dc signals.1"2 Linear fiber interferometric sensors are susceptible to low-frequency environmental perturba- tions, which prevent the detection of intended ...
440
OPTICS LETTERS / Vol. 12, No. 6 / June 1987
Passive stabilization of a fiber-optic nonlinear sensor by using a sampling scheme K. P. Koo,* F. Bucholtz, and A. Dandridge Code 6570, Naval Research Laboratory, Washington, D.C. 20375-5000
Received January 23, 1987; accepted February 26, 1987 A new passive stabilization scheme using a synchronous sampling technique has been demonstrated for nonlinear fiber interferometric sensors. Passive stabilization is achieved by signal normalization derived from multiple time samples of a single output.
Recently there has been increased interest in nonlinear fiber-optic sensors for measuring low-frequency or
dc signals.1"2 Linear fiber interferometric sensors are susceptible to low-frequency environmental perturbations, which prevent the detection of intended signals at low frequencies. Nonlinear sensors permit the translation of intended signals from their basebands to the sidebands of a carrier signal at a frequency above the environmental noise band. This carrier signal must be of the same nature (e.g., a magnetic-
field carrier in magnetometers) as the field signal to be detected so that only signals of the same nature as
the carrier signal will be frequency upshifted. Then low-frequency environmental perturbations will not affect the measurement of low-frequency field signals. However, nonlinear sensors require a large carrier signal for high sensitivity. As a result, the large output signals at higher harmonics of the carrier signal frequency can overload the processing electronics and thus limit the sensitivity of the sensor. One approach toward solving this problem is to use a synchronous sampling technique.3 In Ref. 3 the fiber interferometer was actively stabilized by using a piezoelectric
transducer (PZT). Disadvantages associated with the active stabilization are the bulky PZT element and the noise resulting from resetting the PZT. Passive stabilization schemes have been reported, and they required either a special optical component 4 (3 X 3 fiber
coupler) or a PZT element.5 In this Letter we report a new passive stabilization scheme for nonlinear fiberoptic sensors. A new passive stabilization or demodulation scheme
that requires no special optical or electro-optical component (i.e., requires a 2 X 2 fiber coupler) or addition-
al system modifications is possible by using a synchronous sampling technique. This passive demodulation scheme using synchronous sampling is particularly
access to synchronous sampling of the interferometer output relative to the carrier signal. Through proper samplings at specific time allocations of the carrier signal, two outputs can be obtained:
One output is
dependent only on the environmental noise signal that is not of the same nature as the test signal, and another output is dependent on a test signal modulated by the same environmental signal. With these two signals, one can use electronic normalization to extract the test signal in spite of large noise signals. The working principle of this sampling demodulation can be explained by the following analysis using the fiber magnetometer response for illustration. Consider an interferometer output intensity
(1)
I, =Ii/2(1+ p cos4) ,
where Ii is the input intensity, p is the interferometer fringe visibility, and 0 is the phase shift in the interferometer. When the interferometer is subjected to both magnetic and nonmagnetic perturbations, the total phase is equal to the summation of all the individual phase shifts corresponding to different types of perturbation. The magnetic phase signal that is due to a magnetic field H on a magnetostrictive element is m= klCHI where k = (2r/X)n{(1
-
2
n /2[P, 2(1 -Y)
(2) -
Pn1,])is the
modified propagation constant of the light beam, Pl and P1 2 are the elasto-optic constants of the fiber core, juis Poisson's ratio of the fiber core, n is the refractive index of glass, 1 is the sensor length, and C is the
magnetostrictive constant. If the total magnetic field consists of a dc component Hdcand an ac component h cos ct at frequency c, then Om
=
C
2C) + 2klCHdch cos ct
suited for nonlinear fiber sensors for which a test sig-
nal X at a frequency co is detected by mixing it with a known carrier signal Y at a frequency
co2 so
that signal
X appears as sideband signals at frequencies (w2 ± I)oA nonlinear sensor translates the low-frequency signal at cOIto higher-frequency signals at co2 ± co1 such that electronic processing with high fidelity can be used. The presence of a fixed carrier signal provides easy 0146-9592/87/060440-03$2.00/0
+ 1/2klCh 2 cos 2cot.
(3)
Let the phase shift that is due to nonmagnetic perturbations be 00. For simplicity of analysis, assume that the frequency components
of 00 are well below c,
Now the total interferometer phase shift can be written as © 1987, Optical Society of America
June 1987 / Vol. 12, No. 6 / OPTICS LETTERS
by choosing the dither magnetic-field amplitude h =
>= (o + ems
0 = 0i + 'k2 + ¢03,
(4)
V(4N + 1)7r/(2kCl), Eq. (11) becomes 2 sin(k + 7r/4)
where
F
01 = ko+klC(HdC2 + h
= (dc components),
=
_
(kClh2 )/2.
Substituting o = q0 + I
Ii
02 + 03
into Eq. (1), one obtains
(5)
Note that 02 contains the desired signal Hdc, k1 contains the nonmagnetic signal 00, and 03 is a well-defined signal with fixed amplitude and frequency. Now, if one samples I/Ii at wmt = 0, 7r,and 7r/2independently, one obtains the sampled signals Ii
Ii
O*
(12)
The passive stabilization scheme using the sampling technique was implemented in a fiber-optic magnetometer as shown in Fig. 1. The fiber sensor configuration was a standard Mach-Zehnder fiber interferometer using magnetostrictive metallic glass as the sensing material.4 The fiber sensor length was 40 cm. The magnetostrictive element was excited by a sinusoidal drive (upper trace of Fig. 2) at 2 kHz, and the corresponding interferometer output showing a peak D1
sin(k1 + A 2 )sin A 1 ], (6)
-
for Hdc
Therefore this normalized signal F is directly proportional to the dc magnetic field Hd, (the test signal) when the fiber magnetometer is operated in the closed-magnetic-loop configurations (i.e., for Hd,
2 2
D2 MM
(ct = -r) = 1 + A2[cos(ol + A2)
2 2
X cos Al + sin(ol + A2)sin A1 ], I (wt = ir/2) = I + P [cos(0 1 - A2 )].
hi
2
(7)
(8)
2
On substracting Eq. (6) from Eq. (7), one finds that the differential output is I
4 kC1Hdch
(Wt = 0) = 2 + k2[cos(k1 + A2 ) X COSA,
-1r/4),
0).
= 2 + 2 [cos(0 1 + 0 3 ) 2 2
X COS 0 2 - sin((k1 + k3)sin 0 2 ].
-
= 2 sin (2klCHdCh)
Al = 2kClHdch,
A2
for N = 1.
F = 2 sinA,
COS2cot = (component at 2co),
03 = A 2
n
cos(l1 -7r/4) smAl
Since sin(ol + -7r/4) = cos(0
(component at co),
= Al cos wt =
02
441
(ct = 7r) -I
Ii
Ii
(wt = 0) = p sin(,01 + A 2)sin Al.
(9)
Note that the sampled output at wt = ii/2 [Eq. (8)] can be electronically offset such that (wt = 7r/2)- 1 = P [cos(q51 - A 2 )]. Ii ~2 2 Furthermore,
by dividing Eq. (9) by Eq. (10) one ob-
-
(Wt= 0)
INTERFEROMETER SAMPLING PULSES
Ii I (wt = 1
-
____
F= i
2 sin(0
MAG. DRIVE
RESPONSE
)-
Ii
DEMODULATED OUTPUT
Fig. 1. Schematic diagram showing the fiber-optic magnetometer and the signal-processing electronics for the passive sampling demodulation scheme.
(10)
tains a normalized output
19(Wt =
LD LASER DIODE FC FIBER COUPLER D1, D2 DETECTOR GI GATED INTEGRATOR MM MAGNETOSTRICTIVE SENSOR MAGNETIC COIL MC
AT cot = 0,7T/2,1T
7r/2)-
+ A2) s
cos(ol - A2)
~~2
Al.
0
(11)
If one sets A 2 = kClh2/2 = (N + 1/4)r for integer N
Fig. 2.
Tr n2
An oscillogram illustrating the setting of the sam-
pling pulses (lower trace) relative to the ac magnetic bias (upper trace) and the interferometer output (middle trace).
442
OPTICS LETTERS / Vol. 12, No. 6 / June 1987
_
ically from that at wt = or,and the differential output was electronically divided by the sampled output at wt = 7r/2. To demonstrate this passive demodulation I(n) - I(0) scheme, a simulated spurious signal at 2 Hz was introL duced on the interferometer using a PZT in addition (MAG. xf NONMAIG.A SIGNA to the desired magnetic signal at 8 Hz (note that the magnetic dither is at 2 kHz). The sampled outputs I (rr/2) x MAG. [Idli (wt =70 - 1./hI (wt = 0)] and Is/hi (wt = 7r/2) are shown in Fig. 3. It is clearly shown that [IJ/Ii(wt = -r) - I0 /Ii(t = 0)] was composed of the 8-Hz magnetic signal and the 2-Hz PZT signal, while the I/Ii(wt = 7r/ 2) contained the 2-Hz PZT signal only. With signal normalization, the normalized output F [expression (12)] contained only the 8-Hz magnetic signal, as shown in Fig. 3(b). To ensure proper normalization, the 2-kHz magnetic-dither amplitude h should be ad(MAG.SIGNAL)
~~~~~~~SGA
_=~~~~~~~~~GA-
1(n/2)
justed suchthat h = J([4N+ 1)ir/(2kCl)]. Comparing
I (n /2)
(NON-MAG.SIGNAL) (b)
Fig. 3.
Top:
sampled outputs I(7r) - I(O) and I(7r/2); bot-
tom: normalized sampled output [I(7r) - I(0)]/I(7r/2) and the sampled output I(7r/2). I(7r)- I(O) contains both magnetic and nonmagnetic signal, but [I(7r) - I(O)]/I(7r/2) con-
tains only the magnetic signal. Notation I corresponds to '0/Ii in the text.
Figs. 3(a) and 3(b), one sees that the removal of the PZT signal or the extraction of the magnetic signal has demonstrated the feasibility of achieving passive stabilization by using this sampling technique. In conclusion, the working principle of a new passive stabilization scheme particularly suited for nonlinear fiber-optic interferometric sensors has been described and demonstrated. This passive scheme utilizes a synchronous sampling technique and signal normalization derived from multiple time samples of a single
output. * Permanent address, Sachs/Freeman Associates, Landover, Maryland 20785.
phase shift, A2 of -2 7rrad was obtained (middle trace of Fig. 2). It should be pointed out that the peak phase shift of 27rrad was chosen so that the sampling
References
pulses can be shown clearly (lower trace of Fig. 2). A
1. A. D. Kersey, F. Bucholtz, and A. Dandridge, Electron.
special feature of this sampling demodulation scheme is its ability to be used in the presence of arbitrarily large 2w phase shifts. The interferometer output was sampled by using three separate gated integrators. As required by Eqs. (5)-(7), the three samples should be taken by setting the gates of the gated integrators at (1) the peak of the sinusoidal drive (wt = 0), (2) the valley of the sinusoidal drive (cot = 7r),and (3) the midpoint between the peak and the valley (ct = 7r/2). The sampled output at ct = 0 was subtracted electron-
Lett. 22, 75 (1986). 2. K. P. Koo, A. Dandridge, A. B. Tveten, and G. H. Siegel,
Jr., IEEE J. Lightwave Technol. LT-1, 524 (1983). 3. K. P. Koo, F. Bucholtz, and A. Dandridge,-Opt. Lett. 1I, 683 (1986).
4. K. P. Koo, A. B. Tveten, and A. Dandridge, Appl. Phys. Lett. 41, 616 (1982). 5. A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, IEEE
J. Quantum Electron. QE-18, 1647 (1982). 6. K. P. Koo, F. Bucholtz, and A. Dandridge, IEEE Trans. Magn. MAG-22, 141 (1986).
