Nuclear Instruments and Methods in Physics Research A276 (1989) 347-358North-Holland, Amsterdam

SCINTILLATING OPTICAL FIBER TRAJECTORY DETECTORS

A.J . DAVIS, P.L. HINK. W.R . BINNS, J.W . EPSTEIN, J.J . CONNELL * M.H. ISRAEL,J. KLARMANN and V. VYLETDepartment of Physics and the McDonnell Center for the Space Sciences, Washington University, St. Louis, Missouri 63130, USA

D.H. KAPLAN and S. REUCROFTPhysics Department, Northeastern University, Boston, Massachusetts 02115, USA

Received 7 October 1988

Measurements of attenuation in several types of plastic scintillating optical fibers give attenuation lengths varying from 0.8 to 1 .5m. By comparing attenuation as a function of wavelength in fibers of different thicknesses we infer the contributions to theattenuation from reflection losses and bulk scintillation losses . We find good agreement between these values and calculatedestimates of attenuation in scintillator . We have also calculated the effective scintillation efficiency of small fibers relative to that ofbulk scintillator (for scintillator with dimethyl POPOP as the waveshifting dye) for the two cases of optically coupled and decoupledfibers. Scintillating fiber ribbons made of 200 ~Lm square cross section fibers were exposed to relativistic iron nuclei at the LBLBevalac, and positional resolution of 70 l m was obtained . Relativistic neon and carbon were also detected in these ribbons . In asimilar exposure of 100 ~Lm fibers to 50 MeV/n nitrogen nuclei at the NSCL cyclotron, Michigan State University, a positionalresolution of about 50 ~.m was obtained .

1 . Introduction

Precision trajectory detectors have always played akey role in experiments involving charged particle de-tection in fields as diverse as high energy physics,cosmic ray astrophysics, nuclear physics, and medicalphysics. However, most present day, high resolution( < 100 ILm) detection devices are difficult to make intolarge area detectors suitable for satellite experiments, orvertex detectors in colliding beam geometry high energyphysics experiments . This is due to complexity, exces-sive interference with the trajectory to be measured,(e .g ., multiple scattering), high power requirements, poorradiation resistance, or the need to contain a gas.

The use of scintillating optical fibers offers a methodthat avoids many of these problems . The fibers can bemade into large area arrays (several square meters)without the problems associated with the multiplexingof many small detector units into complicated mosaics.Multiple scattering is small ; for example a one millime-ter thick layer of polystyrene (PS) or polyvinyltoluene(PVT) fibers constitutes only 0.25% of a radiation length .The fibers are rugged and have good radiation resis-tance (as opposed to that of silicon microstrip detectorsand their associated electronics) . The power consump-

* EFI/LASR, University of Chicago, Chicago, IL, USA.

0168-9002/89/$03 .50 © Elsevier Science Publishers B.V .(North-Holland Physics Publishing Division)

347

tion depends on the readout device but is generallyrelatively low. They do not require a gas containmentvessel which can be important for some experiments .Additionally, multiple tracks can be simultaneously re-corded if an appropriate readout device is utilized .

At Washington University, we are presently develop-ing fiber detectors for use in cosmic ray astrophysicsexperiments. The scintillating optical fiber isotope ex-periment (SOFIE), an instrument being developed atWashington University in collaboration with the Uni-versity of New Hampshire for high altitude balloonflight to study the cosmic ray isotopic abundances inthe charge range from silicon to iron, will utilize scintil-lating fiber trajectory and range detectors [1-6]. Thetrajectory detector consists of six layers of 250 lint fiberribbons, the largest of which has dimensions of 1 .2m X 0.6 m, and will measure three pairs of x,y coordi-nates as particles penetrate through the detector stack.The range detector is constructed of multifibers whichare fused together into ribbons and stacked to make asolid block. The multifibers are 1 .5 mm square andconsist of a 15 X 15 array of 100 gm square fibers . Therange detector has dimensions of 12 cm X 5 cm X 100em thus providing a detector with about 6 X 105 indi-vidual fibers . We are also studying the use of large area(1 mZ module) fiber trajectory detectors made of 100Itm fiber ribbons for use on the NASA particle astro-physics magnet facility (Astromag), a cosmic ray facility

34 8

for the study of antiparticles and isotopes, presentlybeing studied for Space Station .

In the context of high energy physics, our group atNortheastern University is pursuing the extension ofthese techniques to the development of very straightribbons with various lengths composed of rectangularcross section fibers for a variety of applications in fixedtarget and colliding beam experiments . We are alsoinvolved in the development of meter long, very straightribbons of 500 l_tm X 1 mm fibers for the calibrationand alignment of a central tracking colliding beamdetector at LEP. We have proposed using rectangularfibers with cross-sectional dimensions of about 200 ~tmX 1 mm as a high resolution multiplicity jump triggerfor heavy flavor identification and as a replacement fordrift chambers . Additionally, we have proposed thedevelopment of meter long coherent arrays of 25 1),mplastic fibers to allow a transverse resolution of 10 ~Lmfor a heavy flavor tagging system at the SSC [7,8] .Heavy flavor particles, such as those containing charmedand bottom quarks, have lifetimes that are typically inthe range 10 -- "-10 -" s. They travel in the laboratoryfor distances that are typically < 1 mm and the decayproducts have impact parameters relative to the decayvertex of typically a few tens of micrometers . To beeffective a vertex detector has to offer a transverseresolution of about 10 ~im or better at the vertex .

In this paper we first review the theory of scintil-lation in bulk plastic scintillators including calculationsof attenuation in scintillator . We then describe labora-tory measurements which characterize the light attenua-tion properties of scintillating optical fibers . From thesemeasurements we calculate the contribution to attenua-tion from reflections and absorption in the scintillator .Using absorption and emission measurements taken onour scintillator we then calculate the effective scintil-lation efficiency of small fibers . This is followed by theresults of exposing a test model scintillating fiber trajec-tory detector to iron, neon, and carbon nuclei from theLawrence Berkeley Laboratory Bevalac relativistic heavyion accelerator. and to 50 MeV/n nitrogen nuclei at theNational Superconducting Cyclotron Laboratory,Michigan State University .

2 . Review of scintillation in plastic scintillator

2 .1 . General properties ofplastic scintillator

Plastic scintillators are composed of a base material,usually polystyrene (PS) or polyvinyltoluene (PVT), andone or more dyes which are added to improve thequantum yield of the scintillator, and to waveshift thescintillation light to longer wavelengths . A minimumionizing, singly charged particle traversing 1 cm of

A.J. Daris et al. / Scintillating optical fiber trgjectorr detectors

plastic scintillator results in the emission of -- 2 X 10 °photons with energy near 3 eV, thus converting -- 3°I ofthe charged particle energy loss into light . Plastic scintil-lator is largely transparent to its own radiated light,though there is some self-absorption by the scintillationdyes, as well as absorption by the plastic base material[9], with attenuation lengths as long as 4 m beingobtained in commercially available scintillator [10] .

The detection of scintillation in fibers differs inseveral respects from that in bulk scintillator . Scintillat-ing fibers transmit only a fraction of the scintillationlight by total internal reflection, about 4.7% in eachdirection along the fiber axis for PS core and acrylicclad fibers [2], and have attenuation lengths of about 1m for fibers with thickness 0.1-1 mm using standarddopings (see section 3 below and ref . [11]) . For the caseof a minimum-ionizing singly charged particle travers-ing a 1 mm fiber, the detection of up to 6 photoelec-trons has been claimed at a distance of 1 m from theparticle traversal [11] . In addition, for small fibers (di-ameters < 500 lr m), the light output per unit pathlength traversed should decrease with diameter, relativeto that in bulk scintillator, for standard scintillatormixes (see section 3 below) .

2 . The scintillation mechanism

The fluorescence mechanism occurs only in certainorganic compounds such as PS and PVT. Two hybridi-zations, called "sp2 " and "spa " are common whencarbon bonds. In sp2 hybridization one of the fourvalence electrons, called a "7-electron", becomes com-pletely delocalized about the molecule . This phenome-non, exemplified by the benzene molecule, leads tofluorescence, which results primarily from transitionsfrom spin singlet excited states to the singlet groundstate of the ,7-electron system . Typical spacing of the7r-states is a few eV . Coupling between the 7-states andthe vibrational states of the molecular skeleton leads tothe splitting of each ,-,-state into a set of vibrationallevels . the spacing of which is usually of order 0.2 eV .The states are then labeled by two quantum numbers,i.e . S,, . where i refers to the electronic excitation leveland j refers to the vibrational excitation level . Fig. 1gives an energy level diagram for a typical scintillatingmolecule (see ref . [12] for a more detailed discussion) .Examples of this spI bonding are polystyrene and poly-vinyltoluene which are commonly used as base materi-als in plastic scintillator, and "BPBD" and "DPOPOP"(or PBD and POPOP) which are commonly used asadditives.

Energy deposition from a charged particle passingthrough the material excites the 7-electrons from thespin singlet ground electronic state (S,,o) to higher states(S ;~) . These molecules quickly decay to the S, t, state viaradiationless transitions . Light emission from this state

A .J . Dauis et al. / Scintillating optical fiber trajectory detectors

Fig. 1 . Singlet ar-electron energy level diagram for typicalscintillating molecule (schematic only). Soo to S, () and S,e toS20 transitions are usually Franck-Condon suppressed (see

text) .

to one of the vibrational levels of the ground state (So,)is fluorescence, or scintillation light.

Plastic scintillator base materials fluoresce by thismechanism. However, scintillator composed only of basematerial is usually not useful . For example, the basematerial used in the fibers described in this paper,polystyrene, has a quantum yield of only 3% . (Note thatthe quantum yield differs from the quantum efficiencyof scintillator quoted previously in that it is the fractionof polystyrene molecules excited to the St� state thatdecay radiatively to the ground state, not the ratio ofthe radiated energy to the total energy deposited by acharged particle.) This low quantum yield is due to therelatively long mean fluorescence decay lifetime (308 ns[13]) of Sre 7r-electrons, and the existence of othercompeting nonradiative decay mechanisms with fasterrate constants . In addition, polystyrene and polyvinyl-toluene absorb their own emission strongly .

It was discovered in the 1940's that more efficientscintillator could be made by mixing solutes (primarydyes) in with the base material. Due to the low quantumefficiency of the base it was first assumed that thesolute alone was responsible for the observed light andthat the base was simply a convenient carrier . It wasalso noted that the more useful solutes absorb lightmost strongly at wavelengths near the peak polystyreneemission, which would seem to point to a radiativetransfer mechanism. This hypothesis was tested bySwank and Buck [141 who found that the dominanttransfer mechanism is, in fact, nonradiative . This trans-fer mechanism, which is known as "Forster transfer"[151, results from the interaction of the donor andacceptor molecular electric dipole moments, giving anenergy transfer probability which is inversely propor-tional to the sixth power of the intermolecular sep-aration . Thus the energy transfer rate goes as the squareof the dye concentration .

The transfer probability also depends on the weightedfrequency overlap integral (Forster overlap integral)

2.3 . Self-absorption and attenuation length

349

between the base emission spectrum and primary dyeabsorption spectrum, thus explaining the observationswhich led to the assumption that radiative transfer wasthe dominant energy transfer mechanism. The effectivequantum efficiency of the base-primary dye system isthus increased by introducing a competing process (For-ster transfer) which is even quicker than the nonradia-tive decay mechanisms for S, 7r-electrons in the basematerial, and leads to radiative decay (e .g., PBD has aquantum yield of 83% [13]).

The required concentration for effective use of theprimary dye (PBD or BPBD) can be estimated bysetting the PBD-polystyrene mean intermolecular spac-ing equal to R �, where R o is the critical transferdistance at which Forster energy transfer and S,deactivation by fluorescence, internal quenching, orother means, are of equal probability (ref . [12], p. 569).This distance is calculated to be about 20 A (ref . [13], p.306), and has a Forster transfer probability of about0.7 . The value of the concentration, CO (mol/1) _3000/4TrNRO~, where N is Avogadro's number, is then0.05 mol/1, or about 1 .5% by weight . This is close to theoptimum concentration obtained in practice .

The concentration required for the primary dye re-sults in very poor transmission of the emitted light,owing to self-absorption by the dye molecule . This is inaddition to the absorption by polystyrene and possiblyby impurities . To circumvent this absorption, secondarydyes are usually added in much lower concentrationwhich absorb the primary emission before a significantfraction is otherwise absorbed . The secondary dye mole-cules then reemit the light at a longer wavelength .Self-absorption by the secondary dye for a given dis-tance in scintillator is much less owing mainly to itslower concentration . For typical dye concentrations, theabsorption lengths for the secondary emission fromDPOPOP, and for the primary emission from BPBD,are expected to be about 2-3 m and 1-2 cm respec-tively as is shown later in this section .

In figs . 2a and b we show the emission and absorp-tion spectra of DPOPOP and PBD in cyclohexane, aninert solvent that is transparent to visible and near-ultraviolet light [13] . The main emission and absorptionbands are clearly separated with some obvious overlapshown at the blue end of the emission . For the case ofDPOPOP, we assign the main emission peak to theFranck-Condon allowed S, o - So, transition, and theshorter wavelength peak to the somewhat suppressedSr ,t - So, transition . The peaks at longer wavelengththen correspond to Sto - Sot, So3, etc . It should benoted that these emission and absorption bands areshifted somewhat to the red when the dye molecules arein PS or PVT.

350

1 .00

0.80

0.40FZ

Z 0.20CFÇc

Fig. 2 .

WAVELENGTH (A)5100 4300 3900 3500 3100

a

WAVE NUMBER (cm_')

A .J . Daois et al. / Scintillating opticalfiber trajectory detectors

018000 22000 26000 30000 34000

Absorption of light near the Sto - Soo peak canresult from the Franck-Condon suppressed Son -> S,otransition . Light absorption near the peak emission (410nm in fig. 2a, and about 430 nm for a PS base material ;see fig . 3) in DPOPOP should result, in part, fromabsorption by the small fraction of ground electronicstate molecules which are in excited vibrational states atroom temperature. Consider, for example, those mole-cules in the Sot state. For such molecules absorptivetransitions to Sto are not as strongly suppressed, and, ofcourse, correspond to the same frequency as the S, o -~So, emission .

Thus, to calculate the expected attenuation length inscintillator we must determine the mean free path forphotons in an ideal gas of DPOPOP molecules (thesecondary dye) . This is given by 1/n'a(v), where a(v)is the molecular cross section for absorption at frequencyv, and where n' is the number of molecules per cubiccentimeter in the Sot state. The photons emitted byDPOPOP molecules and subsequently absorbed by otherDPOPOP molecules are reradiated with a 93% quantumefficiency [131 . Thus the effective cross section for pho-ton loss is obtained by multiplying a(v) by 0.07, thefraction of photons which are absorbed and not reradia-ted .We assume that a(v) for Sot - St0 absorption is

roughly the same as that for the peak absorptionfrequency; i.e., that e(v) = 5 X 10 4 1/molcm (see fig .2a), which corresponds to a cross section of about1 .9 X 10-16 emz. n' is given by n' = (g'/g)B - n, wheren is the density of DPOPOP molecules at 0.011% dop-ing (1 .7 X 10 17 em -3 ), and where B is the Boltzmannfactor exp(-hw/kT), with T as room temperature(293 K) and with hav as the Soo to SDt energy dif-ference. (g'/g) is the ratio of the rotational degener-acies of the levels . (This is taken to be 1 . Distinctrotational levels are normally not resolved in spectro-photometric studies of DPOPOP and BPBD . From fig .2 we see that the peaks assigned to the Sto --> Soo transi-

Emission and absorption spectra are shown for (a) DPOPOP in cyclohexane, and (b) PBD in cyclohexane . Adapted from ref.[131, Graphs 123C, p. 306 and Graph 119C, p. 299. Used with permission of the publisher .

tions have approximately the same magnitude of broad-ening, thus justifying a ratio of about 1 .)

From fig . 2a the energy difference, hdv, is about1300 cm -1 or 0.16 eV . The Boltzmann factor is then1 .66 X 10 -3 and n' is about 2.8 X 10'4 molecules/cm3.This then gives a mean free path of about 2.7 m forself-absorption of peak emission frequency DPOPOPlight. It should be noted that the Boltzmann factor isquite sensitive to the temperature assumed in the calcu-lation. Including other known uncertainties in the calcu-lation we estimate that the calculation should be accu-rate to about +40% .

For comparison with the measured scintillator at-tenuation length we must also include the effects of PSabsorption and reflection losses . In the next section wewill show that our measurements show good agreementwith this calculated value.

For the case of BPBD (the primary dye) emission wehave performed a similar calculation in which we usedBerlman's data [13] for PBD since we do not havecorresponding data for BPBD . Assuming a BPBD con-centration of 1 .1% results in an expected attenuationlength of about 1 .6 cm. The considerably shorter at-tenuation length results mainly from the PBD numberdensity being 100 times that of DPOPOP . Other dif-ferences are that a PBD molecule is 18% lighter than aDPOPOP molecule, and the quantum yield of PBD is83% .

3. Properties of scintillating optical fibers

3.1 . Scintillating fiber characteristics

The plastic scintillator which is used in our fibers ismixed and polymerized at Washington and consists of apolystyrene base doped with a primary dye (butyl-PBD)and secondary dye (dimethyl-POPOP) . In our "stan-dard" scintillator the BPBD and DPOPOP concentra-

48 _w

4400 4000_' 1 .00

WAVELENGTH3600

(A)

3200 2800 260048

FI Sm-'SOl L

c 0 .80 PBD36 36

} 0 .60 A13SORPTION

24 F FMISSION 24Z

0.40

12 r Z 0 .20,12 L

I l' b XX

0 0 L.- ~ ' I I 1 I I I 020800 24800

W WAVE28800 32800 36800NUMBER (crtiI)

tions are respectively 1 .1% and 0.011% of the poly-styrene by weight . We have measured the emissionspectrum and find that it peaks at about 430 nm . It isessentially that shown by the curve labeled "5 cm" infig . 3 . We have also measured the relative scintillationefficiency of the scintillator in bulk. Samples of ourscintillator and NE102 were excited in separate testsusing a 90 Sr source, with the resulting light emissionbeing viewed by a photomultiplier tube . We find ourscintillator to be about 70% as efficient as NE102. Thescintillator is clad with an acrylic tube to make thepreform from which the fibers are drawn. The fibersdescribed in this paper were drawn by Fibre OpticsDevelopment Systems, Inc. [16] . The fibers are square incross section and have a cladding thickness which is 5%of the fiber thickness.

3.2. Attenuation length measurements

One of the most important properties of fibers is thescintillation light attenuation length . Attenuation is theresult of self-absorption by the secondary dye as de-scribed above, absorption by the polystyrene itself, andreflection losses as the photons are lightpiped down thefiber . We have measured attenuation lengths in ourfibers using an ultraviolet source to excite the scintilla-tor (X = 365 nm with band width 8 nm), and a mono-chromator/ photometer system (Instruments S.A .monochromator, model H-20 and Pacific Instrumentsphotometer, model 110) controlled with an Apple IIcomputer . The photometer was fitted with a HamamatsuR928 photomultiplier tube . The combined detectionefficiency is reasonably flat over most of the wavelengthrange of importance, having an extreme variation of25% .

To measure the attenuation length, the UV excita-tion source was directed transverse to the fiber axis atvarious distances from the fiber end which was viewed

A.J. Davis et al. / Scintillating optical fiber trajectory detectors

Fig . 3 . Light observed after transmission of scintillation lightthrough fiber . Each curve is labeled with the distance the light

traversed through the fiber before detection .

by the monochromator/photometer system . Fig. 3shows light emission spectra obtained using a 1 .5 mmsquare fiber for various transmission distances. Theseemission curves are corrected for the detector efficiencyvariations with wavelength . It is evident that the shorterwavelengths are attenuated much more strongly thanthe longer wavelengths . This is believed to result fromthe increased overlap of the DPOPOP absorption andemission bands (section 2.3), as well as from PS absorp-tion .

3.3. Reflection coefficients and attenuation lengths .

351

From these data we obtain the attenuation in thetotal number of photons by integrating over all wave-lengths. In fig . 4 we have plotted the fractional numberof photons remaining, integrated over all wavelengths,versus distance transmitted through the fiber as mea-sured along the fiber axis . Curve A corresponds to thedata shown in fig . 3 for a 1.5 mm square fiber, and givesan overall attenuation length of about 1 .5 m ; curve Bwas obtained in a similar manner for a ribbon of 150l,.m square fibers ; curve C is for a ribbon made of 200wm square fibers with 0.033% DPOPOP (labeled 3 x )instead of our standard 0.011% ; and curve D is for a 1 .5mm multifiber consisting of a 15 x 15 array of 100 l..msquare fibers drawn together (standard mix) .

In fig . 5 the light intensity taken from the curves infig . 3 for particular wavelengths is plotted as a functionof distance traversed in the fiber . The straight linesindicate an exponential loss of photons for a singlewavelength, as expected, and the attenuation length for

zz-1 05W

z00

0z0

a

10A i -Smm smgle fiberB i50N .m fiber ribt-

200N rn 3 x , bbon. . 15mm -B&ber

25 50 75 100 125 150DISTANCE (cm)

Fig. 4 . The fraction of photons remaining as a function ofdistance for (a) a 1 .5 mm single fiber, (b) a 150 ~Lm fiberribbon, (c) a 200 Irm fiber ribbon with 3 times the normalconcentration of the secondary dye, DPOPOP, and (d) a 1 .5mm multifiber consisting of a 15 x 15 array of 100 ILm fibers.

352

4 .0

w 2 .0

z0azw

á 1 .0

IO

0I0 20 40 60

DISTANCE (cm)

Fig. 5 . Light intensity plotted as a function of transmissiondistance for various wavelengths in a 1 .5 mm fiber .

that wavelength can be taken from the slope of thecorresponding line . In fig . 6 we have plotted theseattenuation lengths (A) versus wavelength (curve A).Curves similar to those in fig . 5 were also obtained forthe 150 ltm and 200 lcm fibers . These curves (notshown) also exhibited exponential attenuations forspecific wavelengths . Curves B and C (fig . 6) give re-spectively the corresponding attenuation lengths for the

440 460 480WAVELENGTH (nm)

500

Fig. 6 . The mean attenuation lengths in our fibers obtained byperforming a least-squares fit to the data in fig . 5 (curve A),and to similar data for the 150 Wm (curve B) and 200 )a m, 3 Xfibers (curve C), is plotted as a function of wavelength. Thecurve labeled Cc,~ was derived using the attenuation lengthsand reflection coefficients obtained from curves A and B, and

presented in figs . 7 and 8.

A.J. Daois et al. / Scintillating optical fiber trajectory detectors

150 ltm fibers and the 200 ~tm (3 X ) fibers describedabove.

From these data we can calculate the reflectioncoefficient of the core-cladding optical interface andthe absorption in the plastic scintillator. For a particu-lar wavelength (X) the attenuation can be written asJix - exp( -

x )R",lowhere n is the number of reflections made as thephotons travel down the fiber, R is the reflection coeffi-cient of the core-cladding interface, X, is the attenua-tion length measured along the fiber axis resulting fromself-absorption by the secondary dye and from poly-styrene absorption (i .e ., the absorption of bulk scintilla-tor), and x is the distance traversed by the photonsmeasured along the fiber axis . The attenuation lengthalong the linear distance traversed by the photons isíA ) ;n = A,,/cos 0, where 0 is the mean angle with respectto the fiber axis of photons lightpiped down the fiber.The refractive indices for PS and acrylic used in thispaper are 1.617 and 1.501 respectively [17] . The meanangle for photons which are lightpiped is calculated tobe 14 .6 ° . The attenuation equation can be written in amore convenient form as

h -

1

ln(R)fo

-exp -x(A,

L

)'

where n = x/L, L is the mean distance between reflec-

0-5

1440 460 480 500

WAVELENGTH (nm)

Fig . 7. The quantity 1 - R, where R is the reflection coeffi-cient, is plotted as a function of wavelength . The reflectioncoefficient was obtained from the measured attenuation lengthsin fig . 6, using the model described in the text. The error barsare not statistical but correspond to the variation in the derivedreflection coefficient obtained when the measured attenuation

lengths are varied by ±10% .

1 1 ln(R)AA

-Ás_

-LA

1

1

In(R)AB-X5-LB

WAVELENGTH (nm)

A.J. Davis et al. / Scintillating opticalfiber trajectory detectors

Fig. 8 . The curve labeled a j;� is a plot of the bulk scintillatorattenuation length as a function of wavelength. It was obtainedfrom the measured fiber attenuation lengths in fig . 6 using themodel described in the text. The error bars are not statisticalbut correspond to the variation in the derived attenuationlength obtained when the measured attenuation lengths arevaried by ±10% . The curve labeled ~'DPOP is the attenuationlength due only to the secondary dye self-absorption, assuming

that absorption in polystyrene is that given in ref . [18] .

tions for photons within the critical angle, and A is theoverall attenuation length for the wavelength X .

To calculate the reflection coefficient and absorptionas a function of wavelength we use the data from the 1 .5mm and 150 pm fibers since the dye concentrations arethe same, but the number of reflections differs by afactor of 10 . From the equation above we write twoequations corresponding to the two fibers .

We assume that R and a s are the same for both fibersat the same wavelength . Then taking the attenuationlengths for a given wavelength (A A and AB) fromcurves A and B in fig . 6, and using the mean distancesbetween reflections of 7.8 mm and 0.78 mm for LA andL B respectively, we calculate the reflection coefficientand the scintillator attenuation length . Note that themean distance between reflections is not calculated forthe mean angle, but rather is the mean value of L =t/tan 9, where t is the fiber thickness averaged over thephoton angles which are lightpiped .

Fig. 7 is a plot of (1-R) as a function of wave-length. The attenuation length, X,;., is plotted in fig . 8,where X, �, _ Xs/cos 0; i .e ., X,; . is the attenuation length

along the linear path of the photons for the meanphoton angle .

The measurements of attenuation in a particularfiber are normally repeatable within a few percent.However, we have found that for different fibers whichare nominally identical in size and scintillator mix, thereare differences in measured attenuation which are about+10% . The reason for these differences is not under-stood, but it is likely something in the productionprocess that is not well enough controlled . To estimatethe error that these variations might have caused in ourderived values for the reflection coefficients and X, ;� ,we have multiplied the measured values of attenuationfor either the 1.5 mm fiber, or the 0.15 mm fiber, by 0.9and 1.1 . We then calculated the reflection coefficientsand X,;., and obtained the values plotted as error barsin figs . 7 and 8. As would be expected, varying theattenuation for the small fiber had the greatest effect onthe reflection coefficient uncertainty, and varying theattenuation for the large fiber most strongly affected thescintillator attenuation length . The largest variations arethose plotted as error bars . The values for 430 nm werenot plotted since they were extremely sensitive to theexact values of the measured attenuation .

Extrapolating the attenuation length curve in fig . 8(curve labeled X, ;�) we obtain an approximate value of1.2 m for 430 nm. Comparing this value with thatcalculated in section 2.3 above (2 .7 ± 1 m for 430 nm),we see that the calculated value is off by about a factorof about 2, indicating that other absorption processesmay be important. In the calculation the implicit as-sumption was made that there was no contribution tothe attenuation by polystyrene . This is certainly anoversimplification . To estimate this effect we have usedthe polystyrene absorption curve from ref. [18] to esti-mate the absorption due only to DPOPOP from thetotal absorption . Although there may be reflection lossesincluded in the polystyrene measurement in ref. [18],they appear to be minimal; thus we have used the dataas presented. The attenuation length in the scintillatorcan then be decomposed into that resulting from thepolystyrene and the DPOPOP using

1 1

1Ts

_TpS

x-.-'O'

35 3

Taking the values for X,;� from fig . 8 we obtain theattenuation length resulting from the DPOPOP alone asplotted in fig. 8 (curve XDPOP ). Extrapolating the XDPOPcurve to 430 nm we obtain an attenuation length of near2 m which gives good agreement with the calculatedvalue (2 .7 ± 1 m) obtained in section 2.3 .

As an independent check on the self-consistency ofthese measurements we have used these reflection coef-ficients and absorption lengths in DPOPOP and poly-styrene to predict what the absorption should be in our

35 4

200 Wm, 3 X fiber. Thus we calculate the predictedattenuation lengths using

1 - 1

1X3 .

~' DPOP/3

A Ps

together with the reflection losses expected for a 200~tm fiber. The results are plotted in fig . 6 (curve C~a,c) .We see that the agreement with our measured values(curve C) is quite good and demonstrates that ourmeasurements are internally consistent .

The reflection coefficients and attenuation lengthsderived in this section are based on the assumption thatthe reflection coefficient is independent of fiber size . Itis possible that this is an incorrect assumption since thedrawing process could change the reflection characteris-tics of fibers with different size . However, we believethat the consistency of our measurements argues againstthis . We also find it surprising that the reflection coeffi-cient is dependent on wavelength, although this is aweak dependence . This could result from imperfectionsin the core-cladding interface which scatter short wave-length photons preferentially .

In addition, it should be noted that in our measure-ments the ultraviolet source directly excited theDPOPOP molecules, thus bypassing the primary dye.Charged particle excitation results in somewhat shorterattenuation lengths since some of the BPBD emission(- 10-20%) is not waveshifted by DPOPOP (i .e ., for400 >_ X >_ 430 nm), and is strongly attenuated .

From the above considerations we observe that forsmall fibers (<_200 ftm) reflection losses are very im-portant and may be dominant over attenuation by thebulk scintillator . This, of course, depends upon thesecondary dye concentration that is used. Secondly wenote that for small fibers with reflection coefficientssimilar to those measured in our fibers, the use of acladding with lower refractive index would improve theamount of light transmitted over long distances ( _> 1 m)only marginally . This is a result of the fact that theadditional photons which are lightpiped undergo morereflections than the photons at smaller angles to thefibers axis . Thus a large fraction of the wide anglephotons will be lost. It is important to improve thereflection coefficient of our fibers if significant benefitsare to be obtained using lower refractive index cladding .

3.4 . Scintillation in smallfibers

The scintillation efficiency in small fibers is expectedto be significantly different from that of bulk scintilla-tor. This is a result of the fact that for usual dyeconcentrations the absorption length of photons emittedfrom the primary dye is of the same order as the fibersize, thus allowing a fraction of these photons to escapefrom the fiber before they are waveshifted by the sec-ondary dye.

A.J. Davis et al. / Scintillating optical fiber trajectorn detectors

To study this quantitatively we have measured theabsorbante, A [19], in a thin slab of polystyrene 325 ~tmthick, doped only with DPOPOP . In fig . 9 we plot themolar extinction coefficient, obtained from our absorp-tion measurements, as a function of wavelength forDPOPOP. In the same figure we have plotted ourmeasured BPBD emission spectrum . In the region wherethe DPOPOP absorbante overlaps the BPBD emission,the BPBD photons will be absorbed by DPOPOP andwaveshifted into the visible, with the longer wavelengthphotons being far enough into the visible so that theprobability of absorption is small.

Using these measurements, we have calculated theefficiency of small fibers relative to that of bulk scintil-lator for two cases ; first for a fiber ribbon or sheet(optically coupled fibers placed side by side to form atwo-dimensional fiber array), and second for individual .optically decoupled, fibers . For both cases we assumethat the energy transfer from the polystyrene moleculeto the primary dye molecule (BPBD) occurs over a veryshort distance that can be neglected in the calculation .We also assume that BPBD emitted photons with emis-sion angle such that they are totally internally reflectedwill be always be waveshifted, since they will traverse arelatively long distance in the scintillator . The re-maining BPBD emitted photons will escape and be lostif they have not been waveshifted before encounteringthe sheet or fiber boundary .

For the fiber ribbon case we assume complete opti-cal coupling between fibers ; i.e ., this is equivalent to aninfinite, two-dimensional sheet of scintillator with thick-ness equal to the fiber size (t) . This is of interest since itapplies to the detector described later in this section.For the case where the energy is deposited uniformlyalong a line perpendicular to the fiber sheet and passingthrough the fiber sheet (see fig. 10 inset), the fraction ofphotons (F) of a particular wavelength íX which are

Fig. 9 . The measured emission band of BPBD (solid line, righthand scale) and the molar extinction coefficient of DPOPOP(dashed line, left hand scale) are plotted as functions of

wavelength .

waveshifted before escaping from the sheet can be writ-ten as

FT (t, xo , 0.)

=1- 2Osinz 0,

+ t° J0,sin 0 cos 0 exp( xp cos 0 ) d0,

where t is the fiber sheet thickness, z = 0 is the lowestedge of the fiber sheet, xo is the absorption mean freepath for that particular wavelength (x o = 1° log (e)/e c),and 0. is the critical angle of reflection .

We used the molar extinction coefficient as shown infig . 9 [19], calculated FX for different wavelengths bynumerical integration, weighted them according to theiremission intensity, and obtained the resulting photonconversion efficiency. This conversion efficiency isplotted versus the product of the DPOPOP concentra-tion and the fiber sheet thickness in fig. 10 (curve A) .

For the case of single fibers with square cross sec-tion, the measured absorbance and emission intensitywere used in a Monte Carlo calculation to obtain therelative efficiency for a particle incident perpendicularto the fiber axis and passing through the center of thefiber. Note that these efficiencies are slightly less thanwould be obtained by assuming emission only at thecenter of the fiber since some of the primary dye

Uw 0.8

w 0.6z0

w 04

u

i0

Z 0.200

A.J. Davis et al . / Scintillating opticalfiber trajectory detectors

- 1 -exp(-

a-Z

sin 0 d0 dz-01

x cos 0

á 00 5 10 15 20 25

C [°a by weight] . t [rnicrons]

Fig. 10 . The efficiency of small fibers relative to that of bulkscintillator is plotted as a function of the product of thesecondary dye (DPOPOP) concentration in percent and thefiber thickness in micrometers . Curve A is for fiber ribbonswith complete optical coupling between fibers (equivalent to atwo-dimensional sheet) . Curve B is for optically decoupledfibers . Both curves were obtained by assuming that a chargedparticle traversed a fiber normal to the fiber axis and passingthrough the fiber center. The inset shows schematically thepassage of a charged particle through a fiber ribbon and theresulting line emission source which was assumed in obtaining

curves Aand B. The fiber thickness is t in the figure .

emission occurs near the edge of the fiber, with theresult that a larger fraction of the photons escape . Theresults of this calculation are plotted in fig. 10 (curve B).

The curve intersections with the y-axis correspond toan infinitely thin sheet (curve A) or fiber (curve B) . Forthe infinitely thin cases, only those BPBD emitted pho-tons which are totally internally reflected are wave-shifted. For the case of the optically decoupled fiber,this is about 9%, consistent with that calculated in ref.[2] (4.7% multiplied by 2 for lightpiping in both direc-tions). For the case of the sheet, 37% are waveshifted,which is again consistent with the fraction that is totallyinternally reflected .

To obtain the final efficiency of DPOPOP photonslightpiped in fibers relative to the bulk scintillator emis-sion, it is necessary to multiply the value taken from theappropriate curve in fig . 10 by the fraction of isotropi-cally emitted DPOPOP photons which are lightpiped inone direction, i.e ., 4.7% . For example, in the case ofinfinitely thin fibers, the fraction of BPBD emittedphotons which result in DPOPOP emitted photonslightpiped in one direction along the fiber is 0.047 x0.094 = 4.4 x 10-3 .

It is clear from these curves that for our standardscintillator DPOPOP concentration, small cross sectionfibers are quite inefficient relative to that of the bulkscintillator. For cosmic ray experiments detecting highlycharged particles such as iron nuclei, this reduced ef-ficiency is not a serious problem. However for experi-ments involving singly charged, relativistic particles itcan be a significant problem. The efficiency can beimproved by increasing the DPOPOP concentration,provided that the resulting increase in attenuation canbe tolerated. For applications where this increased at-tenuation is not acceptable it may be possible to usedifferent scintillation dyes, such as the class of dyesdiscussed by Renschler and Harrah 1201, which do nothave a significant overlap of their absorption and emis-sion bands, and can therefore be used in high con-centrations . Although these dyes have lower quantumefficiencies than those we are using for high concentra-tions they have the advantage that the emitted light ismuch more localized than for more standard mixtures .

4. Measurements using fiber detectors

35 5

In this section we describe tests performed at theLBL Bevalac heavy ion accelerator, and at the NSCLCyclotron Laboratory at Michigan State University, tostudy the positional resolution that can be obtainedwith scintillating fiber trajectory detectors.

In our first test at the Bevalac, the detector wasexposed to beams of iron, neon, and carbon, withenergies 1600, 580, and 610 MeV/n respectively . Thedetector consisted of eight fiber ribbons of various types

356

ChargedParticle

Scintillating OpticalFiber Ribbons

ImageIntensifier

ITT4144

Fiber Optic Reduceriemm - il mm

Data Out

Fig . 11 . Scintillating optical fiber detector arrangement used inour Bevalac test . The scintillating fibers are proximity focusedonto a fiber reducer which is also proximity focused onto animage intensifier . The intensifier output is coupled to a CID

array using a fiber optic reducer .

which were 2.5 cm in width and 75 cm long . Eachribbon was attached using vinyl adhesive to a 13 ltmthick Mylar substrate which had been stretched on analuminum frame. The fibers within a ribbon were opti-cally coupled. The spacing between ribbons was theframe thickness, 0.6 cm . The detector stack was orientedso that the beam line was at a 10 ° angle with respect tothe perpendicular to the plane of the fibers . The ribbonoutputs were proximity focused using optical couplinggrease onto an intensified CID video camera (fig . 11).The data were taken with the beam traversing the fibersat a distance of 45 cm from the image intensifier input.

Event recording was triggered by a coincidence be-tween two 2.5 cm wide scintillator paddles placed infront of the ribbon stack. The CID video signal wascontinuously read into an 8-bit analog-to-digital con-verter . Upon recept of a coincidence signal, the imageintensifier was gated off, and a video frame from theCID camera was processed. A video frame consisted ofan array of pixels with 244 rows and 377 columns, withonly those pixel intensities above a software settablediscriminator level being recorded .

Fig. 12 shows tracks of three iron nuclei traversingthe detector stack, recorded as different events, andsuperimposed onto one video frame for comparison .The position of the eight ribbons on the CID array isshown with dashed lines in the figure, with the fiber sizein micrometers given at the left of each line . The 200and 300 ltm ribbons labeled 3 X were made fromscintillator with a concentration of 0 .033% (by weight)of the secondary waveshifting dye DPOPOP to increasethe effective scintillation efficiency . The ribbons wereonly crudely lined up, thus resulting in the zigzag ap-pearance in fig. 12 of a straight line trajectory . We notethat the three tracks shown here appear to be nearlyparallel .

To determine the intrinsic precision with which wemeasured the iron particles positions, we have analyzed

A.J. Davis et al. / Scintillating optica! fiber trajectory detectors

244,

Vl

XaT

00

50

t (ALM)

300 ~3x-

150 -

2003x

150

_ �, . _ �E _ W -- -

3003x l

1

1

1

0 4 8 12 16 20 24DISTANCE (mm)

x (pixels)Fig. 12 . Tracks of three iron nuclei which have been superim-posed onto a schematic of the fiber ribbon arrangement . Thefiber size in micrometers is indicated at the left of each ribbonposition . The label 3 X denotes a secondary dye (DPOPOP)

concentration of 0.033% .

data from the three ribbon layers labeled 200 ltm, 3 X .For each track the y-pixel intensities in a particularribbon were summed to give an intensity distributionalong the x-axis . The weighted mean of this intensitydistribution was then calculated and taken as the bestestimate of the particle position for each of these threelayers . We interpolated between the outer two coordi-nates, labeled x t and x, in fig . 13b, by connectingthem with a straight line, and then found the residualdistance (Ox) between that interpolated position andthe actual position on the x, layer . In fig. 13a we plot ahistogram of the residual distance and obtain a calcu-

(b) I

x3

377

Fig . 13 . (a) Distribution of residuals obtained for the 200 ltm,3 X ribbons exposed to relativistic iron nuclei at the Bevalac asshown in fig . 12 . The residual is illustrated in the inset (b) anddescribed in the text . The resolution of 85 ltm for this residualdistribution corresponds to a positional resolution of 69 ltm in

the fiber ribbon .

40wuI- 30

x

á0

201-wm G�- 85 pril

o x -69 hmz 10

-, i L-1 I200 400 600 800

Ax (microns)

lated rms standard deviation of a = 85 [im. This uncer-tainty in i1 x can be related to the positional uncertaintyin a single layer as follows. Since

XI + X3

thenz z

z ax + a.,aar= 4

+

If we assume ax =az= = ay , we obtain a, ; = (2/3) 1 /2

xa,,,, for the uncertainty in a single layer . Thus, fora,,= 85 ~.m the resolution in a single layer is ax, =69!rm. This resolution is very close to that expected from200 l.Lm fibers which are optically decoupled (i .e.200/ 12 = 58 p, m) . For our fibers which are opticallycoupled, in principle, the position can be determinedmore precisely since we measure the mean of the lightintensity distribution . The fact that we did not getbetter resolution than that expected from decoupledfibers may mean that our coupling between fibers is notas good as we thought it was, or that systematic effectsare slightly degrading the resolution .

We have not analyzed our neon and carbon datafrom the Bevalac because of problems with multipleevents in each frame, but note that we easily detectedboth neon and carbon nuclei with the same detector,although it was necessary to increase the image intensi-fier gain above that used for the iron data .

In our second test at the NSCL Cyclotron Labora-tory at Michigan State University a similar detectorwith ribbons made of 100 gm square fibers was exposedto nitrogen nuclei with 50 MeV/n. Fig. 14 shows thedistribution which was obtained . From the full widthhalf maximum of the distribution, we obtain a distribu-

w

au_0

100

80

V

ir 60

40

200 400 600 800 1000

AX (microns)

A.J. Dauis et al. /Scintillating opticalfiber trajectory detectors

a,,, = 64 pin

a, = 52 ~Lm_y

Fig. 14. Distribution of residuals obtained for the 100 pmribbons exposed to 50 MeV/n nitrogen nuclei at NSCL . Theresolution of 64 gm for this residual corresponds to a posi-

tional resolution of 52 wm in the fiber ribbon .

tion resolution of aAx = 64 l.Lm and a positional resolu-tion ax = 52 pm.

5. Conclusions

We have performed measurements of the attenuationproperties of scintillating fibers and find attenuationlengths of 0.8-1 .5 m for various types of fibers. Thecontributions to the attenuation from reflection andbulk scintillator absorption have been obtained fromour measurements, with reflection coefficients varyingbetween 0.9999 and 0.999 and attenuation lengths in thebulk scintillator varying from about 1 .6 to 4 m forwavelengths between 440 and 500 nm . An extrapolationof these measured values has been shown to be con-sistent with calculated values of the attenuation lengthfor bulk scintillator . A calculation of the effective scin-tillation efficiency of small fibers relative to that of bulkscintillator has been performed using a measured molarextinction coefficient for DPOPOP and emission spec-trum for BPBD . This is shown to be an importantconsideration for detectors using small fibers . A scintil-lating fiber detector was constructed and tested usingrelativistic iron nuclei to determine the positional reso-lution which could be obtained . A resolution in positionof about 70 [Lm was obtained using 200 ~Lm fibers . Thisis close to the resolution of 58 ltm predicted for opti-cally decoupled fibers (i .e., the fiber width of 200pm/ 12 ) . Fiber ribbons made of 100 l_Lm fibers weretested by exposing them to 50 MeV/n nitrogen nucleiand a resolution in position of 52 ~Lm was obtained .Although this resolution is quite good, it is distinctlyworse than 100 ~Lm/ 12 indicating that systematiceffects (such as deviations in parallelism of fibers withinthe ribbon) are broadening the resolution . We believethat these can be reduced in future tests by developingtechniques for making the ribbons straight . Both theWashington University and Northeastern Universitygroups are currently involved in research toward thisgoal .

Acknowledgements

35 7

We wish to acknowledge the excellent work by P.F .Dowkontt and M.A . Olevitch of Washington Universityon the electronic data acquisition hardware and soft-ware systems. In addition we thank Tony Thomas ofWashington University for his work on scintillationefficiency in small fibers. We would also like to thankLarry Harrah of Sandia National Laboratories for help-ful conversations about absorption in POPOP mole-cules . We are indebted to the personnel at LBL andNSCL who made our accelerator tests possible . Weparticularly want to thank H.J . Crawford and I . Flores

358

at LBL, and R. Blue at NSCL . The work at WashingtonUniversity was supported in part by NASA grantsNGR 26-008-001, NAG 5-846, NAGW-122, and NASAcontract NAS5-28657, and in part by the McDonnellCenter for the Space Sciences at Washington Univer-sity . The work at Northeastern University was sup-ported by NSF grant NSF PHY-8517612.

References

also, Atomn. Tekn. Ruhbezhom 11 (1987) 40 (in Russian) ;W.R . Binns, J.J . Connell, M.H . Israel and J. Klarmann,Proc . 19th Int. Cosmic Ray Conf ., La Jolla, vol. 3 (1985)p. 272.

[4] W.R . Binns, J.J . Connell, J.W . Epstein, P.L. Hink, M.H .Israel and J. Klarmann, Proc . 20th Int. Cosmic Ray Conf .,Moscow, vol. 2 (1987) p. 391 .A.J . Davis, J.W . Epstein, P.L . Hink, M.H . Israel, J. Klar-mann, J.J . Connell and W.R . Binns, ibid ., p. 394.

[61 J .J . Connell, J.W . Epstein, M.H . Israel, J. Klarmann,W.R . Binns and J.C. Kish . ibid ., p. 398.

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S. Reucroft, SSC Workshop, Berkeley, Ca . (1987).I. Leedom, SSC Workshop, Berkeley, Ca . (1987) .L.R . Allemand, J. Calvet, J.C . Cavan and J.C . Thevenin,Nucl . Instr . and Meth . 225 (1984) 522.

[101 D.R . Nicoll and M.J .C . Ewer, in : Organic Scintillatorsand Liquid Scintillation Counting, eds. D.L . Harrocksand Chin-Tzu Peng (Academic Press, New York andLondon, 1971).

[11] H. Blumenfeld, M. Bourdinaud and J.C . Thevenin, IEEETrans. Nucl . Sci . 33 (1986) 54 .

[121 J.B . Birks, Theory and Practice of Scintillation Counting(Pergamon, 1964).

[19] The molar absorption coefficient is related to the crosssection as follows:

where e is the molar extinction coefficient, c is theDPOPOP concentration in mol/l, t is the slab thicknessin cm, and 1, is the initial light intensity.

[20] C.L . Renschler and L.A . Harrah, Nucl . Instr. and Meth.A235 (1985) 41 .

[1] W.R . Binns, in : Genesis and Propagation of Cosmic Rays,eds. M.M . Shapiro and J.P . Wefel (D . Reidel, 1988) p.391.

[2] W.R . Binns, M.H . Israel and J . Klarmann, Nucl . Instr.and Meth . 216 (1983) 475 ; also ibid., Proc . 18th Int.

[13]

[14][15][161

I.B. Berlman, Handbook of Fluorescence Spectra ofAromatic Molecules (Academic Press, New York, 1972).R.K . Swank and W.L . Buck, Phys . Rev. 91 (1953) 927.T. Forster, Ann. Phys . 2 (1948) 55 .Fibre Optics Development Systems, Inc., 427 Olive Street,

Cosmic Ray Conf., Bangalore, vol. 8 (1983) p. 89 . Santa Barbara, CA, 93101, USA.[3] W.R . Binns, J.J . Connell, P.F. Dowkontt, J.W . Epstein, [171 D.E . Gray (ed.), American Institute of Physics Handbook,M.H . Israel and J. Klarmann, Nucl . Instr. and Meth . 3rd ed . (McGraw-Hill, New York).A251 (1986) 402; [18] J . Kirkby, CERN Report CERN-EP/87-60 (1987) .