A fiber–optic interferometer for in situ measurements of plasma number density inpulsed-power applicationsL. M. Smith, D. R. Keefer, and N. W. Wright Citation: Review of Scientific Instruments 74, 3324 (2003); doi: 10.1063/1.1582389 View online: http://dx.doi.org/10.1063/1.1582389 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/74/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in High velocity flyer plates launched by magnetic pressure on pulsed power generator CQ-4 and applied in shockHugoniot experiments Rev. Sci. Instrum. 85, 055110 (2014); 10.1063/1.4875705 Fiber optic two-color vibration compensated interferometer for plasma density measurements Rev. Sci. Instrum. 77, 10F325 (2006); 10.1063/1.2336437 Fiber optic catalytic probe for weakly ionized oxygen plasma characterization Rev. Sci. Instrum. 72, 4110 (2001); 10.1063/1.1409567 Thermal tuning of a fiber-optic interferometer for maximum sensitivity Rev. Sci. Instrum. 70, 3542 (1999); 10.1063/1.1149947 Optical probing of fiber z -pinch plasmas Phys. Plasmas 5, 682 (1998); 10.1063/1.872778

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A fiber–optic interferometer for in situ measurements of plasma numberdensity in pulsed-power applications

L. M. Smith,a) D. R. Keefer, and N. W. WrightThe University of Tennessee Space Institute, Tullahoma, Tennessee 37388-9700

~Received 20 January 2003; accepted 17 April 2003!

A fiber–optic-based interferometer has been designed, constructed, and applied to plasmameasurements in pulsed-power systems. The beam from a 1310 nm solid-state diode laser is coupledinto a single-mode fiber and split into two beams, one of which was passed through an acousto-opticmodulator to frequency shift the light. Both beams travel through approximately 30 m of fiber, withthe probe volume consisting of a short air or vacuum gap in the probe beam fiber where the light iscollimated and collected by lenses. The beams are then recombined on a photodiode, producing atime-varying sinusoidal intensity signal that is phase modulated with the presence of a plasma in theprobe volume. This configuration allows for remote measurements of plasma electron numberdensity, and is robust with respect to vibration in the plasma source and electromagneticinterference. Tests indicate that phase measurement accuracies of60.045 rad corresponding tonumber density accuracies of61.231019 m22 at 1310 nm are achievable with this device. Adescription of this interferometer, including refinements needed to achieve these accuracies, ispresented along with the results of tests performed on a coaxial plasma gun. ©2003 AmericanInstitute of Physics.@DOI: 10.1063/1.1582389#

I. INTRODUCTION

Interferometry is a well established diagnostic tool forthe nonintrusive investigation of plasmas.1 Because thechange in refractive index due to an electron gas with num-ber densityNe is given by

n82152l2Neq

2

8p2meeoc2, ~1!

the phase shift experienced by light in passing through sucha gas is given by

w522p

l E ~n821!dl5lq2

4pmeeoc2E Nedl, ~2!

where the integration is taken along the beam path throughthe plasma. By combining the light through the plasma witha reference beam of the same or similar wavelength, an in-terference pattern in the light intensity is obtained that pro-vides temporal and spatial information about the electronnumber density within the plasma.

Interferometry is especially useful in pulsed-plasma ap-plications, since a single beam of light~e.g., from a laser!can probe the plasma along a specified path and the resultingsignal is a phase modulated sinusoid.2 An interferometer forthis purpose operating in heterodyne mode was developed byWeberet al.3,4 and has proven effective both in isolated con-trolled investigations of plasma sources3 andin situ diagnos-tics of plasma opening switches~POSs!.4 It consists of a

Mach–Zehnder interferometer with one beam modulated byan acousto–optic modulator~AOM! so that a time-varyingphase-modulated intensity distribution is incident on thedetector.5 The reader interested in the historical developmentof heterodyne interferometry may wish to consult the refer-ences cited in the articles by Chuvatin,3 Weber,3,4 orJacobson.5

A modified version of this interferometer design utilizingtwo probe beams was recently used6 to investigate theplasma ejected from a cablegun, a device consisting of acoaxial configuration of conductors separated by an insulatorand electrically pulsed to inject plasma into a POS. Accuratemeasurements of path-integrated electron number densitywere obtained at locations 25 and 50 mm from the cablegunmuzzle, thus providing an estimate of the effective plasmavelocity. Data for the buildup of plasma in front of a con-ducting plate were also acquired. Further development of thisfacility produced a method for acquiring radial scans of theplasma jet and provided a performance analysis of alternatematerials and geometry for the cablegun.7

The utility of this method of interferometry applied topulsed plasma studies is thus well established by previousexperimental work. However, all prior interferometers haveutilized the standard Mach–Zehnder arrangement, consistingof mirrors and beam splitters with light beams propagationalong paths through air or vacuum. While such an approachis suitable for controlled laboratory conditions, it has beensubject to problems associated with vibration, and data ac-quisition has been hampered by the effects of electromag-netic interference from the nearby pulsed power sources.These drawbacks, along with other logistical considerationsconcerning access, virtually prohibit their use forin situmeasurements in a large pulsed power facility.

a!Author to whom correspondence should be addressed; electronic mail:msmith@utsi.edu

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 74, NUMBER 7 JULY 2003

33240034-6748/2003/74(7)/3324/5/$20.00 © 2003 American Institute of Physics

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Recently, McFarland and others at Alameda Applied Sci-ences Corporation developed a fiber–optic interferometer foruse in pulsed power plasma studies.8,9 While this design hasbeen used for measurements on the DECADE POS, it has thedrawbacks of requiring careful alignment to null the interfer-ometer immediately prior to data acquisition, and difficultyin data analysis due to the drop in signal amplitude duringthe tests. The heterodyne interferometric approach helps toalleviate these difficulties.

A prototype fiber–optic-based heterodyne interferometerhas been developed and tested to overcome these difficulties.This interferometer consists of a solid-state diode laser witha wavelength of 1310 nm coupled into a single-mode fiber.The light is then split into two paths directed down twoseparate fibers, one of which contains an AOM that fre-quency shifts the light by 40 MHz. The probe beam fiber isapproximately 30 m long to allow remote access to theplasma volume, while the reference beam fiber is matched inoptical path length to the probe beam to minimize any loss offringe visibility due to coherence effects. The only free spacepropagation is through a small plasma probe volume, wherethe light from the probe beam fiber is collimated by one lensand collected and recoupled into the fiber by another identi-cal lens. The light from the probe and reference beam fibersis then combined and coupled into a photodiode whose out-put is recorded with a digital oscilloscope. The entire appa-ratus, except for the fibers for the probe and reference beams,is assembled on a 36 cm by 43 cm platform that can be easilymoved to a location safely removed from the plasma source.

This interferometer has been designed, constructed andtested in the laboratory. Several refinements, including polar-izing filters and a precision path length adjustment mecha-nism, were found necessary to optimize signal-to-noise ratio.The result is a fully operational unit that has been applied tothe same cablegun plasma test facility as presented in Refs. 6and 7. These tests yielded measurements of phase with anaccuracy of60.045 rad corresponding to a path-integratedelectron number density accuracy of61.231019 m22 at theoperating 1310 nm wavelength. It is felt that these tests dem-onstrate its applicability to actual pulsed-power plasma diag-nostic measurements.

In Sec. II, a detailed description of the interferometer ispresented, together with the method of data reduction. Sec-tion III presents the tests performed and the results of thosetests. Section IV presents a discussion and recommendationsfor use of the interferometer in pulsed power applications.

II. THE INTERFEROMETER AND ITS OPERATION

Figure 1 shows the basic configuration for the fiber–optic interferometer.~In what follows, the manufacturer andmodel number are given in parentheses after each componentdescription. Also, several operating devices associated withthe actual usage of the interferometer, such as the powersupplies for the laser and AOM and the data acquisition sys-tem are omitted for clarity.! The output from a 1310 nmpigtail-coupled solid-state diode laser@Power Technology,PPM~LD1398!F2# passes through beamsplitter/coupler B1~Newport, F-CPL-L12135-P! and is separated into two

beams. One beam, the probe beam, is frequency shifted by40 MHz via an AOM~IntraAction, FCM-401E6C!. This lightpropagates approximately 15 m to the plasma probe volume,where it is collimated by lensC1 ~Thorlabs, 50-1310-FC!,passes through the air or vacuum gap and plasma, and iscollected by a similar lensC2 and coupled into another 15 mlength of fiber. The other beam, the reference beam, propa-gates through a length of fiber with the same optical pathlength as the probe beam.~This is represented in the figureby a loop of fiber.! The beams are then recombined inbeamsplitter/couplerB2, and the superimposed light coupledinto a solid-state photodiode detectorD ~Terahertz Technolo-gies, TIA-950!. The voltage signal from the photodiode canbe viewed and recorded with a digital oscilloscope.~Fiberlengths and connectors were supplied by L-Com and FiberInstrument Sales.!

The field component for the reference beam can be writ-ten ao cos(2pnot), whereno is the optical frequency of thelight. Similarly, the probe beam field component can be writ-ten bo cos@2p(no1Dn)t1w(t)#, whereDn represents the fre-quency shift introduced by the AOM andw~t! denotes thephase shift introduced by the plasma. The time-averaged in-tensity resulting from the superposition of these beams isthus given by

I ~ t !5 12ao

21 12bo

21aobo cos@2pDnt1w~ t !#. ~3!

By ac coupling the voltage from the photodiode~which isproportional to the incident intensity!, the time-varying termin Eq. ~3! is extracted, and consists of a phase modulatedsignal that can be demodulated to determine the phasew~t!by the method described below. From it, the path-integratedplasma electron number density can be found from Eq.~2!.

Demodulation of the phase is carried out by essentiallythe same method as that described in Ref. 6. Data are ac-quired at a sampling rate of 250 Megasamples/s and process-ing is carried out digitally off-line. A separate line feed fromthe AOM modulator is used to determine the carrier fre-quencyDn, which although specified as 40 MHz, must bedetermined to high precision for the demodulation process.

FIG. 1. Component configuration for the fiber–optic interferometer.

3325Rev. Sci. Instrum., Vol. 74, No. 7, July 2003 Fiber-optic heterodyne interferometer

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Pure sinusoids at this frequency@cos(2pDnt) andsin(2pDnt), respectively# are generated and multiplied by theexperimental photodiode signal to form in-phase and quadra-ture components at dc, where they are filtered by a zero-phase finite impulse response digital filter to remove higherorder harmonics and noise. For this application, a 1001-tapequiripple design was used with a passband from 0 to 375kHz and a stopband from 1.25 MHz to the Nyquist fre-quency, 125 MHz. The arc tangent of the ratio of quadratureto in-phase outputs from this filter is computed, yielding thedesired phase information. Zero reference phase is found byaveraging the data over a known time interval in which noplasma is present in the probe volume. Phase unwrappingmay also be applied to remove any 2p discontinuities in thedata.

Although the preceding describes the fundamental prin-ciple of operation of the interferometer, several refinementswere found necessary to make it operational in practical ap-plications. Neutral-density variable attenuators labeledA1andA2 in Fig. 1 ~Fiber Instruments Sales, FIS F1-0822FC!were inserted in the reference beam and immediately beforethe detector to control the depth of modulation and overallintensity level, respectively. In addition, it was found duringtesting that the AOM significantly affected the polarizationof the light passing through it, sometimes resulting in a lossof signal. Variable polarizing filters shown asP1 andP2 inFig. 1 ~Fiber Control Industries, FPC-3! were placed in boththe signal and reference beam paths. These are manuallyadjusted to maximize the output detector signal immediatelyprior to data acquisition. Finally, due to the coherence prop-erties of the diode laser, as well as other properties of thelight not fully understood at this time, the signal level wasfound to be extremely sensitive to path length differencesbetween the signal and reference beams. A precision adjust-able variable delay unit as shown~General Photonics, VDL-001! was placed in the signal beam to provide fine control ofthe path length. This is also manually adjusted prior to dataacquisition to maximize the output signal level.

III. TESTING AND VERIFICATION

After all components were assembled and the interfer-ometer was constructed, initial performance tests were con-ducted to establish its basic operating characteristics. Inter-ference fringe visibility is controlled by the beamattenuators, the variable delay unit, and the polarization fil-ters. After all electronics are turned on and allowed to warmup and stabilize, these adjustments are made manually in thatorder to maximize depth of modulation in the sinusoidal out-put signal.

It is particularly important that the variable delay beproperly set, since the mutual coherence properties of thesignal and reference beams produce distinct sharp ‘‘spikes’’in the fringe visibility. This property was measured and ispresented in Fig. 2, which shows fringe visibility plotted as afunction of path length difference. Although the peaks in thisplot are quite narrow, it is a simple procedure to adjust thevariable delay unit to maximize output depth of modulation,and the setting remains stable for over 30 min, providingadequate time for data acquisition. As can be seen from thefigure, a depth of modulation over 90% in the output isachievable with this interferometer.

Once the adjustments are made to maximize fringe vis-ibility, data can be acquired, digitized, and analyzed. A digi-tal storage oscilloscope serves as the data acquisition andstorage unit, and data are downloaded to a digital computerfor processing and analysis. Phase demodulation of the sig-nal is carried out by the method discussed previously, and theresult converted to a time-varying path-integrated electronnumber density via the multiplicative relation given in Eq.~2!. Numerous tests of this prototype fiber–optic interferom-eter have been performed to determine its performance char-acteristics.

To establish the applicability of the fiber–optic interfer-ometer in pulsed-plasma measurements, it was utilized in thesame experimental facility as that in Refs. 6 and 7. Plasmasfrom a copper-core Teflon-insulator cablegun were injected

FIG. 2. Depth of modulation of theoutput signal as a function of thechange in path length as set by thevariable delay unit.

3326 Rev. Sci. Instrum., Vol. 74, No. 7, July 2003 Smith, Keefer, and Wright

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into the probe volume and data acquired and processed todetermine path-integrated electron number density in thebeam path as a function of time. For comparison, data werealso acquired using the previously developed air–path inter-ferometer. Note that data for the fiber–optic interferometerwere obtained with 1310 nm wavelength light, whereas datafor the air–path interferometer were obtained with 633 nmHeNe laser light.

Data were acquired 25 mm and 50 mm downstream ofthe cablegun muzzle, and were digitized and processed inidentical manner. Figure 3 shows example results of thesetests. Number density versus time curves from the fiber–optic interferometer are shown in solid lines, while thosefrom the air-path interferometer are shown in dashed lines.The higher peak amplitude curves are those corresponding tothe 25 mm downstream position, while the lower amplitudecurves are those for the 50 mm position. Data from thefiber–optic interferometer were acquired from two separatefirings of the cablegun, while data from the air–path inter-ferometer were acquired simultaneously from a single firing,albeit one different than either of the two used to obtain thefiber–optic data.

Note that a time delay exists in both pairs of curves dueto the propagation time of light in the optical fibers. Whilethis time delay was calculated at 150 ns from the fiber lengthinvolved, it is not exactly reproducible due to ‘‘jitter’’ in theelectronic trigger circuitry and the effects of the large noisespike that appear at the leading edge of the pulse from theair–path interferometer. This noise spike is the result of elec-tromagnetic interference from the spark–gap switch used infiring the cablegun, and its effects are greatly reduced by useof the fiber–optic interferometer, since its detection electron-ics are more remotely located from the cablegun firing cir-cuit. Estimates of the uncertainty in timing based upon nu-merous firings of the cablegun are approximately 70 ns forthe fiber–optic interferometer, as compared with approxi-mately 150 ns for the air–path interferometer.

Even with the time delay taken into account, the curves

in Fig. 3 are not identical due to two factors:~a! the plasmaoutput from the cablegun exhibits noticeable shot-to-shotvariations7 and~b! effects of measurement noise can corruptthe demodulated phase signal. Statistical analysis of null datasets ~no plasma in the probe volume! has shown that theeffects of measurement noise the fiber-optic interferometerphase data can result in a 3s error bar of approximately60.045 rad corresponding to a number density error of61.231019 m22 at 1310 nm. The air–path interferometerphase data have been found to have a 3s error bar of ap-proximately60.027 rad corresponding to a number densityerror of61.531019 m22 at its operating wavelength of 633nm. Thus, the primary source of the discrepancy between thecurves shown in Fig. 3 is the shot-to-shot variations in thecablegun output.

With all sources of differences between the interferom-eter techniques considered, the fiber–optic interferometercan be said to produce data in close agreement with the pre-viously established air–path interferometric method, and insome aspects more accurate, owing to its lowered suscepti-bility to electromagnetic interference. The agreement of thisfiber–optic method to that of the other established technique,along with its resistance to electromagnetic interference,demonstrate that it is as good, if not a better, method forpulsed plasma diagnostics, and is more robust with respect tovibration and environmental factors.

IV. DISCUSSION

A fiber–optic Mach–Zehnder interferometer operating inheterodyne mode has been designed, constructed, and testedfor its applicability to pulsed-plasma diagnostics. Laboratorytesting of this interferometer has shown that it is quite robustwith respect to vibration and electromagnetic interference atthe plasma site and can achieve an accuracy of60.045 radcorresponding to a path-integrated electron number densityerror of 61.231019 m22 at 1310 nm. Still, some care must

FIG. 3. Path-integrated electron num-ber densities at 25 and 50 mm from aplasma cablegun as measured by thefiber–optic interferometer operating at1310 nm~solid lines! and air–path in-terferometer operating at 633 nm~dashed lines!.

3327Rev. Sci. Instrum., Vol. 74, No. 7, July 2003 Fiber-optic heterodyne interferometer

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be taken to adjust beam amplitudes, polarization filters, andthe variable delay unit in order to maximize depth of modu-lation in the output signal.

While this effort has established the proof of principleand applicability of this interferometer, it has not yet beeninstalled in a production pulsed plasma facility. Plans areunderway to install and use this interferometer or one of asimilar design in the DECADE nuclear weapons effectssimulator located at Arnold Engineering Development Cen-ter. In addition, some further investigation may yield im-provements to its operation. It is not certain that single-modefibers are required for this purpose, and so multimode fibersmay be substituted with equal or perhaps superior perfor-mance. Also, the attenuator, polarization, and delay adjust-ments could perhaps be automated or incorporated into afeedback control system to facilitate its usage in industrialenvironments. Still, in its present form, it has been proven tobe a useful diagnostic tool for plasma studies.

ACKNOWLEDGMENTS

This work was supported by the US Air Force underContract No. F40600-00-D-0001, Task 01-06, Arnold AFB,TN.

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3328 Rev. Sci. Instrum., Vol. 74, No. 7, July 2003 Smith, Keefer, and Wright

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