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Fluorescence lifetime sensor usingoptical fiber and optical signal processing

William Heuywon Park

A thesis submitted in confonnity with the requirements for the Degree ofMaster of AppIied Science, Graduate Department of Aerospace Science andEngineering, in the University of Toronto

@Copyright by William Heuywon Park 1998


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AbstractI propose in theory and demonstrate in experiment a fibre optic sensor whichmeasures fluorescent Iifetime and fiber length using an all optical signalprocess-hgscheme. The schemeuses a double modulation homodyne method to produceauto or cross correlation in fequency domain. Because t ehninates the neefor high bandwidth optical detection and electronic processing, it has the p c ~tentiai of superior performance with less complexity than conventionai time orfrequency domain fluorometers. To demonstrate, fiber length of 50.28f .27mand fluorescent lifetimes of 28.3f .5ns and 360f 8ns are rneasured with only4MHz bandwidth. Furthemore, the fluorescence collection ac iency of multi-mode fiber is derived for single and double fiber configurations. And the effectof optical fiber on excitation and fluorescence is analyzed- Aho, possible appli-cation in the cure monitoring of epoxy resin is addressed.

Fluorescence lifetime sensor usingoptical fiber and optical signal processingby

William Heuywon ParkMaster of Appiied Science

Aerospace Science and EngineeringUniversity of Toronto1998


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AcknowledgementsThis hesis isdedicated to my familywho stood by and endured with me throughIong iliness and even longer recovery. 1 used to take health and family forgranted; but I found tha t they are the most important things in the world.

Experiment was performed in Ontario Laser and Lightwave Center at theUniversity of Toronto, and 1wish to arknowledge the fnendly people there, Dr.Ad Hubert, Ed Kammermayer,and Victor Isbrucker. A h , 1am grateful to SteveBrown of Chemical Sensor Group in Erindale campus at U of T for collectingthe fluorescence spectrum and decay.

Finaily, 1would iike to thank my supervisor, Dr. R M Measures, for givingme a chance to explore the topics of fibre optic fluorescence sensor which, 1believe, has many interesting applications in bioengineering and medical fields,even though it has Little to do with our lab's smart structure program.


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AbbreviationsA 0AODAOMBSB WDFTEOMFTIFIOMLOMMFNAOFDROTDRQYRFRUSMFSPA

acousto-opticdriver for AOMacousto-optic moduiatorbeamsplit erbandwidthDiscrete FourierTransformelectr-p tic moddatorFourier Transfonuiat errnediate kequencyintegrated optic moddatorlocal osciUatormultimode fibernumericaI apertureoptical frequency dornain reflectometeroptical tirne dornain reflectometerquantum yieldradio fiequencyruthenium tris-bipyridy1 dichloride,hexahydratesinglemode fiberN-(3-sulfopropyl)acridinium, inner sait


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Contents1 Introduction 72 Multimode Fiber 9. . . . . . . . . . . . . . . . ..1 Mode Propagation in Steady-State 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..2 Dispersions 10. . . . . . . . . . . . . . . . . . . . . . ..2.1 Modal Dispersion 10. . . . . . . . . . . . . . . . . . . . ..2.2 Material Dispersion 11. . . . . . . . . . . . . . . . . . . ..2.3 Waveguide Dispersion 11. . . . . . . . . . . . . . . . . . . . . . ..3 Rayleigh Backscattering 11. . . . . . . . . . . . . . . . . . . . . . . ..4 Fkesnel Backreflection 12. . . . . . . . . . . ..5 Fluorescence Collection by Direct Coupling 12. . . . . . . . . . . . . . . . . . . . ..5.1 Liouville's Theorem 12. . . . . . . . . . . . . . . . . . . . ..5.2 Collection Efficiency 13. . . . . . . . . . . ..5.3 Coilection Efficiency of Single Fiber 15. . . . . . . . . . ..5.4 Collection Efficiency of Double Fibers 15. . . . . . . . ..6 Fluorescence Collection by Evanescent Coupling 16. . . . . . . . . . . . . . . . . . . ..6.1 Evanescent Excitation 16. . . . . . . . . . . . . . . . . . . . ..6.2 Collection Efficiency 173 Fluorescence System 18. . . . . . . . . . . . . . . . . . . . . . . . ..1 Fluorescent Response 18

. . . . . . . . . . . . . . ..2 Determining Lifetime in T i e Domain 19. . . . . . . . . . . ..3 Determining Lifetime in Frequency Domain 194 Acousto-Optic Modulator 22. . . . . . . . . . . . . . . . . . . . . . . ..1 Acoustic Perturbation 22. . . . . . . . . . . . . . . . . . . . . . . . ..2 Diffraction fficiency 234.2.1 Raman-Nath AOM . . . . . . . . . . . . . . . . . . . . . . 24

4.2.2 Bragg AOM . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3 Modulation Bandwidth . . . . . . . . . . . . . . . . . . . . . . . 25Signal Processing 27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..1 Signal Flow 27. . . . . . . . . . . . . . . . . . . ..2 Auto and Cross Correlations 29

. . . . . . . . . . . . . . . . . . . . . . ..3 TimeDomain Responses 30. . . . . . . . . . . . . . . . . . . . . ..4 Estimation of Parameters 34. . . . . . . . . . . . . . . . . . . . . . . . . ..5 Estimation of Error 346 Experiment 366.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 36

6.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366.2.1 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36


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. . . . . . . . . . . . . . . . . . . . . . . ..2.2 AOM and AOD 39. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..2.3 MMF 41. . . . . . . . . . . . . . . . . . . . . . . . ..2.4 SPAandRU 436.2.5 LO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45. . . . . . . . . . . . . . . . . . . . . . . . ..2.6 PIN Detector 46. . . . . . . . . . . . . . . . . . . . . ..3 Jhperirnental Procedures 46. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4 Data Analysis 48

7 Conclusions 56A Formula and Tables 58. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. l Definitions 58. . . . . . . . . . . . . . . . . . . . . . . . . . ..2 Impulse Function 58. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..3 Solid Angles 58. . . . . . . . . . . . . . . . . ..4 Table of Fourier 'handorrn Pairs 59. . . . . . . . . . . . . . . . . ..5 Decomposition into Fourier Series 60. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..6 rmswidth 60. . . . . . . . . . . . . . . . . . . . . . ..? Fiber-twFiber Coupling 61B FIuorescence Application in Cure Monitoring 62

. . . . . . . . . . . . . . . . . . . . ..l Epoxy Resin and Composite 62. . . . . . . . . . . . . . . . . . . . . ..2 Fluorescence during Cure 63. . . . . . . . . . . . . . . . . . . . . . . . . . ..3 Cure Monitoring 64Bibliography 65


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List of Figures. . . . . . . . . . . . . . . . . . .iber tip with an angled cleave 12

Excitation and collection of fluorescenceusing single fiber . . . . 14Excitation and collection of fluorescenceusing double fibers . . . 14. . . . . . . . . . . . . . . . . . . . .raph of F ( L ) and G(L.s) 16

. . . . . . . . . . . . . . . .-level mode1 of fluorescence system 18. . . . . . . . . . . . . .urvey of fiequency domain fluorometers 21. . . . . . . . . . . . . . . . . . . . . .iffraction at Bragg angle 24

. . . . . . . . . . . . . . . . . . .iffraction at non-Bragg angle 24. . . . . . . . . . . . . . . . . . . . . . . . . .ignal flow diagram 28Square-wave excitation and fluorescent response . . . . . . . . . . 28Simulation of Resnel backreflection fiom 50m fiber . . . . . . . . 31Simulation of SPA fluorescence ming 50m fiber . . . . . . . . . . 32Simulation of RU fluorescence using 50m fiber . . . . . . . . . . . 33Schematic of experimentai setup . . . . . . . . . . . . . . . . . . 37. . .ictures of optical (top) and electrical (bottom) equipments 38Picture of inside AOM . . . . . . . . . . . . . . . . . . . . . . . . 40. . . . . . . . . . . . . . . . . .ransfer function of AOM/AOD 41. . . . . . . . . .hernical formula for SPA (left) and RU (nght) 43Absorption and emission spectrum for SPA (top) and RU (bottom) 44Calibration data for LO's voltage-to-frequency conversion . . . . 45. . . . . . . . . . . . . . . . . . . .C-coupled lowpass detector 47. . . . . . . . . . . . . . .h ~ l e r ~ ~ ~ - c o u & iandpass deteetor 47

6-10 Aligning AOM for first p a s (top) and second pass (bottom) . . . 476.11 Pictures of SPA (top) and RU (bottom) fluorescence . . . . . . . 496.12 Raw data for Fresnel backreflection from 50m fiber . . . . . . . . 506.13 Raw data for SPA fluorescence using 50m fiber . . . . . . . . . . 516.14 Raw data for RU fluorescence using 50m fiber . . . . . . . . . . . 526.15 Raw data for Fkesnei backreflection h m 9m fiber . . . . . . . . 536.16 Fluorescence decay of SPA and Fluorescein . . . . . . . . . . . . 556.17 Fluorescence decay of RU and Fluorescein . . . . . . . . . . . . . 55

. . . . . . . . . . . . . . . . ..l epoxy resins DGEBA and TGDDM 63B.2 curing agents DDS and DDM . . . . . . . . . . . . . . . . . . . . 63


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Chapter 1IntroductionMany have used optical fiber sensor and fluorescent lifetime to measure suchparameters as temperature, pH, O2 oncentration, etc. Th e optical fiber allowsone to excite and coilect the fluorescent signal from a remote medium that mayotherwise b e ciifficuit to access. The lifetime of fluorescence decay is chosenbecause the decay mechanism is weU understood, is sensitive to its molecujarenvironment, and is mostly independent of the intensity and the wavelengthof both excitation and fluorescence. In combining opticd fiber and fluorescentlifetime, the sensors represent a significant development not o d y in fluorescencefield, but also in other sensing applications where the parameter of interest canbe measured from an optical signal whose profiie and mechanism are simiiar tothe fluorescencedecay.

Unfortunately, al1 the sensor implernentations, so far , suffers hom 3 majorproblems:

1. The couphg between the optical fiber and the fluorescence has not beenstudied anaiytically. The fluorescent coupiing is important in determiningthe amount of fluorescence that is collected by fiber, and in evaluating theperformance and potential of optical fiber sensor.

2. The waveguide effect of optical fiber on the excitation and the fluorescencesignais has not been quantified. Unlike the hee-space which it replaces, theoptical fiber generates Rayleigh scattering, Ftesnel reflection, dispersions,modal interference, wavelength dependent attenuation, coupling loss, in-cidental luminescence, etc.

3. Most of signal processing for the lifetime is done electronically in eithertime or frequency domain, using expensive components and complicatedarrangements. The main advantage of electronic signal processing is thatamplification, filtering, and other signai conditioning can be done. As theMetirne gets shorter, it requires faster detection and higher bandwidthsignal processing. This becomes more difficult t o accomplish with theequipments that are cmently anilable.

1address these problems in my thesis with the emphasis on understanding thefundamentah, rather than on reciting a list of possible applications or on per-forming characterization of actual materials.In my thesis, 1propose in theory and demonstrate in experiment a fibre opticsensor which measures fluorescent lifetbe and fiber length using an aii opticalsignal processing scheme. A continuouslaser beam is intensity modulated by anacousto-optic modulator and is launched into a multimode fiber. At the far-end,


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the optical fiber coUects either fluorescent response fiom which to measure thelifetime or fiesne1 backreflection from which to measure the length. The return-ing signal is intensity modulateci again by the modulator and is detected usinga lowpass detector. Although the fluorescent lifetime is the main parameter ofinterest, the fiber lengthmust be aiso measured because the use of optical fiberinevitably introduces propagation delay.The first and second problems are addresseci by deriving the fluorescencecollection efficiency for single and double fiber configurations, and by ana imgthe effect of optical fiber on the propagating signais. The results are obtainedrnainly for multimode fiber, but they can be useful for singiemode fiber as well.

To address the t h i d problem, the signal processing scheme uses a doubleoptical modulation homodyne method to produce aut o or cross correlation infrequency domain. The length and Metirne parameters are estimated by data fit-ting auto and cross correlation modei directly in frequency domain. My schemeeiiminates the need for wide bandwidth opticai detection and high frequencyelectronic processing, whde at the same tirne, reducing the component count andsimplifyingthe experimentd setup. I t has the potential of superior performancewith less complexity than conventional time or frequencydomain fluorometers.


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Chapter 2Multirnode FiberIn this chapter, 1will present some basic expressions which are helpful in under-standing the workings of multimode fiber (MMF) and occasionally singlemodefiber (SMF).Consider a MMF with core radius a and index profile

where Ml = ni sinBM = ni = is knom as numericd aperture,and eEt4s half-angle of acceptance aperture inside the fiber. 2 common typesof fiber are step-index fiber (g = w) in which the core index stays constant nland pambolc-index fiber (g= 2) in which the core index decreases parabolicallybtom nl to na.

2.1 Mode Propagation in Steady-StateA t steady-state, optical power can be propagated only in guided mode withkon2 < P < b n l , where B is th e propagation constant along the fiber axis.[Marcuse, Ungar, Cheo, hatak].The total number of guided modes is

N=--= v2/2, tepg+2 2 v 2 4, parabolicwhere V = koaM. Since diffuse source, such as LED and fluorescence, wiiilaunch equal power into each mode, fibers with equd number of modes wiilcamy equd amount of power. If Pm is the propagation constant of mth-ordermode, then the number of modes with Dm c 3 < konl is

which can be r e h t t e n for the propagation constant as

Since each mode propagates with dEerent velocity v,that a mode takes to travel distance L is [Cheo,Marcuse, = &/d&,, the timeGhatak, Cowar]


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where C = (~,/lV)g/(g+*), and small A is assumed in Eqn 2.4. Ignoringhigherorder terms, the difference between the fastest time (( = 0) and the slowestt h e ('t= 1) is Ln

c a2/2, parabolic= (2.6)One can ais0 describe propagation conditions in terms of geornetnc optics.

By cornparhgEqn 2.4 and B, =kmlos& where8, is the angle between rayvector and fiber axis, one obtains [Ungar, Barnoski, Cheo]

which explains concisely much of the experimentaily observeci phenomena inMhfF'. Furthemore, outside the opticd fiber, the far-field angular (8) depen-dence and the near-field radial (r)dependence of normalized power are (Barnoski]

where is haif-angIe of fiber aperture in air. As expected, the power distri-butions for stepindex fiber ( g = oo)are uniform; that is,P(8)= P(r)= 1,2.2 DispersionsIn this section, 1 eview only the broadening of rms width (a) ue to 3 types ofdispersion associateci with optical fiber: [Cheo,GhatakJ

Modal dispersion (a l ) is caused by the fact that Merent mode travels atdifferent speed.Material dispersion (oz)s caused by the fact that refractive index n(X)varies with wavelength.Waveguide dispersion (03) is caused by the fact that waveguide parameterV depends on A.

For MMF, 01 is usuay dominant, but 0 2 makes contribution in fluorescencemeasurement where source spectral width is large. For SMF, dy 02 and a3are applicable. The dispersions are uncorrelated with one another. And if thefiber is operating iinearly, the rms width of total dispersion becomes [Gowar]

2.2.1 Modal DispersionFortunately for stepindex and parabolic-index MMF, the modai impulse re-sponse tums out to be a square pulse [Marcuse]; that is, when an impulse exci-tation is launched into the fiber, the propagating modes are distributed evenlybetween the fastest mode and the slowestmode. Then, using Eqns 2.6 and A.53,the rms width of modal dispersion becomes

01= - = - step


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Since modal coupling tends to reduce pulse broadening in exchange for increasedat enuation, the modal dispersion exhibits square-root dependence with distanceafter travelling mti ca l length of L, = 1/47,. [Cheo, Gowar]

where a, is th e rms width at L,, nd 7, is steady-state attenuation c oefficient.2.2.2 Mater id DispersionThe rms width of materiai dispersion is [Cheo, Ghatak]

where n(X) s the core index and as is th e spectral rms width of source. Anempi ri d acpression of n(X) nd n"(X) for pure silica are [Ghatak]

where p = X x 106is wavelength in hm], n''(A) = n"(li)/p2, and

2.2.3 Waveguide DispersionWaveguide dispersion is relevant only for SMF. An empirical expression forstep-index SMF s [Ghatak]

2.3 Rayleigh BackscatteringConsider an impulse excitation of unit energy travelling down an optical fiber.The spatial profile of excitation is sirnply E(z)= e-Tz, where 7 s the totai at-tenuation coefficient due to Rayleigh scattering (r,a and absorption (y,).In [ z , z + dz] interval, y.E(z)dz is lost to scattering, of which only S-y,E(z)dzis coilected back into fiber. Assuming Rayleigh scattering is isotropic at l e s tover the acceptance aperture of fiber, the collection efficiency is given as

S = 3g A, for MMF [Kg, K33,Ungar]4(9 + 1)- 3a2--2,,9 A' for SMF [KlO, 11, 33]where w is the spot size of Gaussian profile that approximatesSMF's undamen-ta1 mode field. SpeQfically,S= 3A/4 for stepindex MMF, nd S = 3A In V/V2for stepindex SMF using Eqn 2.36.

S i c e the attenuation is same for backward and forward propagation, thebackscatterecl energy arrving at z = O fkom the interval [t, + &] is dE , =S7.e-2Tz&. The impulse response h ( t )= dEs / d t is simply the rate of scattered


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Figure 2.1: Fiber tip with an angleci cleave

energy returning back to the launch point. Then, using 22 = d / n for 2-waypropagation in an optical fiber of length L, he impulse and frequency responsesof Rayleigh backscattering are [KlO,K13, K14, K32]

2.4 Fresnel BackreflectionAt a cleaved end of MME' as iuustrated in Fig 2.1, the cleave angle 8 deter-mines how much of Ftesnel ref'iection, which is normdy produced due to theindex difierence between nl and no, is coiiected back into the fiber. Using EqnA.63 with small angle approximation (@,OEui< 1)or from Ref [K12], the totalbackrefiection coefficient can be writ ten directly as

if RQ and RL0)and far-end ( 2backreflection are

are the reflection coefficients respectively at near-end (z== L), then the impulse and frequency responses of Fresnel[K13, 14, K32]

2.5 Fluorescence Collection by Direct CouplingCoupling between diEuse source and optical fiber has been studied using Li-ouville's theorem and ray optic assumption, mainly in the context of taunchingLED nto MMF [Hl]. y extending the results of LED-tefiber coupling, 1derivethe efEciency of collecting fluorescence through MMF, whether the excitation iscanied by the sarne fiber or by another. O hers have studied the case of singlefiberp6,H7, Hg] nd double fibers [H3, 4, H8, HlO], al l utiiizing brute forceintegration with complicated geometry. My approach yields simpler yet morecomplete solutions.2.5.1 Liouville's TheoremLiouville's theorem uses canonicd conjugate variables of Hamiltonian mechan-ics. For ray optics, it begins with Format's principle on optical path length,


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[Hl, Marcuse]E

y , =)& = L ( Z . y, I , = extremum (2.23)where 2 = &/&, y1 = dyldz, and 8 s = &z +


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Figure 2.2: Excitation and co11ection of fluorescence using single fiber

Figure 2.3: Excitation and collection of fluorescence using double

+ excitation

t 2u+2s+


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Fluorescence As shown in Fig 2.2, the phase volume of fluorescent source a tz = z emitting into 2 hemispheres is I = GASR, , where '4. = na2 ( l+~ / b ) ~nd R, = 2a. The phase volume of fiber at z = O is T t = n:AfQwhere A f = ?ru2and RI = irsin2 EU Then, the collection efficiency is

2.5.3 Collection Efficiency of Single FiberConsider aLWlluminating a conical volume with ha-angle 0Et4as shownin Fig 2.2. lui an absorbing medium, the excitation profile dong 2 axis isI ( z )= Ioe-Q', where a is bu& absorption coefficient and Io is the initial inten-sity over the core area 4. In [z, + d z ] interval over cross-section area A (% ) ,aI(z)dt is absorbed and QYd(r )& is emitted as fluorescence, of which odyqcQYckI(z)dz is coiiected by the fiber. In travelling back to z = 0, fluorescencesuffers from various attenuations which are lumped into another coefficient f l(usudy negligible).Using Eqn 2.28, the overd collection efinciency for single fiber becomes

where x = (a P )zand L = (a P ) are normalized distances. Asymptotically,F ( L ) - L a s L + 0,and F ( L )- 1 2 / L a s L -+ W. Sirnilar result has beenobtained for backscattering from buik medium [H2, ulshaw].2.5.4 Collection Efficiency of Double FibersConsider 2 identical and parallei MMFs whose cores me separated by 2s distanceas shown in Fig 2.3. Excitation is carried by one fiber and fluorescence iscollected by the other. The derivation for double fibers is same as for singlefiber, except that the collecting fiber does not "sees" the entire cross-sectionA ( z ) but ody the overlap area B(z ) beginning at = s/ anom = bsla. Thisreduces rl, in proportion by

Then, the overaii collection efficiency for double fibers becomes

L # - in tG ( L , ) =lrr(-1+ x R &where x = (a+B)z . L = (a+ B)b, x0 = Ls / a are normalized distances, andcos($/2) = (L x o ) / ( L+2).


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Figure 2.4: Graph of F ( L ) and G ( L y ) with s = O and s = 1.440- F(L)s forsingle fiber. G(L, ) is for double fibers with no cladding so tha t the fiber corestouch ech other. G (L ,1.44~)s for double fibers with reaiistic dimensions of62.5pm cladding radius and 2 5 . 6 ~ore radius, just We the MMF used in myexperiment.

F(L)nd G(L, ) are eduated using Romberg numericd integration [Press]and plotted in Fig 2.4. Since F ( L ) > G(L, ) for aii L > O, as expected,single fiber coliects more fluorescence than double fibers. The assumption ofzero separation (s = O), even though unrealistic because cladding is present inmost optical fibers, establishes the upper limit of collection efficiency for doublefiber configuration. Whea a real cladding dimension of MMF (s = 1.44~)sconsidered, the efficiency decreases by an order of magnitude.

2.6 Fluorescence Collection by EvanescentCou-pling

In order to maximize evanescent couphg in MMF [I9], the cladding is removedso that the core is in direct contact with sample (no)which acts as the rnissing"cladding". Similady in order to rne evanescent coupiing in SMF [I11], thefiber isheated and stretched so that the core forail practical purpose disappears,and a new optical waveguide is formed by the cladding (na) cting as "corenand sample (no) cting as "cladding". Since typicai sample index is not equalto the dadding index, there is coupiing Ioss [Il& 15, 1161 due to AH mismatchat the beginning and a t the end of sensing region.2.6.1 Evanescent ExcitationThe ample absorbs emescent power just as it does in the case of bulk excita-tion. But, because the sample experiencesonly p fraction of the total power, theabsorption coacient decreases to 7 = a p and the d t a t i o n profile becornesI ( z )= ~ e - ~ ' .or a SMF or MMF with weakly guiding stepindex profile, the


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cladding fraction of mode power is [Cheo, Ghatak]

where u2= k$p: - 12, 3 = 12 - && u2a2+w2a2= V2, and Bessel functionKl()epresents the radial field of mode order I in the dadding.

By stimming over all N = V2/2modes in stepindex MMF, the claddingfraction of total power propagating in MMF becomes p8, 19, after minor cor-rectionl

In the case of SMF, there is oniy one mode to consider, nameIy 1 = O. However,it is much easier to work with a Gaussian approximation than with the exactBessel function. For stepindex SMF, he radial field of fundamental mode canbe approximated by [Snyder]

where w is the spot size of Gaussian profile and a is the core radius. Then, thecladding fraction of mode power in SMF becomes a simple ratio of integrais,Pl1 /na $2(r)rdr - 1P = - -2a21w2 =-22.6.2 Collection EfficiencyThe collecting fluorescence through evanescent coupling can be thought of asthe inverse of evanescent absorption; the amount that "tunnels" back into aguiding mode is proportionai to the evanescent field intensity of that mode.Hence, MMF is expected to have higher collection efficiency than SMF becauseof the simple fact that MMF supports many modes and SMF supports only one.

Using Eqn 2.36, the collection &ciency for stepindex SMF is given as [Ill]

Thisexpressionwas derived with 2 assumptions- irst, the indexes of fiber andsample are similar (nl = n2 a no); econd, the wavelengths of excitation andfluorescence are close enough (A, x X p ) so that their modal fields are similar.

Unfortunately, there is no comparable analytical expression for MMF. Thecollection efficiency of weakly guiding stepindex MMF [IIO] and general s t e pindex MMF p12, 1131 has been studied using numerical simulations. For bulksource distributeci uniformly throughout the sample, f l , a V since oniy high-order modes have appreciabie penetration into the cladding. For surface sourcelocated at the fiber-sample interface, II, cc V2 since every mode has a reasonablepower at the interface. But, the exponentiaily decaying source profile whichoccurs in evanescent excitation has not been studied so far.


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negative, the input and output must be biased above O. This is important forsinusoidd input and outputx(t) = 1+ a os(2lrf t), la1 5 i (3-3)

cos(2s t - an-' (2rf s ) )= l + a (3.5)where the constant term has been normalized to 1.

3.2 Determining Lifetime in Time DomainThe fluorescent Iifetime of sample can be measured in time domain using pulseexcitation. Because of finite pulse width, finite detector bandwidth, A-bias, andother problems, it is a standard practice to measue fluorescence fcom both thesample and a reference using the same setup. This arrangement is outlined in

where 1(t ) is laser excitation, d(t) is detector response, h(t) = e-'1' is sample re-sponse with lifetime r, &(t) = ed t lT r ci refereace response with lifetime r, , z(t)is measured reference iuorescence, and y(t) is measured sample fluorescence.Mathematicdy, it can be described as

This problem is solved by iterative convolution in which the measured data{xi, i ) is fitted directly to the convolution models. m e r convolvingh, (t) withEqn 3.7 and h(t)with Eqn 3.6, the residual fiinction

is minimized for the least-square estimator of r. Since the reference IifetimeT, is a fixeci constant, this is a 1-D minimization probtem which can be solvedby Brent's method press], for exampIe. Although one convolution needs tobe calculateci for every new s point, the convergence for 1-D problem is usudyfast. Because of its simplicity and flexibility, this method is preferred over directdeconvolut on met ho&.

3.3 Determining Lifetime in Requency DomainThe fluorescent lifetime of sample can be measured in frequency domain using si-nusoidal or harmonic excitation. Typically, sinusoidal excitation is generated byrnodulatinga continuous wave source; and harmonic excitation is derived fioma train of pulses which decomposes into hamonic series. 3 signals are involved


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in general- xcitation z ( t )with fundamental kequency f and harmonics n ,fluorescent response y ( t ) , nd LO signal z ( t ) at frequency f, .

where, from Eqns 3.3 and 3.5,

If the frequency f is low enough, the amplitude factor (ml and phase shift( p i are measured directly from Eqns 3.9 and 3.10-But if the frequency is hi&,heterodyrre or homodyne method is used, where LO signal z ( t ) s mixed with RFsignalsz(t)and y(t),either inside or outside photodetector. Subsequent Iowpassfilter produces "down-convertetinLF signals X( t ) and y ( t ) at a sufliciently lowfiequency so that ml and ip t can be measured using a lockin amplifier. Inheterodyne method, fo * I and the IF signals are at frequency4 = f - o ;and in homodyne method, f, = f i and the IF signals are DC:

UsuaUy, the data are sampled at more than one frequency, either by changingf, to near any of the harmonics or by changing f itself.

Once {m, p) data set has been obtained, the Metirne T is determineci eitherthrough linear regression of [P4]tan p = la r, l / m 2= 1 + (2a )* (3.13)

against the frequency f,or through minimization of residual function

where mi and vi are measured at frequency fi, nd m(fi) and cp ( fi) re cal-cdated from Eqn 3.12. For an example, m and cp that will be produced atf = lMHz are

Fig 3.2 lists papers, in the order of increasing bandwidth, which use sinu-soidal or harmonic excitation to measure fluorescent lifetime in the fiequencydomain. 1should point out that since fluorescence system is treated as linear andtime-invariant, a Network Analyzer (some with 20GHz bandwidth) can performall the signal processing and can in principle replace most of the equipments de-scnbed in the papers. But, Network Analyzer is very expensive, and the papersbasically talk about cheaper alternative of measuring the sinusoidai response.Main advantages of frequency domain method over time domain method arethat high detection bandwidth and deconvolution of sample response are notrequird.


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Figure 3.2: Survey of frequency domain fluorometersRefi 1 m a x k e q 1 source 1 data

Sinusoidai ExcitationEOMLEDLEDAOMEOM

D2 LampEOMEOMQuartz AOMHarmonie Exitation

synchrotron radiationmode-locked aser + AOMmode noise of CW lasermode-lockedlaser

pulsed laser diodemode-locked asermode-locke aser


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Chapter 4Acousto-Optic Modulator1 used PbMo04 acousto-optic modulator (AOM) in m y experiment because itwas cheap and available. Others [N9, N10,N12,N15, N16, N17,NI81 have useddifferent optical modulators to implement various schemes in which the doublemodulation of optical signal is the key feature just as in my own correlationscheme. The choice depends on factors like modulation bandwidth, operatingwavelength, compatibility with optical fiber, and,most of dl, cost and availabil-ity. In this section, 1 review o dy those aspects of AOM elevant to amplitudemodulation, since that is how 1 use it.

4.1 Acoustic PerturbationAcousto-optic (AO) interaction can be modelled as inelastic scattering betweenincident optical photon (w ,k) and acoustic phonon (0, ),producinga diffractedphoton that is "upshifted"(w+, k+) if the phonon is absorbed or "down-shiftedn(w-,-) f an identicai phonon is emitted. [Korpel, Magdich, Yarivj

The phase-matching conditions determine diffraction angle, polarizat ion, fie-quency shift, and propagation constant. But the modulation of optical signai isachieved through the difEaction efficiency.

Outside the scattering site, incident wave E and difEracted waveE'propagateas separate and uncoupleci plane waves. Inside the scattering site, however, Eand El waves are coupled through acoustic perturbation which is producedaccording to the weU-known strain-optic relation, [Ghatak, Magdich]

where p is strain-optic constant and S is strain field set up by the acoustic wave.Because of syrnmetry in the tensor components, matrix notation [.II[ and vectornotation ( - ) i can be converted from one to the other, dependhg on the context.Then, the coupled wave equation becornes [Magdich, Ghatak, Yariv]

where


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The degree of coupling between the inadent and dfEacted waves is givenby scaIar pagdich, Ghatak, Yariv]

where e and e' are unit vectors of E and Et respectively. Usually, the acousticand opticai waves are aligned with AOM's axb , so that (e'lA[e] le) d e c t s onlyone element from AM. Using appropriate scalar parameters in e = c6n2andA(l/n2) pS , the change in refractive index due to acoustic perturbation ispagdich, Ghatak, Yariv]

where M2 = n6$ /p : is a figure of merit for AOM, A is area of transducer, andfi = ( A U . ) ( ~ J ~ ~ )s acoustic power. Fkom experimental point of view, A n isthe most important parameter because it influences ail optical manifestationsof A 0 interaction.

For example, consider longitudinal acoustic wave dong t n PbMoO* whichis an uniaxial crystai with 4/m point symmetry:

Then, the acoustic perturbation as given by Eqn 4.4 is

Because A[] is diagonal, the diffracteci and incident waves have the same po-larization; otherwise, there wodd be no A0 coupling. The scalar Ae and Anthat are selected depend on the orientation of E and K. Therefore, from Eqns4.5 and 4.6,

4.2 Diffraction EfficiencyAOM can be either Bmgg or Raman-Nath type depending on [Ghatak, Korpel,N25]

K2L 27rALQ=-=- Q < 1, for Raman-Nathk nA2 Q 1, for Braggwhere K is acoustic wavevector, k is optical wavevector, and L is transducerlength.


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Figure 4.1: Diffraction at Bragg angle for upshift case (top) and down-shift case(bottom)

Figure 4.2: Diffraction at non-Bragg angle for upshift case (top) and down-shiftcase (bottom)

4.2.1 Raman-Nath AOMIn Raman-Nath AOM, multiple scattering takes place because the acoustic di-vergence is greater than the diffraction angle. If eo is the angle of incidencewith respect to the acoustic nomd, the diffraction efficiency (q )and angle (8)of mth-order beam are [Ghatak, Korpel, N25,Yariv]

where J,() is standard Bessel function, and Alp = kpAr~L/cos8~s opticalphase shift eaused by An over the interaction length.When O0 = O for example, 100% of 0th-order beam is difiacted out atAip = 2.40; maximum 34% diffraction into 1st-order occurs at Aip = 1.84; andmaximum 2496 diffraction into 2nd-order ccursat A p = 3.05. Naturally,higherorders exhibit progressively lower efficiencies. Due to its low efficiency and lowbandwidth, Raman-Nath AOM appears ody in specialized application (N24J.


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the difEraction output becomes pagdich, Goutzoulis]

= 1+a sinc(fdf,,) c o s ( 2 ~ f , t ) , uniform beam (4.18)- 1+oe-.'f;/~f2-cos(2nfmt), Gaussianbeam (4.19)

where P( ) is the spatial FT of optical beam profile p ( z ) . The 3dB point or50% modulation depth occurs at

0.60fm,, uniform beamf 3 d ~ 0.75fm,, Gaussian beam


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Chapter 5Signal Processing5.1 Signal FlowFig 5.1 depicts the block diagram of my aii optical signal processing scheme:

1. LO signal x(t) is rnodulated onto DC laser intensity by AOM.2. 1-way propagation in optical fiber introduces At/2 delay.3. At the far-end, fiesne1 reflection x(t -At/2) or fluorescent response y(t -At/2) couples back into the fiber.4. On the return path, the fiber introduces another At/2 propagation delay.5. Second optical modulation by AOM mixes the LO signal z ( t ) with thereturning signal, giving z( t ) z( t- At) or x(t)y(t- At).6. The mixed signai is integrated by lowpass detector, producing auto corre-lation &,(-At) or cross correlation&,(-At).

The goal is to determine the fiber length (L) by analyzing the auto correlationwhich cornes from Fresnel backreflection with impulse response h(t)= 6 ( t ) ,andto determine the fluorescent lifetime ( 7 )by andyzing the cross correIation whichcornes nom SPA or RU fluorescence with impulse response h(t)= e - t / T .

AU signals are periodic, either sinusoidal or square-wave, with frequencyf = 1/T. Since the propagation delay At = 2Lnlc is fixed by the fiber Iength,and since it is the modulation frequency that is being varied in my experiment,the co rdat ion s turn out to be functions of f :

This epresents a fundamental change of domain which does not easily lend itseifto the conventional techniques of (stationary) random variable. Ait hough timedomain responses ca n be inferreci from inverse FT of correlations, it is simplerto estimate L and T directly in iiequency domain.


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Figure 5.1: Block diagram of signal flow in my experiment. Auto correlation(top) is produced when measuring Ftesnel backreflection,and cross correlation(bottom) is produced when measuring SPA or RU fluorescence.

detector&.(-At) 4 *Z& 1-z(t - +) 4 t )

detector* - A j,-:& /

Figure 5.2: Square-wave excitation x(t) and fluorescent response y ( t ) of singlelifetime system

laserfiber 4* At/2

.x(t - F ) l ( t - At) z(t)z(t - At)


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5.2 Auto and Cross CorrelationsSquare-wave excitation is used extensiveiy in my experiment because the simple"on/off States are easier to generate, e s p d y with nonfinear moduiator likeAOM.But its analysisis based on sinusoidal case. The sinusoidal input z(t ) andthe fluorescent response y(t) are &en by Eqas 3.3 and 3.5. Now, consider anideai (equalon/off) square-wave excitation at fiequency f = 1/T,as iliustratedin Fig 5.2. The waveformusing Eqns A.48 and A.49. is decornposed into more convenient Fourier series

By superposing Eqn 3.5, the fiuorescent response to the square-wave excitationis

00 4( - cos ( 2 m t - a n - l ( ~ m f r ) )~ ( t ) = l + x - (5.6)odd rn dl+ 2rm T ) ~which, as shown in Fig 5.2, rises and falls exponentiaiiy between the maximumB = 1+ anh(T/4r) and the minimum A = 1- anh(T/4r).Then, the correlations defined by Eqns 5.1 and 5.2 becorne, for sinusoidalcase

a2cos (27rf At + tan-' (27rf 7))Rdf) 1 + dl + (Zr r ) 2and, for square-wave case

00 8 cm (2amf ~t + t a K 1 2 m ))&,cf) = l + 1-* m 2 (5.10)odd m dl+ 2 m T)?The effect of finite bandwidth on the shape of correlation cannot be ignoreci.First, he AOM hq ue nc y responseis sinc(0.6 / s d ~ )kom Eqns 4.18 and 4.20,where beam profile for both the laser beam and the MMF output are assumecisufiiciently uniform. After 2 passes thmugh AOM, he fkequency signai is atten-

uated by sine2 0.6f 3ds ) .Second, the cosine series is truncated after 36MHzbecause very little contribution cornes from higher fiequencies due to bandwidthand lifetime attenuations. Therefore, the auto and cross correlations must becorrected to, for sinusoidai case

a2&, (f) = 1 t 2 sinc2 w) cos(v)a2a,cn = i +- ~ ~ c ~ ( w )cos(v + an- l(u))2 ,/m


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Figure 5.3: S i d a t e d AC component of&( f ) for Fresnelbackreflection undersquare-waveexcitation (top) and sinusoidal excitation (bottom), with L = 50mand f s d ~= 8MHz


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Figure 5.4: Simulated AC component of &,(f) for SPA fluorescence undersquare-wave excitation (top) and sinusoida1excitation (bottom), with L = 50m,f J d B = 8MHz, and r = 30ns


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Figure 5.5: Simulated AC component of & f ) for RU fluorescence undersquare-wave xcitation (top) and sinusoidal excitation (bottom),with L = 5m,fsds = SiMHz, and T = 350ns


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which estimates the parameters kom time domain responses. In my correla-tion scheme, however, the parameters are gtimated by data fittinga,f ) and&.(fi directly in the hequeney domain, thereby circumventing the resolutionconstraint of DFT formalism.

5.4 Estimation of ParametersThe uto correlation of Eqns 5.11 and 5.13 and the cross correiation of Eqns 5.12and 5.14 can be modelled as y = &= (f ;L) nd y = R, f , ), where fiberlength L and luorescent Iifetime T are unknown parameters. Fortunatdy, the2 parameters can be determined sequentially. First, the least-square estimatorof L is found by minimizing residual function

where Yi is the actual measurement of auto correlation due to Resnel backre-Election at frequency fi, and &=(fi) is calculated fiom the analytical model.Second, the least-square estimator of r is found by mhimkhg residuai function

where y; is the measurement of cross correiation due to SPA or RU fluorescenceat frequency fi , and &,(f;) is calcdated from the model.In each case, the data fitting reduces to 1-D minimization problem whichW solved by Brent's method [Press]. When evaluating the residual in Eqns5.21 and 5.22, the measured and the calculated data are standardized, st bysubtracting linear regression iine from the data, and then by normalizing thedata to zero mean and unit standard deviation.

5.5 Estimation of ErrorThe accuracy and the confidence intervai of estimation can oniy be establishedthrough ensemble average. Conceptually, the '%ruenparameter Uttue is statisti-cally reazed, dong with other random processes or errors, as an experimentaldata set D l iom which an estimation a1 is obtained by data fitting to a model.However, because of the random components, V 1 s not an unique realizationof ut,, . There are infinitely many other redizations V2, s - from whichestimations a2,a3, are obtained. After sufficient number of data sets, theensemble of ai would describe some probabiiity distribution about utruc in theparameter space. [Press]

I f { a i ) is a sample of parameter estimations, then the true parameter isapproximated by ensemble average: [Gut man]

where tN-1;a/2s a point in Student-t distribution with N -1degree of fieedornand 100(1- a)% confidence interval, and a and sa are the usuai mean andstandard deviation,


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-&O, if ( b * )is a sampleofestimations oranother parameter b, the Merencea - is approximated by [Guttman]

where


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Chapter 6Experiment6.1 Experimental SetupThe experimental setup of my correlation scheme is outlined in Fig 6.1; andthe optical and electrical equipments are shom in Fig 6.2. The purpose ofthis experiment is to demonstrate a novel optical signal processing scheme formeasuring the lifetime of fluorescence decay. Because the optical fiber introducesround-trip propagation delay, the fiber length is also measured using F'resnelbackreflection fiom the far-end.-4 continuousAr laser beam passes through halfwave rotator (X/2) and polar-king beamsplitter (BS), and is focused by a Iens onto acousto-optic modulator(AOM) at its Bragg angle. AOM modulates the intensity of laser beam in si-nusoidal or square-wave whose frequency is ramped in time by local oscillator(LO). The resulting 0th-order beam is spatiaiiy filtered by adjustable iris andlaunched into multimode optical fiber (MMF) y a standard fibre optic couplerequipped with 10X objective.

At the far-end, the optical fiber collects either Fresnel backrefiection or ffu-orescence from SPA or RU solution, and guides it back tu AOM. he returningsignai is focused by the fibre optic coupler onto AOM again at its old Braggangle. The 0th-order beam of this second intensity modulation is collimated bythe lem, filterd by uis and interference filter, and finally detected by a lowpassPIN diode detector. A digital oscilioscope coiiects the voltage input to LO as"inputn data and the voltage output from PIN detector as "output" data, anduploads to computer for data fitting.

When me a s m g Fiesnel backrefiection as the auto correlation, my schemeresembles a hybrid of modulation OFDR and correlation OTDR, ecause thecorrelation is measured as function of modulation frequency. When measuringfluorescent response as the cmss correlation, my scheme resembles frequencydomain fiuorometer, because the Metirne is determineci through its sinusoidalresponse.

6.2 Components6.2.1 LaserArgon laser was pre-configured for single-he and single-fiequency operation atwavelength X = 45?.9nm, with bandwidth Au = 3 M h , and coherence lengthLcor = c / A u = 100m. Its output was linearly polarized and was stable atl5mW f .5% without optical feedback problem. The laser polarization was


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Figure 6.1: Schematic diagram of experimental setup. Ali components are fromOntario Laser and LightwaveResearchCenter (OLLRC) r Department ofmec-tricd Engineering at U of T.

SPARU

10XAODAOMAr laserBS

detectorfilterX/2lensL OMMFoscilloscopePIN

SPA

I I,amp * oscill* ,scope

cornputeru10X objective fibre optic coupler (Newport)140MHz quartz os dator driver (NEC OD-8802)Lead Molybdate (PbMo04) acousto-optic moduiator(NEC OD-8813)Argon laser (Spectra-Physics 2020-05)Broadband polarization beamsplitter cube (NewportlOFC16/PB.3)Low-noise J-FET nput Quad OpAmp (TL 074)Interference bandpass iters (Melles Griot 460f Onm,550 Jr ZOnm, 600f 0nm)Broadband polarization rotator (Newport PR-550)Bi-convex o p t i d g la s lem (Newport KBX 076)4MHz Pulse /Fbct ion Generator (Wavetek 187)51 2pmdiameter core multimode fiber (Corning 1517)lOOMHz digital storage oscilioscope (Tektronics 2230)Blue enhanced PIN diode (Silicon Detector Corp. SD200-22-12-041)Programmable Ramp Generator (Burleigh RC-43)Ruthenium tris-bipyridyl dichloride, hexahydrate(Molecular Probes R-1498)N-(3-sulfopropyl) acridinium, inner salt (MolecularProbes S-460)


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Figure 6.2: Pictures of optical (top) and electrical (bottom) equipments


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rotated by hahave (X/2) plate formaximum transmission through beamsplitter(W -Because of very long coherence Iength, Fresnel backrdection coming outof MMF contains speckle pattern which is local fluctuation of intensity due tointerference amongst modes. In addition, 6082 "humming" vibration fiom thelaser cooiing mechanism contributes to the fluctuation by inducing an acousticperturbation of fiber index. But, since there is no mode dependent couphganywhere in the signal path, the total intensity over entire optical beam shouldbe constant despite the local phase noise. Nonetheles, some intensity noise maybe introduced because, as the fiber optic launcher expaxiences the vibration, itsfocused spots move about over the fiber end-face and over the AOM aperture.6.2.2 AOM and AOD.4cousto-optic modulator (AOM) nd its matching driver (AOD) were salvagedfrom old LWC aser fax machine. AOM, shown in Fig 6.3, consists of LeadMolybdate (PbMo04) crystai with 633nm anti-refiection coating and lOmmLithium Niobate piezoelectric transducer. AOD is 140MHz quartz oscillatorwhich is amplitude modulated by a R F mixer. Since the acoustic speed is va =3.63km/s dong f axis (B12,CRC,N251, 140MHz carrier frequency producesacoustic wavelength of A = 25.9pm. The AOM is Bragg type because Q =17> 1.PbMoOs is tetragonal(4/m point group) systemwith strain-optic coefficientat 633nm p12, CRC, Yariv]

It is interesthg to note that nfpi3= nJm3holds true for PbMoOc throughoutits optical spectrurn [B12]. This means that, from Eqn 4.10, the Bragg diffrac-tion is isotropie and independent of polarization between E and K. Since BSrefiects (TE) wave polarized aloag 1 nd transmits (TM) wave polarized dong2, n3 acts on the laser excitation on the first p as , and nl acts on the retumingsignal that actually reaches PIN detector. The relevant refiactive indexes (inbold) and their Bragg angles are [Bass]

The transfer function of AOM/AOD is plotted in Fig 6.4. In order to obtaina linear response fiom GOM, the electrical input to AOD must be biased atthe linear portion of traasfer function. The best sinusoidal outpu t with 25dBharmonic suppression was observed with 2.2 f .OV input to AOD. For square-wave modulation, biasing does not matter since it works on simple "on/offprinciple. Few parameters of Oth-order beam tha t have been measured a t 458nmare


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Figure 6.4: Normaiized output inteosity of Othorder beam kom AOM in re-sponse to input voltage to AOD

normalizedoutputfkom AOM

input to AOD [VI

The Bragg condition is not M y atis6ed in m y experiment mainly due tooptical divergence and Mependence. Especially, the A-dependence of s a c -tion efficiency becomes important when measuring SPA and RU fluorescenceat 550nm and 600nm respectively, since AOM was aiigned at 458nm for boththe laser excitation and the returning signals. The efficiency decreases notoniy because of the longer wavelengths, but also because the old incident an-gle (O0 = 0.214") no longer matches the new Bragg angles. Using small angleapproximation in Eqn 4.15, I )I decreases from 90.5% at 458nm o

The optical divergence of returning signai will reduce the diffraction effi-ciency even further, because AOM difnacts oniy those portion of the focusedbeam that satisfies Bragg condition- i n addition, since the half-angle diver-gence (0.86") of 10X objective is greater than the Bragg angle (0.51),0th and1st order beams of returning signal overlaps. This reduces the signal modula-tion depth and contributes to intensity noise, because the PIN detector is notintegrating over the entire 0th-order beam.

The double p a s through AOM is compiicated by

4 a = KA8L

a dinerent Bragg angle and efficiency for excitation (at 458nm) nd fluores-cence signal (at 550nm or 600nm),Mixent focal Iength for 10X objective (1.48cm) and lens (20cm), and

550nm (SPA)1.50

different beam profile for first pass (nearly pa rde l laser beam) and secondpass (11.5O MMF aperture).

600nm (RU)2.62

These asymrnetries mean tha t optimal coupliig condition for one way does notautomaticdy Iead to optimal coupling for the other way. A compromise isunavoidable.6.2.3 MMF1used 50m long step-index MMF with 25.6pm core radius and 62.5prn claddingradius. Some of material da ta at 458nm are


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The attenuation coefficient a t 458nm was dculated from 2.3dB/km given at850nm, using the f a c t that most of the propagation loss occurs through Rayleighscattering where 7 c R om Eqn 2.18, the impulse response of Rayleighbackscattering is an exponential decay 6 t h "Lifetime" of 0 . 7 7 ~ . lthough thecritical length in Eqn 2-11is 40m, it is convenient to take L, = Born which isequal to the fiber length.

F'rom Eqns 2.10 and 2.11, 1-way propagation in MMF produces modal dis-persion of ol= 0.66ns. and 2-way modal dispersion increases to clfi = 0 . 9 3 ~This limits the spatial resolution to

Also, the use of 550f 0nm and 600f 0nm interference fiiters t o isolate SP.4and RU fluorescenceisequivalent to having40nm spectral sourcewhich producesa substantial materiai dispersion according to Eqn 2.12. Then, using Eqn 2.9,the total dispersion for fluorescent signai adds up to d ? ~ : .

55Onm (SPA) 600nm (RU)0.6611s 0.661~

Fortunately, the total dispersion of SPA and RU signais are insignificant com-pared to their lifetimes of about 30ns and 350ns.Maximum scattering takes place when the excitation is continuous and con-stant, because the entire length of fiber acts as scattering source. And maximumreflection occurs when the fiber end-face is clean and perpendicular. If the ex-citation input z(t) = 1 is launched into MMF, hen the steady-state outputcoming back is y(t) = h(t)*x(t) =H(0). Using Eqns 2.19 and 2.22, the Fkesneiand Rayleigh components of the outpu t are

When the fiber tip is held in air (no= 1.0), kesnel refiection is about lOdSabove Rayleigh scattering. When the fiber tip is imrnersed in aqueous solution(no = l.33), Fresnel reffection falls below scattering; but, this is irrelevantbecause fluorescence ismeasured a t different wavelength. Fresnel reflection fromthe far-end and Rayleigh scattering are depolarized for al1 practical purposeand are split 50/50 by BS. However, Ftesnel reflection from the near-end is stilipolarized and passes straight through BS.Because the laser excitation has shorter penetration in RU solution than in

SPA, the RU fluorescence is "closer" and has better coupling to the fiber end-face. Nonetheless, QY must be included when calculating the total amount offluorescence that is collecteci. Using no = 1.33 and b = a/ anom = 168pm inwater, the total collection efficiencies for SPA and RU fluorescence become


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Figure 6.5: Chernical formuia for SPA (Mt) and RU (right)

I'here is about 5dB clifference between SPA and RU signais. Considering thatfiber attenuation, diffraction efIiciency, AOM attenuation, fl te r attenuation,and PIN diode responsitivity are ail A-dependent, mostly in RU'S favour, thefinal signals shouid be of similar magnitude. Fhrthermore, had 1 used doublefiber configuration in my experment, the fluorescent signais would be 9-13dBlower since G (L ,1.44~) 0.0023 for SPA and G (L ,1.44a) = 0.0078 for RU.

Comparing the collection efficiency of fiesne1 refiection (RL)nd fluores-cence (QYrl,)at the far-end, the Fkesnel backreflection is 23dB higher than SP.4fluorescence and 27dB higher than RU luorescence. This is consistent with ex-perimental observation of few p W for F'resnel signal and few n W or both SPAand RU signals.

Yeliow-orange luminescencepl61 is obsemed from the fiber's plastic buffer.Fortunately, even though this luminescence can be seen easily by naked eyes?its contribution at 550nm and 600nm is below the noise flmr of PIN detector.This is due to very poor evanescent coupling between the cladding source andthe propagating modes in the core.6.2.4 SPA and RUSPA and RU compounds were selected based on their single exponential decay,long lifetime, visible absorption and emission spectnun, large X shift, high QY,stable photochernistry, easy preparation, and low cost. While SPA is a reguiarfluorescent compound, RU is fundamentally a phosphorescent compound whoseemission is greatly enhanced by spin-orbit coupling due to heavy-atom pertur-bation. Structurally, RU is &-transition metal cornplex with 2,2'-bipyridineligand in octahedral configuration. Pertinent transitions in the visible spectrumare met al-teligand charge- ransfer states (MLCT) which are formed when e-is excited from metal's d-orbitai to ligand's n'-antibonding orbital. Referringto Fig 3.1, the absorption state is l (MLCT) and the emission state is the spin-forbidden (MLCT). (B131

Chernicd formula for SPA and RU are shown in Fig 6.5, and their absorptionand &ion spectnun are included in Fig 6.6.The SPA and RU solutions areprepared as air-saturated aqueous solutions at room temperature, and in ratherheavy concentration to maximize the fluorescence. Some pertinent materialdata are [Probes]


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Figure 6.6: Absorption and emission spectnim for SPA (top) and RU (bottom)


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Figure 6.7:Calibration data for LO's voltage-to-frequency conversion

molecular massconcentration cE , a at 458nm

QY7

LO is basically a voltage controlled oscillator, converthg input voltage (V )to output frequency (f). The calibration data for this conversion is recordedrnanually using lodcin amplifier' and fiequency counter2,and is plotted in Fig6.7. Linear regression gives [Guttrnan]

with f in p z ] and V in (VI. A stable and accurate frequency generation isessentid to my correlation scheme; regrettably,LO exhibited some thermai driftwhich Limits the degree of accuracy that can be achieved in m y experhent.

SinceLO frequencyis sweptMMH z every second, the modulation frequencythat the laser excitation experiences in the first pass is different fiom that thereturning signal experiences in the second pass due to propagation delay A t =2Lnlc. For 50m fiber, the differenceisAf = (4MHz/ls)0.5ps 2Hz. This beatfrequency is ciifficuit to deal with because it appears as slow swing of the entiresignal baseline.

'Stanford Resead System SR5302Ftuke 1900A


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6.2.6 PIN DetectorFig 6.8 shows the schematic diagram of detector that 1used in the experiment.Essentially, it is DGcoupled lowpans transimpedance amplifier with the PINdiode in photovoltaic mode (OV bias) so that diode m e n t (1)is proportionalto optical power (P), JPnkins]

where RA = 0.2-0.3A/W is the respoasitivity of diode for 45-OOnm. Theha1 output signal becomes

By trial and error, the upper limit of fo, f3 = 160Hz seemed sufficient to filterout noise without excessive smoothing. Bowever, the circuit in Fig 6.8 is "home-maden; and, as such, the effects of improper grounding and stray capacitanceare unavoidable even under the best of circumstances.Unfortunately, after al1 the experiments were done, 1realized that detectorin Fig 6.9 wouid have been h p l e r and better. It is AC-coupled bandpass circuitwith the final output signal

Since the correlation output is repeated every ramp intervai, this ramp frequencyconstitutes the lowest kequency component of output signal. Also, the outputsits on top of large DC bias. The bandpass detector, with low cut-off (fi) setto the ramp frequency and with high cut-off (fo) set sufficiently high but nottoo high, would filter out the large DC bias, slow drifts, and fluctuations whichplagued my expriment.

6.3 Experimental ProceduresPreparations involving sample solutions, fiber, laser, LO, and AOM alignmentsare summarizedas foUows:

SPA/water (458pM) nd RU/water (468pM) olutions are prepared usinglaboratory grade water.Both ends of approximately 50m long MMF are stripped of plastic bufferwith Polystripp~,leaned with acetone, and cleaved with a fiber cleaver.Since fiber coupling depends critically on the quality of end-face, it isimportant to obtain a cut that is flat and perpendicular at l e s t acrossthe fiber core.The Ar laser output is set to 15mW at 458nm.Ramp generator is set to ramp W V t every 1 second interval, and LOconverts this to a correspondhg frequency ramp 0-4- every second.Fig 6.10 (top) illustrates the aligning of AOM for the fi st pa s. The Arlaser beam is focused by lem so that the spot size at AOM is within itsactive aperture. The iber coupler is adjusteci for maximum coupling intoMMF by monitoring the optical power corning out of the far-end.


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Figure 6.8: DC-coupled Iowpass detector, using blue enhanced PIN diode andlow-noiseJ-FETnput Quad Op-Amp

1-teV converter Amplifier DC remover Lowpass filtervo= -ROI Vz

1+ f fo 1 +if f 3

Figure 6.9: Simpler AC-coupled bandpass detector

1-to-V converter 1 AC coupling 1 Amplifier

Figure 6.10: Aligning AOM for first pass (top) and second p a s (bottom)

+ aser


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Fig 6.10 (bottorn) illustrates the aligning of AOM or the second pass. .Arlaser is Iaunched from the far-end o simulate and make visible the pathof retuming signal. The fiber coupler is adjusted until the focused spota t AOM is within the same aperture that the first pass went through,thereby maintaining the same Bragg angle. Basicaiiy, AOM is geometri-cally aiigned for optimum performance at 458nm; he subsequent decreasein performance at 550nrn and 600nm is accepted as a compromisein returnfor easier alignment.

The experimental procedures of a c t ud y measuring Fkesnel backrefiection(for fiber Iength) and fluorescent response (for SPA and RU lifetimes) are asfollows:

1. Decide on the type of measurement. When measuring Fkesnel reflection,the fiber tip is held in air. When measuring fluorescent response, thefiber tip is immersed in SPA or RU solution as shown in Fig 6.11. Thismaxirnizes the collection efEciency, and represents the simplest configura-tion because there are no external components to aiign. Of course, whenchanging hom one measurement to another, the fiber tip must be washedthoroughly with distiUed water-

2- To reduce contamination of signal, 460f Onm interference filter is placedin front of PIN detector when measuring Fkesnel reflection, 550 f 0amfilter when measuring SPA fluorescence, and 600f 0nm filter when mea-suring RU fluorescence.

3. The gain, reference bias, and bandwidth of PIN detector, desaibed in Fig6.8, are detennined by trial and error. Generdy, F'resnel signal was fewpW, nd SPA and RU signals were both about few nW.

4. Fiilally, both the ramp input and the correlation output are sampled withdigitking oscilloscopeusing built-in exponential averaging algorithm. Thedata set is then uploaded to computer for data anaiysis and ensembleaveraging. Raw data for Fresnel reflection, SPA fluorescence, and RUffuorescence are shown in Figs 6.12, 6.13, and 6.14, respectively.

5. So f a t the opticai fiber is nomindy 50m long. In order to assess theresolution in fiber Iength measurement, 1.01m is cleaved off the far-end,making the fiber 49m long nominally. F'resnel reflection is then measuredby repeating steps 1-4. A raw data for this is shown in Fig 6.15.

1 tried to collect as many sets of data as possible within the time allocatedby OLLRC ab. Unfortunately, 1managed to coiiect only 35 da ta sets for 50mfiber, 16 da ta sets for SPA fluorescence, 13 da ta sets for RU fluorescence, and 10data sets for 49m fiber. Collecting more da ta sets will help, of course. But a fun-damentai improvement in the accuracy and confidence of parameter estimationcan only occur when better quality equipments are used.

6.4 Data AnalysisWhen the bottom graphs in Figs 6.12, 6.13, and 6.14 are compared to the topgraphs in Figs 5.3, 5.4, and 5.5, one can see that there is very good corre-spondence between the experimental measurements and the calculated models.Using Student-t values for 95% confidence interval (a= 0.05), the length of


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Figure 6.12: Raw data for Resnel backrefiection from 50m fiber. The voltageinput (top) to LO and the correlation output (bottom) from PIN detector areshown for onecompleteramp period. The excitation waveform was square-wave-


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Figure 6.14: Raw data for RU fluorescence using 50x11 iber. The voltage input(top) to LO and the correlation output (bottom) from PIN detector are shownfor one complete ramp period. The excitation waveform was square-wave.


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Figure 6.15: Raw data for Fresnel backreflection fkom 49m fiber. The voltageinput (top) to LO and the correlation output (bottom) from PIN detector areshown for one co mp lete ramp period. The xcitation waveformwas square-wave.


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50x11and 49m optical fibers are estimated to be

The 0.27m uncertainty for LS0is close to (rms)modal dispersion limit of 0 . 1 bin Eqn 6.2,and represents almost 2 orders of magnitude improvement over theDFT esolution of 13m in Eqn 5.20. Unfortunatdy, the tm e merence of 1.01mbetween 50m and 49m fibers lies outside the confidence interval.

The lifetime of SPA and RU fluorescence are estimated to be6.64(SPA) = 28.3f .5ns t- (tls:o.ozs)-n (6.10)

46.7(RU) = 360f 8nst (ti2;o.ozs)-T3 (6. i l )The SPA and RU lifetimes were also determined in time domain, using a con-ventional pulse excitation setup in Chernical Sensor Group at Erindale campusof University of Toronto. The excitation source was N p aser with 10x1spulsewidth at 337m. Fluorescein was used as reference because it exhibits a stablesingle lifetime of 3.8-4.3ns [A7, A81 over the a i o n pectrum of interest. Thefluorescent decays are shown in Fig 6.16 for SPA-Fluorescein pair and in Fig6.17 for RU-Fluorescein pair. Setting the reference lifetime at 4.0ns in Eqn 3.8,the estimated Metimes are

(SPA) = 2 9 . 2 ~ ~.1%(RU) = 379ns90.1%

which are consistent with Eqns 6.10 and 6.11, s weH as,with the d u e s citedfrom Iiterature in Section 6.2.4.


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Figure 6.16: Fluorescence decay of SPA sample y ( t ) and Fluorescein reference

O tirne index i [0.2ns/step)

Figure 6.17: Fluorescence decay of RU sample y ( t )997

and Fluorescein reference

tirne index i [2.0ns/step]


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Chapter 7ConclusionsIn my thesis, I demonstrate a fibre optic sensor for measuring fluorescence life-t h e , in which the main signal processing is performed entirely by optical de-vices. It has severai distinct characteristics and advantages when cornpared tothe conventional time dornain and frequency domain fluorometers:

A single optical fiber is used to c q he laser excitation and to coUectfluorescent response or Fresnel backrefiection. This gives remote mea-surement capability which is important for the development of fibre opticsesors.The optical signal passes twice through AOM which acts as an opticalbidirectional mixer. Since the double modulation occurs at almost samefrequency, the signai processing is basically a homodyne scheme. Be-causeAOM is the only active component, system bandwidth can be easilyupgraded by replacing it with another opticai modulator of higher band-width.The DC output from the PIN detector becomes auto or cross correlation.The detector s bandwidth is independent of modulator s bandwidth dueto somewhat unusuai change of domain brought about by the correlationoperation. Because only DC component from AOM mixing is measured,the PIN detector does not have problems associated with wide bandwidthopticai detection and high frequency electronic signal processing.Since the modulation frequency of AOM s rampeci, the input and outputdata are repeated at every ramp period and are measure as functions offrequency.Continuous wave excitation has lower peak power than pulse excitation,so that there is l e s likeiihood of damaging a sample.

0 Although the experiment uses buik components, the system is simpleenough to be integrated into a single "in-line" device.

hthermore, I address theoretical problems involved in using optical fiber toexcite and coilect fluorescence from remote medium. The fluorescence couplingaciency of multimode and singlemode fiber is derived, and the waveguide d-fect of opticai fiber on the propagating signals is anaiyzed in detail. 1 hopethat the foundation laid in this thesis heips reader to understand better theworkings of optical fiber sensor, whether it is for measuring temperature, pH,O2 oncentration, or even epoxy resin cure [See Appendix BI.


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Fkom experiment, 1 have successrully dete&ed the fluorescent lifetimeof N-(3-sulfopropyl) acridinium (SPA) and rutheniwn tris-bipyridyl dichloride(RU), and the fiber length of mdtimode optical fiber sensor. SPA and RU com-pounds were chosenbecause they have a stable single Metime, visible spectrum,and relatively high quantum yield; and multimode fiber was chosen becauseit has large core which facilitates better coupling. The main results of dataanalysis are as follows:

My correlation scheme gives an order of magnitude improvement over the con-ventionai DFT method. The uncertainties represent the usual 95% confidenceintervai for ensemble average. UtimateIy, the resolutions are limited by opticalfiber dispersions; od y modal dispersion is present in fiber length measurement,but both modaI and materiai dispersionsare present in fluorescent iifetime mea-surement.

The lifetimes are consistent with literature values and with the values decon-voluted from pulse excitation method. Unfortunately, however, the fiber lengthshows poor intemal consistency, since the actual 1.01m that is cleaved off thefar-end is estimated as 1.75fO.Mm at 95% confidence. This inconsistency isattributed to the drift and fluctuation of modulation frequency coming fromLO.

The coupling efficiency of F'resnel backreflection is at least lOdB greater thanRayleigh backscattering, and 23-27dB greater than SPA and RU fluorescence.This is consistent with experimental observation of few pW for Fresnel signal andfew nW for both SP.4 and RU signals. In coliecting SPA and RU fluorescence,as expected, the single fiber configuration is 9-13dB more efficient than doublefiber configuration.

AOM s the key component in my correlation scheme, because i t performs themodulation of laser excitation in the k t ass and the opticaimixing necessaryfor auto and cross correlations in the second pa s . Using one AOM for bathfunctions allows the signai processing to be done as much as possible in opticaidomain with minimum extemal components. Diffraction efficiency and Braggangle depend on the input wavelength. Due to phase-mismatch, the Braggdiffraction decreases fkom 90.5% efficiency for laser excitation (458nm) o 61%efficiency for SPA fluorescence (550am)and o 35% efficiency for RU luorescence(600nmj.The efficiency decreases even more if optical divergence is considered.

The merits of my fibre optic fluorescence lifetime sensor become obviouswhen one realizes that an experirnentai setup with only 4MHz bandwidth is Ca-pable of measuring fluorescent lifetime of 28.3f .5ns and 360f 8ns. Shorterlifetimes can be measured by simply upgrading LO and AOM o a higher band-width, with no changes to the other components, experimentai Iayout, or dataanalysis. Although the 4MHz bandwidth is rather low for practicd applica-tions, it is suficient for the purpose of my thesis which is to demonstrate a newconcept in optical fiber sensor, fluorescence lifetime measurement, and opticalsignal processing.


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Appendix AFormula and TablesA.1 Definitions

A.2 Impulse F'unctionThe impulse hinction d(t)has the foliowingproperties: [Brigham]

d ( t ) = 0 , t # OL ' ( t ) = 1lald(at)= d(t)

h(t)d(t-a)= h(a)d(t- a)d ( t - a) * d ( t - 6)= d ( t - a+ b ) )

A.3 Solid AnglesConsider a conical aperture dong i axis with ha-ang le 8,o that dS is diner-entiai sphtxicai area normal to the radius vector il is angle between i and i,and dS cos8 is dinerential plana area normal to i. The sphe7ifol solid angle of


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aperture is

and the planor solid angle is defineci a s [W yatt]d S cos8 Irn = ~ - =2 Je J ( rd8) (rshf ld#)cae=nSin28 (A .14)@=O 4=0 r2

A.4 Table of Fourier Transform PairsThe foiiowing Fourier Traasform pairs

have been selected fkom Ref prigham, Bracewell]. If a function is d&edwith conditional domain, then it is zero outside the domain and is equai to themidpoint at the discontinuity.

(even) + (0 )(od4 + (O)(0) + (even)

(0 ) + ( o W

(A.16)(A.17)(A. 18)(A.19)(A.20)(A.21)(A-22)(A.23)(A.24)(A.25)(A.26)(A.27)(A.28)

(A.29)

(A.30)(A.31)

(A.32)(A.33)( A - 3 4


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n ( t ) A sinc(f) (A.35)~ ( t )A sinc2(f) (A.36)

cos(2irat) A J ( f -4 6 ( f+42 (A.37)sin(2irat) & d ( f - a)- 4 f +4 (A.38)22

t/'.> O A 7 (A.39)1 + j 2 r f re-ltl/r & 27 (A.40)1+ ( 2 s f ) 2e-rt2 e-z r f2 (A.41)

e - t 2 / a z a f i e - r 2 a 2 f 2 (A.42)6(t- At) + d(t+At)

2 & cos(2s at) (A.43)1-e-(ltl-At)/rl ~tl> ~t COS (2s At + tan-' ( 2 s T)2r JI (2 s T ) ~ (A.44)

A.5 Decomposition into Fourier SeriesConsidera waveforrn z ( t )which consists of (h ( t ) , tl < T / 2 )repeated at every Tinterval or at frequency 1/T.The time domain expressionand the correspondingcomplex Fourier series are [Brigham]

Applying FT to both sides and solving for on,

If h ( t ) is real and even, H( )is &O reai and even. Then, the complex seriesbecomes a cosine series,

00

r ( t )= 0 0 +1 0 , cos(F)n=1

A.6 rms Widthbot-mean-square (rms)width of function h(t)is definecl as [Bracewell]

c2= ( t2)- t) * (A.50)where

( t)= = - W O )/* h(t)dt 27rjH O)


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Appendix BFluorescence Application inCure MonitoringB . l Epoxy Resin and Composite

4The term epozy refers to molecule containing -&c- ring structure. The cureprocess breaks open the epoxy rings and converts epoxy monomers into networkof crossIinked polymers which is characterized [Ency] by high adhesive strength,low sbrinkage, good mechanical and thermal properties, high chemical and cor-rosion resistance, and good electrical insulation. To bring about some optimumcharacteristics, most commercial epoxy reins contain proprietary mixture ofepoxies, curing agents (hardeners), accelerators, diluents, Mers, flexibilizers,and impurities (dyes, solvents, etc.) [Ency, Lubin]. Th e generic chemical for-mula of 2 popular epoxies and curhg agents are shown in Figs B. 1 and B.2, orwhich the ring opening reaction occurs mainiy between the tenninal glycidylgroup and the primary amine group a s foilows:

One mportant application of epoxy resin is in composite [Ency] where strongand stifF fibers (usualiy glass,boron-tungsten, graphite, or Kevlarl) are dignedin epoxy rein rnatrix. Most composites are manufacturecl by baking in an ovenunder pressure. Temperature provides heat needed to initiate and maintain theepoxy cure reactions, and pressure compacts the fiber matrix by squeezing outexcess resin and gas pockets. Typically, the cure cycle follows a &ed time-tem-perature-pressure profile [08], even in the presence of chemical variation in resinmixture, unequal distribution in composite laminates, ciifference in preparationor storage, and other practical situations that corne up in the real world.The fixed cycle is simple and cheap to implement, but the quality of com-posite varies from batch to batch. Obviously, the composite daes not attain itsoptimum properties when the epoxy resin is not M y ured; f ihermore, m e -acted epoxy resins serve as sites [O131 or crack nitiation and propagation. Thequaiity can be improved by using some feedback control which requires monitor-ing of parameters (temperature, pressure, viscosity, capacitance, conductance,

'Kevlar, also k n m a P P T ~ ~oly(pphenyleneterephthalamide), ia trademark ofDupont


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Figure B.1: Generic formula of 2 epoxy reins: (top) DGEBA or digIyudylether of bisphenol A, and (bottom) TGDDM or tetraglycidyl diamino diphenylmet hane

Figure B.2: Generic formula of 2 curing agents: (top) DDS or diamino diphenylsulfone, and (bottom) DDM or diamino diphenyl methane

acoustic impedance, refractive index, IR absorption, fluorescence, etc.) that af-fect or indicate the sta te of cure.

B.2 Fluorescence during CureIf A and k are, respectively, rates of radiative and non-radiative decays fioman emitting state of molecule, the quantum yield (QY) and the lifetime (r )offluorescence are defined as

The radiative decay remains fairly constant, but the non-radiative decays, suchas rotational and vibrationai relaxations, are idluencecl by the molecular en-Wonment. A t the beginning, an uncure epoxy resin exhibits high rnolecularmobility which means fast k, low QY, nd short T. After full crosslinking poly-merization, a cured epoxy rein exhibits low moIecuIar mobility which teads toslow k, high QY, nd long T .

If the conversion from uncureci to cured sta te occurs hornogeneously through-out the rein, then QY and T would increase smoothly during cure. However,rom phosphorescence studies [O 0,011,0 21, ESR spectroscopy [O21, andelectron and optical microscopy [013],he initial formation of network and thesubsequent growth in crosslinking are found to be nucleation process, in wbichthe cure proces occurs heterogeneouslp or locally with distinct boundary be-tween the 2 states. Therefore, QY increases because the cured domain growsat the expense of the uncured domain, but T remains constant because theunderlying nature of A and k within each domain do not change.


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[PZ21V Vadde, V Sriniva

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