an analysis of a fiber-optic magnetometer with magnetic feedback

1680 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. LT-5, NO. 12, DECEMBER 1987

An Analysis of a Fiber-optic Magnetometer with Magnetic Feedback

U

K. P. KOO, A. DANDRIDGE, F. BUCHOLTZ, AND A. B. TVETEN

Abstract-The magnetic feedback nulling technique in a fiber-optic magnetometer is analyzed both theoretically and experimentally. Re- sults indicate that high nulling efficiency requires large closed loop gain, and large signal-to-noise ratio requires system bandwidth no larger than the signal bandwidth. Large linear dynamic range, freedom from magnetic hysteresis, and long term stability are achievable.

I. INTRODUCTION

S ENSING of magnetic fields using a fiber-optic interferometer has been demonstrated [1]-[4] using mag-

netostrictive metallic glass. In particular, a magnetic feedback scheme has been employed [5], [6], [SI, [9] in these fiber magnetometers to improve their performance. Improvements include an increase in the linear dynamic range, high suppression of magnetic hysteresis associated with the magnetic material, and improved long-term stability. This paper presents an analysis of the fiber-optic magnetometer with magnetic feedback nulling and dis- cusses some of the important operating parameters. Also, experimental results are presented to illustrate the key features of this technique.

11. SYSTEM CONFIGURATION A schematic of a typical fiber-optic magnetometer is

shown in Fig. 1. This system consists of a standard fiber interferometer plus the driving electronics to the magnetic coil for ac and feedback biasing. The purpose of the ac bias is to provide a high-frequency carrier for the low- frequency magnetic test signal through the quadratic magnetostrictive response of the metallic-glass sensing element. The output of the phase sensitive detector, which is proportional to the low frequency magnetic test signal, is used as a feedback to a magnetic coil to nullify the effect of the magnetic test signal on the transducer. The Mach-Zehnder interferometer is made up of a 2 X 2 fiber coupler as splitter and a 3 X 3 fiber coupler as combiner for passive stabilization of the fiber interferometer. The magnetic field sensing element is a strip of metallic glass (5-cm-long 1.2-cm-wide 25-pm-thick) bonded onto a single-mode fiber. The three interferometer outputs are

Manuscript received June 10, 1986; revised January 29, 1987. K. P. Koo was with the Naval Research Laboratory, Washington, DC

20375-5000. He is now with Sachs Freeman Associates, Landover, MD 20785.

A . Dandridge, F. Buckholtz, and A. B. Tveten are with the Naval Re- search Laboratory, Washington, DC 20375-5000.

IEEE Log Number 8714992.

a D3

Fig. 1. A schematic of the experimental arrangement of a fiber-optic magnetometer with low frequency magnetic feedback. LD-Laser diode, FC-fiber coupler, NM-magnetostrictive material (e.g., metallic glass), D l , 2, 3-p-i-n diode detectors, SPE-signal processing electronics, LIA-lock-in amplifier.

detected by three p-i-n diodes and then electronically processed to stabilize and linearize the output signal [7]. The processed signal is followed by a phase sensitive detection (PSD) locked to the ac magnetic signal at an ac bias frequency w0/27r = 820 Hz. The frequency chosen cor- responds to a region of flat frequency responses of the ribbon for stability, rather than at a resonance. The PSD output is amplified, integrated, and fed back to the bias magnetic coil. The external test magnetic signal is simulated by a second magnetic coil collinear with the bias magnetic coil. For ease of display, the simulated external magnetic signal is either a slow triangular signal at w,/2a = 0.02 Hz or a step signal. The output signal is taken from the amplified PSD output and is proportional to the external magnetic field. To understand how this feedback system works, consider the following analysis.

111. SYSTEM ANALYSIS

The entire fiber magnetometer with the magnetic feedback nulling can be represented by a signal flow diagram as depicted in Fig. 2. Here, signal A represents the ac magnetic bias (dither) signal at frequency wo, X is the low frequency external test magnetic signal at us, B is the feedback signal, Y is the processed interferometer output and 6 is the magnetic error signal which serves as input to the sensing element represented by a dimensional response function Y = kVLC [ e l 2 . A derivation of the quadratic magnetostrictive response of an amorphous magnetic material is given in [4]. From the signal flow chart, one

0733-8724/87/1200-1680$01.00 @ 1987 IEEE

KO0 et a/.: FIBER-OPTIC MAGNETOMETER WITH MAGNETIC FEEDBACK 1681

refercncc

output

LIA

Fig. 2. A system signal flow block diagram for the magnetic signal. The feedback loop for interferometer stabilization is not included. Magne- tostrictive response is represented by Y = kLC(e)’ . Phase sensitive detection is represented by the combination of a mixer and a low-pass filter. F is electronic gain, M is oersted per volt conversion factor, Vis radian per volt conversion factor.

can generate the following coupled equations:

~ ( w ) = A ( @ ) + X ( w ) + B ( w ) ( l a )

y ( t > = k l . ‘ ~ ~ [ e ( t ) l ’ (1b)

( 1 4 - K [ X ( 4 + B ( 4 1

B ( w ) = 1 + iwr

Here, (la) and (IC) are in the frequency domain while (lb) is in. the time domain because y ( t ) is a nonlinear response to x( t ) and, as such, does not have a general transfer function. Variables in lower case represent time domain functions while corresponding variables in upper case represent Laplace transforms of the time functions. Equation (IC) will be derived later. The symbol represen- tations are

K k

C H I A I 7

w F V

M

2 kFVMLC 1 A I = closed loop gain, propagation constant of the lightwave in the fiber

magnetostrictive constant, total magnetic field at the sensor, amplitude of the ac magnetic dither field, time constant of the lock-in amplifier, the operating frequency input to the filter, electronic feedback gain, radians per volt conversion factor of the optical

oersteds per volt conversion factor of the feed-

core,

receiver,

back magnetic coil.

The feedback network is represented by the state variables E , Y, D , and B in response to inputs X and A . To obtain the ouptut signal B, we expand the magnetostrictive response function y ( t ) as

y ( t > = ~ ~ c ~ ~ [ e ( t ) l ~

= VkLC[a(t) + x ( t ) + b(t)]’

= KkLC[a2(t) + X 2 ( t ) + b2(t)

+ 2 a ( t ) x ( t ) + 2 a ( t ) ’ b ( t )

+ 2.44 b ( t ) ] . (2)

Note that E ( w ) is the Laplace transform of e ( t ) and signal A is the ac magnetic bias field at wo chosen to be

large compared to the frequency w, of the external test magnetic field (i.e., wo >> w,). The PSD extracts only the signal component amplitude at frequency wo (i.e., the underlined terms 2kVLCu( t ) x ( t ) and 2kVLCa( t ) b( t ) in (2) ) and then multiplies it with a low-pass filter transfer function 1 /( 1 + ~ w T ) , where r is the time constant of the single-pole low-pass filter. Solving (la)-(lc) for B , one obtains

-K/( l + K ) B ( w ) = X ( 4

1 + iw[r / ( l + K ) ]

X W 2 for K << 1

and substituting this result back to (la) and (lb), one obtains

E ( W ) = A ( w )

1 + i o [ T / ( 1 + K ) ] - K/(1 + K ) +

1 + iW[T/(l + K ) ]

/ A ( w ) + X ( w ) ; for K << 1

1 for K >> 1

= \ or

for - 1 S K

<< 1, and K >> 1. (4 ) UT

It can be seen from (3) that for sufficiently high feedback gain, the signal B approaches that of the external field X with an effective ti,me constant of r/( 1 + K ). Therefore, the bandwidth of the closed loop system is de- termined by the effective time constant and not by PSD time constant alone. The above analysis will be used to explain the key features of a fiber magnetometer using the magnetic nulling technique.

IV. EXPERIMENT To illustrate the key features of this magnetic nulling

technique and its relation to the analysis, the following experiments were performed.

1) Tracking efficiency and system response time were measured as a function of closed loop gain K . Consider the response of the feedback signal B ( t ) to a step input X ( t ) = X , for t > 0. The response B ( w ) in the frequency domain is

B ( w ) = K/(1 + K ) X0 { 1 + iw[r/(1 + K ) ] }

1682 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. LT-5, NO. 12, DECEMBER 1987

Taking the inverse Laplace transform we obtain the time response

Now, one can define the “tracking efficiency” as a mea- sure of how closely B ( t ) approaches the input X ( t ) in the steady state ( t >> 7 / ( 1 + K ) . According to (6) the tracking efficiency is simply K / ( 1 + K ). By measuring the response B ( t ) as a function of K , one can determine the tracking efficiency and the response time of the system as a function of the closed loop gain K. In our system, I/ = 1 V/rad and M = 0.04 Oe/V, C = 2 X 10-6/0e2, k = 0.8 X lo7 rad/m, L = 0.1 m and IA I = 0.25 Oe. With the PSD time constant set at 0.3 s, a magnetic step signal X of 2 mOe for a duration of 30 s was applied to the sensor. The response amplitude and the response time of the feedback signal were measured as a function of the feedback gain K . Response time was taken as the time required to reach 90 percent of the final value of X . This response time is equal to 2.37 of a first-order filter with time constant T. A typical oscilloscope trace of system response to a step magnetic field of 13 y ( 1.3 X loF4 Oe) is shown in Fig. 3. The tracking ability of the feedback signal B to the input X and its response time depend on the system gain K as predicted in (6). This was verified from our results shown in Fig. 4. For the tracking efficiency as a function of system gain K, the agreement between experimental results (crosses in Fig. 4) with theory (solid line in Fig. 4) was quite good. The experimentally measured system response time (circles in Fig. 4) slightly disagrees with the values predicted by the model at the high gain region K > 10. The reason for this is probably due to our first-order approximation of the frequency response of the closed loop system. However, the experimental data did illustrate the relation between the system gain and the amplitude and time responses. For maximum tracking ability and fast response time, high system gain was required. In our case, faithful tracking (i.e., B = X in (3)) occurs at a system gain approaching K = 10. To increase the signal to noise ratio, one can increase the PSD time constant r at the expense of a longer response time while maintaining K fixed, which is equivalent to reducing the bandwidth of the system.

2) The removal of the effects of magnetic hysteresis and the suppression of irregular magnetostrictive response of the sensor sample was examined by choosing a “bad” transducer which exhibited large magnetic hysteresis and field dependent irregularities as shown in Fig. 5 . Here, the PSD output with no magnetic feedback was recorded as an external “sawtooth” magnetic field X was applied. With magnetic feedback, the feedback signal was used as the output. In the case whewthe feedback gain K was small ( K << 1 ), the magnetic sample would experience a magnetic field perturbation E = X + A as indicated by (4). Therefore, the feedback signal would follow the magnetic response characteristics including hysteresis and irregular

Fig. 3 . An oscilloscope trace of the feedback signal B / M for 7 = 30 s, K = 5, ( A I = 185 mOe, input X = 13y.

x x 0.3

1 0 . 2 4

0.1 1 10 100 lo00

CLOSED LOOP GAIN. K = 2kFMVLC I A 1 Fig. 4. Plots of the experimental data for the tracking efficiency (symbol

“x”) and the system response time (symbol “0”) of signal B as a function of closed loop gain K . The solid curves are theoretical predictions from (6).

NO FEEDBACK

Fig. 5 , An X- Y plot of fiber-optic magnetometer response ( Y-axis or ver- tical axis) to a slow “sawtooth” magnetic field X (X-axis or horizontal axis) with no magnetic feedback.

field dependent response of the magnetic sample-a sup- pressed version of the response with no feedback. How- ever, as K increased, tracking efficiency improved result- ing in less hysteresis and fewer irregularities. This trend of improvement is illustrated in Fig. 6. The linear response of the feedback signal B with respect to the applied field X when K > 10 indicated the usefulness of this magnetic feedback nulling technique in eliminating magnetic hysteresis and irregularities. In fact, the feedback signal

KO0 et al.: FIBER-OPTIC MAGNETOMETER WITH MAGNETIC FEEDBACK

WITH FEEDBACK

- -1 0 1

. . x ( W

Fig. 6. A set of X-Y plots of the fiber-optic magnetometer response to a slow “sawtooth” magnetic field for magnetic feedback gains G < 5 and G = 5 , 10 and 20.

B followed the input signal X as predicted by (3) when K >> 1.

3) The linear dynamic range of a sensor element that has a quadratic field dependence response is normally limited to the field region where the quadratic properties hold. For metallic glass materials of the shape and type (Metglas 2605 S2) that were used here, the linear region is limited to magnetic field amplitudes less than 1 Oe (i.e. , I Hdc I < 1 Oe). However, by using the feedback scheme, low frequency magnetic fields at the sample are nulled. Hence, the linear dynamic range will be unlimited theoretically but in practice will be limited to the nulling magnetic field that can be generated by the feedback magnetic coil driven by conventional electronics. In our experimental system, the dynamic range is about lo6 limited by the electronics. This translates to a measurable magnetic field from 0.5 X Oe to - 5 Oe.

4) Factors that can affect the stability of the fiber optic magnetometer are shown in (5). With no magnetic feedback (i.e., for K << l ) , the fiber magnetometer output is Y = kVLCA2 + kVLCX2 + 2kVLCAX. It can be seen that any time-dependent changes in C, L , and A in addi- tion to drift of the interferometer scale factor V will lead to long term drift in the output open-loop Y. Hysteresis in the magnetostrictive response of the Metglas will cause C to change depending on the magnetic history of the metallic glass. Small fluctuations in the dither magnetic field amplitude will cause A to change. Thermal strain will cause L to change. With magnetic feedback ‘and sufficiently large closed loop gain ( K >> 1 ) as shown in (3), the feedback signal B has a steady-state response equal to the external magnetic field X .

V. LONG TERM STABILITY

Another important factor in determining the stability of the overall system is the stability of the interferometer/ demodulator combination. Many methods have been de- veloped to demodulate the interferometric output and, in this work, both active and passive homodyne techniques were employed. The purpose of the demodulator is to lin- early convert the optical phase shift into a voltage. The

1683

initial test used the passive homodyne technique. A 3 X 3 coupler was used to generate two signals phase shifted by 90” and these two signah were processed by a differ- entiate cross multiply circuit. This technique provides a linear phase detection capability between - 10 rad and 1 prad at typical frequencies. For short term measurements ( < 1 h), similar to those made in Fig. 3-6, the demodulator scale factor V (voltdradian) using this techniques was stable to within - 5 percent. However for the long term measurements necessary to characterize the magnetometer, factors including the laser power output, laser coupling to the input of the interferometer, and loss of fringe visibility due to laser coherence and changes in the polarization mixing efficiency, lead to variations of the scale factor V of greater than 5 percent over a 2-h time period. Although the scale factor could be stabilized using an AGC and a pilot tone applied to the interferometer, it was decided to implement a closed loop active homodyne demodulation approach. In this approach, a feedback voltage, proportional to the optical phase difference in the interferometer is applied to a PZT around which a length of fiber in the reference arm is wrapped. Similar to the magnetic feedback approach, the correction voltage applied to the PZT locks (in this case) the interferometer to the quadrature point, the gain in the feedback loop is then maximized. Now the optical phase shift is measured by monitoring the feedback voltage applied to the PZT. Variations in laser ouput, coupling, and interferometer fringe visibility now appear only as variations of the gain bandwidth product of the system rather than variations in the scale factor of the demodulator.

The scale factor of the interferometer was monitored continuously for 26 h (a portion of the run is shown in Fig. 7), the deviation of a 10-mrad test signal was less than 1 percent. Measurement over a five-day period con- firmed this stability. However, measurements of the magnetometer (34.2-mOe rms dither field at 850 Hz) in the open loop configuration showed variations of up to 5 percent in a 12-h period corresponding to drifts of approxi- mately 300 nT. To demonstrate the performance of the closed loop configuration, the magnetometer was run for 13 h (with a 150-nT calibration step), and the results are shown in Fig. 8. The magnetometer long term stability was < 10 nT over 13 h, an improvement of a factor of 30 over the open loop configuration.

VI. CONCLUSION

The magnetic nulling technique in a fiber-optic magnetometer was analyzed using a simple system model. Ex- perimental results were presented to illustrate key attrac- tive features of the nulling technique. Sufficiently large feedback gain should always be used to ensure that the output signal B follows input X (high tracking efficiency). Longer system response time can be traded off for higher signal to noise ratio by increasing the time constant in the phase sensitive detector (i.e., narrower bandwidth). Large linear dynamic range and freedom from magnetic hyster-

1684 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. LT-5. NO. 12, DECEMBER 1987

INTERFEROMETER IPZT) SIGNAL

I

10 mrad

MAGNETIC SIGNAL

~ PZT 1% IA l /v’2 = 34.2 mOe

X = 75.6 mOe

ZERO

x = 75 rnOe

I

Fig. 7. Long term magnetometer stability in the open loop configuration. Stability of fiber-optic interferometer itself was ( < 1 percent) over a period of 12 h (upper trace) compared with the 5-percent drift in the output of the open loop magnetometer.

X = 150 nT Drift c 10 nT

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3

TIME Ihr l

Fig. 8. Long-term magnetometer itability in the closed magnetic loop configuration. Drift was less than 10 nT over a period of 13 h. A calibration step of 150 nT was applied.

esis were possible. An improvement of a factor of 30 in the long term response stability was obtained using the magnetic nulling.

REFERENCES [I] A. Dandridge. A. B. Tveten, G. H. Sigel, Jr., E. J. West, and T . G.

Giallorenzi, “Optical fiber magnetic field sensors,” Electron. Le?[. , vol. 16, pp. 408-409, 1980.

[2] K. P. Koo and G. H. Siegel, Jr., “Characteristics of fiber-optic magnetic-field sensors employing metallic glasses,” Opt. Lett., vol. 7 , pp.

[3] K. P. Koo, A. Dandridge, A. B. Tveten, and G. H. Sigel, Jr., “Fiber- optic dc magnetometer,” J . Lightwave Technol., vol. LT-1, no. 3, pp.

[4] J. E. Livingston, “Magnetomechanical properties of amorphous metals,” Phys. Stat. Sol., vol. 70, pp, 591-596, 1982.

[5] K. P. KOo, G. H. Sigel, Jr., A. B. Tveten, and A. Dandridge, United States Statutory Invention Registration, no. H94, July I , 1986.

[6] A. D. Kersey, M. Corke, and D. A. Jackson, “Single-mode fiber-optic magnetometer with dc bias field stability,” J . Lightwave Technol., vol. 3 , p. 836, 1985.

171 K. P . Koo, A. B. Tveten, and A. Dandridge, “Passive stabilization scheme for fiber interferometer using ( 3 X 3 ) fiber directional couplers,” Appl. Phys. Let?., vol. 41, pp. 616-618, 1982.

334-336, 1982.

524-525, 1983.

[8] C. J. Neilsen, “All fiber magnetometer with magnetic feedback com- pensation,” presented at SPIE Conf. Fiber-optic and Laser Sensors, San Diego, CA, Sept. 18-23, 1985.

[9] K. P. Koo, F. Bucholtz, and A. B. Tveten, “Stability of a fiber-optic magnetometer,” IEEE Trans. Magnet., vol. 22, p. 141, May 1986.

K. P. Koo (S’71-”77) was born on March 30, 1949. He received the B.S. degree in electrical engineering from the University of Illinois, Chi- cago, in 1972. and the M.S. and Ph.D degrees in electrical engineering and applied physics from Case Western Reserve University, Cleveland, OH, in 1975 and 1977, respectively.

At Case Western Reserve University, he worked on waveguide C 0 2 lasers, laser Stark spectroscopies, and Stark-tuned optically pumped far-infrared lasers. From 1977 to 1978 he was with

theBrookhaven National Laboratory where he worked on laser atmospheric pollutant monitoring systems using Raman and optoacoustic techniques. From 1978 to 1980 he was affiliated with John Carroll University conducting research on various aspects of optical-fiber sensors. In 1980 he joined the Naval Research Laboratory in Washington, DC. He is now with Sachs Freeman Associates, Landover, MD. His current research interests include fiber couplers and passive and active stabilization schemes for fiber interferometric sensors, particularly in the magnetic-field area.

Anthony Dandridge was born in Kent, England on November 11, 1951. He received the B.S. and Ph.D. degrees in physics from the Sir John Cass School of Science and Technology, City of London Polytechnic, England.

His postgraduate and postdoctoral research work included flow bire- fringence, viscometric, and light-scanning studies of short-chain polymers. In 1979, he was a Lecturer in Physics at the University of Kent, Canter- bury, England. Since 1980, he has been associated with Georgetown Uni- versity, Washington, DC, John Carrol University, Cleveland, OH, and the Naval Research Laboratoy, Washington, DC. His research work covers fiber-optic sensor systems as well as the noise and spectral characteristics of semiconductor lasers. He has authored and coauthored over 50 journal and conference publications.

Dr. Dandridge is a Fellow of the Royal Astronomical Society.

KO0 et al.: FIBER-OPTIC MAGNETOMETER WITH MAGNETIC FEEDBACK 1685

Frank Bucholtz was born in Detroit, MI, on April 14, 1953. He received the B.S . degree in physics from Wayne State University, Detroit, MI, in 1975, and the Ph.D. degree in physics from Brown University, Providence, R1, in 1981. His postgraduate work included structural studies of magnetic and fast ionic conducting borate glasses using nuclear magnetic resonance.

From 1981 to 1983 he was an NRC Postdoc- toral Research Associate at the Naval Research Laboratorv. Washington. DC. where he con-

Alan B. Tveten was born in Wolf' Point, MT, on January 24, 1934. He received the B .A. degree from Concordia College, Moorhead, MN, the M.A. degree from the University of Nebraska, Lincoln, and the Ph.D. degree from Colorado State University, Fort Collins.

Before joining the Naval Research Laboratory, Washington, DC, in 1979, he worked as a Physics teacher at Dana College, Mankato State Univer- sity, Mankato, MN, and Colorado State Univer- sity. He has done research in secondary electron ., - .

ducted research in the area of ferromagnetic devices for microwave signal emission in metals, magnetic susceptibility of rare earth oxides, and remote processing. Since 1983 he has been a member of the Optical Sciences Di- sensing using light scattering from aerosols. Since 1979, he has been work- vision at Naval Research Laboratory. His current research interests include ing with the fiber-optic sensor and the optical information-processing groups fiber-optic sensors and the magnetic properties of materials. at -the Naval .Research Laboratory, Washington, DC.

an analysis of a fiber-optic magnetometer with magnetic feedback

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