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					                                                     15 March 2000




                                      Optics Communications 176 Ž2000. 105–112
                                                                                                     www.elsevier.comrlocateroptcom




  A precision fiber optic displacement sensor based on reciprocal
                           interferometry
        Fang Ruan, Yan Zhou ) , Yee Loy Lam, Suohai Mei, Chinyi Liaw, Jun Liu
    Photonics Research Group, School of Electrical and Electronic Engineering, Nanyang Technological UniÕersity, Nanyang AÕenue,
                                                     Singapore 639798, Singapore
                    Received 24 August 1999; received in revised form 21 October 1999; accepted 29 December 1999



Abstract

    A fiber optic nanometer range displacement sensor has been developed based on reciprocal interferometry, a concept
widely used in fiber optic gyroscopes. Its configuration is similar to a Michelson interferometer but with only one of the two
arms used. The principle of operation is the interference between the reflected light wave from the fiber end and that from a
reflective object. As both the reference and the sensing light waves travel through the same optical path except for the air
gap which is the distance to be sensed, the system is thus reciprocal and insensitive to perturbations introduced to the fiber
path. While the system is very simple, it has demonstrated substantially improved immunity against environmental
perturbations over the conventional Michelson interferometer. Our experimental results have shown that the interference
behavior agrees well with its mathematical model. The system has demonstrated a resolution of 5 nm. The influence of
temperature change and PZT induced phase shift to the fiber has been studied and the results have shown that the system is
indeed insensitive to these perturbations. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Fiber optic sensors; Position sensors; Displacement measurement; Optical reciprocity; Interferometry




1. Introduction                                                        w1–3x as well as integrated modes Ževen and odd.
                                                                       interferometers w4–6x have mainly been reported. A
   Position sensors with excellent performance in the                  conventional Michelson interferometer is based on
micron or sub-micron range are in high demand in                       the interference between a reference arm and a signal
many fields, such as the wafer industry. There are                     arm as shown in Fig. 1. In principle, the length of
various methods to realize the displacement mea-                       the two arms should be identical to achieve the
surement. Optical interferometry is one of the widely                  highest fringe visibility. In practice, the length differ-
used methods in this field because of its high preci-                  ence of the two arms has to be at least matched
sion, and in this respect, Michelson interferometers                   within the laser source coherence length. In the case
                                                                       when a low-coherence-length laser source Žwith a
                                                                       coherence length in the millimeter range or less, such
  )
    Corresponding author. Tel.: q65-790-6466; fax: q65-791-            as a diode laser. is used, a mismatch can lead to the
2687; e-mail: eyzhou@ntu.edu.sg                                        deterioration of the signal to noise ratio or even the

0030-4018r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 0 3 0 - 4 0 1 8 Ž 0 0 . 0 0 4 8 2 - X
106                                      F. Ruan et al.r Optics Communications 176 (2000) 105–112


                                                                        present case and a circulator replaces the coupler.
                                                                        The circulator routes the input optical wave from
                                                                        Port 1 to Port 2. The reflected interfering waves that
                                                                        are coupled back to Port 2 are routed to Port 3
                                                                        without being partially coupled back into Port 1. In
                                                                        essence, the configuration resembles a Fizeau inter-
      Fig. 1. Conventional Michelson fiber optic interferometer.        ferometer, but it is a fiber-based version with low
                                                                        finesse due to the low reflectance of the fiber–air
                                                                        interface, the low coherence length of the semicon-
disappearance of the desired signal. Another issue of                   ductor laser used, and the diverging cone nature of
great concern is the effect of external perturbations                   the emitted light beam from the fiber end. Ideally,
on the optical path length of the signal carrying                       the circulator should not couple any light wave back
optical fibers. A conventional Michelson interferom-                    to the laser cavity, to ensure the stability of the light
eter configuration is very sensitive to environmental                   source. However, in practice, there is always a tiny
perturbations, because these perturbations generate                     amount of light feedback. In order to further prevent
different deviations in the optical path length of the                  back-reflection-induced relative intensity noise
two arms. This configuration is therefore too noisy                     ŽRIN., an isolator is placed immediately after the
for practical use. The effect of external perturbations                 laser source. The air gap distance establishes the
is reduced in integrated sensor. However, integrated                    optical phase difference between the reference reflec-
modes interferometers face a number of difficulties                     tion and the sensing reflection, which in turn deter-
in fabrication, alignment and assembling. In this                       mines the power of light monitored at Port 3 of the
paper, we have adopted the concept of reciprocity,                      circulator.
which is fundamental to designing low noise inter-                         The detected optical power at the output of the
ferometric fiber optic gyroscopes, to a fiber optic                     sensor can be represented by:
position sensor ŽFOPS.. The modified Michelson
configuration ensures reciprocal interferometry. The                                     (
                                                                        Io s Ir q Is q 2 Ir Is cosDF                         Ž 1.
system configuration and its working principle, in-
cluding theoretical simulation results, are described.                  where Ir and Is are the optical powers of the refer-
Our experimental results show that the system has a                     ence light wave and sensing light wave respectively,
resolution of about 5 nm and its reciprocity makes                      and DF is the optical phase difference between
the output almost non-responsive to environmental                       these two waves. DF is proportional to the air gap
disturbances of temperature variation and others, me-                   distance x, and can be expressed by:
diated by induced phase shift.
                                                                        DF s 4 p n 0 xrl                                     Ž 2.
                                                                        where n 0 is the refractive index of the air gap and l
2. System configuration and theoretical study
                                                                        is the wavelength of the light source.
   Fig. 2 shows the configuration of the modified
Michelson interferometer. The reflected light from
the air–object interface at the far end of the air gap
is partially coupled back into the fiber Žsensing
reflection. and it interferes with the Fresnel reflec-
tion from the glass–air interface at the fiber end
Žreference reflection.. Although multiple reflection
occurs within the air gap, the effect of subsequent
reflections to the primary ones is found to be negligi-
ble. In contrast to a conventional Michelson interfer-
ometer, only one of the two arms is employed in the                                  Fig. 2. Schematic of reciprocal FOPS.
                                          F. Ruan et al.r Optics Communications 176 (2000) 105–112                                                                107

   Assuming that the laser input optical power into
the fiber is Ii , the power of the reference light Ir can
be calculated using Fresnel law, which approxi-
mately yields:

                          2
           n1 y n 0
Ir s   ž   n1 q n 0   /       Ii f 4%Ii                        Ž 3.


where n1 f 1.46 is the fiber core refractive index.
    To obtain the expression for the sensing light
wave power Is , which is a function of the air gap
distance x, the numerical aperture of the fiber, and
object reflectance etc., we consider the simplified
case in which the single mode fiber is perpendicular                     Fig. 4. Simulation result of the relationship between sensor output
                                                                         I0 r Ii and air gap distance x.
to the object surface and Is is only a function of x.
We assume that the light wave emanating from the
                                                                         the proportionality relationship between optical
fiber end can be regarded as a point source S in free
                                                                         power passing through the two spherical caps, the
space and is emitted within the acceptance cone of
                                                                         ratio of Is over Ii is thus,
angle um , as shown in Fig. 3. The reflected light
from the object is then equivalent to that from a                         Is                SA EF
                                                                             s 96% = 96%          .                    Ž 4.
point source SX , where SX is the mirror image of S                       Ii                SAG H
Žtherefore SD s DSX .. Taking the reflectance of the
                                                                         Mathematically:
object as ideally unity, the power of the reflected
light from source SX is thus 96% Ii . A spherical                        SA EF   2 p rh1   h1
                                                                               s          s .                                                                    Ž 5.
surface centered at SX can be drawn across the fiber                     SAG H   2 p rh 2  h2
end such that the radius of the sphere is r s SX E s                     Assuming that x is the air gap distance to be mea-
SX F s SX G s SX H s SXA. Let SAEF and SAGH repre-                       sured and d is the diameter of the sensing fiber core,
sent the areas of the spherical cap AEF and AGH of                       as can be seen in Fig. 3, we have:
height h1 and h 2 , respectively. Considering the 4%
loss of optical power at the air–fiber end interface                                               (
                                                                         h1 s ASX y BSX s Ž 2 x q 0.5drtan um . q Ž 0.5d .
                                                                                                                                                 2                 2

each time the light exits and re-enters the fiber, and
                                                                                                    y Ž 2 x q 0.5drtan um .                                      Ž 6.
                                                                                     X         X       X
                                                                         h 2 s AS y CS s AS Ž 1 y cos um .
                                                                                 (                                 2
                                                                               s Ž 2 x q 0.5drtan um . q Ž 0.5d . Ž 1 y cos um . .
                                                                                                                                             2


                                                                                                                                                                 Ž 7.
                                                                         Substituting Eqs. Ž2. – Ž7. into Eq. Ž1., we get:
                                                                         Io                                2 x q 0.5drtan um
                                                                          Ii               ž
                                                                               s 4% q 92% 1 y
                                                                                                   'Ž2 x q 0.5drtan u           m.
                                                                                                                                     2
                                                                                                                                         q Ž 0.5d . 2
                                                                                                                                                        /
                                                                                                                   4p n0 x
                                                                                  Ž 1 y cos um . q 0.384 cos   ž       l         /
                                                                                 =
                                                                                  (ž     1y
                                                                                                       2 x q 0.5drtan um

                                                                                               'Ž2 x q 0.5drtan u      m.
                                                                                                                            2
                                                                                                                                q Ž 0.5d . 2
                                                                                                                                                 /      Ž 1 y cos um . .



  Fig. 3. Simplified schematic diagram for the derivation of Is .
                                                                                                                                                                 Ž 8.
108                                    F. Ruan et al.r Optics Communications 176 (2000) 105–112


                                                                           light coupled back to the fiber is less when the object
                                                                           moves away.


                                                                           3. Experimental results

                                                                              In our experiment, the sensing probe was held on
                                                                           a multi-axis translation stage, a polished wafer was
                                                                           used as the object and was mounted on a nanoposi-
                                                                           tioner. The nanopositioner incorporates active error
                                                                           compensation, capacitive displacement sensor and
 Fig. 5. Measured response of the sensor as a function position.
                                                                           DAC interface, thus it can be controlled to establish
                                                                           position measurement with a resolution of 1 nm. The
                                                                           probe was aligned perpendicular to the wafer and
                                                                           separated from it with a very small air gap. The
In our case, an E-TEK pigtailed laser diode with an
                                                                           probe and the nanopositioner were mounted on a
emitting wavelength of 1.55 mm is used as the light
                                                                           baseplate and put in an environmental chamber on
source, and the single mode fiber has a numerical
                                                                           top of a vibration isolation table to isolate external
aperture of 0.1 and a diameter of 9 mm. By substitut-
                                                                           variation that can influence the stability of the dis-
ing these values into Eq. Ž8., the output signal can be
                                                                           placement set-up.
plotted as a function of x and the result is shown in
Fig. 4. It can be seen that the sensor output is a                         3.1. Sensor response
raised cosine with a period of lr2 and there is a
downward trend as the gap distance increases. This                            Our first experiment was to test the sensor re-
trend can be easily understood from the fact that the                      sponse versus position. In the experiment, the




                                                   Fig. 6. Position resolution test result.
                                      F. Ruan et al.r Optics Communications 176 (2000) 105–112                               109


                                                                     fixed, although the fluctuation is within the step size.
                                                                     Thus, the estimated position resolution of our sensor
                                                                     is about 5 nm.

                                                                     3.3. Sensor stability

                                                                         An experiment on our sensor’s long-term stability
                                                                     was also conducted when the wafer was fixed. In this
                                                                     experiment, both the output of the sensor and tem-
                                                                     perature inside the sensor-containing chamber were
                                                                     monitored as a function of time, and data were
                                                                     collected at a sampling rate of 1 datars for 24 h. The
             Fig. 7. Sensor stability test result.                   result is shown in Fig. 7. It can be seen that the
                                                                     sensor output drifts with time, the drift is strongly
nanopositioner was operated in close loop Žwith ac-                  correlated with the chamber temperature and it is
tive error compensation. and was controlled to move                  recoverable when the temperature recovers. This can
at a step of 5 nm within a full moving range of 20                   be explained by the fact that the air gap was estab-
mm. The position signal of the wafer together with                   lished with mechanical fixtures which expandrcon-
the sensor output was recorded at each step. The                     tract in dimension when the temperature changes.
results were plotted in Fig. 5, where the x axis is the              The output change of our sensor is thus to a certain
position of the wafer in mm, and the y axis is the                   extent the response to the displacement change in-
sensor output in volts. By comparing Fig. 5 with the                 duced by temperature.
theoretical results within the same position change as
shown in Fig. 4, it can be seen that they show the                   3.4. Sensor immunity to external perturbation ap-
same behaviour. The envelopes of the oscillating                     plied to the fiber
curve in both cases show a downward trend as the
                                                                         As has been described above, our sensor is theo-
displacement increases and the numbers of peaks in
                                                                     retically immune to external disturbances introduced
these two figures are the same. Thus our experimen-
                                                                     to the fiber by design. To verify this, further experi-
tal results show good agreement with the theoretical
                                                                     ments were conducted to investigate the sensor out-
model. The difference in their initial sensor output
                                                                     put behavior under externally induced length change
amplitude is due to the fact that the fiber–wafer gap
                                                                     to the fiber caused by both PZT stretching and
distance cannot be precisely set at absolutely zero
                                                                     temperature change.
during the experiment and hence would be of a tiny
but arbitrary amount.
                                                                     3.4.1. Phase shift induced by a PZT fiber stretcher
                                                                        A PZT fiber stretcher tightly wound with 20 m
3.2. Sensor position resolution test
                                                                     fiber was added to the optical path as shown in Fig.
   In order to investigate the position resolution of                8. By varying the drive voltage to the PZT, the
the sensor, the sensor was operated at one of its most
sensitive bias points. A computer program was used
to control the nanopositioner to generate a ‘ladder’
shape movement with a step size of 5 nm. The
nanopositioner was kept stationary for 5 s after each
step, while the output of the sensor and the nanoposi-
tioner monitor were sampled every second. The posi-
tion signal of the wafer and the sensor output are
plotted in Fig. 6. It can be seen that the data from the             Fig. 8. Configuration of sensor immunity test under external
sensor output fluctuates when the nanopositioner is                  perturbation induced phase shift.
110                                 F. Ruan et al.r Optics Communications 176 (2000) 105–112

sensor’s immunity to this phase shift induced by the
fiber stretcher could be studied.
    Calibration of the PZT induced phase shift was
first carried out using a Mach–Zehnder interferome-
ter as shown in Fig. 9. The PZT fiber stretcher was
inserted in one arm, and a fiber coupled acousto-optic
modulator ŽAOM. together with a fiber coil of the
same length as in the PZT stretcher was used in the
other arm to enable a heterodyne detection. A polar-
izer and a depolarizer were inserted to improve the
signal-to-noise ratio and reduce polarization-fading
effect. The length of the two arms was matched
within the coherence length and the interference-                       Fig. 10. PZT stretcher phase response versus its voltage.
beating signal was generated. The PZT drive voltage
change causes an optical phase shift and thus results              voltage changed from 0 to 10 V, corresponding to a
in the phase change of the interference-beating sig-               phase shift from 0 to 3p Žusing the coefficient 0.9
nal. A modulation analyzer was used to demodulate                  radrV obtained in Fig. 10., the sensor output re-
the phase change.                                                  mained fairly stable. Note that the sensor output
    Owing to the fact that the modulation analyzer                 noise has been enlarged and in fact output variation
can only demodulate an ac phase signal, a 2 kHz sine               is about "25 mV which is within the noise level as
wave signal was applied to the PZT. The output of                  indicated in Fig. 6.
the modulation analyzer was recorded while the am-
plitude of PZT drive voltage was increased from 0 to               3.4.2. Phase shift induced by temperature change
20 V in steps of 0.5 V. The results are plotted in Fig.               In order to investigate the sensor’s immunity to
10, where the x axis is the amplitude of the PZT                   temperature variation applied to the common optical
drive voltage and the y axis is the modulation ana-                path, the 0.6-m length of the sensing fiber was coiled
lyzer output. It shows that the PZT phase response is              and heated by a 50 W-power resistor. A thermistor
linear with respect to its voltage with a coefficient of           was placed near the fiber to monitor its temperature.
0.9 radrV.                                                         The sensor output together with the thermistor’s
    To assess the immunity of the position sensor, the             reading were collected at a sampling rate of 1 datars
PZT fiber stretcher was then added to the sensor as                when the temperature of the sensing fiber was in-
shown in Fig. 8. A 20 mHz sawtooth signal was                      creased from room temperature to 808C. As can be
applied to the PZT, its amplitude together with the
output of the sensor were recorded. The results are
shown in Fig. 11. It can be seen that when the PZT




Fig. 9. Mach–Zehnder based PZT phaservoltage coefficient mea-
surement set-up.                                                        Fig. 11. Sensor behavior under PZT induced phase shift.
                                  F. Ruan et al.r Optics Communications 176 (2000) 105–112                                    111




                                Fig. 12. Sensor behavior under temperature induced phase shift.




seen in Fig. 12, there is only a tiny dependence of                should be possible if the noise from the laser and the
the average sensor output on the change of tempera-                electronic circuit can be further reduced.
ture. The sensor’s output variation is about 50 mV,
which is only slightly above its noise level. It should
be noted that under such an amount of temperature                  4. Conclusion
change, the expansion of the fiber would be 16.5 mm
Žassuming a thermal-expansion coefficient of 5 =                      A precision position sensor based on reciprocal
10y7 r8C w7x. and this would result in a change of                 optical interferometry with a resolution of 5 nm has
the optical phase in the order of about 20p rad. The               been demonstrated. The experimental results agree
same amount of temperature change, if applied only                 well with the mathematical model. The most attrac-
to the sensing arm of a conventional Michelson                     tive advantage of the system is its excellent immu-
interferometer, would cause a measurement error of                 nity to environment perturbations due to its recipro-
about 8 mm.                                                        cal nature. In addition, the very simple configuration
                                                                   of the system makes it very compact.
3.5. Sensor noise

   Finally, we would like to mention that the noise                References
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