Detection of x rays with a fiber-opticinterferometric sensor

Fabrizio Barone, Umberto Bernini, Maurizio Conti, Alberto Del Guerra, Luciano Di Fiore,Mauro Gambaccini, Raffaele Liuzzi, Leopoldo Milano, Guido Russo, Paolo Russo, andMatteo Salvato

A fiber-optic Mach-Zehnder interferometer was used for x-ray detection. A single-mode, polarization-preserving silica fiber is exposed to a high-flux x-ray beam (x-ray tube for diagnostic radiology, 30 kV,16.8-keV average energy, 17-40-mA anodic current), modulated at f = 9 Hz by a chopper with steelblades. The energy absorbed produces a modulated temperature rise that induces a phase shift in thepropagation of a He-Ne laser beam with respect to the unirradiated arm of the interferometer. Wemeasured the linearity of the temperature rise with the energy released to the fiber and the linearity of thepeak amplitude at frequency f in the power spectrum of the interferometric signal with the anodic currentof the x-ray tube. A possible application of this technique to synchrotron radiation monitoring isdiscussed.

Key words: X rays, fiber-optic sensors, synchrotron radiation.

Introduction

In recent years fiber-optic sensors have been pro-posed for the detection of a variety of physical quanti-ties, e.g., pressure, temperature, strain, rotation, andmagnetic field.' In a previous paper2 we proposed anovel application for fiber sensors, namely, a fiber-optic interferometer for high-intensity x-ray beamdetection. The principle of operation is that of afiber-optic temperature sensor: when irradiated, thetemperature of the fiber increases to an amount thatis dependent on the absorbed fraction of the beamenergy. This is the so-called generalized photother-mal effect, i.e., the heating of a sample after interac-tion with an electromagnetic (or particle) beam.3In the x-ray region, the photothermal effect in metalsamples has been demonstrated in recent years byMasujima and co-workers,4 5 who used a photoacous-tic apparatus with microphonic detection and a

F. Barone, U. Bernini, M. Conti, R. Liuzzi, L. Milano, G. Russo,P. Russo, and M. Salvato are with the Dipartimento di ScienzeFisiche, Universith di Napoli Federico II, I-80125 Napoli, Italy. L.Di Fiore is with the Istituto di Fisica Nucleare, I-80125 Napoli,Italy. A. Del Guerra and M. Gambaccini are with the Diparti-mento di Fisica, UniversitA di Ferrara, and the Istituto Nazionaledi Fisica Nucleare, I-44100 Ferrara, Italy.

Received 29 June 1992.0003-6935/93/071229-05$05.00/0.c 1993 Optical Society of America.

chopped synchrotron radiation (SR) source to detectthis temperature rise in metal samples.6 A photo-acoustic detector for x-ray dosimetry has been used atthe Photon Factory [National Laboratory for HighEnergy Physics, (KEK)] Synchrotron Radiation Facil-ity, Tsukuba, Japan both for white7 and monochro-matic x rays.8 For low-energy x rays (< 20 keV),this temperature rise is due mainly to thermalizationof photoelectrons that are produced by interactingphotons. The mechanism for heat generation insidea solid sample has been investigated in detail theoret-ically:9 it is due to electron-electron interactionsand then to electron-phonon interactions in thecrystal structure, following the absorption of primary(incident) or secondary (fluorescent) photons and theproduction of photoelectrons and Auger electrons.As an alternative to a photoacoustic detector, wepropose the use of a silica optical fiber for x-rayabsorption. The final effect of irradiation is a rise inthe temperature of the exposed fraction of the fiberand then a change of its optical path length, ni, thatcould be detected interferometrically (e.g., in a typicalMach-Zehnder scheme). For fused-silica fibers thelarger contribution to this change comes from thetemperature dependence on the refractive index nrather than the fiber length 1. Although the probabil-ity for x-ray interaction in silica is reasonably highonly below 100 keV (Fig. 1), in principle doped-glassoptical fibers can be used as an x-ray energy absorber

1 March 1993 / Vol. 32, No. 7 / APPLIED OPTICS 1229

Q

80U

Z0

I GlUUUU,__ _ _ l- _ 1000 - S__

100 -

10 ____ __ __ _ _

1 _

0.140 10 20 30 40 50 60

ENERGY (keV)70 80 90

age energy fluence on the sample in one cycle is P =Ey/2f, then

D E(P en2f p

and from Eqs. (1) and (3) the temperature rise (C) ina modulation cycle is

2 fc p

100

Fig. 1. Mass linear attenuation coefficient of fused silica.

to increase the efficiency of photon absorption forhigher photon energies. We point out that such asensor is not able to detect single photons or even lowphoton flux densities (m-2 s). For example, forfused-silica fiber-optic interferometric sensors,with typical values for temperature sensitivity(AO/IAT 102 rad m' 0 C-1) and for an extremephase sensitivity of AO 10-6 rad, a temperature riseas low as 10-80 C for 1 m of fiber irradiated could bedetected. At 20 keV, where the fraction of absorbedphotons incident normally to a 250-jim (outer diame-ter) fused-silica fiber length is - 10%, this wouldcorrespond to at least 107 photons absorbed in thislength of fiber.

Principle of Operation of the Fiber Sensor

Let us assume that a monochromatic excitation beam,intensity modulated at frequency f (Hz) (50% dutycycle), is incident on a sample of fiber with diameter d(m), length I (m), density p (kg M- 3

), specific heat c (Jkg-'0 C-1), orthogonally to the fiber axis. We definethe following: E is the photon energy (keV, J), (p isthe photon flux density (-

2 s), 'I is the energyfluence (J m-2), D is the average absorbed dose in thefiber (J kg-'), [Len/P is the mass energy absorptioncoefficient of fused silica (

2 kg-'), and Xq is thefraction of absorbed energy that is converted intoheat.

If EabS is the total energy absorbed in the irradiatedfiber, its temperature increases by an amount givenby

A TIEabs _ TjD(1AT = d2 c1pc c

If charged-particle equilibrium holds, the absorbeddose in a medium is related to the photon energyfluence T by (see Ref. 10, Chap. 4)

D F len

p(2)

We assume that the same relation holds to a goodapproximation for irradiated fiber. Since the aver-

(4)

Thus, at a fixed energy E, AT is directly proportionalto the beam flux density. For example, for a silicafiber (see Table 1) with an outer diameter d = 250pm, with E = 10 keV and a photon flux density p =1015 m-2 s'l (e.g., SR source), modulated atf = 10 Hz,we have (see Ref. 10, Appendix D.3) Pen/P 2 m 2 kg-1

(neglecting the doping, e.g., with germania, of thefiber core). Then the expected temperature rise is-2.1 x 10-40C, the average absorbed dose is 1.6 x10-1 J kg-1 , and 1.7 x 10-5 J are absorbed in a 1-mlength of irradiated fiber. We assumed that most ofthe absorbed energy in 250 Pim of SiO2 is convertedinto heat (i.e., - 1).1 To confirm these estimates,we performed a preliminary experiment at KEK witha SR source (Photon Factory) to measure this photo-thermal signal in a silica graded-index optical fiberwith gas-microphone detection. 12,13

The temperature rise AT in the fiber sensor afterirradiation produces a phase shift AO in the probelight beam of wavelength that propagates in themeasurement arm of a Mach-Zehnder interferome-ter with respect to the propagation in the unirradi-ated reference arm. This phase shift is related to thetemperature rise AT produced in the irradiated fiberby

dO 2rn dl dn\_d- ___ 1 T+jT (5)

where n is the refractive index of the fiber and I is thelength of fiber irradiated. For silica fibers the changein refractive index dominates the thermal expansionof the fiber (see Table 1); then

dO 27r dn

ldT dT (6)

Hence, when we use a He-Ne laser source (633 nm)

Table 1. Physical Properties of Fused Silica

Density p 2.2 x 103 kg m-3

Specific heat c 7.5 x 102 Jkg-'C-1Temperature coefficient of the refrac- 10-5C-

tive index dn/dTLinear thermal expansion coefficient 10-7 0C-

d/l/dTMass energy absorption coefficient 2 m2 kg- 1

at P'en/P 10 keVRefractive index at 633 nm 1.457

1230 APPLIED OPTICS / Vol. 32, No. 7 / 1 March 1993

. . . _=-

. I

1 nrlnn

(3)

the sensitivity dO/ldT is of the order of 102 radC'm-'. By combining Eq. (4) and approximation (6),we have

2rr dn (2rr dn -rE Fen\AO -- lAT ---- l P. (7)X dT X dT 2f p

These calculations show that, by illuminating 1 m offiber, a phase sensitivity of the order of 10-2 rad isneeded to detect a temperature rise of 10-40C.Because of the low frequency and the high-amplitudedrift of the interferometer output that are caused bythermal, mechanical, and acoustic ambient fluctua-tions, this sensitivity can be achieved only with asuitable feedback control of the interferometer, thatis, locked on a certain phase relationship between thetwo arms. In this closed-loop operation mode, areasonable signal-to-noise ratio can be obtained.

Experimental Setup

The experimental setup of the prototype Mach-Zehnder fiber interferometer is shown in Fig. 2. Inthis figure L is the laser source, BS a beam splitter, Ca chopper, P is a half-wove retardation plate, 0 is amicroscope objective, PZT is a piezoelectric trans-ducer, OF is a polarization-maintaining optical fiberand D is a photodiode. It is mounted on a 1 x 0.5 x0.02-M3 aluminum plate and has fiber arms of 5-mlength. A linearly polarized He-Ne laser beam (633nm, 6 mW) propagates through a single-mode, polar-ization-maintaining (bow-tie) fiber (York HB600).A short length of the reference arm is glued along astack of piezoelectric actuators to control the relativephase of the light in the two arms with an appliedpositive voltage. This consists of the sum of amodulating signal at 4.7 kHz and a low-frequency(= 1-Hz bandwidth) actuating signal. The high-frequency component produces a modulation of therelative phase at the interferometer output. A coher-ent demodulation technique' provides a signal that isproportional to the relative phase fluctuations in theinterferometer output. This signal is low-pass fil-tered, amplified, and then fed back to the piezoelectrictransducer (unity gain at 1 Hz) to lock the interfer-ometer on a dark fringe. This servo system allows

X-ray beam

C II

Fig. 2. Experimental setup.

the interferometer to be operated continuously forlong intervals, unaffected by low-frequency fluctua-tions, which can be as high as several radians in fewseconds. Finally, the useful measurement band-width ranges from a few hertz to - 100 Hz. Thesensor was usually operated by chopping the x-raybeam below 10 Hz, where the signal is higher [seeapproximation (7)]. The performance of the detectorwas preliminarily tested2 by using an Ar+ laser beam(514 nm) to heat the fiber with a power density of 3X 103 W m-

2, with a sensitivity of 10-3 rad Hz-'/2

at a modulation frequency of 8 Hz.A 4-m length of fiber of the measurement arm was

exposed to x rays by using a research mammographicx-ray unit. This fiber was wound in air between twosupporting rods 7 cm apart, placed at a distance of 8cm from the focal spot of the x-ray tube. Betweenthe x-ray source and the fiber, an electromechanicalchopper with 0.5-mm-thick steel blades modulatedthe beam at a frequency f = 9 Hz. The energyspectrum of the x-ray beam is dominated by a line at17.4 keV (molybdenum anode, K, line); the meanphoton energy is 16.8 keV. The anodic current wasvaried by as much as 40 mA; the accelerating voltagewas kept fixed at 30 kV. The specific photon fluxdensity was 4.1 x 1013 m-2 s-1 mA-'.

Results

Figure 3 shows a semilog plot of the power spectraldensity (V Hz-1/2) of the demodulated interferometricsignal, below 24 Hz, when the x-ray tube was oper-ated at an anodic current of 30.3 mA. The spectrumdrops approximately with an f-1/2 dependence. Thelarge peak at 9 Hz in the interferometer output that isdue to the x-ray heating beam is clearly evident. Apeak at 8 Hz was superimposed for calibration byapplying a sine modulation to the piezoactuators; avoltage amplitude of 9.66 x 10-1 V Hz-1/2 produced aphase shift of 5 x 10-2 rad Hz-1/2 (height of the

2.98 V/4Hz

0. kHz_ _ 12.207 HzTop = 2.98538 U/4Hz 5 dB/div Undo: Inning

rad/'qHz

Fig. 3. Power density spectrum of the relative phase fluctuationsof the interferometer (no. of averages, 3). The first peak at 8 Hz isthe calibration peak (corresponding to 5 x 10-2 rad Hz-l/2 ) andthat at 9 Hz (where the cursor is located) is produced by themodulated x-ray beam. Anodic current of the x-ray tube, 30.3mA; accelerating voltage, 30 kV. The acquisition time for onespectrum is 16.4 s (150 modulation cycles). Horizontal scale, 2.44Hz/div; vertical scale, 5 dB/div; top value, 2.98 V Hz-l/ 2

= 1.54 radHz- 1 /2 .

1 March 1993 / Vol. 32, No. 7 / APPLIED OPTICS 1231

calibration peak). This allows power spectral den-sity values to be converted into phase shift values[and into an estimated temperature rise by usingapproximation (6)]. Figure 3 shows that the signal-to-noise ratio achieved is 10 dB (two grid divisions)at 9 Hz, and the minimum detectable phase shift is

20 dB below the calibration peak, corresponding toan estimated noise level of a few mrad Hz-'/ 2. Theheight of the 9-Hz modulation peak is related to theamount of energy absorbed per modulation cycle andis proportional to the photon flux density [see approx-imation (7)]. To compare this peak value with thoseobtained at different times with different anodiccurrents, we normalized the peak height to the heightof the corresponding calibration peak at 8 Hz andthen expressed it as phase shift values (rad Hz-'/ 2).Figure 4 shows the plot of this phase shift versus theanodic current of the x-ray tube. The current inmilliamperes is converted into photon flux density inm_2 s-' and shown in the upper scale. A linear fit(solid line) was superimposed to the measurements,which indicates a good linearity of sensor response inthe explored current and flux density ranges. Theestimated noise level for all sets of measurements was5 x 10-3 rad Hz-'/ 2 . This corresponds to a mini-mum detectable temperature rise of AT 10-51C(1-Hz bandwidth) with this sensor. The slope of thebest-fit line is 1.2 x 10-17 rad Hz-'/ 2 M2

s.

Discussion

We used a fiber-optic Mach-Zehnder interferometeras the detector of a high-flux density ( 10'5 m_2 s-')x-ray beam (16.8-keV average energy). A point sen-sor was realized by exposing the total length of 4 m offused-silica fiber, and beam detectability plus linear-ity of response versus beam flux density was observed.The detector operates in open air in the presence oflarge coupling to ambient noise, mainly temperaturefluctuations, air currents, and acoustic background,that forces the use of a suitable fringe-locking system.

Photon flux density (nf2 )15

0.0 0.4 0.8 1.2 1.6 2.0 x 1 0

6s' N

0$:1

S.

0.03

0.02

0.01

0 1 0 20 30

Anodic current (A)40

Because of this condition the apparatus is extremelysimple and easy to use.

In the description of the principle of operation ofthe proposed x-ray fiber-optic sensor we did not takeinto account the spectral distribution of the x-raybeam, the high birefringence of the optical fiber used,the presence of the acrylic fiber jacket-consideredequivalent to fused silica as for x-ray attenuation andthermal properties-and we made a charged-particleequilibrium assumption in the estimate of the ab-sorbed dose in the fiber. These assumptions lead toa linear relation between the interferometer outputand the photon flux density [see approximation (7)].The linearity of the phase shift AO versus the fluxdensity (p of the x-ray beam was experimentallyconfirmed quantitatively. In fact, the coefficientAO/!p calculated from approximation (7) is 1 X 10-17rad M2 s, and the measured value is 1.2 x 10-17 radHz-1/ 2 M2

S.

The sensor we propose is a type of integrating,calorimetric dosimeter for x rays (see Ref. 10, Chap.14). The level of absorbed dose measured is of theorder of 10-2 J kg-'. In this respect, it shows asensitivity level better than the existing dosimetersbased on thermocouples and thermistors; the latterare useful for large doses (> 10 J kg-').

The basic idea for this study is that bare opticalfibers can be used as high-flux x-ray detectors in ageometrical arrangement-such as a linear array ofplane-parallel fibers-that could also give one-dimensional geometric information on the spatialdistribution of the beam. In this configuration, thelimiting spatial resolution could be the diameter ofthe fiber itself; as an alternative, a single fiber couldperform a scan across the x-ray beam so as to realize abeam position monitor for high-flux sources (e.g.,SR). In this respect, a fiber-optic wire scanner forSR could be used as an alternative to conventionalphoton beam position monitors with metal wires'4' 6

because of the high x-ray transmission through afused-silica fiber (Fig. 5) and the wide range ofdetectable photon energies. (Indeed, the sensor re-sponds even to visible light if the flux is high enough.)

I00

.0'0

,_0

.0

0

C.250

Fig. 4. Phase shift of the interferometer output power versus theanodic current of the x-ray tube. The current is converted tophoton flux density in the upper scale. The solid line is the linearbest fit to the measurements. The x-ray beam was chopped at 9Hz.

0.1: - __ _ V -.< > ~~~~~~~~0 2 5 0 m m

0.01 -o _ r _- - _ _ -0125m m;~~~~~~~~~~. it

0.001 i I I :n=nnno U 1U ZU ;JU '4+ O1 bU /U

Photon Energy (keV)CU YU 1 UU

Fig. 5. Fraction of absorbed photons in 0.125- and 0.250-mm-thick pure fused silica as a function of photon energy.

1232 APPLIED OPTICS / Vol. 32, No. 7 / 1 March 1993

w~ I I I

I I~~~~~~~

0

Major drawbacks seem to be the necessity of choppingthe x-ray beam and the expected radiation damage tothe optical fiber after prolonged exposure to highfluxes.'7 As for the required length of fiber to irradi-ate, an increase in the interferometer's sensitivitywould allow a correspondingly shorter fiber arm.

In conclusion, a fiber-optic x-ray sensor could offerseveral advantages: (1) wide energy range (from softx rays to hard y rays by using doped-glass fibers), (2)high fluxes (e.g., SR sources), (3) one-dimensional andtwo-dimensional spatial information obtained fromfiber arrays and multiplane fiber stacking. Howev-er, the optical fiber dosimeter is an integral sensorand not a single photon counter, i.e., the number ofincident photons must be so large that the energyabsorption, and hence the temperature rise, is greatenough to be detected. We believe that the sensitiv-ity of our prototype dosimeter can be increased by 1 or2 orders of magnitude by using a more compactmechanical and optical setup and operating the detec-tor under vacuum.' 8

References1. T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, Jr.,

J. H. Cole, S. C. Rashleigh, and R. G. Priest, "Optical fibersensor technology," IEEE J. Quantum Electron. QE.18,626-665 (1982).

2. F. Barone, U. Bernini, M. Conti, A. Del Guerra, L. Di Fiore, P.Maddalena, L. Milano, G. Russo, and P. Russo, "A fiber opticinterferometric X-ray dosimeter," in Fiber Optic and LaserSensors IX, R. P. DePaula and E. Udd, eds., Proc. Soc.Photo-Opt. Instrum. Eng. 1584, 304-307 (1991).

3. A. C. Tam, "Applications of photoacoustic sensingtechniques,"Rev. Mod. Phys. 58, 381-431 (1986).

4. T. Masujima, "Photoacoustic x-ray absorption spectroscopy,"in Proceedings of the 5th International Topical Meeting, P.Hess and J. Pelzl, eds., Vol. 58 of Series in Optical Sciences(Springer-Verlag, Berlin, 1987), pp. 19-24.

5. T. Masujima, Photoacoustic X-Ray Absorption Spectroscopy,Vol. 147 of Topics in Current Chemistry (Springer-Verlag,Berlin, 1988).

6. T. Masujima, H. Yoshida, H. Kawata, Y. Amemiya, T. Katsura,M. Ando, T. Nauba, K. Fukui, and M. Watanabe, "Photoacous-tic detector for synchrotron radiation research," Rev. Sci.Instrum. 60, 2318-2320 (1989).

7. T. Masujima, H. Kawata, Y. Amemiya, N. Kamiya, T. Katsura,T. Iwamoto, H. Yoshida, H. Imai, and M. Ando, "Photoacous-

tic x-ray absorption spectroscopy (PAXAS) I: instrumenta-tion and detectability," KEK Photon Factory Activity Rep. No.4 (National Laboratory for High Energy Physics, TechnicalInformation and Library, Tsukube, Japan, 1986), p. 314.

8. M. Hoshi, T. Masujima, C. Nagoshi, Y. Sugitani, T. Sano, S.Sawada, H. Kawata, Y. Amemiya, M. Ando, "Applications ofphotoacoustic spectroscopy to dosimetry of synchrotronradiation," KEK Photon Factory Activity Rep. No. 4 (NationalLaboratory for High Energy Physics, Technical Informationand Library, Tsukube, Japan, 1986), p. 313.

9. M. E. Garcia, G. M. Pastor, and K. H. Bennemann, "Theory forthe photoacoustic response to x-ray absorption," Phys. Rev.Lett. 61, 121-127 (1988).

10. F. H. Attix, Introduction to Radiological Physics (Wiley, NewYork, 1986).

11. X. M. Tong, T. Watanabe, H. Yamaoka, and H. Nagasawa,"Hard x-ray interaction with materials," Rev. Sci. Instrum.63, 493-495 (1992).

12. P. Russo, T. Masujima, H. Shiwaku, T. Inagaki, S. Kawano, T.Hiraga, and M. Kadoyama. "Photoacoustic measurement ofthe temperature rise in a silica fiber-optic upon irradiationwith x-ray from a synchrotron radiation source," KEK PhotonFactory Activity Rep. No. 8 (National Laboratory for HighEnergy Physics, Technical Information and Library, Tsukube,Japan, 1990), p. 61.

13. P. Russo and H. Hirayama. "EGS4 user code for simulation ofsynchrotron radiation photoacoustic experiments," NationalLaboratory for High Energy Physics (Tsukuba), KEK InternalRep. No. 90-19 MR (National Laboratory for High EnergyPhysics, Technical Information and Library, Tsukube, Japan,June 1990), pp. 1-36.

14. B. A. Karlin, P. L. Cowan, and J. C. Woicik, "X-ray, soft x-rayand VUV beam position monitor," Rev. Sci. Instrum. 63,526-529 (1992).

15. E. L. Brodsky, K. J. Kleman, G. Roberg, D. Rioux, R. Patel, andH. Hochst, "Implementation and test of a synchrotron radia-tion position monitor at a user beam line," Rev. Sci. Instrum.63, 519-522 (1992).

16. T. Mitsuhashi, A. Ueda, and T. Katsura, "High-flux photonbeam position monitor," Rev. Sci. Instrum. 63, 534-537(1992).

17. B. D. Evans, G. H. Sigel, Jr., J. B. Langworthy, and B. J.Faraday, "The fiber optic dosimeter on the navigationaltechnology satellite," IEEE Trans. Nucl. Sci. NS-25, 1619-1624(1978).

18. D. A. Jackson, A. Dandridge, and S. K. Sheem, "Measurementof small phase shifts using a single mode optical interfer-ometer," Opt. Lett. 5, 139-141 (1980).

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