA, the detection 

bandwidth 8 IS 1 Hz. the responslvlty ;r of the photodlOde IS approximately 0.5 

A!W at 633 nm, the operating temperature T IS 3000 K and the load resistance 

IS R~ = 10 kn We further assume that the optical power through the spatial 

filter at quadrature IS Po: = 1 uW USing these values we may calculate the 

minimum detectable change In optical power through the spatial filter using 

equation (23.10) We thus find 

If we now substitute thiS value Into equation (3 1.14) and assume (X = 0.78 as 

discussed In section 2 4 we find that a reasonable minrmum detectable strain 

expected for a typical MDS/9-633 sensor IS 

,- 0-9 I L..lE:mm ~ 1 m,m 

The MDS/9-633 sensor IS thus seen to be a highly sensllive strain detector It 

is not, however, as senSitive as say a Mach-Zehnder interferometer since 

modal domain aensors are based on differential modal phase modulation, 

. whereas the Interferometer IS based on absolute phase modulation [2]. By 

sacnflclng some sensItivity, though the modal domain sensor Will likely gain 

3 0 MODAL DOMAIN SE~SING 43 
Increased stability and Immunity to environmental nOise over the 

interferometer. making modal domain sensors. In general. a more practical 

approach to strain detection," many real world situations. 

3.2 The MDS/9-850 Sensor 

Similar to the MDS/9-633 sensor. It has been observed that when 850 nm light 

from a semiconductor laser diode IS Infected into a 9 pm core diameter fiber 

a symmetric two lobe pattern can be created at the fiber output which 

oscl"ates as a function of aXial stram Considering the same fiber as discussed 

in sectIOn (3.1) we see that the normalized frequency at ;'3 = 850 nm is 

v = 2405 1215 nm = 34-1 

850nm 

From Figure 4 we find that this allows for the propagation of only the U'" and 

VII modes. including all degeneracies We WI" now show for the case of 

x-polarized Injection that the oscillatory two lobe pattern is caused by the 

interference of the U'OI and even LPII modes 

From equation (22.4) ~e see that the electric f'},Jds In the fiber core of the 

x-polarized LPOI and even LPn are. respectively 

3.0 MODAL DOMAIN SENSING 
l32 1) 

and 

(322) 

USing equation (3.1.2) we can find the intensity distribution created by the 

Interference of these modes to be 

In equation (3 2 3) ~/3 = /30' - /3" , ~1jJ = 1/10' - tV" and I" = Y,/2. In addition, 

from Figure 4 we can find that bOl = 0.730 and bl1 = a 325. so that If equations 

(22.9) and (22 10) and Figure 4 are used with V = 3.44 • n, = 1.458. 

a = 4 5 pm and ;,c = 850 nm we calculate ~p to be ~/3 = 1.1x101 m-'. 

Note that in equation (3 2.2) the first term is the intensity of the LPo, mode alone 

and the second term is the intensity of the &;" mode alone While the third term 

anses due to the interference of the .Po, and LPI1 modes. For diSCUSSion 

purposes let us rewrite equatIOn (3.2.3) as 

3.0 MODAL DOMAIN SENSING 50 

- __ - ... ..:--__ .=-s:~:- __ -_-_ ... -_ 
---

(3 2 4) 

Notice that I,{r) is aZimuthally symmetnc while 12(r, 4» has a maximum at 

4> = 0 and 4> = rt. The third term 13{r, cP, z) also has a maximum at 4> = 0 but 

has a minimum at ,_, = rt In addItion 13(r, (P, z) IS modified by the 

cOSl~pz - ~(j) term whIch vanes between -1 and + 1 as Z IS vaned. Thus we 

can see that for proper choices of A, and A~ we should expect to see an output 

intensity pattern consisting of two lobes. one of whIch gets bnghter as z vanes, 

while the other gets dimmer. Figures 16-22 help visualize thiS behaVior. 

FIgures 16 and 17 show the intensity dlstnbutions of I,(r) and '2(r. </», 

respectively. \',hlle FIgure 18 shows a sketch of the LP,. mode. whIch IS sImIlar 

In the coordinate ¢ to the output of the MDS/9-850 sensor at quadrature. 

FIgure 19 shows I,(r) ~ I:(r,~) when 13(r, 4>. z) = 0 , while Figure 20 shows 

13(r, ¢, z) at a maximum. Finally, Figure 21 shows the entire intensity 

dlstnbution of equatIon (3 2.4) when 13(r, ¢, z) IS a maXimum, With Figure 22 

being a three dimensIonal plot of I,lr) + 12lr, <j)) when l:(r, <p, z) = O. In these 

figures It IS assumed that A, = 2A2 , WIth all but FIgure 18 shOWing plots 

normalized to I,(r) haVing a maximum intenSity of unity. The choices of AI and 

Az are somewhat arbitrary and give Indications as to the ratio of the input 

power eXisting in each mode. Here the choice of ~ = 2A, was done to 

p-nhance the visuallzatlo.l of the behaVIor of the two lobes as a function of 

strain, which has been observed. This choice was made after evaluating 

3 0 MODAL DOMAIN SENSING 51 

-

-

• 
severdl plots of equation (3 2 3). with the amplitude coefficients taken as 

parameters With A2 ~ 2A, It was seen that the calculated output rntenslty 

• 

dlstrrbutlon of the MOS/9-850 sensor most closely agrees with experrmental 

observation One must realize. however. that the ralio Az/A, will be 

determrned by source Input conditions and must be some moderate value 

greater than one If A2/A, IS less than unrty the '-":, mode will dominate and 

only a srngle lobe will present at the output. If A;:A. IS much greater than unrty 

only negligible power Will eXist rn the '-"0' mode and thus no interference Will 

take place For convenrence we Will proceed under the assumption that 

Some further comments concerning Figures 16-22 should be made. First. It 

should be noted that all line graphs are plotted in the plane where J,(r) • 

I=(r. ¢) and IJ(r. ¢. z) have maxima. Second. all the unrts of the S~2· -

dimenSIOns rn Figures 16-22 are in microns. Third. the 3-D plot in Figure 22 

is only valid In the region ",.-here r = ,./x2 + Y" ~ 4.5 pm And finally, the 

sketches of Figure 18 are included to give a better visualization as to how the 

pattern caused by '-"01 and '-"II modal interference will appear as seen looking 

toward the fiber end face As With similar plots in earlter sections, these plots, 

With the exception of Figure 18, were generated With aid of the matenal In both 

Append,~ C and Appendix O. 

3 0 MODAL DOMAIN SENSING 52 

"'--.. -~ 

-=. .... -~.. - ~~ ~.-- .. ,. -
- ... __________ ~,.._ ...... _ V"' .... :-.... ....- ---.. -. 

At this POint It should be easily seen how this modal Interlerence phenomena 

can be used 3S a sensor mechanism If one adjusts the Input conditions In 

such a way that 13(r, ljJ, z) IS zero at the fiber output end face, a maxImum 

sensitivity quadrature pOint will have been c"eated If one then momtors one 

of the peaks at this quadrature POint by spatially filtering out all but a small 

portion of the output pattern at this peak, a change In optical power through 

the aperture of the spatial filter will be dIrectly related to any perturbations In 

the fiber 

Notice now that In FIgure 21 If we mOnitor the peak of a lobe, then a maxImum 

mtenslty at some amount of strain Will occur at r ~ 2.38 um In the maximum 

mtenslty plane If we choose the lobe at say If> = 0 and If It can be shown that 

2( Uo,r ) 2( U"r ) Jo -- + 4J1 - a· a (3.2.5) 

at r ~ 2.38 p'm, for A2 ~ 2A., then we can obtain the reduced form for the core 

field intensity, equation (323), as 

I = l/o{1 + cos(oP z - ~vi)} 

or 

" 

1 2( ilfJ z - 011 ) = p cos 2 (3.2.6) 

3 0 MODAL DOMAIN SENSING 53 
where ['0 has Incorporated IOtO It the terms of equation (3 2 5) after belOg 

factored from equation (3 2.3) and where Ip = 21' ~ represents the peak intensIty 

of a lobe. Indeed. by recalling the fIber parameters and uSing FIgure 3 we can 

show for r ~ 2.38 um that the quantitIes of equatIon p 2 5) are the same to 

wIthin 48 percent. wIth Az ~ 2A,. so that the above slmpllftcatlon of the core 

IOtenslty function IS valid 10 the regIon of a lobe peak at either qJ = 0 or 

0= 1: The only difference. recall. In these two loces IS that one will IOcrease 

In intensity while the other decreases for small amounts of strain. Also, since 

the peaks of I~(r. 0). 13(r. </>. z) and I.(r) + I:(r, o. z) don't pFecisely a\lgn WIth 

one another. With the peak radius of 12(r.o) belOg the largest, It IS expected 

that the above Simplification of the core intensIty function should be valid for 

reasonable ratios of A2/AI > 2 In the reglo~of the lobe peaks at 0 = 0 and 

~ = n. Therefore from now on It WIll be assumed that we are diSCUSSing a 

sensor system In which the IOput has been adjusted so that two lobes of equal 

intenSity are observed at the output under a no strain situation Further, It will 

be assumed that the ratio A:! AI IS some reasonable value so that the 

interference takes place and that In the region about the peaks of the lobes the 

intensity can be approximated by equation (3.2.6). 

We recall that by using equation (2.4.6), we can Include in equation (3.2.6) the 

photoelastlc effecl.s of the fiber under strain. at the radial coordinate of a lobe 

peak, to gIve 

3.0 MODAL DOMAIN SENSING 54 
2( ~/l £z L,:x ~ t.!>o ,) = fp cos 2 \ 

(32.7) 

where ¢o = - rr/2 If we consider that we are momtonng the lobe which 

Increases with strain from ( = (:12 under a no strain situation. We recall that 

at quadrature IJ(r, ~ z) = 0 and we have two lobes of equal intensity, one of 

which Increases while the other decreases as a function fo strain. Using the 

same arguments as were used to arrive at the results of equations (3 1 14) and 

(3.1.15), we can show for small changes of strain, as averaged over the gage 

length of the sensing fiber. that ~£, can be measured from quadrature With the 

MDSi9-850 sensor as 

for the case of static strain and 

.J.f., = 

..lV 

Vol..l/l L,:x) 

..\Vpeak cos(wtl 

VQ luP L,:x) 

(328) 

(3.2.9) 

for the case of small amplitude time harmonic strain and small peak 

displacement vibrational strain. Note the Similarity of these results (only up 

<- takes on a different value) and those of equations (3.1.14) a;Jd (3.1.15) even 

though the sensing techniques are rather different The sensitiVities of the 

3.0 MODAL DOMAIN SENSING 55 

- ~-• ..T -
MOS/9-850 and MOS/9-633 sensors are also comparable and equations (3.2 8) 

and (3.29) may be used to detect ~ .l£, from quadrature If there IS an initial 

strain In the fiber 

As expected. uSing a laser diode in a modal domain sensor provides several 

advantages. First. due to the fundamental mode (LPot) not needing to be 

extingUished for proper sensor operation. It IS much easier to align the input. 

Also. since informatIOn will be taken from the sensor by mOnitoring the 

intensity variations of a lobe peak. alignment of the Q-POlnt of the sensor IS 

expected to be relatively simple. In addition. laser diodes are light weight. 

physically small and It IS possible to find highly linearly polarized laser diodes 

operating at ;0 = 780 nm that are relatively inexpensive 

Although the preceding analYSIS has been for;' = 850 nm. it IS still valid for 

any source wavelength such that V < 3.8 so that the LP2t mode IS stili cutoff. 

For 10 = 780 nm. V=3 75 In addition. for ;'0 = 780 nm. ~f3 ~ 1 lxlQ-1 m-' as With 

850 nm injectIOn so that sensitivity IS preserved. 

The only apparei1t drawback to uSing laser diodes as sources is that they 

require special viewing equipment to observe the infrared radiation. ThiS 

problem may, however, be overcome through the use of small, light weight 

!! 

in-line detection techniques presently under investigation. And finally, as ' 

laser diodes may be operated in a pulsed fashion. It may be possible to 

3 0 MOOAL DOMAIN SENSING S6 

, . 
:,.t:------ -

sImulate the use of a beam chopper 10 a detection system so that 

signal-to-nolse ratIo may be preserved for low frequency nOIse as would be 

: 

present If there was, say, excess thermal drIft. 

3 0 MODAL DOMAIN SENSING 

-.. 
---

nl.-GLAD 

n,-CORE 

. ceRE 

Figure 10 A SImplistIc look at modal Interference 

3.0 MODAL DOMAIN SENSING 

END F"ACE 

J 

• I 

. ' 

~ -, .. 

sa 
CUTOF"F" PLOT 

ID:VPI TEST ~ 

TYPE. EErJD 

iRICk FrSER 2B-JAN-8? 13:58:53 

d 

SMM~~~~~~~TTTT~~~~~~~~~ 

3 

2 ,"\ I \ 

E _1",,, I \ 

I \ ... 

~ " ~ 

, ." !,," t i'-,-, -, -, :-: "--' ...... , __ ..... ' :--"--'~ .aD ! ao 1. 2~ "0 1. 60 

W~ve 1 ength (I.IM \ 

Cutcff Havelength=l2J5. 

VRP!RBLE ==E~-~RE PRTTECN ~7 :~~c n~ 

I;): ,'FI ,PIC- =-IE'ER 2~-JAN-B7 ::::;-:::: 

p 

(I 

W 

E 

R 

I.~~---------------------------------------------~ 

1.0--------- ------ --,~----...---­

a.s -- --... )..~-

0.-1 -

O. Z ---I 

,I 

, 

I 

I 

'I 

." 

,/ 

~.D~------------------------------~ .00 .a5 .10 .15 .20 .25 

Numerlcal Aperture 

Mode ~leJd Olameter=ll. 1472 

• 

FIgur. 11. FOA-2000 fiber optiC analyzer data 

3.0 IIODAL DOMAIN SENSING 59 

, -

-.. 
____ -- __ --- ___ ------- _____ -- ____ ~ __ _ ---..-~ ... n ••• '-... .--~~~-.. - --- .. ~r- ;-

z 

0.31 .J 

I , 

. 

. 

1 

O ... a i 

\ 

Q 

• 

F"l9ur

• 12. The MOSI9.633 background IntenSIty term 

3 0 MODAL DOIIAlH SENSiNG 

.. so 

-1 .. 5: 

-11.50 

-11.::10 

60 
t~--:--.:- - .. 

z 

c. e ~ 

-c. ~ e 

\ 

I 

OR!GtNAn PAGE IS 

OF. FCOR Q1] .\LIT'l 

_, so 

,"--" J , .. , ..... ' 

'L..,' 

/ .. sc 

I 

I 

I I t ,- I -'" 

j 

I 

-~ -~ 

_~.sc 

Flgu

rw 

13. ",. M0SJ9.633 strain I'/'IOdulated lntenSlt1 term 

3 0 ,.OOAL DOMAIN SENSING 

61 
1. CS • 

C ;3 : 

\ 

\ 

I 0.35 .... 

- - - -~ - -

, SO 

,. 

FIgure 14. The total MD519-633 output IntensrtY distribution 

30 MODAL DOMAIN SENSING 

• 

62 

I 

f7
.' 

ROTATION 

(0) 

~----------~----------------------~ (~ 

Figure 15. Axial YJew of the MOS/S-633 intenSIty distribution 

30 MODAL DOMAIN SENSING 
_0.] 

o 

Q. 

-' ° c 

LP01 

/ 

/ 

/ 

/ 

lNTE.N5ITY 

i i 

J : : 2 2 

s j s ~ 

RADIUS S ~ 

Flgur. 1&. The LP Of mode Intensity distribution of the MDS/9·850 sensor 

30 MODAL DOMAIN SENSING 

CR!GINAI; PAGE IS 

O~ fOOR Qm\Ll'Ol 

J 

. 

• 64 

--• -----::--- -.'--'''-._-.:. -
II' 

LP II INTENSITY • 5. 

j 

: .... I 

I 31 

I 21 

/ >- "] \ 

~"I / 

\fl - 0'1 . .. \ / :2 w_: \ 

\ Ul J 7.,' \ 

\ }- OS; I' 

2 I :::j 

D.. ., 31 

.J 0 ~. 

a .1 

a 01 

I 

I I 

, , C 2 :l : :l 2 2 

5 0 5 :: :! :: 5 :: 5 :: ! 

RADIUS 

figure 17. The LP" mode Intensity dlstllbutlon of the MDSJ9..850 sensor 

• 

3 0 MODAL DOMAIN SENSING 

_ - _~ .. __ . -:s::..:..~ --_- -

3 

:l 

\ 

\ 

, 'I 

5 0 

65 

~ 

..... - -- - -.. 
. Ii 

-

LoP .. "'~':'~:~I1'Y 

V:a 3."S~'P 

9/11~ ...... __ ,1IaA 

ft. - I .. sa D- 3U 

NA- I 

CL 

Ct.-lCl?!AL ~ !._::~ rs 

OE f.OOR Ql!rl.LITY 

, 

" rCA ,. 

--~-------+--~~~--------~x 

\,.-" 

,. 

Flgur. 18. The LP ff mod. Intensrty panern '" 

3 0 MODAL DOMAIN SENSING 

I 

I 

I 

T 

, , 

, , 

-... -- ... -.. ~ ----- --~ -

z 

t.x 

NOTE 

,. 

~ crt-r_ca. 

Z. 

-
INTENSITY 

\ 

~ l 2 :: D ~ 

5 (, 5 0; :: 5 ~ : ~ -

-

RADIUS 

Figure 19. MDS/9-850 Intensrty vanatlon of 1.(r)+I.(r,cj.), at quadrature 

• 

3 0 MODAL DOMAIN SENSING 

-- ~ -.:::-' -_ .... $ .... , ..... _- - ~ 
CROSS TERM z~.~--------------------------~r----------------------------- I .~ 

1 .: 

I ,-

1 .! 

J S! 

1 .i 

I 1-

1 Z' 

1 :1 1 :J 

0': o ,: 

o 7! 

~ :l.S: 

o !i 0'·1.1 t- 0.2 

o 11 

en ~.:~' ----------1-----------..; en -~ .- / 0-0 i: I a: -0 ~: 

(,) :~ ~; / -05-

-0. ,! 

-4.': 

-0 ;! 

-I =: -I :-: 

::'~l 

-1'~1 

:!::! 

-1 .. ,! -I ;: 

-I S: 

-2 C!~----~------------_r--,_~r_--__ ~--------------~--~--~--- 4.32 I :I 0 

5 ~ 5 C 5 fl 5 0 5 

RADfUS 

o 

223 

esc 

3 ~ .. 

5 0 

• 

F'1gU'" 20. Intensity vvkllon of the MDSJ9·8S0 "OSS term I.(r,~.z), •• maximum 

3.a MODAL DCIIAIN SENSING !l8 
TOTAL " 01 "1 ' 8 

: :1 >- ~: }-" , 2-

- ,.11 

\I) nl :z 2 e 

2 '1 \1126 I- 2 2 , st 

Z 2.' _ 2 21 2] 

2 0 

-1 : :1 ~ ; ~j 

5::1 1.3 F 12 II 

I 0 

0"1 0.1 

o , 

C O.S Sl o • 

~J] o lJ o O' I 

q II 3 3 2 I 

5 C 5 C 5 5 0 

INTESNS\TV 

/ 

I 

/ 

i 

:I :I 0 Z 2 3 

5 0 5 0 5 0 5 0 

RADIUS 

3 II 

s 0 

\ 

\ , 

\ I 

5 

FIgure 21. Tatallntensi~ pattern of the MDSJ9.850 output when l.tr.+.z) i. maxImum 

3.0 MODAL DOMAIN SENSING 

.. 

~- -
! 

\ \. es "\ I 

\ 

\ 

I 

1.2S t 

c.s; 

3 0 MOO"'\. DOMAIN SENSING 

... :0 

70 

___ --- _.----
4.0 MDS/9-633 SENSOR EVALUATION 

Although an MDS/9-633 sensor system will have practical limitations. it IS easy 

to construct a wor~ Ing sensor system based of the MDS/9-633 techmque using 

readily available optical laboratory equlpmenl In addition. by evaluating t .. -

MDS/9-633 sensor one can obtain insight about the practical aspects ana 

performance characteristics of modal domain sensors in general. We begm 

with a description of the experimental system used to evaluate the MDS/9-633 

sensor technique. 

The experimental setup is shown diagrammatically in Figure 23 As seen. tr .. 

emission from a He-He gas laser is focused through a microscope objective 

onto the end face of a 9pm core diameter fiber held in a fiber positioner. This 

fiber is of the same characteristics as the fiber discus-r~ed in section 3.1 and is 

attached in sequence to a static stram control d6vice. a piezoelectric PZT 

'.0 MDS19-633 SENSOR EVALUATION 71 
cylinder. a canttlever beam and a holding post at the output. The static strain 

control device Simply conSists of two plastic disks on which the fiber IS wound. 

one of which has an attached push rod and is mounted on a rotateable base. 

As seen In Figure 24. tension IS applied to the fiber between the two disks as 

force IS placed on the push rod via a micrometer screw. In addition. so as to 

aVOid appreciable bend loss m the fiber. the radius of the disks was 

approximately three Inches 

The PZT cylinder following !he statiC stram control device had wound upon It 

several turns of the 9 um core dIameter fiber and obtained Its excitation from 

an external Signal generator As WIth the statIc strain control deVice. the 

purpose of the PZT cylinder was to aid In aligning the sy&tem quadrature pOint. 

For reasons to be discussed later. however. only the PZT cylinder was able to 

help achieve this goa\. 

After the PZT cylinder, the fIber was attached. along With a resistive strain 

gage. to a cantilever beam. Appendix A presents a detailed analYSIS of the 

strain characteristics of a loaded canhlever beam, as well as a discussion of 

the geometry of the fiber path on the beam necessary so thal the strain 

Induced In the optical fiber IS Identical to that induced in a reSistive strain gage ~ 

placed at the geometric center of the beam surface. The reader is encouraged 

40 MDSJS.633 SENSO~ EVALUATION 

- ....... -- ~- ...... 

72 
to review Appendix A before proceeding. Referring to Appendix A, the 

dimensions of the cantilever beam and the optical fiber path were chosen as 

L = 0288m 

L, = 00254 m 

b = 0 071 m 

h = 0 0022 m 

r = 00159 m 

where L IS the beam length, L-L, IS the length of the straight fiber segment"" 

and r is the radiUS of the curved portion of the fiber. with band h being the 

beam W1dth and thickness. resper.tlvely With this geometry the change In 

average stram Induced m both the cptlcal fiber and the resistive stram gage 

IS given as a function of load by 

3mgL ~£ = 

Ebh2 (4.01) 

as shown in Appendix A. where m IS the change in initial load mass and g is 

the acceleration due to gravity. Young's modulus E for the beam depends Of" 

the beam material and as our beam was constructed of alumin .. 

E = 6 9x1010 Pa, In addition, for this beam the Poisson's rallo is v= 0.33, while 

the gage length of the fiber on the beam IS 

L, = 2(L - L,) + rtr = 0.575 m . 

4.0 MDSJ9..633 SENSOR EVALUATION 13 
Further, the opttcal fiber was mounted to the beam unstnpped to prevent 

breakmg and both the fiber and resistive stram gage were bonded to the beam 

uSing thermal-set epoxy 

The output end of the fiber sensor was attached to a hold 109 post positioned 

a few centimeters from the photodetectlon circuit The detection circuit 

consisted simply of a photodlode, reverse bIased at nme volts, mounted on an 

x-y-z posltionrng stage Load resistance was prOVided vIa a decade box In 

additIOn, epoxied to the front of the photodiode (UOT model PIN-100) was an 

IriS whIch served as a spatial flltenng deVice. Fully open the 1rI~ was 1 2 cm 

10 diameter and when closed a 1.0 mm aperture remamed. TYPically, spatial 

filtering was done with the iriS closed; however. the actual size of the spatIal 

filter aperture IS mostly Irrelevant as long as it IS small with. respect to th_ 

output intensity distribution being monrtored. 

Not shown is the Wheatstone bridge and amplifier CircUit used to detect small 

changes in resistance of the resistive strain gage. The output of this circuit 

and the photodetector were both connected In parallel to a digital voltmeter 

an oscilloscope and a spectrum analyzer for data collection purposes. 

addition, the entire system, except for measurement equipment, was mounted. 

to a floatmg (pne~matlca"y supported) optical table. 

4.0 MDSJ'9-633 SENSOR EVAlUAnON 74 

f 
~lnal!y, throughout the diSCUSSions to follow no account Will be given to any 

system nOIse artslng from sources other than the photodetectlon circuit and Its 

associated load resistor In addition, It Will be assumed that the bondmg of 

both the optical fiber and the resistive stram gage to the cantilever beam IS 

perfect with no sheartng of the fiber Jacket occurmg as stram IS applied These 

assumptions Will not likely be valid outside of a laboratory environment 

4.1 Resistive Strain Ga1e Evaluation 

As the resistive strain gage IS a commonly used and well accepted instrument 

for measunng stram It was decided that a resistive stram gage would be used 

as a standard with which to compare the performance of the MOS/9-633 

sensor. It was therefore Important to evaluate the performance of the resIstive 

stram gage used in our sensor system prtor to all other measurements. As 

mentioned preViously, the resistive strain gage was placed at the geome!r.~ 

center of the cantIlever beam surface, so that as a function of load, the inc_ 

stram charactenshcs of the gage follow equation (4 0.1). In addition, as shown 

in Appendix B. the change in average strain in the beam as measured by the 

resistive strain gage IS given by 

40 MDSI9-633 SENSOR EVALUAnoN 

, 

\ 

/ 

7S 

I 

.. 
(4 1 1) 

where V.'" IS the negatIve voltage measured (for ~osltive strain) at the output 

of the inverting amplIfIer following the Wheatstone brtdge CirCUIt. The bndge, 

recall IS used to allow small changes In strain to be detected. In addItIon the 

Input v,,, to the bridge CirCUIt. as supplIed by a regulated power supply, WPmeasured (0 be 100 V. whIle the gam of the amplifIer was measured to be 

I R6/R51 = 179.78. IndIvIdual values of R, and R, were measured to be 

102834 MQ and 572 a kQ. respectIvely. These measurements and other 

sImilar ones to be presented later were made on a Solartron model 7061 

dIgItal voltmeter that was capable of dIsplaYing seven slgnlficanHiigits. 

The specifIc resIstive strain gage used was manufactured by 

Micro-measurements Corporation and had a nominal resistance Ro of 120.0 

± 0 18 Q. In addItIOn. the gage factor Sg was gIven as 2095 ± 05 at 3000K 

while the transverse senSitivity factor kt was gIven as kt = 0.006. Finally •. 

POIsson's ratios In equat!on (4.1.1) are given as Vo = 0.285 and v = 0.33 and 

represent the POIsson's ratios of the factory gage calibration beam and the 

aluminum experimental test beam. respectively Refer to Appendix B for 

• 

further details. 

40 MDS/9.633 SENSOR EVALUAnON 76 

•• 

J 
" 

In order to evaluate our resIstive strain gage, the beam was inltally loaded 

with a 200 gram mass uSing the loading technIque depicted In Figure 2S(b). 

ThIS was done to take any Nslack" out of the system. The gage resIstance was 

then measured and the other resistances of the bridge cIrcuit adjust3d 

(tnmpots were used) so as to null the output. Additional load mass was then 

added to the beam with readings of Vout being taken as the excess load mass 

reached the values of 5, 10.20.30.40.50 and 100 grams. This procedure was 

repeated several times and a representative plot of data depicting the 

measured versus Induced change in average beam strain is given in Figure 

26. In partIcular. note the regressIon polynomIal calculated for thiS data. fJ. ~ 

IS seen. the calculated slone of the line devIates only slightly from the 

case of unity slope In addItIon. the y-axIs crossing value can be shown to 

very closely correspond to the measurement uncertainty of the resistive strain 

gage. 

If we now conservatIvely assume that our Solartron volt/ohm meter is 

uncertain to within plus or minus one dIgit In the fourth decimal place (for a 

given scale factor) we may calculate our minimum change in s 

measurable with the resIstive strain gage using the procedure outlined Ir. 

Appendix 8. With dV:ut = :: 10-4 V, v'n = 10.0 ± 10-4 V ,R, = 572.0 ± 10-4 k!l and 

R. = 102.834 == 10-' M!l we find that our minimum detectable change in ~ 

average beam strain is illm,n = 0.21 J.lm/m. as measured with the resistive 

.0 MDSI9-633 SENSOR EVALUAT10N n 

c-3 
·~ 

... 

.. 

.. strain gage. As this value also represents tWice the absolute measurement 

uncertainty of the reslstrve strain gage (even with no applied load) It IS seen 

that the y-axIs crossing of the regression polynomial of Figure 26 very closely 

matches with the predicted value. We therefore see that our resistive strain 

gage prOVides a lustrflable strain measurement standard. 

4.2 Dynamic Strain Measurements 

With confidence now gained In the performance of the resistive strain gage, 

the next task was to rnvestlgate the performance of the MOS/9-633 sensor. A 

discussion will be given in this section relating to the modal domain sensor's 

abilities to serve as a dynamiC stram measurement deVice. Sections 4.4 ai 

4 5 will discuss static strain measurements. 

DynamiC strain was induced in the cantilever beam uSing a setup as shown In 

Figure 2S(a). As is seen. the action of the vibration exciter (BrGel & Kjcer type 

4809) was transmitted to the beam vIa a push rod. The ball and socket jOint 

was used so that the deflecting force on the beam remained normal to the 

surface and so that the shaft of the Vibration exciter was not subjected to any 

off axis ~tress. Notice. however, t~at this setup does not provide a way by 

which the force on the beam or the beam tip deflection can be measured as it 

'.0 MDSJ'I.&33 SENSOR EVALUATION 
I .. 

vibrates. All IS known IS that the beam can be caused to vibrate at the 

frequency of the signal Input to the vibration exciter and that the amplitude of 

this vibration may be vaned (in an uncallbrated way) by adjusting the mput 

Signal amplitude. For thiS reason It was important that the resistive strain 

gage behave properly so th-t the MDS/9-633 sensor readings could be 

compared to a reliable standard. 

It was decided that as the beam vibrated the amplitude of the sinusoidallv 

varying average beam strain, or peak average strain, would be the quantity to 

be measured For the modal domain sensor. we have from section 3.1 that the 

measured peak average strain IS given as 

'(peak = 

Vpeak 

(4.2.1 \ 

For the resistive stram gage we have from Appendix B that this same quantity 

is measured as 

(42.2) 

Note that in equations (402.1) and (4.2.2) we are considering that the beam is 9 

initially unloaded and that V ~.~ and Vp correspond to the amplitudes of the 

~ 0 MDS19-633 SENSOR EVALUAnON 79 
( 

.... 

sinusoidal signals generated at the output of the MDS/9-633 and reslst!ve 

strain gage sensors. respectively 

To avoid both resonance conditions and damping of the vibration induced into 

the cantilever beam It was decided that the beam would be excited at as far 

below Its fundamental frequency of vibration as possible This frequency was 

determined by plucking the beam and allowing It to vibrate freely (with the 

push rod removed) and by then mOnitoring the output of the resistive strain 

gage sensor on a spectrum analyzer As seen in Figure 27 the fundamental 

frequency of vibration was measured to be 21.6 Hz. Since the vibration exciter 

could not be reliably operated below 10 Hz this was chosen as the eXCitation 

frequency for dynamiC stram measurements 

To conduct the experiment the fiber launch conditions were adjusted until ~ 

rotating three lobe pattern was observed. This was often facilitated _, 

adjusting the tension In the length of fiber between the spools of the static 

strain control device. although no good explanation for thiS effect presently 

eXists. The photodetector was then typically moved toward the fiber till the 

pattern just filled the open iriS (a somewhat arbitrary act) and the Q-point was 

set using the PZT cylinder. 

It was observed that when the PZT cylinder was excited at its oresonance 

frequency of 38.5 kHz an apprecIable small signal sinusoidal strain could be 

4.0 MOS19-633 SENSOR EVALUAnON 10 
( 

I 

imparted to the fiber. causing a small sinusoidal response at the photodetector 

output The Q-POlnt of the system was then set by using an x-y positioner to 

position the closed IriS over the POint of the pattern that gave the highest 

amplitude and least distorted sinusoidal response. This proved to be the most 

reliable way of settIng the quadrature POInt and Figure 28 shows a highly 

aligned MOS/9-633 output signal observed durIng such an alIgnment. The top 

trace IS the modal domain signal and has a peak-to-peak voltage of 80 mV. 

The bottom trace 15 the input to the PZT cylinder and has a peak-to-peak 

voltage of five volts. Both traces are at 385kHz. 

Conceivably. It should be possible to set the O-pOInt by locatIng the IriS 0._ 

the peak of a lobe and causIng a static strain in the fiber so as to cause the 

pattern to rotate to the point where the iris is located half way between the 

maximum and minimum of a lobe. In practIce this proved to be difficult. 

though. as It was often difficult to align the input In such a way that the three 

lobe pattern rotated properly through more than about twenty to thirty 

degrees. This was fIne for small signal work but made alignment of the Q-point 

difficult using the "bulk effect" technique just descnbed. Therefore only the 

"small signal" method of setting the Q-point, uSing the excited PZT cylinder. 

was used. 

40 MDSJ9·633 SENSOR EVALUATION 81 

- ..... --~ 
------- ~ .... 

With the Q-point properly set. data was taken by recordmg the peak voltage 

out of each of the sensors on the cantilever beam, for varymg amplitudes of 

the signal mput to the vibration exciter, at the 10 Hz peak observed on a 

Spectrum analyzer. Recall that for all dynamic measurements the beam 

excitation IS at 10Hz. Plots of some of this data. converted to stram 

measurements using equations (42.1) and (4.2.2) are given m Figures 29, 30 

and 35 with several polaroid photos corresponding to the data of Figure 30 

bemg shown m Figures 31-34. These shall be discussed shortly. 

For t"~ data of FIgures 29, 30, and 35, the load resistance was 50 k.Q and t~c> 

mput to the Wheatstone bridge V" was taken from a nme volt battery. Tn~ 

value of CL was taken to be :t = 0.78 in equallons (42.1) and (4.2.2), as per the 

discussion of section 2.4, although this value will be seen to change when 

static strain measurements are undertaken. Recall also that· ilP = 1.2x10" m-I 

for the MDS/9-633 sensor. In addItion, so as to make the data sets 

independant, the pattern and quadrature point were readjusted before eacn 

set of data was collected. For the data sets of Figure 29, 30 and 35 the Q-pomt 

voltages Va for the MDSi9-633 sensor were 12 V, 0.55 V and 0.35 V, 

respectively. Since the sensitivity of the MOS/9--633 sensor directly depends 

on the Q-point value of optical power through the spatial filter aperture, It is 

easy to see wh¥ the y-axIs crossing IS at a much higher value of stram in 

Figure 35 than it is in Figure 29, Note, however, the linearity and near unity 

4.0 MDSJ9.&33 SENSOR EVALUAnON '2 
~ r 

f~ , i ~ t 

i ". 

1':1 

t 

} 

t 

----------------------------------.. 

slope of all data In Figures 29 30 and 35. Especially note that the y;-axis 

crossings of the extrapolated data In each of these figures agrees well with the 

minimum expected detectable average bE-am strain calculated in section 3.1 

Figure 31 shows a spectrum analyzer trace for both the MDS/9-633 sensor (top 

trace) and the resistive strain gage (bottom trace) at a paint where the beam 

excitation IS small. Note the output of each ~ensor IS precisely at 10Hz and 

that the MDS/9-633 sensor has a much higher signal to noise ratio than the 

resistive strain gage sensor, thus indicating that the modal domain sensor WI 

be able to provide strain measurement data long after the resistive strain gage 

has reached Its minimum. Also. the spectrum analyzer gave the amplitude of 

each detected Signal In dBV RAtS so that peak voltage was calculated using 

the conversion 

(42.3) 

Furthermore, the data of Figure 31 corresponds to the first blackened data 

point in Figure 30 and is seen to be at the low end of the usable range of the 

resistive strain gage. Similarly, the polaroids of Figure 32 correspond to the. 

second blackened data point of Figure 30 and are the result of a larger beam 

excitation. All data shown in these photographs were averaged eight times for .. Visual purposes only. Finally, 'Figures 33 and 34 show the Vibration exciter 

input signal and the noise floors of the strain sensors at quadrature with no 

4 Q MDSI9-633 SENSOR EVALUATION 83 
r 1\'-

excitation, respectively The bottom trace in Figure 34 corresponds, at 10 Hz, 

to the noise H04 5 dBV RMS) of the MDS/9-633 sensor, while the top trace 

corresponds to the noise (-86.0 dBV RMS) of the resistive strain gage sensor. 

Using equations (4.2.1), (42.2) and (4.23) it is easily seen that these noise 

t 

i 

J 

figures correspond to minimum detectablE' average beam strains of 

L = 2 8xl0-! m/m and & ~ 0.1xl0-i m/m for the MDS/9-633 and resistive 

strain gage sensors. respecttvely. This IS in very good agreement With the 

predicted minimum detectable strains for each sensor and lends validity to the 

j assumption of negligible excess environmental noise. 

I There are two final comments to make before moving to the next section. First, 

It should be mentIOned that the maximum tip deflection never exceeded more 

than a few millimeters for all dynamic measurements. Second. although no 

values for beam displacement have been given, this can be calculated If the 

average strain in the beam is known using the relation 

(42.4) 

where d is the beam tip displacement from its undisturbed position. L is 

length of the cantilever beam and h is the beam Jhickness [1]. For the modal 

domain sensor, this gives us 

'.0 MDSI'S-633 SENSOR EVALUATION 
, 

.. 

-- ---------------

d = __ V_pe_a_k _ ( 43Lh2) • 

VQ~P L,1l \ 

where the beam is assumed to be mitially unloaded . 

4.3 Extraneous Dynamic Modulation 

--~. ----... 

(42.5) 

At this point it is reasonable to wonder if there are any effects other than 

rotation of the three lobe mtens/ty dIstributIon whIch gIve rise to the sIgnals 

discussed m the prevIous section. In order to investIgate this. a properly 

rotating three lobe pattern was obtained and the detector positioned. with the 

iris fully open, so that the pattern filled the area of the detector face. The t: 

was then caused to vibrate at 10 Hz using the vibration exciter, with data taken 

as peak voltage readmgs at the output of both the photodetector and the 

resistive strain gage sensor cirCUIts. Figure 36 shows this data taken for a 

senes of varying signal amplitudes mto the VIbration exciter. The data is 

plotted as millivolts of extraneous modulation out of the photodetector versus 

resistive strain gage detected strain. 

Figure 37 shows polaroid photos of the spe".:trum analyzer traces for large (top 

photo) and moderate (bottom photo) beam excItations. These correspond to 

•. 0 MOSl9-133 SENSOR EVALUAnoN 
, 

,-

f 

their respective blackened data points in Figure 36. Similarly, Figure 38 shows 

a polaroid photo of the spectrum analyzer trace for small beam excitation and 

corresponds to the blackened data point nearest the origin in Figure 36. For 

all photos in Figures 37 and 38 the top trace shows the output of the resistive 

strain gage sensor while the bottom trace shows the extraneous modulation 

output of the photodetector. Figure 39 sliows the noise floors, with no 

excitation, for the measurements of extraneous modulatIOn. Agam, the top 

trace corresponds to the nOise of the resistive strain gage (-88 dBV RMS) while 

the bottom trace corresponds to the noise of the photodetector output (-99.5 

C1BV RMS) 

In a tYPical measurement Situation, recall, the iriS Will be closed, leaving"'-

a 1.0 mm aperture. This means thal with the diameter of the iris open bem~ 

12 cm, only one 144"1 of the pattern is spatially filtered in a normal 

measurement situation. ThiS spatial filtering also takes place at approximately 

the average intensity of the pattern. at quadrature. so that the extraneous 

modulation figures shown in Figure 36 will be divided by 144 for measurement 

situations such as those described in section 4.2. For the largest extraneous 

modulation reading of Figure 36 (-62.1 cBV RMS or 1.11 mV), the 

corresponding value after spatial filtermg is 7.7J.LV (-105.26 dBV RMS). This is 

easily seen to be well within the noise of the optical sensor output. even as 

shown in Figure 34. We thus conclude that the results presented in section 42 

40 MDSI9-633 SfHSOR EVALUATlOH 
are entirely due to three lobe rotation and that extraneous modulation effects 

are entirely negligible. 

As a final commp.nt for thIs section, it has been suggested that, though small, 

the extraneous modulation effects are due to bend loss. If this were true, 

however, a peak at 20 Hz would be found due to bend loss occunng when the 

fiber both goes Into tensIon and compression as the beam vIbrates, but no 

such "peak was observed. A more likely reason for the extraneous 10 Hz 

modulation is that some 10Hz excItation is being transmitted to the floattng 

table as the cantilever beam IS forced to VIbrate. Because the 10 H~ 

extraneous modulation figures are small, though. It is eVident that the fie 

table is properly performing Its function of excess Vibration suppression, as 

expected, even though a VIbrating structure is attached rigidly to It 

4.4 Static Strain Measurements (First Attempt) 

It was also of interest ~o study the static strain measurement capabilities of tr,_ 

MOS/9-633 sensor. As with the resistive strain gage evaluation measurements, 

the cantilever beam was loaded as shown in Figure 25{b), with masses 

, 

periodically added to the basket in excess of an imtialload mass of 200 grams. 

Now, however, the change in average beam strain, as measured by the 

4.0 MDSJ9-633 SEH$OR EVALUAnoN 87 
'-- .... ~ 

MDS/9-633 sensor, was to be compared to the known mduced change in 

average beam strain caused by varying the load mass. Recall that the Induced 

change in average beam strain IS given as 

3mgL 

Ebh 2 (4.4.1) 

where m IS the change in load mass. Further recall that this same quantity. 

as measured by the MDS/9-633 sensor IS given by 

(4.4.2) 

as was shown IS section 3.1 and where 6/1 = 

As before, the input to the optical fiber was adjusted until a properly rotating 

three lobe pattern was observed and the Q-point was adjusted, with the initial 

load mass In place, U' '9 the excited PZT cylinder. Mass was then added to 

the basket and .lV measured (thiS time through use of a strip chart recorder) 

as the excess load mass reached 50, 100, 150. 200, 250 and 300 grams. It we:. 

observed, however, during early static loading tests that there was 

appreciable pattern drift over a period of a minute or so. It IS believed that this 

drift IS attributable to the static strain control me.:hanism and due in part to 

jacket shear for large amounts of induced static strain {recall It \"3S mentioned 

• 0 MDSJ9.633 SENSOR EVALUATION 

.. 
-- - .... ", --.....- - -,.-- -~------.,----...... ---------- -} 

earlier that obtaining a rotatmg three lobe pattern was often facilitated by 

tensioning the fiber uSing the static strain control device). As the need fo. 

loadmg, unloadmg and settling the basket make the procedure for taking static 

stram data much more lengthy (1-2 minutes) than the procedure for takmg 

dynamic stram data « 30 seconds) It was necessary to fully release the 

tension of the fiber m the static stram control device when static stram 

measurements were to be attempted 

In addition, prellmmary plots of measured versus induced stram data gcwe 

regression lines whose slope was ~ften noticeably different from Untty. This 

was believed to be due to the physical parameters leading to the calculation 

of :x, in equation (4.4 2), not bemg precisely known for the fiber bemg used. 

In an attempt to directly measure.., )€. launch conditions were adJusted until 

a three lobe pattern was obtained WhlCI exhibited proper rotation over greater 

than 300°. With the fiber between the spools of the static strain control device 

just taut, the tension in the fiber was increased by turning the micromet~~ 

screw until the pattern rotated 1200 (lobe peak to lobe peak). The change 111 

the micrometer setting was then recorded and the tension in the fiber qUlckJy 

. released. This procedure was repeated several times and It was determined 

that the micrometer was advanced an average of 691.um for 120° rotation. The 

4.0 MDSJ9·&33 SENSOR EVALUATION 89 
I 

change in length ~L,:o of the f.ber between the spools was therefore 

approximately 

-1( 691 um ) ~L'20 = r, sin r2 = 564.75.um • 

where r, = 7 62 cm and r: = 9 32 cm reprpsent. respectively. the radius of the 

rotaiJng spool and the length of the push rod. This indicates that a change '" 

length of 141 19 .um .s needed to cause a rotatIOn from quadrature to the 

nearest lobe peak (a 30° rotation). 

From equation (3 1 11) we can solve for the change," fiber length required to 

cause pattern rotatIOn from quadrature to the nearest lobe peak as 

(44 ~' 

where. recall. ~p = 1 2x104 m-I for the MDS/9-633 sensor. With 

~L:::I = 141.19 .um we can thus solve for x to find :z = 092. on average. for our 

fiber. 

New data was now taken for 2=0.92. With RL = 50kO. See Figures 40 and 41 

for plots of this data and note the near unity slope for each of these figures. 

In addition. the quadrature point voltage Va was 25.8 mV and 23.1 mV for the 

data of Figures 40 and 41. respectively. 

~.O MDSJ9.633 SENSOR EVALUAnON 90 

- -.. ~ -
r 

It IS Interesting to note that the highest POint on the regressIOn line of Figure 

40 occurs at ~l, = 1045 um!m or .1L, = .1l.L, = 60.1 um. This indicates thelt 

". the response of the MDS/9-633 sensor stays linear for ilV, in equation (4.4.2), 

approximately as large as 066V;; The dynamic range for thiS linear response 

region can thus be found. m decibels. as 

DR = 10 log I ~max 

OPmm 

DR = 10 log 

o 66Po (4 4.4) 

where i1Pm1n was given In equation (23.10) and where Po is the optical powt:. 

through the spatial filter aperture at quadrature. Recall that the voltage at the 

output of the photodetectlOn CirCUit is directly related to the optical power 

through the spatial filter by the photo diode responsivity ::;f and the load 

resistance RL.' USing the system parameters used in section 3.1 to determine 

the minimum detectable stram of the MDS/9-633 sensor we thus find that the 

dynamic range of this sensor, in the lu'ear region, is approximately 52 dB. 

'0 MDSI9·633 SENSOR E'.II.LUATJON 91 
r 

4.5 Static Strain Measurelnents (Second Attempt) 

Due to the dnft problems encountered uSing the static strain control device 

shown In Figure 24 It was deCided that this deVice would be redeSigned and 

additional static strain measurements attempted. Shown In Figure 42 IS the 

resulting new static strain control deVice. As seen. a length of optical fiber IS 

attached to t\".'o aXially aligned mounts. one of which exhibits aXial translation 

as the motor shaft turns The motor used was a 200 step per revolution 

stepPing motor and connected between the motor shaft and the movat-'-

mount was a #2 threaded rod with fiftY-SIX threads per Inch As the ga~_ 

length of fiber between the two mounts was measured to be L, = 0522 m. then 

for every step applied to the motor the change in Induced average stram in the 

fiber was t:\l = 4345 J,lm/m 

This new static strain control device prOVided several advantages. First. the 

induced strain m the fiber was purely aXial. as opposed to the axial and 

possibly transverse strains mduced in the fioer wound on the spools of the . 

static stram control deVice. Second. t:'ere was a very Simple relation between 

the number of steps applied to the motor and the strain induced in the fiber, 

, 

as discussed above. Most importantly. though. was that there was no jacket 

shear in the fiber between the stationary and movable mounts This effect was 

40 MDSJ9.633 SENSOR EVALUATION 92 
r 

' . 

. "

I 

eliminated by first stripping the fiber of Its Jacket at the pOints where it was 

clamped and by then bondmg directly to the bare fiber a length of stainless 

steel tubing. Due to the more ngid nature of the stainless steel tubing and the 

epoxy used to bond It to the bare fiber the, induced strain was more faithfully 

transmitted to the optical f'ber, with no relaxation of the tension occuring due 

to elasttc stretching of the polymer Jacket. Indeed, It was observed that 

negligible pattern dnft occurred over a penod of several days with the fiber 

under Significant tension. The only disadvantage to uSing tne neN static strain 

control device was that the fiber betwe~n the clamps had a tendency to break 

Just at the pOint where the fiber eXited the stainless steel tUbing This is 

believed to be due to slight aXial misalignments of the fiber mounts causing 

high stress concentrations m the regIons of these breaks. 

As before, the Input to the fiber was aligned such that a three lobed intensity 

distribution was present at the output that exhibited pure rotation. Pains were 

taken to ensure that the alignment was such that this rotation would occur ave: 

most of a full revolution Then, uSing a linear x-y positioning stage the spatial 

filter aperture was positIOned over the peak of a lobe, with steps then being 

applied to the motor to cause the pattern to rotate to the point where the 

spatial filter monitored the pOint located half way between the maximum and 

minimum intensity paints of a lobe. Due to the discrete nature of the increases 

in applied strain, though, the proper quadrature point was often overshot. 

4.0 MDSJ9-a33 SENSOR EVALUATION 93 
requiring final alignment uSing the x-y positIOning stage With the operatmg 

point thus properly set. strain was measured as additional steps were given to 

the motor 

As before. the strain measured by the MOS/9-633 sensor followed equation 

(4.42). In addition. as before It was noticed that plots of preliminary measured 

versus Induced strain data gave a linear regression line with slope different 

from unity when :t was taken as :x = 0.78. By fitting only the first POint of . 

preliminary data to a regression line of unity slope it was detemllned that 

:x = 0 86 was a more acceptable value. Assuming 'l = 0.86 additIOnal data was 

taken and IS shown In Figures 43 and 44 

Two final comments are necessary. First. the method by which ex 

determined for the data plotted In Figures 43 and 44 is admittedly questionable 

due to the preliminary data used to determine :x possibly not being 

Independant from the data subsequently taken and presented There simply 

was no way in which a reliable and independant determination of ex could be 

determined with the setup used. Indeed. an independant determination of the 

photoelastic coeffiCients used to calculate a is likely to be an Involved task :n 

itself. It IS believed. however. {"at photoelastic effects must be considered as 

the fiber is subjected to strain and that the analysis leading to equation (4.4.2) 

40 MDSJ9-633 SENSOR EVALUATION 94 
, 

I 

, 

I 

I 

~ 

------------

is correct The value of :x. however. and its constituent terms IS very much 

open to question_ 

The other comment necessary IS that this second round of static stram 

measurement data was taken uSing a UOT model 81 Optometer This 

Instrument directly displayed the optical power passing through the spatial 

filter aperture and inCident on the face of the detector head. As per tldiscussion In section 3 1 leading to the result of equation (3.1.14), however. 

UP and Pc may be directly substituted for tlV and Vo in equation (4.4.2). The 

value of P:; was 0.13 uW and 0.16 uW for the data plotted In Figures 43 and 44. 

respectively. 

4.0 MDS19-633 SENSOR EVALUATION 
l 

; 

• ! 

~ 

~ 

..... 

L - - - - - - '-r-t-==';';""'+-r-' 

:'::-- ~~ .. -~ ? :-~':-~ :3 

~.E Z:;C: .. ;-_:~::y 

_________ J 

STATIC STAAl.., J 

CDIoITltOl. ~".C;. 

pZT CVLINO£R 

:~e.1"4rION~'" ~ ~T41t) 

OPTICAL. ~&L~ 

~Tlv& S1'RA'" 6ACIIa (~e«eD 

e.«.eentc.ALL.'f 

eUl/~, A.o,jD l't-At@ 

~(J OJ.UL 

PM-fi/Col~Y 

.uN OIT A 

IN 

~ 

1'1& 

~f;1'1It1G. C~ OF ~ CAHflL.I?VIlR MAM) 

Figure 23. Uperlmental MDSI9-&33 system 

.0 MDsn.633 SENSOR EVALUATION 95 
· I 

J 

l;-

t: 

f 

, - --- --- - - -~--- - .-.- ..-.. --...... 

OUTPUT 

(I) (Il 

(I) SPOOL ON WMICH OPTICAL. r:'IOe.R IS WOUNO 

(11 OPTICAL FINIt UNOtaR "'N~IO" 

(3) Aleuo MOUNT MTWU". SPOO~ • O9'rICAL 'T~.L. 

(iI) Rl~IO MOUNT aeTWUN ~L r. ItOTATAa&.~ .... 

(5) RO'rATAeL.5 -.ua 

(61 O"~CAL. TA8L.& 

('f) MIGRO .... Taa SCMW OIlVIC~ 'n) PaOYIOji ~ 

ON TH& ~ ROO 

(8) PUSH ROO 

F1gure 24.. First static strain control deylCe 

4..0 "'DSI9-633 SENSOR EVALUAnON 

INPUT 

97 
GLA~P 

(0) 

LlJa.,CAT&P kL~ 

AN P 5oGiC.liT ..7OINT' 

F=~~ VI'IATION ucrra" 

(INPUT VIA 516N~ 

,....i::s::::::z:'L:. ~t4UA TO .. ) 

{OrT1CAL§ ""NTlLEV"", ",AM ~ 

8A~&T IN WNICH IUIOWtJ 

MA~.5 A~& PI.A~r> S:O~ 

STATIC L.tlAD'NCir PU~~~&S 

I , / I / 1 ; } I ; J ; I 1 I I I I I I I I I I I I I I I ) 1 I 1 

FIgure 25. loading schemes 01 Ute expenmental MDSJ9.633 sensor system 

40 MDSJ9..633 S£HSOA EVALUATION 91 
,. 

I 

\ 

I 

: 

v 

% 

• 

~ 

: 

to 

• I, 

.. 

: 

-- - "" ~ ,- - -

48 r 

I 

3S~ I 

3~ .,:;1 

.. 1 

1 

i 

I 

] 

, 

,. 

: 

Ii 

RSC OUBRIlfIVH OtlTIl 

-

.~-

15 Zil 

, ", 

,'" ". 

25 

IH»UcrD stRAIN (ual .. > 

39 

TrlE REG~ES5IO~ FOL~NOMI~L OF L:NE 

( ~.=1~E-011 + \ 9.8~~E-0~).~ 

ThE VARIANCE - ~.704E-02 

FIgure 21. Resistive strain g~ cahbrationlevalu.tion data 

40 MDSJ9.633 SENSOR EVALUAnON 

--_ ... --------, 

1 

J5 4~ 

99 
ORlGYNAI: FA"GE! is' 

OE POOR QUALITY: 

4.0 MI)S/9·633 SENSOR I!:VALUATION 100 
.. 

,. 

ORIGINAJ; ? A"'G"£. IS 

OF POOR QtrAUTY. 

Figl.lrlt 28. Highly aligned MOS/9·633 $(!fl$l)f output (sell!! text for details) 

4.0 MOSf9..633 SENS,OR EVALUATION 101 
.... e: s :1 

" f 

\ 

f 

: 

., 

;: 2SE!i'£4, ... CP04,4 

K 1G$;&33 V5. RSC stMIM MrASURDCOOS (RIAL 1) 1.,T-----______________________________________________ ~ 

, 

3J 

,../" 

/ I /' I 

/ ! ./ I ,/ 

0( =.78 

i 

111 

T~E ~EGRE3SIO~ POL,NOMI~L OF LI~E 1 

\-6.875E-0:1 + ( 9.688E-01i*A 

TnE VARIANCE - 2.42=E-03 

Flgur. 29 MDSJ9.633 dynamIC strain measurement d8ta (trial " 

40 MDS19-633 SENSOR EVAlUATION 102 
. " 

---- ,,- ---.. _-

IlC HDS/633 YS. RSC stRAIN MIilSURDIDfTS iTRlilL 2) 

6 

1 U i ... 

I / 

I , 

I , . 

. SJ , 

.- i ,. 

/ 

I , . 1 ., 

,. 1 . . I I . \ , I 4~ 

: / 

, 

" , . ., . .. . 6-

.. 

c: , .. .. 3_ 

po . ~ i / 

/ ~ 

(II I /t: 

I'l I / . '" I . \ ZJ 

v. 

:: 

I .. 1 -r 

L ... ., I .., :rJ 

I Y 

" 0( :.78 I , . 9' , I 

Q t i l 4 5 ~ 

RSG StR~IH lllah.) 

---- . ! • \.."~:",!..-. -. "" .a ... 

• 

FIgure 30. MDSIS-£33 dynamIc st.aln measurement data (trial 2) 

4.0 MDSI9-&33 SENSOR EVALUATlON 103 
PRlGINALPAGE IS' 

DE :rOOR QUALITY 

Fl~IJr~ :31. MDsrl,S33 and resistive strain gage outputs for small excitation 

4.0 MOSlSll.633 SENSOR EVALUATION 

\ b) 

104 
O:':UGfNAL PAGE IS 

QE fOOJ!t Ql.1AIJXXj 

Figure 32. 1II105{9·633 <lmd ft'lsistiv(ll Irtrsin Lll!gl!: outputs for largt1l excitation 

4.0 MDSJ9-633 ~IENSOR EVALUATION 

(0..) 

HIS 
Figuro 33. Input signlll of th~ vibration ellcit"f 

4.0 MDSI9·633 S;£NSOR EVALUATION 106 
f1gUflJ 34. NO!$@ nOOflll of th(l MDS/S·633 and re$istivf! strain gage sensors 

4.0 MDSI9·G::i3 SENSOR EVALUAnON 107 

L 
" r 

, 

r 

~ 

v 

% 

• 

I 

.. 

.. 

... 

II 

It 

, 

II " 

II 

~ 

I 

At tIM/'ll ¥s. ItSC StAAl" tmlSURDlDftS (tRIAL 3) 

18 I :i' 

9j .; 

/ , 

I /' 

/ .I' 

:J 

, 

,//' 

,.,/" 

, , , 

I " I ", 

'1 , , 

, , 

, , 

! , . , 

, I 

51 , 

/ 

I ;' 

./' 

~ ,/'D 

I / 

,.I' 

3~ / 

,.I' 

.,.! 

2j i], oJ 

I _if' 

Ij If' l/ 0< =.16 

8, i ~ I i ; i 

3 • $ .; 1 8 

ISC stRAI" h.w'.) 

ThE ;:;EGRE.35IO~ FO,-t:'llOi'lIHL Or LHJE 1 

\ 1.07 =E-CIJ + , 1.0:aE+00J.X 

ThE VARIANCE - 1.406E-0~ 

Fi9ure 35. MOS/9-633 dynamIC strain meuurement data (tnaI3) 

9 

4..0 MDSJ9.633 SENSOR EVALUAnON 

ORIGINAL; PAGE IS 

OF POOR Qt1AI.roJ 

19 

108 
'i 

:i 

~ ~ 

, " 

r 

" 

11I 

J 

.: 

lot 

,J 

0 

, 

.. 

.. " 

0 

Z 

'" .. 

c: 

. 

-. 

-

ORIG~~.!.~ ?X~ I5 

OE P.OOR QUAUTY 

U1RAHEOOS AC MOIMlLAtlON 1.~-;-_____________________ ---. 

I 

l~ 

I 

I I 

I 

.~j 

, , 

'l 

,c 

, , 

/ 

~/ ... _/u 

/.0 

. ./ 

9",' 

r I i 

~ i 2 S 

RSC STRAIN (uMl .. ) 

TnE VARI~NCE 4.0~5E-04 

FIgure 35. Extraneous dynamIC modulatIOn 

40 MDSJ9.633 SENSOR EVALUATION 109 
ORIGINAL PAGE IS 

0.1 roaR QUALITY; 

Figur'!l 37. ElItMllllHl.!lB modulation signals for largfl and moderat(! excitations 

4.0 MOSI9·633 SENSOR EVALUAilON 

(0..) 

( b) 

110 
OlffGlN"A!! PAGE m 

OF. POOR QUALITY 

FiglJrl!l 3a. txtfllnttOus dynamic modult1tthm signals for small beam excitation 

4.0 MDSJ9·633 SENSOR EVALUATION 111 
~00l' . .\!: ?~ r3 

D! 'pGOR QL~AiXry. 

FlgUllll 39. EX!tnafl~OUIll (;ynlllmic modulation noh';1il floors 

.t.O MDS19-633 SENSOR EVALUATION 112 
p 

~ , 

J 

.j 

! 

1 

• 

~ 

• E 381 I 

zJ 

I 18~ 

I 

Q I 

18 

I 

28 

OLD StAtIC StRAIN COHTIOL DAt~ (til~~ 1) 

, 

48 

, 

6i 

i 

7i 

ACTUAL FUll STRAIN (ul.) 

j 

88 

0<: = .92. 

ThE ~EGhESSrON FOLT~OMIHL OF Lr~E 1 

\ 1.Q~4E+00) + , 1.019E+00)lX 

ThE VARIANCE - 4.704E+00 

"19\1,.. 40. MDSJ9.633 static strain measurements (first attempt tnaJ 1) 

.0 MDSJ9.633 SENSOR EVALUAnON 

118 

t13 
, -- - C'~i~_""':''''1-' ;'~_o,J.:..,.~ 

:':;' r,~O:\. Qu:.~17Y 

OLD ST~TIC Sr~iH COhl~L ~TA (TRIAL 2) 

1111 

11 ,,' 

,-

,a~ .- /,.~ 

,-

, 

I . 

, 

.. I ,-

I 811~ / . - \ ,/ 

I I ./' 

· I 

· 78J 

/ 

.. ~, 

I .. ,r 

% ! -'" 

• , ,/' 

II: 69~ I: I .. '" I r ,,/' -' II 

5~ .- ..,-

Q ,-

, 

.- .. I , , : I 

: 48~ . . ~ ,- e 

'I JIl~ t , , i , 

28~ /" 

/ 

i ,,~l'J , 

I , 

19~ .- , , 

.-

" I .' ot. =.92-

e1 

Q 18 211 

THE 

. 39 411 511 611 711 88 

ACTUAL flSfR STRAIN (wVlI) 

\ 7.o1-:E··:l: .. - \ y..';J:·E-')l ., 

;ME ~A~i~.CE - ~.:i~E·v~ 

F"JgUr. 41. 1IDSJ9-533 static straan measunmMttS (first .Uempt; bUt 2) 

40 IIDSJ9.&33 SENSOR EVALUATION 

98 ll)j 

• 

I 

,,//} 

i 

I 

I 

11~ 

114 
--- <~------------~ 

SIDE. VIEW 

<D ~ c.aNT12O\.. £L&CrItON'C5 

(j) DC. MCr'I'OA ~ STaPPtN6 ~ 

~ ~~Ii SHAFT 

8~.-oo 

S MOYA8I.& MOLltn' 

~ OPTICAL Fleu'1t) .. ST1IAINaD 

& 6TAT'ONASt'f MOUNT' 

~ .~N CQNTItQ.LaR a45e PLAT~ 

<i CLAMPS 

Ftgurw 42. Redesigned static strain control dnice 

4 0 MDSJ9.133 SENSOR EVALUAT10" 115 

e • ., 
55T-______________________________________________ HiM STATIC STRAIN CONTROL DATA (TRIAL 1) ~ 

5 

4S 

I , I 

ZI1 25 39 3S 

KfUAL nBER StRAI" (u..t.> 

ThE ~EG~ESSION FG~iNOMIAL OF LINE 

I 

4S 

\ 1. 785E-Ol) + ( 9. 947E-.)1) *', 

ThE VARIANCE - 5.671E-01 

Figure 43. MDSJ9.433 smO,1: sInin me.aurernents (sv.ond attempt: tna11) 

U MDSf9.(i33 SENSOR EVAl.UAnON 

sa 

116 
-

.. 

, 

\ 

, 

, 

.., 

Z 

~ 

Z 

.. 

II 

A 

.. 

z 

: 

., 

c 

;: 

E 

55 

511 

I 45~ 

4a~ 

I 

I 35J 

31i1~ I 

I 

I 

I 

25

1 c:a~ 

15., 

18~ I 

i 

~i 1 

I 

HEW StAtIC StRAIN COHtJOL DATA (tIIAL 2) 

/I YI 

...' I 

'" I )Y 

9 1 

i ~----S--~19----1~~--~2~r---2~5--~3i----3~5----48----4-S---S-Ii1----5S 

ActUAL FrSD StRAIN (u.v.) 

'ME v.:.;;r":'NCE 

• 

4 0 MDS19-633 SENSOR EVALUATION , '\ . -.,....-- ~ .. -. --_ ... \ 

117 
I 

L 

5.0 CONCLUSION 

Modal domain sensors usmg 9 um core diameter fiber at source wavelengths 

of 633 nm and 850 nm have been thoroughly described. The mode content of 

the most commonly observed intensity distributions at the fiber/sensor 

outputs, for each wavelength. have been discussed and the resulting str 

modulated behavior of these intensity distributions has been proven from first 

principles. In addition. It has been shown how thiS strain modulated behavior 

may be used as a strain detection mechanism and suggestions have been 

made concerning how micro-optlcal components can be used to construct a 

MOS/9-850 sensor. 

The linear and highly sensitive nature of modal domain sensors has also been 

predicted and experimentally venfled for small amounts of strain and the 

dynamic range of a typical modal domain sensor has been calculated. 

5 0 CONCLUSION 118 
[ 

I 

i 

Furthermore the many advantages and disadvantages of the various modal 

domain techniques have been addressed In great detail. 

It IS hoped tnat future work with modal domain sensors will Involve a t:omplete 

experimental evaluation of a MDS/9-850 sensor and that further investIgations 

Will result In the realization of additional in-line micro-optical 

inJection/detection techniques for modal domain sensor use In additIOn. an 

Independant study 1n~0 the values of the individual photoelasllc coeffIcIents of 

the optical fiber used In th~ previously described expenments should be 

undertaken with a parallel study undertaken to determme the radial changes 

of the core :ndex of refractIOn as a function of stram and how this Will affect the 

propagatmg modes. 

Finally, It was assumed m section 42 that for quasi-static Induced beam 

Vibrations at frequencies well below the fundamental natural frequency of 

Vibration, with small peak beam tiP displacements, that the cantrJever beam 

stress-stram relatrons held Just as If the beam was statically loaded. With 01"'" 

a sinusoidal multiplicative factor appearing for the quasi-static stram case 

was also assumed that only tne fundamental mode of vibration was excited. 

Although the correspondmg nature of the experimental results and the 

theoretical predIctions as to the behavior of the MDS/9-633 sensor lend 

5 0 CCNClUSION 119 
validity to these two assumpttons. further investigation may be necessary to 

finally prove that these assumptions are valid. 

120 

5 0 CONCLUSION 
I 

L 

APPENDIX A: Strain Characteristics of Loaded 

Cantilever Beams 

One of the simplest and most fundamental ways In which a newly developed 

strain sensor may be evaluated is by attaching It to the surface of a cantilever 

beam which IS placed under load. If the beam is construded from some 

homogeneous matenal, such as aluminum or steel then the strain 

characteristics of the beam are qUite easily descnbed as a function of load, 

thus making the loaded cantilever beam a convenient strain standard. 

Consider for instance the cantilever beam of Figure 45. Assuming the 

is made of a homogeneous material, the stress at any location on or within ••. -

beam is given by 

• MgZ 

(J = I CPa] , 

APPENDIX A: StraIn Chanct.rlstlCS of Lo"d Canttlev.r aeams 

-- ..... _ 7'- .. _- - .-

(A.1) 

121 
[ 

where z is the distance above or below the neutral axis. M~ = F x t IS the 

bending moment and I IS the moment of inertia given as 

(A 2) 

If we now consider only the surface which IS m tension when the beam IS 

loaded we fmd that the surface stress (1M is 

(J~r = (A.3) 

Recallmg that stram £. is related to stress by the relation £. = (1/E • where E IS 

the modulus of elasticity. we see that the strain along the tensed surface. of the 

cantilever beam IS 

(A.4) 

Note that this result indicates that the strain along the surface of the beam 

Increases linearly as a function of t. being zero at the free end and be .. _ 

maximum at the clamped end. The average strain in the beam thus occurs at 

t = L/2. Also note that by changing the sign of the strain relation in equation 

(A.4) one can descr~e the strain induced i~ the beam surface being 

compressed. The negative sign Simply indicates the compressional force. 

APPENDIX A. StraIn Characteristtcs of Load.d Cantll.".r aeams 122 

L - ---~ -
r 

& 

,. 

... 

" I 

I 

-------------------. - - -- - --

Often. though. one is Interested In the change m average stram m a situation 

where the loading force IS changed by varying masses attached to the beam. 

We will call this change In average strain dt whIch is simply gIven by 

3mgL ~t = 

Ebh 2 (A.S) 

where m IS the change In mass. g is the acceleration due to gravity and the 

fact that average stram occurs at {= L/2 has been used. This quantity can 

easily be measured by a resistive strain gage placed at the geometric centt. 

of the beam surface [12] 

A.1 A verage Strain Induced in an Optical Fiber 

In the evaluation of fiber optic stram sensors it is often desirable to loop a 

sensing length of fiber along a cantilever beam as indicated in Figure 4f; 

Since the output of an optical fiber strain sensor is actually a measure ot 

average strain m the fiber sensor length (more commonly called the gage 

length) we can calculate the average change in strain. ~ • to which the fiber 

IS subjected along its path by evaluating 

APPENDIX A: Strain Chartctensttcs of loaded Cantil ... , Beams 123 
j£, = jL 1 r

L

, = -L £.d{. L, f "0 

(A.G) 

where ~L IS the total elongation of the fiber path and L, IS the gage length. 

Usmg equatIon (A 4) we can evaluate ~L as follows· 

jL = 2J' £x de.J,. r £x ef( 

AS "SC 

jL = 2fL 6F! d! _ 2r C· 2 _6_F_(L_, _-~r_c_o_s_O_' sm t;J dQ 

L, Eh'b '0 Eh'b 

~L Gmg 2 2 2 = --(L - L, ~ 2L,r - r ) 

Eh 2b 

(A.7) 

Note that a simple transformation from rectangular to polar coordinates was 

necessary to integrate the strain effects in the curved portion of the fiber. Now, 

by dividing equation (A.7) by the fiher gage length and iecalling that m is the 

change in load mass we fmd that ~l, IS 

APPENDIX A: Strtlln Characteflstu:s of Loaded CantIlever Beams 124 
Smg 2 2 2 

d£{ = 2 (L - LI + 2L,r - r) . 

Eh bL, (A 8) 

.-" t where 

(A 9) 

Notice In equation (A 8) that If r= L, so that the curved portion of fiber lust 

touches the free end of the cantilever beam then 

..le, = (A 10) 

which, if L, == 2L, IS approximately the same result expressed in equation (A.S). 

More precisely, if we choose Lr. Land r properly, it is possible to make the 

... 

.. i results of equations tA.S) and (A.8) express the same quantity. Assuming L 

and L, to be fixed. we can solve for r as follows: 

Smg 2 2 2 3mgL -----(L - L1 + 2rLI - r ) = Eh 2

bL, Ebh 2 

2 2 2 L L - LI + 2rL1 - r = 2 (2(L - L,) + nr) 

2 ( :rL ) 2 r -r 2L '

-T -(L,L-L1) = 0 

APPENDIX A:. Strain Characteristics of Loaded ~ntJle,",r Beams 125 
(A.11) 

These last considerations are Interesting m that they demonstrate that by 

usmg simply loaded cantilever beams an optical fiber stram sensor can be 

subjected to known strain effects while havmg its performance evaluated 

simultaneously against more commonly used strain sensors such as resistive 

stram gages. Finally. It should be mentioned that due to the relatively 

insensitive nature of both resistive stram gages and optical fibers to 

transverse stram. no considerations in the prevIous formulations have been 

given to transverse beam contractions (13). 

APPENDIX A~ Strain Characteristics of Loaded Cantllevera.am. 12& 
b 

" 

~ I 

GLAMPEO 

aND 

/ 

b 

1.-: 

F. L.OADINC':a ~ORGe. 

l- • &E ......... l-£NGT ... 

b • 8&.AM WIOTIof 

h. BeAM "wIC)(NES5 

~ NIW'TJtAlAXIS 

-x 

Z c DISTANGIi ~.., ""EU~L .4)CIS 

FIgure 45. eancn.".r beam geometry 

APPENDIX A; Strain CharacterIstICS 01 Load~ CantJlftu..8.ams 121 
r 

r 

I F. L 

"ICAL ~I.£a SaHSO" - LI 

B: 

;t----------L~---------.: 

c 

,0 t 

1. • I jCLAMPEO E.ND s:R£& &NO 

1... c:.ANTIL£VU &UM L5NCilTH 

1..-L.1 • L£Nc:.TH O~ F'18ea WWIGM I~ STfU-ICaHT 

b. BeAM WIP'TW 

r. RAOIIA~ Of: CURVED FI8&R 5>IOH 

Figure". Optical fiber and reSlsllYe main gage placement .,.rameters 

APPENDIX A: Strain ChMacteristlcs of Loaded CantiJe..,.r aeamJ 128 

11 
.. 

1 

, 

, 

i 

I 

1 

! 

! 

~ 

APPENDIX B: The Resistive Strain Gage 

Lord Kelvin fIrst observed that a change In stra!'1 Imposed on a wire is 

accompanied by a change In resIstance ~R of the wIre The relationshIp 

between resistance change ~ and strain t can be derived by considering a 

uniform conductor of length L, cross-sectional area A. and resistIvity p. The 

resistance R of such a conductor IS given by 

R = pL 

A 

DIfferentiating equation (8.1) and dIvIding by R gi\tes 

However. 

dR 

R = 

APPENDIX B: The ResIstive StraIn C;lge 

dp dL 

P + L 

dA 

A 

(B 1) 

(B~) 

123 
. 

; 

. 

' . .. 

w " - ---..r. - ............. __ . __ e ____ 4 _____ _ 

dA 

A (8 3) 

under elastic deformations where v IS the POisson's ratio of the conductor 

matenal The strain sensitivity SA of the conductor IS defined as 

dR/R 

dLJL 

Substituting equations (B 2) and (B.3) mto equation (8 4) gives us 

1 ,., 2( dL ) ..... - ~\ - \ T . 

(84) 

l8.S) 

The last three terms of equation (B.S) are due to dimensional changes In t~o 

conductor The first term is due to changes of resistivity with strain. The last 

term is usually neglected for elastic strains since It IS small « 0 1£1 compared 

to the other terms ( - 1.60). The dcnvatlon of (8 5) IS modified slightly for 

large strains since the conductor undergoes plastic deformatlon [13]. 

APPeNDIX 8: 'Th. ReSist"'. Strain Gage 130 
l"' ..... ~:;~.. ~ »+V"lFY'*"q- COt ••• 5 ¥ 

-- - - -- - - -- - - -

B.1 Strain Gage Calibration 

In practice equation (8 5) IS not very useful smce It IS only valid for a single 

filament conductor and because the first factor which describes the change of 

resistivity With respect to stram IS often unknown. TYPically the conductor at 

a resistIve stram gage IS formed IOta a gnd to recuce ItS size as shown in 

FIgure 47 This causes the gage to exhibit sensitivity to both axial and 

transverse stram The response of a surface mour.ted gage that is '5ubjected 

to a aXIal s!rc:.n ~.1 a transverse stram E:. and a shearing stram ~~ can be 

expressed by 

dR 

R (8.6) 

where S~. Sr and S, are the sensitivities of the gage to aXial transverse and 

shearmg strains, respectively In general. the gage sensitivity to sheanng 

stram is small and thus neglected so that 

dR R = S..(E:a ~ kr£t) • (57) 

. 

where kt = S~S~ IS defined as the transverse senSItivIty factor for the gage. 

APPeNDIX 8: The "eSJstrve Strain Gage 131 

• 
I 

, . 

Strain gage manufacturers provide the transverse sensItivity factor kt and a 

calibration constant known as the gage factor for each gage. The gage factor 

Sg represents the calibration constant for a batch or lot of gages and IS 

determined by testing sample gages drawn from a lot of gages In a given 

production run Reslstc:.nce change dR expenenced by a gage IS related to the 

gage factor and the aXial strain by 

dR 

R (B 8) 

The stress field In the calibration beam used for the determination of ~ is 

always unaxlal. therefore the gage IS subjected to a biaXial strain of 

(B.9) 

where \'0 = 0.285 is Poisson's ratio for the cahbration beam material. 

Subshtuting equation (8 9) Into equ=3hon (B 7) and companng with equation 

(B.8) yields 

or 

(B.10) 

APPENDIX B: The ReslstlYe Stram Cage 132 
1 

", 

1 

r 

I 

Therefore when the stram gage IS used to measure unaxlal stram in a material 

other than the calibratIOn beam we see that 

or 

dR 

R = 

(8 11) 

where \ 15 the POisson s ratio of the structure to which the stram gage IS 

attached. It should be eVident from equation (8.11) that the calibratIOn 

procedure used to determme k, and S. allows transverse stram effects to be 

"calibrated out' of the actual stram gage measurement [13] Also. it should 

be eVident that the change m average strain In a loaded cantilever beam as 

deSCribed In AppendiX A could be measured Lsmg a resistive stram gage 

placed m the geometric center of the beam by usmg the relatron 

(8.12) 

where R is the imtlal gage resIstance (often measured). v is POisson's ratio of .. 

the test material and OR is the measured change in gage resistance 

APPENDIX B Th. Reststt ... stratn Gage 133 

-- --,,....-------------- --- -- -- --- ---- -- ...... .r: 
r 

f 

I 

t I. 

i 

i 

B.2 The Use of Wheatstone Bridges to Measure dR 

In order to enable small changes in strain and therefore small changes m 

resistance to be measured In a resistive stram gage. a Wheatstone bridge 

circuit with an amplifier output stage IS often used. A constant-voltage 

excitation Wheatstone bridge CircUit IS shown m Figure 48. For this bridge 

Circuit. the error voltage Eo IS given by 

Eo = lB.13) 

Equation (8 13) mdlcates that the Initial error voltage Will vanish (Eo = 0) If 

(B.14) 

When equatron (8.14) is satisfied. the bridge is said to be balanced. This 

means that the small unbalanced voltage caused by a change m resistance of 

any arm of the bridge is measured from a zaro or near-zero condItion. This 

small signal can easily be amplified to significant levels for recording. 

If a single resistive strain gage IS placed in the bridge circuit a mdlcated in 

10 

Figure 48, a voltage ~Eo developes at the input to the amplifier stage when the 

nommal resis!ance of the gage R IS changed by an amount ~ Such changes 

APPENDIX B The ReSistive Stnlln Gage 134 
f 

, 

~ 

4 -1 

m resistance are m general due to stram or temperature variations: however 

m the following analysis the change m OR due to temperature effects will be 

assumed negligible. 

If the fixed resistors R2 RJ and R4 are chosen to have the same resistance 

value as the nommal reslstan.:e R of the resistive stram gage. we have that 

(8 15) 

"Jhere 

jR/R 

'7 = (8 16) 

Substituting equation (8 16) anto equation (8.15) we fand that 

~o = jR!R ) -~-J-'R-T-2-, Vm 

~o = 1 ~ ( 2 )'V 4 R IlR/R + 2 In 

APPENDIX B. The Resistive Stram Cage 135 

--
I 

I 

I 

r 

r 

J 

I 

I 

I 

J 

r 

\ 

where the binomial expansIOn (1 .,.. a)-I::: (1 - a) has been used since 

tYPically .lR «R Continuing. 

~2 

--2- Vm 

8R 

(B.17) 

Since the second term of equation (8 17) IS very much smaller that the first. 

we have 

1 .lR = 4 TV,n 

The output of the Invertmg amplifier IS then given by Ihe relation 

V!)(Jt 

R-

= __ 'J ~£o = 

Rs 

1 

4 

(B.18) 

(8.19) 

where Rs IS chosen large enough so as not to cause slgmflcant loading of the 

bridge network and where a near-zero Inilial condition IS assumed for Mo 

(i.e .. the bridge IS assumed to ~e Inlhally balanced) [14]. 

8y substituting equatIOn (8.12) into equation (8 19) and then rearranging 

terms we flnd that the change in average strain induced in a resistive strain 

gage is given ,by 

APPENDIX B The ReSIst ... ,. Strain Gage 136 

- ." ...;:::.- .... _- - -
~[ SgRs (8.20) 

Due to the linear nature of resistive strain gages. WheatstJne bndges and 

simple inverting amplifiers. the peak change In average strain as Induced in a 

resistive strain gage by a sinusoidally varying strain field is given by 

.JR- [ 

Sg;6 ] . (8.21) 

where the negative sign has been dropped in equation (821) since V"' which 

represents the amplitude of the smusOIdally varymg output voltage. is 

Independant of phase Considering once agam the case of measunng the 

change In average strain In a cantilever beam we see that equation (8.20) will 

be most useful when the beam IS subjected to a static load and that equation 

(821) will be most useful when the beam IS forced to Vibrate under the 

Influence of a Sinusoidally varying load. 

Finally, In order to investigate the minimum detectable strain for a resistive 

strain gage used in a detection network such as that of Figure .48, we 

differentiate equation (8.21) and divld~ by dip to obtain 

. dRs 

+ --Rs (B.22) 

APPENDIX B. The Resisdwe Strain Gage 137 
------- -------------- ---~----~- . 

where In equation (B 21) k \ 0 and v are assumed to be constant and where 

dRs. dRs and dSg represent manufacturer stated tolerances on the values R,. 

• « R. and Sg. respectively. Also. dVp and dV,,, represent the inaccuracies of 

measunng Vp and V n on. say. digital voltmeters. oscilloscopes or spectrum 

anallzers By then setting the ratio dJ.£~1 J.£;I equal to unity and solving for 

V;. we will have a minimum value of Vp needed for reliable measurements 

whIch when substituted Into equation (6.21) will gIve the minimum reliable 

value of ~£p MInimum detectable strain values on the order of 10-' are not 

uncommon for resistive strain gages used in typical measurement situations. 

wIth hIgher sensItivities expected In cortraled laboratory envIronments [13] 

... 

: 

... 

I, 

APPENDIX B: The ResistIve Strain Gage 138 
,--

I 

I 

I 

L 

, 

h 

GOt-.! .... e.CT TO 

WHeATSTONe. eRID<:a1iE 

ResiSTIVE STRAIN C2A.<:aE. 

Figure .s7. A resistive strain gage 

_PPENOIX B: The ReSistive Strain Cage 

- "-- ~ 

139 
" 

I 

+ 

Eo 

R,= RE51~TIVE $TRAlN 6A6E 

-R"/AS a AMPLIFIE~ 6A1t.I A 

FIgure Q. A Wheatstone bridge circuit with amplifier 

APPENDIX B: The ResastlVe Strain Gage 

+ 

VOUT 

140 
ta'--. 

r 

l-

• 

APPENDIX C: Bessel Function Numerical 

Expansions 

The following numerIcal expansions for Jo(x) and J.(x) can be used to aid in 

,: 

plotting modal intensity patterns [151. 

whe:-e 

. 

, 

A = 2.2499997 

B = 12656208 

APPENDIX c: B~ssel Function NumerlQl ExpanSJons 1~1 
'. 

~ 

/:. 

. 

.. " 

1-

l~ ~ 

'. 

c = 03163866 

D = 0.0444479 

E = 0.0039444 

F = 0.0002100 

and 

where 

G = 0.56249985 

H = 021093573 

I = 0.03954289 

J = 0.00443319 

K = 00003i761 

L = 000001109 

The.5e expansions gIve eight sIgnificant digIts for -3 ~ x ~ 3. For reasonable 

departures of I x I ~ 3 these expansions also give very good results for plot' 

purposes. 

APPENDIX c: aessel Function Numeru:a' EzpanSions 142 
-~-. ~ ----.... ------- ------.... -,. --~~oot-n ____ ~.-_~_~~_-. _ _ --.-J 

APPENDIX 0: FORTRAN Programs 

The following FORTRAN programs are useful for generating the data needed 

to create the hne and surface plots of the vartous intensity dlstnbutlons of 

Interest in modal domain sensing. 

APPENDIX D FORTRAN Programs 143 
ccccccccccccccccccccccccccccc~ccccccccccccccccccccccceeecceeeeeeccceecce 

e c 

c THIS PROGRAM GENERATES THE VALUES WHICH WHEN PLOTTED RESULT C 

C IN THE LINE PLOTS WHICH DESCRIBE THE TWO LOBE PATTERN OF C 

C INTEREST IN MODAL DOMAIN SENSING C 

C C 

cecceeceececcccccecceecececececccecccccccccceccececeeccecceecccceccccccc 

c 

c 

c 

c 

c 

C 

C 

e 

C 

c 

c 

C 

C 

REAL JO(100).J1C100).XVAL(100).I.J.K.L 

A = 0.56249985 

B = 0.21093573 

e = 0.03954289 

D = 0.00443319 

E = 0.00031101 

F = 0.00001109 

G = 2.2499997 

H = 1.265620a 

I = 0.3163866 

J = 0.0444479 

K = 0.0039444 

L = 0.0002100 

RBAR = -4.59 

DO 10 N = 1.100 

RBAR = RSAR + 0.09 

XVAL(tD = R8AR 

Xl = 62S-R5AR/3.0 

XO = .400_RBAR/3 0 

JO(N) = 1.0 - G.(XO-~2) + H.(XO •• 4) - I.eXO--6) 

$ + J.(xo •• a) - K.eXO-.I0) + L-eXO--12) 

J1(N) = (0.5 - A.(XI--2) + 8-eX1 •• 4) - c.eXl--6) 

$ + D*(Xl •• a) - f-CX1-.10) - F-(X1 •• 12» 

$ .3.0.Xl 

10 CONTINUE 

DO 20 N = 1.100 

OUT = eJO(N) •• 2) 

$ + eJ1CN) •• Z) 

$ + e2.0-JO(N).J1(N» 

HRITEe08 •• ) XVAlCN'.OUT 

20 CONTINUE 

STOP 

END 

APPENDIX O· FORTRAN Programs 144 
cccccccccC:CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

c C 

C C 

C THIS PROGRAM CALCULATES THE VALUES WHICH WHEN PLaTED CREATE C 

C THE THREE LOBE PATTERN OF INTEREST IN MODAL DOMAIN SENSING. C 

C NOTE THAT THIS ROUTINE EXHIBITS HIGHEST ACCURACY WHEN THE C 

C ARGUMENTS OF THE BESSEL FUNCTIONS ARE IN THE RANGE (-3,3). C 

C C 

C (THIS ROUTINE USES THE LP11 AND LP21 EVEN AND ODD MODES!!!) C 

C C C ••••••••••••••••••••••••••••••••••••••••••••••••••• C 

C .. •• C 

C ••• GO ~OWN S8 LINES TO CHANGE PLOT PARAMETERS'" ••• C 

C •• •• C 

C ••••••••••••••••••••••••••••••••••••••••••••••••••• C 

C C 

C C CCCCCCCCCCCCCCCCCCCCCCCCC~CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

C 

IMPLICIT DOUBLE PRECISIO~ (A-Z) 

INTEGER N,H 

C 

A = 0.5624993500 

B = 0.2109357300 

C = 0.0395423900 

0 = 0.0044331900 

E = 0.0003176100 

F = 11. 0000110900 

G = 2.2499997000 

H = 1.2656208000 

I = J 3163866000 

J = J. J4444HODO 

K = ~.J039444000 

L = 0.0002100000 

C 

PI = 3.14159265400 

C 

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 

C C 

C C 

C C 

C CHANGE THESE PARAMETERS TO MODIFY THE PLOTS COMPLETELY. C 

C A1 AHD A2 ARE THE AMPLITUDE TERMS. OTHETA IS THE RELATIVE C 

C PHASE TERM AND Z IS SOME DISTANCE ALONG THE FIBER. C 

C (PHOTDELASTICITY IS NOT CONSIDERED IN THIS PROGRAM.) C 

C C 

C C 

A1 = 1. 000 

A2 = 1.000 

OTHETA = 0.1003 

Z = 0.000-4 

C 

C C 

C C 

l C 

APPE"OIX 0 FORTRAN Programs 145 
J 

L 

eeeeeeceeeeececeeeeeeeeeeeecceeecccceeceeeeeceeecececcececceeeecceeccece 

c 

e 

c 

c 

c 

c 

$ 

c 

$ 

$ 

c 

c 

$ 

$ 

e 

$ 

$ 

$ 

$ 

c 

C 

20 

C 

C 

10 

C 

Bl = I.Z0D4 

X = -4.7501DO 

Y = -4.7501DO 

DO 10 N = 1,37 

X = X + 0.Z5DO 

DO 20 H = 1,37 

y = y + 0.Z5DO 

RSQR = (X •• Z) + CY.lEZ) RBAR = DSQRTCRSQR) PHI = DATANZ(X,Y) 

Xl = .688DOlERBAR/3.000 

XZ = .906DOlERBAR/3.0DO 

JOZ = 1.000 - GlE(XZlE.Z) + H.(X2-.4) - I.(XZ.lE6) + JlE(XZlElE8) - KlECXZ--IO} + L-(XZlElEIZ) 

JIZ = (0.500 - AlECXZ--Z) + SlE(XZlE_4) - C-CX2lElE6) 

+ DlE(XZwwS) - E.(XZ.-IO) + F-(XZlE.IZ» .3.0IlOlEXZ 

JZ = (JIZJEZ.000/(XZJE3.0DO» - JOZ 

JI = CO.5DO - AlECXl.JEZl + BlE(XllElE4l - CJE(X1JE.6) + OlECXllElEa) - ElECXllElEl0) + FlECXllE.lZ» 

lE3.0DOlEXI 

IIHENS = (CAllEJl )UZ) 

+ C CAZ.JZ)UZ) 

+ (Z.000JEA1JEAZJEJlJEJZ-DCOS(3.0DOlEPHI - BUZ + DTHEl':' 

WRITE(8.-) X.Y.INTENS 

CONTINUE 

Y = -4.7501DO 

CONTINUE 

STOP 

END 

APPENDIX D FORTRAN Programs 1~ 

--- --- -- ... _- ----~ 
References 

1 Butter. C D and G B Hocher Fiber OptICS Stram Gage. Applied 

OptICS Vol 17. No 18 15 September 1987 

2 CuI shaw. Bnan: Optical Fibre Sensmg and Signal Processmg. Peter 

Peregrlnus Ltd , London. 1984. 

3. Shankaranarayanan. N K., Mode-Mode Interference In Optical Flbt:,_ 

AnalysIs and Experiment. M.S. ThesIs, VPI, 12 March 1987. 

4 Shankaranarayanan. N K .• et al: Mode-Mode Interference m AXially 

Stramed Few-Mode Optical Fibers. Proceedings. SPIE. San Diego, CA. 

August. 1987 

5. Ehrenfeuchter. P A: Modal Domam Detection of Vibration m Beams. 

M.S ThesIs, VPI. December 1986 

6. Shankaranarayanan. N K., et al. Optical Fiber Modal Domam 

Detection of Stress Waves. Proceedings. IEEE Ultrasonics Symposium, 

Williamsburg, VA. November 1986. 

7. Chenn. Allen H .• An Introduction to Optical Fibers, McGraw-HIli Book 

Company. New York, 1983 

8. Safaai-Ja~l. A.: Optical Waveguide Theory (EE 5980 Class Notes). VPI 

Department of Electncal Englneermg. Fall Quarter. 1987. 

References 147 

...I 

t! 

)( ~ __ - ... ::-__ --s--;:;..VL:-~,..-- ---- _____ = ____ £ ... ~.--------------------------.----~----------~--~~-
9 Keiser, Gerd. Optical Fiber Communications. McGraw-HIli Book 

Company, New York. 1983 

10 Gloge, D, Weakly GUldmg Fibers. Applied OptiCS, Vol. 10, No. 10, 

October 1971. p 2252 

11 Safaal-Jazl. A., A Study of Interference Patterns m Few-Mode Optical 

Fibers, Internal Report, VPI Department of Electrical Engineering. 

December 1987 

12 Tlmoshenko, S. Strength of Materials. D Van Nostrand Company. 

Inc, New York, 1940 

13. Kobayashi. Albert S, ed. Handbook on Experimental MechaniCS. 

Prentice-Hail, Inc. Englewood Cllfts. NJ. 1987 

14 Nilsson, James W, Electric CirCUits, Addison-Wesley Publishing Co , 

London, 1983 

15 AbramOWitz, Milton and Irene Stegun. eds Handbooy 

Mathematical Functions. Dover Publications Inc, New York, 1972. 

16 Designers GUide to Fiber OptiCS. AMP Incorporated, Harrisburg, PA, 

1982. 

References 148 

----------
J 

Vita 

Bradley D. Duncan and 

attended Abingdon HIgh School In Abingdon. VIrginIa He receIved the B.S. 

and M S. degrees In Electrical Engineering From VirginIa Polytechnic Institute 

and State University In Jt 'ne, 1986 and May, 1988, respectively. His resear-.... 

interests include intrinsic fiber optac sensor techniques and optical •. _ 

sensor system design. 

Mr. Duncan is a member of the IEEE Lasers and Electro-Optics Society. 

~-r"'UyI~ ~ ~J< ./} ..... ~ 

'5/$.I "!~ 

, ./ ,,, 
, 

J 

APPENDIX E - Paper Abstracts from smart structures Workshop 

(Blacksburg, VA) - Apr1l 1988 

... ..:. - ... - ....... _ _ -s-,..-__ .. -.::- =---:- -:- ~ - --
-- ---------------......- .... 

TABLE OF CONTENTS 

Introduction to Smart Structures • • • • • • • • • • • • • • • 1 

Materials Issues for Smart Structures ••••••••••••• 3 

Experimental Analysis of Smart Structure Materials by 

Full-Field optical Techniques • • • ••••••••• 4 

Large Deployable Antennas in space as Smart Structures • • • • 7 

Active Trusses for Structural Control • .8 

Development of a Novel 'Adaptive/Smart Composite Material' 

Using Nitinol 'Fibers' ••••••••••••••••• 10 

F~ber Optic Methods for Structure Monitoring ••••••••• 12 

Modal Interference Techniques for strain Detection 

in Few-Mode Optical Fibers • • • • • • • • • • • 

Applications of OTDR Methods to Structural Analysis • 

Acoustic F~ber Mehtods for Structural Monitoring • 

Acoustic Emission Detection in Smart Materials • 

• 14 

• 15 

.17 

.18 

Fiber optic Assessment of Impact Damage in smart Materials •. 20 

Control and Signal Processing Design Issues in 

Smart Structures • • • • • • . • • . • • . • . . • • 22 

~ 
• I 

Introduction to Smart Structures 

Dr. Richard O. Claus 

Director Flher &. Eectro-Optics Re~earch Center 

Protessor. Electncal Engmeering 

'Smare "1Otelhgent" or '30ef.se-ahk" ~:.-uctures are structures which comain their o\,.n 

sensors, actuators and cOIT.?l!tatlon ~d control hardware. Although smart structure 

concepts may be applied to me dcslp and Implementation of buildmgs. dams, bndges, 

plpehnes and ships. rece::.t researc:: efforts have been concentrated on potentIal 

aerospace applications 10 aa\ anced ~rcraft, launch .. ehicles, and large space-based 

platfonns. 

Ylrgmia Tech has been 1000hed In scart structures research since 1979 WIth sustamed 

support from the NASA Lar.gley Rese:::ch Center, Snnmonds Precision/Hercules and the 

Vlrgmia Center for Innovathe Techno~ogy. In 1979 and 1980, Virginia Tech participated 

In the first documented smart structure c~:penments, conducted at NASA Langley, which 

demonstrated the use of embedded optcal fiber sensors for the measurement of strain in 

low temperature composite materials. Since then Virginia Tech has worked on the 

development of optical fiber interferOI::etric, blackbody, evanescent, modal domain and 

time domain sensors for the evaluation of composite cure, in-service structural 

component monitoring, nondestructi .. c materials evaluation, and damage detection and 

e',aluation. 

At the same tlffie. Virginia Tech faculr: •• students and staff ha .. e cooperatively df'\eloped 

~nd demonstrated effective embedcro actuators for structural shape modification. 

e\-perimentallyanalyzed the micromec:::amcal problems associated with embedded sensor 

and actuator elements In ad\anced composites, developed computational and cortrol 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29, 1988 

~ __ ~ --__ i7 

1 

-..:fA 
~y~tem architecture concepts for smart structure applications. and consIdered the 

Integration of these mterdlsclphnary problems in specific aerospace stl ucture de~lgns. 

This Smart Structures Workshop re\iews the major non-propnetary accomplishments In 

this area by Virglma Tech dunng the past several years and 10 parucular highlights the 

recent results of the past several months More than a dozen brief techmcal diSCUSSIOns 

Jre followed by a \\orkmg panel dIscussiOn lunch period and afternoon laboratory 

demonstrations of Implemented smart structure concepts. 

Smart Structures Workshop Abstracts • Virginia Tech _ April Z9, 198& 

. , 

2 
r , 

L.. 

, . 

III 

, 

, 

a 

r. 

. 

I 

- - - -------" 

Materials Issues for Smart Strudurcs 

Dr. Garth L WIlkes 

Professor 

Chemistry 

The term "smJ.f[ ... tructure~" ~'Jrr ~s the ImplIcation that a gwen matenal or "structure" 

\\hen provideu a particular ~tlmlilus. will generate a specific response. What the specific 

stimuh are as well as the nature and magmtude of the re;)ponse will depend upon the type 

of "smart structures" deSired for a given apphcatIon. 11115 brief talk will focus on matenal 

parameter considerations with respect to generatmg sman structures and will Illustrate a 

number of specific cases by e\ample. While a somewhat hIgher emphasiS will be given to 

those concerned WIth pol~menc based matenals. discussion will also consIder those based 

on either metalliC or cer~mlc systems as \\-ell Fmally, some new directions toward the 

development of new h) bnd or complex matenal structures will also be outlined. 

.. 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29, 1988 

3 
Experimental Analysis of Smart Structu~e ;,Iaterials by Full-Field Optical Techmques 

Dr Robert Czarnek 

AssIstant Professor 

Engineering SClence and Mechanics 

The concept of integration of sensing and controlhng de\1ces wlth load carryIng elements 

h.l5 been implemented in the form of so-called "smart structures". In a smart structure, 

~ensors and actuators are embeuded In the material that the elements of the structure are 

made of. The materials used to make these structures are m05tly fiber-reinforced 

composlles. Probably the most efiectl\e type of sensors used in smart structures are made 

of optical fibers embedded bet\\een the layers of the structural fibers. The optical fiber 

deforms together wah the composite element ~nd modulates light passing through the 

fiber. allOWIng the detection of dangerous stram levels in the structure as well as failure 

of the material 

The presence of the opucal fiber embedded in the material makes sense only If it does not 

diminish the performance of the matenal. Composite materials on the m.Jcromecharucs 

level are extremely complex structures and their behavior is still not fully understood. 

The Interaction between the fibers in a layer and the layers in the material causes strain 

le\els much higher than those predlcted analytIcally. Imperfections of the manufactunng 

process comphcate the situation e\ en further, introducing strong nonuniforrnity into the 

strain distribution in the material An optical fiber introduced as an element of such a 

complicated structure brmgs even more unknO\\'ns into the materials analytical model 

SOale preluninary e"<penments have been performed on graphite epoxy coupons with 

opueal fibers embedded m the dlrection perpendicular to the direction of the load. T".,'o 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29, 1988 <1 

- )1' 
r , 

.., 

'. 

III 

I 

, 

, 

i 

• . 

~enSJllvlty moire interferometry with a sensltlvlly resolution on displacement 

l11easurementli of 100 nanometers The measurements were performed on the edges of 

the specimens Strams as high as :CC \\ere detected in the vicmJty of the fibers at a load 

equal IO 50% of the calculated f:ulure load. Figure 1 Illustrates fringe patterns 

representing: 

(a) the hOrizontal displacement field and 

(b) the vertical dlsp!acement field at thiS load level in the specimen with the optical 

fiber embedded bet\veen the fibers runmng ill the 0 degree direction. The 

concentratIon of high strains near the optical fiber IS clearly viSible. 

Corresponding patterns were recorded for a specimen with the other layup. 

The results of the performed e\p~nrr.ents show strong strain concentration around the 

embedded sensors and a very strong de;Jendence of the strain concentration factor on the 

layup of a composite member. The magrutude of the effect of the embedded components 

on the strain distnbutIon m the structural elements suggests a strong need for an extensive 

e\penmental and analytical program on the determination of the influence of embedding 

optiCal sensors on the behavior of composites and on providing a means for reducing 

undeSIred effects. 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29. 1988 

-- . 

5 
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(a) (b) 

Figure 1. 

Smart Structures Workshop Abstracts Il\l Virginia Tech mJ April 29, 1988 6 
Large Deployable Antennas in Space as Smart Structures 

Dr \\' .lrren L Stutzman 

S.nelhte CommUnicatIOns Group 

Professor. Electrical Engineenng 

\lany space-based projects are planned mto the next century that reqUlre large 

antennas These antennas are most often reflectors and occaSIOnally pbased arrays. In 

either case, the antenna 1S up to many meters m e~tent anc must be deployed m space 

Performance depends crit1cally on t'le accuracy of the antenna shape. Antennas do not 

deploy accurately and also are subject to d1stortions \\-b1le in space, primanly m the 

form of thermal grad1ents Therefore. sensmg and control are necessary. Witb large 

scale antennal structures the sensmg. control. and computing funcuons are best 

lmegrated lI:to the desIgn. creatmg a smart structure. This paper w1ll focus on the 

large space antenna as an 1deal candIdate for smart structure realization. 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29, 1988 7 
.-

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Active Trusses for Structural Control 

Dr Harrv H Robertshaw 

Associate Professor ~fechan1cal Engmeenng 

and 

Dr Charles F Remholtz A~slstant Professor ~Jech~n1cal Engmeerlng 

Structures that can change their configuration, termed variable geometry trusses 

(VGTs) or active trusses, are bemg studied for their many applIcatIons· active control 

of structural VibratIOn, pOIntmg of structures or substructures, or performing roboticlike tasks. In fact, given a structure that can move actIvely, the dIstinction between a 

robot and a structure becomes blurred 

\\ e are presentl~ usmg two forms of acti\ e structures to control the Vibration of 

contmua attached to them. We have performed planar and spatial Vibration reduction 

e\penments '\-lth £\\0 configuratIons for the actl\e truss. 

The planar expenments have been conducted with one plane of a tetrahedraltetrahedr<ll (T-T) truss controlhr~~ :l beam that is constrained to almost planar motion. 

The spatial e>.periments were performed \\lth an octahedral-octahedral (0-0) truss 

(rucknamed the geodesIc truss) con troll 109 a rod. In each case the trusses had t~ree 

degrees of freedom embodIed in three lmks of vanable length actuated by machme 

scre\\s dn\-en by dc motors The motton of th(' lmks wen! sensed with resistive o 

transducers and the motIons of the beam and the rod were sensed using strain gages. 

The equatIOns of motion for the systems \\ere Imeanzed about an operatIng point and 

an LOR optimal control la\\ \\as applIed \\lth mdIvldual estImation of most of the 

Smart Structures Workshop .\bstracts • Virginia T~h • April 29. 1988 8 
needed r.lle terms. Slgntficant \'Ihratlon reuuctlon was ohserved with reasonable 

correl.ttion \\ ith the analyses. 

The spattal truss \\ as abo used ttl pertorm a rudimentary robotic task: wnting letters 

wlm a pen placed at the end of a rigid raj attached to the structure. This robotic task 

Imohed solving the m\erse k.mematlc equations for the needed link lengths in order to 

follow the reqUired "p~th" to \\ me the letters. For the geodeSIC truss, the solution of 

both the forward and the inverse kmematlcs IS iteratl\'e. A reasonable amount of effort 

has gone mto optllllizmg theses nerame procedures. 

Addmonally. \\ e ha\ e studied kmematIcs of most of the dlfferent possible 

configurations of the basic .mIt of \ anable geometI) trusses. The advantages and 

dIsadvantages of these different forms are determmed based on: ease of solution of 

the kinematic equ:ltions, possIble \\orkspace of the trusses, loads Involved during 

quasi-static and dyn~lTIlc maneu\ers. and possible kInds of motions available from the 

structure. 

9 Smart Structures \\orkshop Abstracts _ \1rginia Tech _ Apri129,1988 

_~ __________________ .m= _________ '-_'_'~_-_'_~_'_~_'~ __ -_-__________ F~===-__ -="~-' 
Development of a Novel'Adapth'ejSmart Composite Material' Utilizing Nltinol'Fibers' 

Cr:lIg A. Rogers 

Associate Professor ~1~chamcal Engineermg 

.-\ novel class of adaptive matenals has been developed and demonstrated at VlrgmJa 

Polytechmc Institute and State t..:m\'~rsity. This class of adaptive materials utilIze a 

shape-memory-alloy (Nuinol) in a lammated, fiber-remforced composite. Adaptive 

matenals are a relatively new class of materIals that have the capability of changing 

their physical g~ometry, or of alterIng their physical properties. The basic concept 

behmd the adaptive material d~"e!oped at VPI&SU is that the shape memory alloys 

are integrated In a bulk materIal (\ e., laminated fiber- reinforced composite, or an 

elastomer) as an actuator for force, mOlIon, and/or variable stiffness. Possible 

applIcations for this class of adaptive materials are: in structures that are part of longduratiOn. unattended space ffil~Slons (for which the material must be able to 

compensate for damage by redlstnbuting the load around failed portIons of the 

structure); in bIOmedIcal applications (such as :lrtificial heart valves and pumps with no 

moving parts), in active vibration control of large fleXible structures, in active acoustic 

control for aircraft to reduce intenor soun1levels, and 1ll robotic manipulators. 

The adaptive response of the material has been demonstrated experimentally by 

controlhng the motion of a fiberglass cantile\er beam. The cantilever beam is a 

uruque composite matenal containing several shape memory alloy fibers (or films) in 

such a 'way that the material can be :;tiffened or controlled by the addition of heat (i.e., 

apply a current across the fibers) A demonst;.ation of the capabilities of this unique 

class of materials will be "resented. Shape memory alloys and the mechanism by which 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29. 1988 

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10 

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they e,hlblt the charactemtlc shape memory effect (SME) will also be explained In 

The basic physical design of the demonstration adaptive/smart composite cantilever 

beam IS conceptually simple. The shape memory alloy fibers are embedded in a 

m.ltenal off of the neutral axis of the beam whIch when actIvated mtroduce a large 

force and subseque ~~ bending of the structure. Before ImbeddlJ1g the fibers, the shape 

memory alloy fIbers are plastically elongated and constramed from contracting to their 

normal or 'memory' length upon curing the composite material wah hIgh- temperature. 

The fIbers are therefore an integral part of the composite materIal and the structure. 

When the fibers are heated, generally by passing a current through the shape memory 

alloy, the fibers 'try' to contract to their 'normal' length and therefore generate a 

umformly dIstributed shear load along the length of the fibers. The shear load offset 

from the neutral a.us of the structure \\ 111 then cause the structure to bend in a known 

and predIctable manner. There are several other configuratioll5 that are currently 

bemg unplemented and ill' estigated 

This presentation will describe the actual prototypes of the novel 'Adaptive/Smart 

Composite Material' and the capabilities of the devices. The basic concepts and 

mecharusms by which the adaptIve response of the material is demonstrated will also 

be presented. several of the technical problems and solutions will be discussed. Lastly, 

the future direction and impact of this technology \\ill be postulated. 

Smart Structures Workshop Abstracts • Virginia Tech _ April 29, 1988 

-- ~ ... ~--:...~.~ .... --- - -

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Fiber Optic Methods for Structure Monitoring 

KImberlv D. Bennett 

Research Associate. Fiber ~\:.: Electro-Optics Research Center 

Electrical Engineering 

and 

Dr. Richard O. Claus 

Director, Fiber & Electro-Orucs Research Center 

Professor. Electrica Engineering 

Structures engineered for mtegrated active control impose demanding requir.!ments on 

system components such as actuators. sensors, and intellIgent control schemes. In 

partIcular, sensors are required to deter.une structural status, both in terms of normal 

operating parameters such as posnio,. strain, or temperature, as well as actual 

matenal mtegrlty. Perhaps the most m~ ure approach for embedded sensing, and one 

readily apphcable to attached sensors.l:1\ohe!) the use of optical fibers. 

Much of the pioneenng \\ork m smart structures. specIfically embedded fiber optic 

sensing in structural materials, was per formed in the early 1980's at NASA Langley 

and Virginia Tech. Presently a number of researchers are investigating the use of fiber 

OptICS for monitoring ground, air, and space based structures.. In addition, a number of 

different mechanisms are being exploitee to perform various sensing tasks. Among 

these are optical time and frequency domain techniques, modal domain sensing, 

absolute and differential fiber interferometry, polarimetry, and various intensity 

modulation methods. Targeted obsef\'ables include both point-ta-point and distributed 

strain measurements, \ibration and structural mode analysis, state of cure in composite 

matenals. temperature monitoring, and damage assessment. 

Smart Structures Workshop Abstracts _ \lrginia Tech _ April 29. 1988 12 

~ - -~ ..... ~' .. :"~~~~~:--.: -~ . ... ... 

--------------------------.. -----------------------------------------=~====~----=~' 
III thl' paper. several general sensmg methods will be reviewed. Emphasis will be 

gl\ en to (hose which have had p.trllcular applicatIOn in smart structures research at 

Virginia Tech. 

Smart Structures Workshop Abstracts _ Virginia Tech _ ApriJ29, 1988 

... =-_:":S: .. !I:-_ ... _ - __ • 

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Modal Interference Techniques for Strain Detection in Few-Mode Optical Fibers 

Bradlev D Duncan 

Gr.lduate Re ... earch ru.~lstant. FIber & Electro-Opucs Research Center 

Electncal Engmeering 

Interference bet\\een the modes of:m optical fIber results m speclfic intenslty patterns 

whIch can be modulated as a functIon of dlsturbances m the optical fiber system. 

These modulatIOn effects are a dIrect result of the differential phase modulauon whlch 

anses due to the dIfference in propagation constants of the constltuent modes. Based 

on these concepts it has been shown how the modulated mtenslty patterns caused by 

\ anous mode groups 10 few-mode optICal fibers (V < 5.0) can be used to detect strain. 

A detaIled discUSSIOn of the modal phenomena responsible for these strain induced 

pattern modulations IS presented and it IS shown that strain detection sensitivities on 

the orde: of 10-10 can be expected for simple systems based on these modal 

interference concepts. Actual strain d~ !ectIOn systems based on the developed theory 

are also proposed and evaluated. 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29, 1988 

~ 

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14 
Applications of OTDR Methods to Structural Analysis 

Russell G. Mav.lr 

Techmcal Director. FI~er & Electro-Optics Research Center 

Electrical Engineenng 

Embedded optical fibers have been proposed as a technique for measuring strain and 

displacement in matenals. particularly composite materials. By measuring parameters 

of the light exiting the embedded fiber. the integrated strain along the fiber can be 

demed. A promising techmque to resolve the stram at discrete locations in a material 

IS optical time! domain reflectomet~ (OIDR). 

OTDR is a measurement technique In \\ hlch a shon pulse of light is launched into an 

optical fiber and IS reflected back to the input end by constituent atoms along the 

length of the fiber The intensity of the reflected light 15 plotted as a function of the 

time dela~ that the light pulse suffers In returrung to the input end of the fiber. Since 

the time delay is linearly related by the speed of light in the fiber to the distance from 

the mput to the reJection. OTDR may be used to accurately determine the location of 

a discrete reflector. 

E'qJeriments at Virginia Tech in 1984 demonstrated the feasibility of using OTDR to 

sense deformation of composite coupons \\ith embedded optical fibers. In those 

experiments, OTDR was used to measure the loss induced by microbends in an 

embedded fiber at a point .... here pressure was applied. The spatial resolution of the 

measure~ent system IS limited by the optical pulse \\;cth. Although the results 

demonstrated the \ alidity of the concept. derh ation of actual fiber or coij'lposite strain 

from rrucrobend loss is difficult. 

Smart Structures ',\'orkshop Abstracts _ Virginia Tech _ April 29. 1988 

.. ..;. - __ ~.;;.~-w... - T15 

.,--
Furtht!r research at tht! Fiber anu Electro-Optics Research Center in 1987 e\tendt!d 

the \\ork and enabled the Jlre~t i11CJ~urement of fiber (and composite) 'itram by 

placmg reflective markers within the t!mbedded fib~r. The markers were fabncated by 

separating the fiber at a pOint. and spliCing the two ends together with an air gap 

bet\\een them. The Fresnel retlectlon from t!-II! refractive index mismatch of the sphce 

YIelds a reflection center that produces a readIly observable mark on the OIDR tr:ice. 

The longitudinal stram of the flbt!r section between t\\O aIr gap sphces IS found by 

measunng the resultmg mcrease m time delay bet\\een the two reflective markers 

correspondmg to the t\\ 0 air g~ps 

Lunitatlons of thIS technIque include a hrrut to the number of air gap splices that molY 

be placed sequentIally on a fiber due to the splice loss and fiber loss budget. A hmit to 

the achIevable spatial resolution e\lsts. traceable to the low energy content of very 

narrow \\idth laser pulses. 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29. 1988 16 
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Acoustic Fibc,· Methods for Structural Monitoring 

Dr. Ahmad Safa.li-Jazi 

Associate Professor 

Electrical Engineering 

TransmIssIon properties of cladded fiber acoustIc waveguides are briefly reviewed and 

compared wIth those of optical fibers.. ApplIcations of acoustic fibers in sensing and 

SIgnal processmg are addressed. Attention is focused on embedded acoustic fibers for 

structural monitoring T\\o schemes for the Implementation of acoustIc fiber sensing 

concept are discussed In one scheme the acoustic fiber sensor functions in much the 

same way as an optical fiber sensor. namely that an external disturbance perturbs a 

physIcal parameter of the fiber yielding a change In amplitude, phase, or polarization 

of the acoustic W3\ t propagating In the fiber. The amount of the change is a measure 

of the external dIsturbance. In a second scheme, acoustic fiber is used in a listening 

mode picking up acoustIc emissions and thus monitoring the health of the structure. 

Ad\ antages of acoustic fiber sensors i.:I certain special applIcations are pointed out. 

Research and development of acoustic fiber phase sensors at the Fiber and ElectroOptics Research Center of Virginia Tech are addressed. 

Smart Structures Workshop Abstracts • Virginia Tech _ Apri129, 1988 17 
L 

Acoustic Emission Detection in Smart Materials 

KImberlv D. Bennett 

Research Associate, Fiber & Electro-Optics Research Center 

Electrlcal Engine.~nng 

and 

Kevin D. Zehner 

Rese..lrch Assistant, Fiber & Electro-Optics Research Center 

Electncal Engineenng 

The morutoring of acoustlc emissIOn (AE) IS an important techruque for the 

nondestructlve charactenzatlon of straIned matenals. Time and frequency domaIn 

analyses of AE events Yield mfo~matIon about the type, geometry, and location of 

defects, as \\ ell as about matenal propertles and how failure may occur. The 

quantitari, e mterprew,tlon of AE e\ ent signatures IS critically dependent upon the 

faithfulness of the aco ... stic transduction and Signal processing system in reproducing 

localized stress \\ave amplitude as a function of time. Altr.ough presently employed 

plezoelectnc sensors are sensithe and reasonably broadband, they are not sUlted to 

embedded measurements, and are highly susceptible to electrical noise. 

This paper reports the detectIOn of acousuc emission signals generated in symmetnc 

cross-ply composite laminates using internal optical fiber sensors. Few-mode optical 

fibers were embedded between different prep reg layers during lay-up, and the resulting 

specimens were cured under pressure l!et\ .. een heated platens. During the original 

tests, samples containing optical fibers laid m the axial direction were loaded in tensIOn 

in specially designed grips. allowing for continuous monitoring of light. Acoustic 

signals "'ere obtained by detecting changes in an optimized modal domain feature 

mherent in the intermodal interference pattern Independent measurements were also 

supplied by a piezoelectric transducer made by Acousti~ Emission Technology 

Smart Structures Wllckshop Abstracts _ Virginia Tech _ April ~9. 1988 

- .. ~ ~ 

- - --..:--- _. ~:- . - -

18 
Corporation Agreement hetween transducing methods was excellent, indicating that 

acoustic emis~lons may be mea~ured uSing fiber optic senstng techmques. 

On-gomg e\periments tn\ l)l\ e samples with optical fiber laid across the direction of 

applied IO.ld. allowing for the use of conventional gnps. although requiring some care 

dunng cure. Collection of AE signals and computational analysis is simplified WIth the 

use of an me\pensive digItal oscilloscope and assocIated computer. Also. the use of 

multiple fibers for the location of AE events IS investIgated. Results of these tests, as 

\\ell as limitations of the method and Implications for the composites industry are 

discussed. 

" 

Smart Structures Workshop Abstracts • \lr&inia Tech _ April!9, 1988 

~_ ..... __ .. I 

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Fiber Optic Assessment of Impact Damage in Smart Materials 

Michael R. Dumais 

Research Assistant, Fiber & Electro-Optics Research Center 

Electrical Engineering 

KImberlv D. Bennett, 

Research AssOciate, Fiber 8i Electro-Optics Research Center 

Electrical Engmeering 

This study investigates the possibility of incorporating optical fibers into a structure 

:Jnd using them to characterize impact damage. It is believed that the ability to 

correlate signal disturbances from optical fibers with physical disturbances would 

proVIde invaluable real-time mformatJon about the reliability of active engineering 

s\stems. 

Previous \\ork In this area. conducted at Virgmm Tech with sup port from NASA 

Langley, General Motors, and the \'Irgmia Center for Innovative Technology, involved 

the use of an embedded optical fiber mesh. Contmuous wave light signals propagated 

through the fIbers in the x and y directions, and \\ere collected by an array of discrete 

photodetectors. Disturbances in the cw output due either to fiber breakage or 

intermod.ll interference were related to various impacts. Disadvantages arise in the 

need for injection of light into multiple fibers, and for multiple detectors. 

In order to simplify the system and quantify impact signals, an exposed optical fib.!r 

ha't1ng a V number of approximately 4.5 was attached to a thick aluminum plate with a 

rigid epoxy. The fiber was excited \\ith monochromatic laser light and its output 

monitored with a pbotodetector. Witt ... the plate inverted and l)ing flat, several trials 

\\ere run in which a steel mass \\as dropped on the plate from difterent heights and 

positions 'oIo;th respect to the fiber sensor. Using a dlgital wa\;eform analyzer, fiber 

output signal changes were captured o\er the course of an impact. With the aid of a 

Smart Structure'. Workshop Abstracts a Virginia Tech a April 29. 1988 

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20 

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computer. Fourier • .lOalysis of the sIgnals was performed. and attempts were made to 

correlate spectral signatures with different types of impacts. Also. output sIgnal power 

densIties were calculated and analyzed with respect to impact amplitude and location. 

After attaching a second fIber to the plate. slmllar drop tests \\ere run and blInd Imp..tct 

location informatIOn \\as extracted by e\almrung the time lag between the dIsturbance 

SIgnals from the two fIt .!rs 

In this paper the limitations of fIber optIC Impact and damage detection are dlscu!''ied. 

and dIrection for future efforts proposed. 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29, 1988 

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Control and Signal Processing Design Issues in Smart Structures 

John C. McKeeman 

AssIstant Profe!lsor 

Electrical Englneenng 

and 

Doug K. Lindner 

AsSIStant Professor 

Electrical Engmeenng 

The ne'\t generation of space structures \\-111 he sIgnificantly dtfferent from the current 

generation of spacecraft. The new space structures will be made of new composite 

materials whIch \\Ill allow them to be of slgruflcantly larger dimensions The Increased 

sIze. In panicu1J.r. along WIth tIghter performance speCIfICatiOnS will require that the 

:.-tructure be deSIgned and bUIlt to functIon as a coheSive umt In WhICh subassemblIes 

strongly Interact to u""'hleve s~stem performance speCIficatIons. The system wide 

Integrauon wIll be achIeved by control loops \"hICh (effectively) coordinate the 

subassemblIes. Such a structure we call a smart structure. 

In thIS paper \\ e examme the system configuratIon of smart structures from a systems 

perspective. To focus the dIscussion we consIder as an e: ... ample structure 3 large space 

antenna, the Hoop Column Antenna We describe the control loops required to 

Implement and maintain the antenna in space. Sp~cial attention is gh en to the 

components required to implement the control system. Se\ eral control design issues 

are hlghhghted. 

To successfully produce this control system. several new computing technolegies must 

be tadored to the applIcations required by each subassembly. At the highest level in 

thIS hIerarchical control system. Artillcial Intelhgence coltpled \\lth Neural Net\,orks 

\\ III control the housekeepmg actintles and gross structure control. At the 10\\ est level, 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29, 1988 ,,', _ ... 
application specific mtegrated circuits will be customized to handle the high 

throughput, high bandwidth requirements for the sensors and actuators. This paper 

focuses on new computers architectures reqUired to implement advanced control 

structure wlthm a intelligent ~tructure. 

c-4 

Smart Structures Workshop Abstracts _ Virginia Tech _ April 29, 1988 

• I 

23 
APPENDIX F - Abstracts from Papers To Be Presented at The SPIE 

Conference (Boston, MA) - September 1988 

t 

t 
~ <' , 

TABLE OF CONTENTS 

Interferometric Measurements of strain Concentration Induced 

by Fiber Embedded in Fiber Reinforced Composites • • • • • 1 

Demonstration of A Smart Structure with Embedded Actuators 

and Sensors For Active Control •••••.•••••• 3 

Full Field Analysis of Modal Domain Sensor Signals 

for Structural Control • • • • • • 

Intensity Pattern Modulation in Optical Fiber Modal Domain 

• • 5 

Sensor Systems: Experimental Results. • . • • • .7 

Smart Structures Program at Virginia Tech •• 9 

Fiber Optic Sensor Systems for Smart Aerospace Structures •.• 11 

-~ J 

I 
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INTERFEROMETRIC MEASUREHENTS OF STR~IN CO!lCENTRATIONS INDUCE!) BY 

A!l OPTICAL FIBER ENBEDDED IN FIBER REINFORCED COMPOSITES 

R. Czarnek*, Y.F. GUo*, K.D. Bennett+ and R.O. ClausT 

* Department of Engineering Sc~ence and Mechani:s 

+ Department of Electrlcal Engineering 

virginia Polytechnic and state University 

Blacksburg, Virginia 24061 . 

The concept of using of optical fibers for sensing the 

nechanical response of conposite structu~es to applied loads has 

'b... 

been inplerented in the fo=n of so-called "sI:lart skins.u An 

c?tical fiber inbedded betNeen the layers of the structural fibers deforI:ls together w~th t~e Cc~pos2te structure and I:lod~lates 

llght pa3s~r.g thrcugh the f~be~. ~his allows for the detectic:! of d<lnqerous str=.!.n levels:.:. -he s~ructure, as ~:ell as 

T~e pres~~ce c: the c~t.!.cal f~~~~ enbedded ~n the material 

15 v1cble only ~f ~t dces not d:.~:nish the perfornance of the 

CC~~o51te nater:.=l C~ t~e ~:crc~echan~cs level is an 

e:..:tre:'ely co:-:plex st~uct:l~e c::d 2:'5 !:;~::=':io~ ~s st~ll not fully 

ur.cerstocd. The interaction te~~ee:: :he cc~posite fibers in a 

layer and the layers ~n the ~ate~~al ca~ses st~ain le~els ~uch 

hlgher than these pre::!:!.cte-i ar.c2.yt:!.c=.::'y. I~perfect1o~s 0: thE: 

l.n~:-oducir.g s~rc-:g nC':1~~.::c!""- .... t:- :n~o ~::e strain dist!"'li:tltior' 0: 

t~e !1ate~!.al. 

1 

1 
., ,~ 

'~'-

" ------------ - - ---- '--'--------

model of the matcr1al. Several 1rnpor~ant questions can a~d 

should be answered before the concept of e~bedding optical f1bers 

can be commercial1z~d. These include u~derstanding ho~ fibers 

influence the strain field 1n a cc~p~site eleoent, and if the 

strain conccntrat1on factors introduced are significant when 

compared to the natural stra1n var1ations wh1ch ar1se fro~ the 

nanufacturing process. strain concentra~ion dependence on the 

layup and position of the opt1cal f1ber is also unknotv"n. 

F1nally, understand1ng of whether the inclusion of optical fiber 

can cause p:=-e!:!.atu!:"e fa:lu!:"e of a CO:::;:~51te element, and ho: ... to 

...... reduce any such effects is necessa:=-y. 

These is ues requ1:=-e ser1CUS expe~1~ental investigation. 

Moire interferoretry is a hiSh sensitlvity ~etho~ yielding full 

f1eld r.easu~e~en~ of 1n-plar.e d!.s;:lace~e~~5. Its sensit1vity is 

l1nlted to 1/2 of a ~avelens~h cf ~~e light used pe~ f~1nge 

the c~de~ o~ 10C n~ 1S star.d~~j l~ the ~?:iSU Photo~echanics Labo~ato~y. The s;:at1al resolut1C~ 15 11~~~ei cnly by the quality 

s~all as 1 nicrc~e~e~ ca~ be succes5fcl:; resolved. 

perfor:-,~3. c~ t::e face of a :::2-;::::si~e, :5 ~'ell as c~ 1ts edse. 

ORIGINAL; PAGE IS 

OF POOR QU"AI.In 

2 
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ORIG!NAD P ~G?; IS 

OF POOR Qtr~ 

DEMONSTRATION OF A SI-tART STRUCTURE tilTH E~lBEDDED 

ACTUATORS AND SE!ISORS FOR ACTIVE CONTROL 

C.A. Rogers*, K.D. Bennett+, n.H. RobertshaN*, and J.e. McKee~an· 

* Department of llechanlcal En;ineering 

+ D~part~ent of Electrical Englneering 

V~rginia Polytechnic Institute and State University 

Blacksburg, V~rginia 25061 

A novel class of "s:::a:::-tll materlals having l!mbedded sensors 

and actuators and appropriate "intelligencell has been developed 

and deruonstrated at Virginia Tech. ~h~s class of adaptive nater1als uti11ze a sh~pe ~e=ory alloy (~itinol) in a laminated, fibe=-rein=orced ccrpos~te as the e~~eddec distributed actuator. 

The basic concept beh~~d t~~ s~~rt ~ater~a:5 developed at V~rgin1a Tec~ 1S t~at the shape ~er=r- allc~ fibers are integ:::-ated 

into a bulk ~ater~al such as a CC~Fosite st=uctural =e=ber, and 

used as actua~ors fo:::- force, ~otion, ar.j, 0:::- variab~e stiffness. 

opt~cal fiber sensors. Pcssi~le appl~ca~:ons fo:::- this class of 

ac.aptlve ~aterl.als are lr. structur~s that are part of 10r:gdurat:o!1 , unattended ~~sSlcns (:or ~~.l.c~ the naterial rust b~ 

able to co~pensate for c.3~age by rad:str:~u~lng the load around 

fa.l.~~j portions of the structur~), ir. b.l.o~edical appl~cat.l.ons 

(s'.:c:-_ as art1f1Cl.<l.l he:l:::-t val\-es and pU~Fs ~·:th r.o .-:oving parts), 

In a~tlve vlbratlc~ control of large f:cxible st:::-uctures, l~ 

, 

3 
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levels, and in robotic nanipulators. 

The adaptive response of struct~ral ~e~bers has been demonstrated in hardware by controll~ng the motion of a fiberglass 

The beacr is a unlque cocposite naterial contain~ng several shape nenory alloy flbars ~n such a way that the 

oater~al can be stiffened or cor.t~olled by the addition of heat, 

created by apply~ng a curren~ across the f~bers. Embedded cptical fibers non~tor the ~ot~on of tr.~ cantilever bean and application-specific intelligent harj~:are has been designed and built to 

control the not~on and/cr v~bra~ion of the structure. 

"" Results fro~ ex~er~=ental 5tudles showing active motion 

control with this novel s~art strcct~~e will be presented. Shape 

memory alloys and the rechanls~ by ~~ich they exhibit the character~stic shape ~er.ory effect (S::~) fo~ use as an actuator will be 

- I explained, as well as ~r.e F~ys~=al ~es~gn and imple~entation of 

t~e e~edded stra~n se~s~ng =~=er op~~cs. The control strategy 

(Le. "~:l-:.ell~ge::ce) \,:'::1 also l::e p~ese:l~ed. Lastly, the fU~t:re 

direc~~o:l and i~p~c~ of th~s ~ec~::21c;i ~ill be postulated. 

4 
FULL FIELD A:lrtLYSIS OF NODrtL DOl-lAIN SENSOR 

SIGNrtLS FOR STRUCTUAAL CONTROL 

K.D. B-'!nnett, J .C. !o!::Keeman, and R.G. Hay 

Fiber and Elec~ro-Optics Research Center 

Virglnla Polytech~lc Institute and State University 

B:acksburg, V1rginia 24061 

When coherent 11ght is la~~ched into multimode optical 

flber, a co~plex interference of the modes occurs~along the fiber 

length, and a speckle pattern res~lts at the output. The exact 

arrange"ent of the speckles depends on the modal ar~angement 

integ=a-ced along the floer, anc. lS !::odulated by local changes in 

gee"et=y and refracti':e :'n:icx pro::1.le. Interrogating tt.e modal 

dc~al~ s1.gnal 0:: an opt1cal f1.cer e~edded or attached to a 

struc~u=e 1.S a ~ell e5ta~l~shed =~~ns of determining pseudesta~lc stra1~ a~d str~ctural v1.t=a:~on frequency and ~ode shape, 

as ~e~~ as rc~~t~r:'~g aceust1.C e~~~:s occurring in the ~aterial. 

cu~put s;-eckle I:'otion. In ac.ditio!"' to 

recess='!"1ly results 1.:1 a lcss c: c;-tlcal pO~'er a~d ~seful 1.nfc=-

~a~:c~. Advance"ert re', 'cr collection has been U:3.c.e thrcu;:: 

ORIGINA'D PA"GE IS 

OF POOR QUALITY 

5 

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. 

. 

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~ ~ -_~_~ . ____ _ - 'c J.,.. ~]l 

In th~5 paper, we report the use of a detector array to 

process the modal doma1n output patterns .• The array ~s linked to 

an ISH-PC, w-hich reduces the data in real tHte. Full field deter~1nat1on of low ~ode speckle rotat1cn due to aX1al strain is 

noted, as well as gross speckle rota~ion i~ multimode f1be~s due 

to bulk f1ber oot1on. Stat1stics of speckle cotion in both lo~ 

an nult1mode fibers has also been lnvest~gated. F1nally, the 

i~portance of this r.ethcd for use in snart structure dynanics and 

control will be disc~s5ed. 

DlUGli"iAL PAGE IS 

011 EOOlt QUALITy 

I 

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INTENSITY PATTERN fotODULATIC!l IN OPTICAL FIBER 

MODAL Dm'lAIN SEnSOR SYSTE:-!S: EXPERIilE:.TAL RESULTS 

Bradley D. Duncan 

Fiber & Electro-Optics Research Center 

virginia Polytechnic Institute and State University 

Blacksburg, Va 24061 

Brian U. Brennan 

Simconds Precision I.S.D. 

Panton Road, Vergennes, VT 05491 

(A5STR.~CT) 

The past several years have giver. rise to oany optical fiber 

sensing techniques to/hich r.-:=.y be e.-played in systems to detect 

-'~h abservables as te~perat~re, press~re, displacement and 

As sens~ng c.e''-1.::e.5, cpt:!.c:!l :::!.cers a::-e a":tractive due to 

t~e~r s~all size, flexib~lity, rugged~ess an1 intrinsic 

In add:"~io:1. tt.eir p::-ccli .... .:ty to be highly 

se::s.!.tive to e~~er!lal peri:~rbat1ans 1S c:.u:.ckly r.lak!.ng optical 

:::oe::-s t~e S2:1S1ng deV1ces a:: choice passb.-€ 

~~::-i!ltrusi .... e sensor applications. 

Si=ply put, cptical fi~er sensc::-s exploit the effects of 

~e::-t~rbat:!.ans a:1d ext€rn~l fac~ors 0:: the ligh~ in the fiber. 

~~;:!::-:!lleled 1r. sensit:!.vity are the r~~se ~cd~lated sensors, a 

c:::'::ssic: .o.::a:-ple 0: \.h4Ch is t!;.e dua::'-:!ber ~!a::~-Zehndcr 

os E:OOR QUALiTY.: 

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i 

~ sensor tends to be ~~lte complex. with 

the reference phase anq quadrature pOlnt often needing to be 

actlvely controlcd. 

By comparison, systems utilizing sl~gle-flber modal 

interference schemes, such as those to b~ discussed in this 

paper, essentially cause the t~o arrs of the interferometer to be 

within the same environnent. This provides for a high C02Qon 

node rejection capacity while affording the system the further 

advantages of sirpliclty and l~creased ruggedness, wi~h no need 

for couplers. Though renaining highly sensiti~e, as will be 

shown, so~e sensitivity wlll be sacrlflcea 1n a single-fiber 

1nt~rfero~eter, or nodal donaln sensc~, due to the fact that the 

sensor nechanisrn will now be based on ciffe~en~ial phase 

::'oc'..!lation. -, 

In a cc::'panion paper ~ det~~led t~eoret:cal analysis 0= the 

~e~al phe~c~ena responsible fo= :te fa= ~e:d i~tensity pattern 

~~~ulatien of varlC~S ne~al do~a~n se~so~ syste:s is presented. 

This pape= \-lill present expe=i:-e:,t3.1 res:.:lts ;.;hl.eh vsr.lfy t!:e 

lth :-cda! co~aln sense= syste:-s. 

.', 
/ 

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-PW .-~ 

- ~-------." 

SMART STRUCTURES PROGRAM AT VIRGINIA TECH 

R. O. Claus and K. O. Bennett, Fiber and Electro-Optics Research 

Center, Virginia Tech, Blacksburg, VA 24061. 

Abstract 

This paper reviews the smart structures and avionics research 

and teaching program at Virginia Tech. Started in 1979 with 

support from the NASA Langley Research Center, this program has 

grown to include interdisciplinary participation between .ore 

than twenty faculty f=om seven departments in the Colleges of 

~ngineering and Arts and Sciences, graduate and undergraduate 

engineering classes which specifically address smart structures 

issues, and directed research programs conducted in~ooperation 

.ith more than a dozen aerospace companies and government 

organizat~ons. 

CUrren~ smart structures research includes major efforts in 

l} the development of embedded and attached optical fiber and 

acoustic fiber sensors for a wide range of applications including 

cure ronitoring, in-service lifetime struc~ural monitoring, 

ncndestructive evaluation, and impact and da~age detection and 

analysis, 2) sensor signal mult~plexing, processing and data 

handling to achieve near real t~~e districu~ed structural 

analysis, and 3) the cotibined use of e~ejded or attached sensc~s 

and actuators to ach~eve conLrolled structural-response. Special 

ca~pus facilities which have been u3ed for this work include an 

I 

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~~~~~~.~~~Mr.~_(_.-. ~~4~--~------~---.~~~~t~.r_#~e"-4.~_4~j~~.~ .. =m1~'2~~'.~_~ .... ~ 

.ical fiber fabrication facility, an autoclave for composite I .~ ,; 

structure fabrication and curing, and laboratories for optical 

fiber sensor development, materials response and nondestructive 

evaluation, structural control testing, and computer engineering. 

The work in all of these areas during the past few years by 

different Virginia Tech faculty, staff, graduate student and 

visiting scientist groups will be reviewed. 

[This work has been supported in particular by sustained 

funding from th~ NASA Langley Research Center, Simmonds 

Precision/Hercules, and the Virginia Center for Innovative 

Technology. ] 

10 

, . 

,.. 

• 

. ... 
I 

--------.~ 

/ Fiber optic Sensor Systems tor 

Smart Aerospace Structures 

W. J. Rowe, R. O. Claus., D. A. Martin+, and D. Tritesl 

Lockheed Aeronautical Systems Company 

Dept. 72-51, Zone 303 

Marietta, Georgia 30063 

ABSTRACT 

Current and projected advances ~n aerospace structures 

technology for such ongoirg programs as the Advanced Tactical 

Fighter, National Aerospace Plane, and NASA/DoD space platfor!l1s 

are used as the starting po~nt for a top-lev~l structural 

nonitoring systems analysis. Performance requirements are 

considered for such structures, and used to identify needs for 

integral sensors and systems. R~sults of recent work are 

discussed, which have de~onstrated the potential for fiber optic 

se~sor syste~s which can assess and repor~ C~ structural 

cond~t~on in real ti=e. The essential syste~ elements are 

de!ine~, and constrai~ts impose~ by ve~icle configurations and 

nission perfo~3r.ce are considered. The resulting development 

needs, for f1ber O~t1c sensors and syste~s to achieve Smart 

Structures in these applications, are stated in conclusion. 

*Fiber & Electro-Cpt1cs Research Center, 6~S Whittemore Hall, 

Virginia Tech, Blacks~urg, VA 2';061. 

+Kelly Johnson Resedrch & Develop~~nt Center, Rye Canyon, 

Lockneed Aeronautical Systens CO~;3ny, P. O. Box 551 

(7';71/211/2), Buroa,k, CA 915~O_ 

#Bl~g. 10';, Org. 62-13, Lockheed ~~sslles & Space Company, 

Space Systems Div1s10n, 1111 Lockheed Way, Sunnyvale, CA 

9';086. 

11 
" . -\ 

, 

APPENDIX G - Invited Lectures 

t 

" 
INVITED LECTURES 

1. "optical Fiber Fundamentals," Proc. Optical Fiber System 

DeS1gn (Madison, WI) February 1988 (R.O. Claus). 

2. "Smart Skins and Avionics," LTV Aerospace (Dallas, TX) 

Februaury 1988 (R.O. Claus). 

3. "Optical Fiber Sensors" (Short Course), MFOC '88 (Crystal 

C1ty, VA) March 1988 (R.O. Claus). 

4. "Fiber Optic Sensors for Materials Evaluation," Hercules 

Research Center (Wilmington, DE) May 1988 (R.O. Claus). 

_IV' 

, 
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~--.---

APPENDIX H - Papers To Be Presented 

t 

• 
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PAPERS TO BE PRESENTED 

1. "Embedded Sensors," Sensor Technology Symposium (Alcoa 

Center, PAl June 1988 (R.O. Claus). 

2. "Intelligent Structures Research at virginia Tech," QNDE (La 

Jolla, CAl August 1988 (R.O. Claus, K.D. Bennett, R.G. May 

and B.D. Duncan). 

3. "Low-Profile Optical Time Domain Fiber Sensors for Materials 

Evaluation," QNDE (La Jolla, CA) August 1988 (R.O. Claus, S. 

Sudeora, K.A. Murphy and K.D. Bennett). 

4. "Advanced Sensors for Smart Materials in Aerospace 

Applications," AIAA Conference (Atlanta, GA) September 1988 

(J.S. Heyman, R.S. Rogowski and R.O. Claus). 

5. "Demonstrat~on of A Smart Structure with Embedded Actuators 

and Sensors for Active Control," SPIE (Boston, MA) September 

1988 (C.A. Rogers, K.D. Bennett, H.H. Robertshaw and J.C. 

McKee""lan) • 

6. "Fiber opt~c Sensor systems for Smart Aerospace Structures," 

SPIE (Boston, MA) September 1988 (W.J. Rowe, R.O. Claus, 

D.A. Martin and D. Trites). 

7. "Full Field Analysis of Modal Domain Sensor Signals for 

Structural Control," SPIE (Boston, MA) September 1988 (K.D. 

Bennett, J.C. McKeeman and R.G. May). 

8. "Intensity Pattern Modulation in Optical Fiber Modal Domain 

Sensor Systems: Experimental Results," SPIE (Boston, MA) 

September 1988 (B.D. Duncan and B.W. Brennan). 

9. "Interferometr~c Measurements of strain Concentrations 

Induced by An Opt~cal Fiber Embedded in Fiber Reinforced 

Composites," SPIE (Boston, MA) September 1988 (R. czarnek, 

V.F. GUo, K.D. Bennett and R.O. Claus). 

10. "Smart Structures Program at Virginia Tech," SPIE (Boston, 

MA) September 1988 (R.O. Claus and K.D. Bennett). 

11. "optical Fiber Methods for the NDE of Smart Skins and 

Structures," SEM Fall Conference (Indianapolis, IN) 

November 1988 (R.O. Claus, K.D. Bennett and B.D. Duncan). 

, 

End of Document