The phosphorescence microphone: A device for testing oxygen sensors and filmsChristina M. McGraw, Hari Shroff, Gamal Khalil, and James B. Callis Citation: Review of Scientific Instruments 74, 5260 (2003); doi: 10.1063/1.1626009 View online: http://dx.doi.org/10.1063/1.1626009 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/74/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Optical dissolved oxygen sensor utilizing molybdenum chloride cluster phosphorescence Appl. Phys. Lett. 98, 221103 (2011); 10.1063/1.3595483 Investigation of microphones as near-ground sensors for seismic detection of buried landmines J. Acoust. Soc. Am. 122, 253 (2007); 10.1121/1.2743155 Highly sensitive organic ultraviolet optical sensor based on phosphorescent Cu (I) complex Appl. Phys. Lett. 89, 161112 (2006); 10.1063/1.2364156 Factors affecting the performance of large-aperture microphone arrays J. Acoust. Soc. Am. 111, 2140 (2002); 10.1121/1.1471895 Lightweight fiber optic microphones and accelerometers Rev. Sci. Instrum. 72, 2816 (2001); 10.1063/1.1372172

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The phosphorescence microphone: A device for testing oxygen sensorsand films

Christina M. McGrawDepartment of Chemistry, University of Washington, Seattle, Washington 98195

Hari Shroff a)

Department of Bioengineering, University of Washington, Seattle, Washington 98195

Gamal KhalilDepartment of Chemistry, University of Washington, Seattle, Washington 98195

James B. Callisb)

Department of Chemistry, University of Washington, Seattle, Washington 98195and Department of Bioengineering, University of Washington, Seattle, Washington 98195

~Received 29 April 2003; accepted 14 September 2003!

A new concept in sound pressure detection, the phosphorescence microphone, is introduced. Thisdevice replaces the diaphragm of a microphone with a thin film of pressure sensitive paint. Dynamicchanges in pressure are detected by monitoring the changes in phosphorescent intensity that are dueto cyclical variations in oxygen partial pressure in the sound wave. To test this new device, theacoustic resonance spectrum of a closed cylinder is measured and compared to the spectrumobtained with a commercial electret microphone. Oscillations in phosphorescent intensity that occurat the frequency of sound are observed, and the magnitude of these oscillations is dependent onsound pressure. Several experiments are presented to confirm that the spectrum obtained with thephosphorescence microphone is due to the oxygen sensitivity of the pressure sensitive paint. Inaddition to detecting sound, this device has shown efficacy in testing pressure sensitive paints forhigh frequency, low differential pressure applications. The phosphorescence microphone was usedto show that selected pressure sensitive paints could detect acoustic pressure changes as small as 6Pa in the frequency range 150–3500 Hz on a background of 105 Pa. © 2003 American Institute ofPhysics. @DOI: 10.1063/1.1626009#

I. INTRODUCTION

In this article, the phosphorescence microphone~PM!, atransducer based on a pressure sensitive paint~PSP!,1,2 isintroduced. A thin film of platinum porphyrin compound isused in place of the diaphragm of the microphone. The phos-phorescent light emitted by the porphyrin is dependent on theoxygen partial pressure at the surface of the film. Thus dy-namic changes in pressure can be detected by observingchanges in the emitted phosphorescent light.

All microphones are based on the transduction of acous-tic energy to electrical energy. In most microphones anacoustic pressure wave causes a flexible diaphragm to move,and the motion of the diaphragm induces a change in someproperty of an electrical circuit. The electret microphone,invented in 1962 by Sessler and West, is in common use.3 Inthis device, the capacitance between two plates, one fixedand one acting as the diaphragm, changes according to thevariation in sound pressure. The electret, a thin layer of po-larized ceramic or plastic film placed between the diaphragmand stationary electrode, obviates the need for an externalbias.

Despite the excellent sensitivity and uniform frequencyresponse of the electret microphone, the last decade has seenrenewed interest in optical microphones. One recent exampleis based on a micromachined interferometer.4 An even sim-pler design relies on intensity modulation in which the dia-phragm oscillation is transferred directly to a beam of light.5

One of the main advantages of an optical microphone is thatit can be constructed with no electrical leads attached di-rectly to the transducer. The transducer is thus immune toelectrical interference. If one incorporates low-loss glass fi-bers, it is also possible to place the photodetector and lightsource several hundred meters away from the microphonehead, making the optical microphone a good choice for usein hard-to-reach or hazardous locations.

In addition to detecting sound, the PM also offers a newmethod for testing the response of PSPs to high frequency,low differential pressure fluctuations. PSP response is typi-cally determined using pressure jump methods,6 shocktubes,7 or, more recently, a chopper-modulated free jet.8

Baron et al.6 developed a pressure jump apparatus to studythe response of PSPs to rapid pressure changes. The responsetime, limited by the rate of oxygen diffusion through thepolymer, is determined from the phosphorescent response ofPSP to step changes in pressure. Using a fast-acting valve,the pressure in a sample chamber is changed from nearvacuum to ambient pressure in 600ms. Similar instruments

a!Present address: Biophysics Graduate Group, University of California,Berkeley, CA 94720.

b!Electronic mail: callis@u.washington.edu

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 74, NUMBER 12 DECEMBER 2003

52600034-6748/2003/74(12)/5260/7/$20.00 © 2003 American Institute of Physics

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were used to measure the effect of paint thickness9 and paintmatrix10 on response time. Although these methods havebeen used to measure submillisecond response times, thepressure changes must be large and are often plagued byringing artifacts. Shock tubes have been used to measurerapid pressure changes for PSP characterization.7 Althoughshock tubes generate smaller pressure steps than those seenwith the pressure jump instruments, the pressure changes arestill on the order of 25 kPa with uncertainties of 0.54 kPa. Anew apparatus was recently developed to study the dynamicresponse of PSPs to high-frequency pressure fluctuations.8 APSP sensing layer was employed to detect 70–80 kPa pres-sure fluctuations at frequencies on the order of several kilo-hertz that were generated by a sinusoidally modulated air-jet.

The motivation behind the development of the presentsystem was the need for a more sensitive method to compareand evaluate PSPs for low-pressure, unsteady aerodynamicapplications. The PM has also been used to measure theacoustic response of a resonant cylinder, determine the fre-quency response of PSPs to small differential pressure fluc-tuations, and test the sensitivity and linearity of PSPs over asmaller pressure range than was previously possible.

II. THEORY

Since the intensity of phosphorescent molecules isquenched by collisions with oxygen molecules, phosphores-cence can be used to measure oxygen partial pressure.11 In1989 researchers at the University of Washington, NASAAmes, and Boeing developed a pressure sensitive paint usingthe phenomenon of oxygen quenching of phosphorescentmolecules dissolved in an oxygen permeable polymer. Thepaint was first used to obtain a continuous pressure map ofan airfoil in a wind tunnel.11 It has since been used to studyaircraft models,2 Navy ship air wakes,12 and automobilemodels.13

A. Pressure sensitive paint

A PSP coating consists of a luminophore~a moleculethat emits light! dissolved in an oxygen-permeable polymer.1

The luminophore used in these experiments is platinum tet-ra~pentafluorophenyl!porphine ~PtTFPP!. When exposed toultraviolet radiation, the phosphorescent PtTFPP moleculesemit light at 650 nm. The intensity of the phosphorescentemission is inversely proportional to the surface pressure.PtTFPP works well as an oxygen sensor because its phos-phorescent lifetime in typical polymers at STP is 10ms. Thisrelatively long lifetime provides ample opportunity for anexcited molecule to respond to dioxygen diffusing into or outof the polymer as the oxygen partial pressure fluctuates.

The quenching of PSP phosphorescence is describedquantitatively by the Kavandi equation@Eq. ~1!#.11 Underconstant illumination and fixed detection conditions, the ob-served phosphorescence intensity is inversely proportional tothe pressure:

I 0

I5A1B

P

P0, ~1!

whereI is the phosphorescence intensity at pressureP, I 0 isthe phosphorescence intensity at a reference pressureP0

~typically 1 atm at 298 K!, andA andB are Kavandi param-eters determined by the particular luminophore/polymercombination.A and B are extracted experimentally by plot-ting I 0 /I versusP/P0 and fitting the resulting data to a linearequation with slopeB and interceptA ~Fig. 1!. The points inFig. 1 are actual data~see Sec. III A!. Once A and B aredetermined, Eq.~1! can be used to determine pressure fromintensity. In practice, Kavandi plots are not linear over awide dynamic range.14

B. Expected pressure and temperature changesgenerated by a sound wave

The pressure change corresponding to a given soundlevel is described in Eq.~2!:15

Dpm5A2rcsI ref10SL/10, ~2!

whereDpm is the maximum amplitude of the pressure wave,r is the density of air~1.21 kg/m3!, cs is the speed of sound~344 m/s at 293 K!, I ref is the reference sound intensity(4.82310213W/m2), and SL is the sound level in dB.

The fractional phosphorescence intensity change causedby a fractional change in pressure can be obtained by differ-entiating both sides of the Kavandi equation with respect topressure

d

dPI 5

d

dP S I 0

A1B~P/P0! D52I 0

@A1B~P/P0!#23

B

P0,

~3!

dI

I 052

dP

@A1B~P/P0!#2

B

P0. ~4!

FIG. 1. Kavandi plot of the pressure sensitive paint used in the phosphores-cence microphone.P0 is atmospheric pressure andI 0 is the reference inten-sity at reference pressureP0 . The Kavandi plot is obtained by monitoringthe steady state intensity of a paint sample inside a sealed chamber as thepressure is varied. Points are experimental data and the solid line is the fit tothe Kavandi equation.

5261Rev. Sci. Instrum., Vol. 74, No. 12, December 2003 Phosphorescence microphone

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Since the paint operates on a background of atmosphericpressure,P'P0 . The Kavandi parameters for the PSP sens-ing layer used in this study areA50.34 andB50.66 ~seeFig. 1!. This gives

dI

I 052

B

~1!23

dP

P052B

dP

P0520.66

dP

P0. ~5!

Thus the relative fractional phosphorescence intensitychanges are about 0.70 times the fractional pressure changes.For a 137 dB sound wave, Eq.~2! gives dP5142 Pa. In thiscase the fractional intensity change due to the pressurechange is 9.231024, a very small number that challengesthe sensitivity of the sensor layer and detection system.

The sound waves also cause temperature oscillationswhich are in phase with the pressure oscillations under adia-batic conditions. Since pressure sensitive paints are sensitiveto changes in temperature, the expected temperature changeof an ideal gas has been calculated:16

dT5Tref

g21

g

dP

P0, ~6!

where Tref is the room temperature~298.15 K! and g5CP /Cv51.42. For a 137 dB sound wave, Eq.~6! predictsa temperature change of 0.124 K in the gas. The sensinglayer used in this study has an average fractional intensitychange of 8.731023 per degree Kelvin~see Fig. 2!. If thetemperature change in the sensing layer is equal to the tem-perature change in the gas, the fractional intensity changedue to temperature oscillations is 1.131023. However, thelarge heat capacity of the sensor layer used in these experi-ments means the actual temperature oscillations in the layerare several orders of magnitude smaller than the temperatureoscillations in the gas. Thus the effect of temperature on

phosphorescence intensity can be safely neglected. This as-sertion is verified in the experimental section.

C. Longitudinal resonances of a tube

The sensitivity of the PM was determined by obtainingthe acoustic spectrum of longitudinal resonances of a closedcylinder. Although the acoustic impedance~pressure dividedby volume flow! is often used as the dependent variable inthe acoustic response of resonant cavities,17 the present studyis limited to measurements of sound intensity as a functionof frequency. The resonant frequencies of a cylinder closedat both ends is given by

n5ncs

2L, ~7!

wheren is the frequency,L is the length of the tube, andn isan integer. Since the tube is firmly closed at both ends, thereis no need to apply an end correction toL. At the resonantfrequencies, standing waves are set up inside the tube andpressure antinodes are present at each end of the tube. Theantinodes represent maximum changes in pressure, so theacoustic spectrum of the tube~pressure versus frequency!yields peaks at the resonant frequencies.

One method of measuring the acoustic spectrum of thetube is to excite it with a short pulse of sound at one end andrecord its response with a microphone placed at the otherend.18 Alternatively, a speaker placed at one end can be usedto excite the tube with sound waves of known frequency andamplitude. When the response is measured with an electretmicrophone placed at the opposite end of the tube the outputvoltage of the electret becomes maximal at the resonant fre-quencies of the tube. With the PM device, the acoustic spec-trum of the tube is measured by replacing the electret micro-phone with a thin film of PSP. The PSP responds tomaximum changes in pressure with maximum changes inphosphorescent intensity. Plotting the intensity of phospho-rescent light as a function of frequency generates an acousticspectrum comparable to that obtained with an electret micro-phone.

Since the lifetime of acoustic energy in the tube is finite,the Fourier time-frequency relationship predicts resonancepeaks of finite width. Furthermore, the width of each peakdepends on thermal and viscous losses at the tube wall.Ilinskii 19 provides a detailed discussion of the effect of en-ergy losses on the width of resonant peaks in acoustical reso-nators.

It is important to ascertain that the intensity changes aredue to changes in oxygen pressure and not to another vari-able. Therefore Sec. III describes a series of tests carried outon the instrument to validate that the measured PM responseis solely due to the oxygen sensitivity of the sensing layer.

III. EXPERIMENTAL SETUP AND RESULTS

A. Preparation and characterization of the sensor film

The PSP is made by dissolving 2 mg of PtTFPP~Por-phyrin Products, Logan, UT! and 0.1 g of MAX, a siliconpolycarbonate copolymer~General Electric, Fairfield, CT,

FIG. 2. Temperature sensitivity of the pressure sensitive paint used in thephosphorescence microphone. The temperature sensitivity is determined bymonitoring the intensity of the paint inside a sealed chamber at constantpressure~1 atm! as the temperature is varied.I 0 is the intensity of the paintat 298 K.

5262 Rev. Sci. Instrum., Vol. 74, No. 12, December 2003 McGraw et al.

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LR 3320! in 10 ml of dichloromethane. TwentymL of thissolution is pipetted onto a thin layer chromatography~TLC!plate~Aldrich, Milwaukee, WI, Z122777! to create a circulararea of dye approximately 0.8 cm in diameter. The TLC plateused to support the film is a 250mm layer of 2–25mmdiameter silica particles attached to a clear polyester backing.The silica particles in the TLC plate cause diffuse scatteringof the exciting light, increasing the path length of each pho-ton. The probability that a photon will be absorbed by thePtTFPP is thereby increased.

The sensor film is characterized for its response to staticchanges in oxygen pressure using a computer-controlled‘‘survey apparatus.’’20 The painted TLC plate is placed insidea temperature and pressure controlled sample chamber. Thesample is excited with filtered light from a tungsten lampwhile the air is evacuated from the chamber. A computercontrolled valve mechanism slowly increases the pressure to1 atm while the temperature is held constant. Changes inphosphorescent intensity are measured with a photomulti-plier tube~PMT! and analyzed on a computer. The excitinglight is limited using a 400 nm bandpass interference filterwith a 40 nm width at half height. The emitted light is iso-lated using a 650 nm bandpass interference filter with a 35nm width at half height. The Kavandi parameters are ex-tracted by fitting the data to a line of slopeB and interceptA~Fig. 1!. Since sound waves are small and superimposed on a1 atm steady-state pressure, only the rangeP/P0

50.98– 1.0 is used in these experiments. Here the plot islinear; over a wider range it is nonlinear.

The survey apparatus is also used to determine the inten-sity change with temperature~Fig. 2!. In this case a constant~1 atm! pressure is maintained while the temperature insidethe chamber is raised incrementally from 293 to 303 K. Thefractional change in intensity with temperature, as deter-mined by the slope of Fig. 2, is28.731023 per degreeKelvin.

B. Experimental setup

A schematic of the phosphorescence microphone isshown in Fig. 3. The resonant tube is a section of PVC pipe~1.14 m in length, 3.5 cm inner diameter!. It is placed on atable with a compression horn driver~MCM Electronics,Centerville, OH, 54-060! at one end and the PM sensinglayer at the other. The PM sensing layer consists of 20ml of

the PSP pipetted on a TLC plate of approximately 1 cm2. Tosecure the painted TLC plate to the resonant tube a 5/16 in.diameter hole is drilled through the center of a PVC tubeend-cap. The painted TLC plate is placed over the hole withthe painted side facing the horn driver. The TLC plate isrigidly fastened to a glass plate in order to secure it andprevent it from mechanically vibrating at the frequency ofthe sound wave.

Data acquisition is carried out on a PC equipped with aNational Instruments data acquisition board~PCI-6110, Aus-tin, TX!. The digital-to-analog converter is programmed toprovide a sinusoidal voltage of varying frequency. Thepower of the signal is increased using an audio amplifier andused to drive the speaker. In the following experiments, thefrequency of the amplified signal is scanned from 150 to4000 Hz in 2 Hz increments. Sound levels of 110–137 dB at790 Hz are used in these experiments. The sound level wasmeasured by removing the PM sensing layer and placing asound level meter~Simpson Electric Company, Model 886,Elgin, IL! through the hole in the tube end-cap.

The paint is excited using a 405 nm LED~Roithner La-sertechnik, Cat. No. HUUV-5101L, Vienna, Austria! and a405 nm bandpass filter. As the paint responds to the oscillat-ing sound wave, the phosphorescent light is modulated at thefrequency of sound. Two convex lenses focus the phospho-rescent light onto a photomultiplier tube~PMT!. The phos-phorescent emission detected by the PMT~Hamamatsu,R928, Bridgewater, NJ! is isolated by a 650 nm bandpassfilter, which rejects stray and scattered light below 630 nmand above 680 nm. The PMT current is converted to a volt-age by an operational amplifier operated in transconductancemode. The time constant for the PMT preamp is 50ms. Theoscillating voltage from the preamp is converted to a digitalvalue by the National Instruments analog-to-digital con-verter, the dc offset is removed, and the signal is analyzed inLabVIEW.

Figure 4 shows the response of the PM and electret mi-crophone to a 790 Hz sound wave. The sound intensity levelwas 137 dB for the PM and 123 dB for the electret. Theresponse to 16 sine wave periods was averaged in order toimprove the signal-to-noise ratio. As expected, the PM signalis noisier than the signal from the electret microphone. Sincethe noise of the PM detector can be described in terms of thephoton shot noise, the signal-to-noise ratio is roughly equalto the square root of the number of photoelectrons collected.With approximately 33109 photoelectrons collected at eachdata point, the expected signal-to-noise ratio is 53104. Incontrast, an electret microphone is limited by the thermal andpreamplifier noise,21 which is much lower than the photonshot noise of the PMT. Due to saturation at high sound levelsit was necessary to operate the electret system at 123 dB,significantly less than the 137 dB sound levels used with thePM.

C. Measurements and limitations

The PM’s sensing ability is compared with that of anelectret microphone~Realistic, 33-1063! by measuring theacoustic spectrum of the tube with both devices. Data is col-

FIG. 3. Schematic diagram of the phosphorescence microphone set up formeasurements of the acoustic resonances of a cylinder.

5263Rev. Sci. Instrum., Vol. 74, No. 12, December 2003 Phosphorescence microphone

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lected for 0.5 s at each 2 Hz frequency increment. The powerspectrum is obtained at each step and the peak amplitude atthe frequency of interest is recorded. Plotting the magnitudeof the power as a function of frequency generates an acousticspectrum of the tube. Phase is not determined in these ex-periments. Four spectra for each experiment are averagedand smoothed using a 5-point moving average filter. Thenormalized resonance spectrum of the tube, as measured byboth a PtTFPP/MAX sensing layer and the electret micro-phone, is given in Fig. 5. Although the electret microphonehas a noticeably better signal-to-noise ratio than the PM, thepeak locations and widths are virtually identical. The factthat the spectra of the tube acquired by the electret and PMare almost identical even though taken at widely different

power levels indicates that the acoustic response is in thelinear range.

Ideally, the tube spectrum is a series of peaks of equalintensity as a function of frequency. However, the horndriver used in these experiments has internal resonances thatcouple with and distort the acoustic spectrum of the tube.The response of the horn driver alone was measured over thesame frequency range using an electret microphone placed 2cm from the horn driver mouth. The resulting horn driverspectrum shows three broad peaks between 650 and 1750Hz. When an acoustic spectrum of the resonant cylinder isobtained, the horn sound intensity is greatest at its internalresonance frequencies. These internal horn resonances distortthe acoustic spectrum of the cylinder and cause the broadhumps centered at 650 and 1750 Hz that are seen in the PMand electret resonant spectra~Fig. 5!.

Several experiments were performed to ensure that theresponse of the phosphorescence microphone was due onlyto fluctuations in oxygen pressure. In the first experiment thetube was flushed with nitrogen for 5 min. The frequency ofthe input sound wave was swept over the same region andthe amplitudes of the power spectrum were recorded as be-fore. The acoustic spectrum in nitrogen is presented in Fig. 6.For the purposes of comparison, the acoustic spectrum of thePM in air is also shown. Figure 6 shows that a large reduc-tion in the signal amplitude is observed when the air is re-placed with nitrogen and no peaks are apparent at resonantfrequencies. Nitrogen does not quench the porphyrin tripletstate so no signal is expected if oxygen quenching is the solesource of signal in the PM. The absence of a measurableresponse from the PM in nitrogen indicates intensity changesare due to cyclical changes in oxygen pressure and not totemperature oscillations that occur at the frequency of sound.

Replacing the PtTFPP in the sensing layer with magne-sium tetra~pentafluorophenyl!porphine ~MgTFPP!, anoxygen-insensitive molecule, provides an additional test ofoxygen sensitivity. PtTFPP and MgTFPP absorb and emitlight at the same wavelength, but MgTFPP is considerablyless sensitive to oxygen since its emitted light~fluorescence!is from the lowest singlet state and has a lifetime of 8 ns.Thus there is significantly less time for the excited state tointeract with oxygen. A sensing layer of MgTFPP~PorphyrinProducts, Logan, UT! in the same silicon polycarbonate co-

FIG. 4. ac response of the~a! phosphorescence and~b! electret microphonesto sound waves at 790 Hz in a cylindrical resonant cavity.

FIG. 5. Resonance spectrum of the cylindrical resonant cavity as measuredby ~a! the phosphorescence microphone and~b! an electret microphone. Thesound intensity level was 137 dB for the phosphorescence microphone and123 dB for the electret microphone.

FIG. 6. Resonance spectrum of the cylindrical resonant cavity as measuredby the PM in air and nitrogen~flat line!. The sound intensity level was 137dB for both cases.

5264 Rev. Sci. Instrum., Vol. 74, No. 12, December 2003 McGraw et al.

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polymer was prepared and placed in the PM. The soundwave frequency was swept over the same region and theamplitudes of the power spectrum were recorded as before.Replacing the sensing layer resulted in a diminished signaland no detectable resonant frequencies. The lack of responsefrom an oxygen-insensitive MgTFPP sensing layer indicatesthat the PtTFPP sensing layer response is caused by changesin oxygen partial pressure that occur at the frequency ofsound and is not due to temperature oscillations or othereffects.

In the final test of the sensing layer’s exclusivity of re-sponse to oxygen, the 650 nm emission filter was replacedwith a 390 nm bandpass filter and the acoustic response ofthe tube was measured with the PtTFPP/MAX sensing layer.Again, signal amplitude diminished and no resonant frequen-cies were detected. Exchanging the emission filter with 390nm bandpass filters prevents the phosphorescent light emit-ted by the paint from reaching the PMT. Any signal detectedby the PMT is due to noise or stray light. Since no change inscattered and stray light was observed, the intensity changesdetected at 650 nm are not due to changes in scattered lightarising from mechanical displacement of the sensing layer.

Equation ~5! predicts the phosphorescence intensitychange caused by a change in pressure. For the PtTFPP inMAX sensing layer and a 137 dB sound wave, the expectedfractional intensity change due to pressure is 9.231024.This value was determined experimentally by measuring thesteady state dc signal and the peak-to-peak amplitude of theac signal at 790 Hz, a resonant frequency. Dividing the peak-to-peak ac value by the dc value gives 10.531024, close tothe predicted value for this sound level. Thus the response ofthe PM to ac and dc levels of oxygen is in the expectedproportion.

To test the linearity of the sensing layer response, thesound level of the speaker was varied between 110 and 137dB. The frequency was swept between 720 and 1000 Hz andthe amplitude of the power spectrum at 790 Hz was recordedat each sound level. Sound level was converted to pressurechange using Eq.~2!. Figure 7 shows that a linear relation-ship exists between relative intensity changes and changes inpressure, as predicted by Eq.~5!.

The frequency response of the sensing layer was deter-mined by dividing the normalized PM peak amplitude by thenormalized electret peak amplitude at each resonant fre-quency. This ratio, in decibels, is given by

dB5203 log10S peak amplitudePM

peak amplitudeelectretD . ~8!

The frequency response data was fit to the transfer functionof a second-order~RLC network! filter.22 The inductive com-ponent in this case arises from the storage of oxygen in thepolymer.23

Figure 8 shows the frequency response of the PtTFPP/MAX sensing layer. Relative to the electret microphone, the3 dB point of the PtTFPP/MAX sensing layer is approxi-mately 2370 Hz. After this point the PM response drops at arate of 20 dB/decade until 3550 Hz, the last detectable reso-nance.

The response time of the paint can be calculated fromthe inverse of the angular frequency at the 3 dB point

t51

2pn, ~9!

wheren is the frequency of the sound wave at the 3 dB point.With a cutoff frequency of 2370 Hz, the calculated responsetime of the PM sensing layer is 67ms. The PM response timeis very close to the 50ms PMT preamp time constant andmay be limited by amplifier distortion. However, since thelifetime of the phosphorescent molecule is 10ms, the fre-quency response of the PSP sensing layer is within an orderof magnitude of being limited by oxygen diffusion throughthe polymer.

FIG. 7. PM response to varying sound levels at 790 Hz.

FIG. 8. Relative frequency response of the PM sensing layer.

5265Rev. Sci. Instrum., Vol. 74, No. 12, December 2003 Phosphorescence microphone

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IV. DISCUSSION

A microphone based on the principle of phosphores-cence has been introduced. Dynamic changes in pressure aredetected by the changes in phosphorescent intensity that oc-cur at the frequency of sound. Furthermore, these pressurefluctuations are due to the PM’s oxygen sensitivity, not me-chanical vibrations or temperature changes.

The PM and a conventional electret microphone werecompared by using each to measure the acoustic spectrum ofa closed cylinder excited by a midrange horn driver. Al-though the spectra are similar~Fig. 5!, the electret micro-phone has a significantly better signal-to-noise ratio. Whilecomparing these two spectra, it is important to consider thatthe PM signal improved greatly upon averaging four spectraand smoothing the result. The need to signal average severalspectra with the PM increases the data acquisition time sig-nificantly as well. In contrast a single electret microphonespectrum is almost noise-free and requires far less soundintensity.

In addition to higher sensitivities, an electret microphoneis simpler to use than the PM. Electret microphones arereadily available, easy to set up, and portable. The currentPM apparatus which used a PMT, pre-amp, and UV lightsource is somewhat bulky and limits the location where mea-surements can be made. In addition, filters and lenses mustbe mounted and aligned each time the PM is moved. A morecompact PM could easily be fabricated, however.

Experiments have shown that the PM is sensitive enoughto detect sound levels of 110 dB (Dp56 Pa) and frequenciesup to 3500 Hz. In contrast, electret microphones have beendeveloped that detect frequencies ranging from 1023 to 2.03108 Hz.24 A typical electret microphone can detect soundlevels down to 65 dB (Dp50.04 Pa) at frequencies of 30–15 000 Hz~Radioshack, Fort Worth, TX, 270-092!. Althoughaveraging more spectra could increase the PM sensitivity, itwould come at a substantial increase in data acquisition time.

Nevertheless, the PM has some advantages over an elec-tret microphone. Electret microphones saturate at high soundlevels. The Kavandi relation@Eq. ~1!# indicates that the in-tensity change will continue to be linear as the sound levelincreases above 137 dB. Indeed at high sound levels the PMexhibits an increased signal-to-noise ratio, unlike the electretmicrophone. Also, like an optical microphone, there is noneed for electrical leads to be placed directly at the trans-ducer.

Another advantage of the PM involves the possible im-aging of sound. Neither the conventional electret microphonenor the optical microphone provides a ready measurement ofthe sound pressure field over a surface. However, the phos-phorescence microphone, used with a sensitive chargecoupled device camera, may be capable of providing a con-tinuous map of the sound pressure on any surface to which

pressure sensitive paint can be applied. One simple applica-tion would be to image the radial modes in a resonant tubeby replacing the PMT with a camera.

The PM was originally designed in our laboratory to testthe efficacy of PSPs for high-frequency, low-speed applica-tions. The frequency response of a sensing layer is deter-mined by dividing the normalized PM peak amplitude by thenormalized electret peak amplitude at the resonant frequen-cies. In the future, this ratio can be used to determine thefrequency response of many sensing layers. A comparison ofthese frequency responses could help identify the best paintsfor demanding PSP applications such as surface pressuremeasurements of insects, automobiles, and low-speed air-craft.

ACKNOWLEDGMENTS

The authors gratefully acknowledge Martin Gouterman,Jonathan Wettlaufer, and Vladimir Chaloupka for valuablediscussions. The authors also thank Roy Olund for his assis-tance with the experimental aspects of this research. Thisresearch was supported by the National Science Foundationunder Grant No. 9980069.

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