JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 4, APRIL 1992
`
`503
`
`Common Path Heterodyne Optical Fiber Sensors
`
`Toshihiko Yoshino, Takaharu Hashimoto, Makoto Nara, and Kiyoshi Kurosawa
`
`Abstract- The common path type of differential heterodyne
`fiber-optic sensing scheme has been developed which uses a
`polarization maintaining fiber as either a sensor or an optical
`lead and a dual-frequency dual-polarization laser beam. The
`sensing schemes are applied to the measurements of temperature,
`strain, force, pressure, rotation rate (gyro), magnetic and electric
`fields, and thin film thickness. The sensing scheme and main
`performances for each measurand are described. High precision
`and high stability as well as good linearity for each measurand
`are demonstrated.
`
`I. INTRODUCTION
`
`By means of optical fiber sensors many physical and
`
`chemical quantities can be measured in a flexible and
`remote manner without undergoing electromagnetic induction
`noises. However, at the present stage of fiber-optic sensing
`technology, high stability and reliability are the most required
`features for practicing fiber sensors. In order to fulfill such
`requirements, the present authors have developed the common
`path type of heterodyne optical fiber sensing in which het(cid:173)
`erodyning two laser beams take a common path in the entire
`sensing system since 1981. The sensing system can measure
`various quantities with good linearity and high stability against
`environmental temperature and pressure variations.
`The key devices for the developed fiber sensors are a dual(cid:173)
`frequency dual-polarization laser beam and a polarization(cid:173)
`maintaining fiber, which are used for a sensor element or an
`optical lead. The combination of the two devices produces
`a stable and precise fiber sensing scheme especially suited
`for polarization based fiber sensors. The developed fiber sen(cid:173)
`sors make it possible to measure various quantities such as
`temperature, strain, force, pressure, rotation rate (gyroscope),
`magnetic and electric fields, displacement, and film thickness.
`The purpose of this paper is to give the detailed descriptions
`of our previous studies on the in-line heterodyne fiber sensors,
`partially reported in the several conferences [1]-[7]. The
`sensing schemes and main performances of the developed
`fiber sensors are described classifying the use of polarization
`maintaining fiber (PMF) into a sensor element and an optical
`lead.
`
`Manuscript received October 31, 1990. This work was partially supported
`by Grant-in-Aid for Special Project Research for Lightwave Sensing from the
`Ministry of Education, Science, and Culture of Japan.
`T. Yoshino is with the Department of Electronic Engineering, Faculty of
`Engineering, Gunma University, Tenjincho, 1-5-1, Kiryu, Gunma, Japan.
`T. Hashimoto is with Tokyo Sokki Kenkyujo Co., Ltd., Aioicho, 4-247,
`Kiryu, Gunma, Japan.
`M. Nara is with Nikon, Nagaodai-machi 4-7-1, Totsuka-ku, Yokohama,
`Japan.
`K. Kurosawa is with the Tokyo Electric Power Inc., Nishi-tutujigaoka 2-4-1,
`Chohu, Tokyo, Japan.
`IEEE Log Number 9106098.
`
`l. Polarizer
`
`Fig. 1. Optical arrangement of heterodyne fiber-optic sensor using polariza(cid:173)
`tion maintaining fiber as sensor element.
`
`II. USE OF PMF AS SENSOR ELEMENT
`The retardation of highly birefringent single-mode fiber, i.e.,
`polarization maintaining fiber (PMF), depends on temperature
`and mechanical forces so that it can be used for temperature
`(e.g., [8]) or mechanical force measurement. Here we present
`a new sensing scheme to achieve high precision for the
`retardation measurement.
`A laser beam consisting of two frequency components with
`orthogonal linear polarization is launched into a PMF with the
`coincidence of polarization axes between the laser and PMF,
`as shown in Fig. 1. The output beam from PMF is passed
`through a polarizer oriented at 45° to the fiber polarization
`axes, II and ..l, and detected by a photomultiplier. Letting the
`propagation constants of the orthogonal polarization modes of
`the fiber be ,B11 and ,81- and the laser frequencies be Ji and h,
`the photoelectric signal is given by
`I= IA11 expi(27rfit - /311L) + A11 expi(27rf2t- B1-L)l 2
`(1)
`
`where L is the fiber length and A11 and A1- are real constants.
`Equation (1) represents a beat signal
`I= ATI + A3._ + 2A11A1- cos{ 27r(f1 - h)t -
`
`(/311 - /31-)L}
`(2)
`
`which can be rewritten as
`
`I= A+ Bcos(27rb..ft - r),
`(b..f =Ji - h; A, B real numbers)
`
`where
`
`r = (/311 - ,81-)L
`
`(3)
`
`(4)
`
`is the retardation of PMF, depending on temperature and
`applied force besides the initial retardation.
`
`0733-8724/92$03.00 © 1992 IEEE
`
`HALLIBURTON, Exh. 1007, p. 0001
`
`

`

`504
`
`JOURNAL OF LIGHTWAVE TECHNOLOGY. VOL. IO. NO. 4. APRIL 1992
`
`The PMF used in this paper is Hitachi Cable's one having
`a beat length of 2.5 mm at 20°C and ,\ = G33 nm.
`The light source used is a home-made frequency stabilized
`transverse Zeeman He-Ne laser operated at ,\ = G33 nm
`(STZL). The laser emits orthogonally linearly polarized two
`modes having a frequency separation from 300 to 400 kHz,
`stabilized within about 1 kHz; the frequency stabilization was
`achieved by the negative feedback of the beat frequency of the
`two modes to the cavity length by means of a cooling fan [9].
`
`A. Temperature
`
`Fig. 2(a) shows the temperature sensing system. In order to
`locate the sensing part at a specified section of the fiber and to
`eliminate the effect of the surrounding temperature variations,
`a differential detection scheme using two PMF's is employed.
`Both a signal fiber and a reference fiber are aligned close to
`each other except the sensing part, where the sensing fiber was
`made longer than the reference one by different lengths L of
`0-4 m; the entire length of the sensing fiber was 10 m. The
`sensing part was inserted in a water bath, heated by a nichrome
`heater inserted in the water. Fig. 2( b) shows the typical beat
`signals (300 kHz) of the sensing and reference fibers. The
`phase difference between the two beat signals is detected by a
`phasemeter. Fig. 2(c) shows the change in phasemeter output
`measured as a function of the change in water temperature
`monitored with a mercury thermometer. In the experiment
`the water bath was heated and natural-cooled many times.
`Somewhat data variations observed in Fig. 2(c) are most
`probably due to the temperature inhomogeneity within the
`bath. The temperature dependence of fiber retardation is given,
`from the average slope of Fig. 2(c), as
`
`(5)
`
`The temperature resolution ~T is proportional to the sens(cid:173)
`ing fiber length L and limited by the fluctuation of the
`phasemeter output, ~r, which was about 0.1°. From (5),
`~T is 0.1° /(114°C- 1rn- 1 L) = 0.009°Cm/ L, or 0.009°C
`for L = 1 m for example.
`Thermal cycling was studied between room temperature
`and 185°C by inserting a 1-m-long part of PMF into an
`electric furnace. Fig. 2( d) shows the measured results in which
`temperature was raised from 30 to 185°C in one hour and fell
`down in natural cooling. A good reproducibility is shown in
`Fig. 2(d).
`
`B. Strain and Force Sensors
`
`Fig. 3(a) shows the strain sensing system. In order to reduce
`the temperature-induced drift, a differential detection scheme
`using two PMF's is again employed. A 27-mm-long part of
`a sensing PMF is fixed on an aluminium plate by a scotch
`tape whereas a reference PMF is aligned close to the sensing
`one but free from the plate. Axial strain was applied to the
`fiber by bending the plate and monitored by a metal strain
`gauge. Fig. 3(b) shows the change in the phasemeter output
`measured as a function of the monitored strain E. The strain(cid:173)
`induced retardation is proportional to the sensor length L and,
`
`(a)
`
`(b)
`
`7DD
`
`o;
`<lJ &DD
`:9.
`&, 5DD
`~ 4DD
`3DD
`
`0
`<lJ
`Ci]
`
`~ .c p.,
`
`2DD
`
`lDD
`
`D
`
`x360°
`
`700
`o; 600
`<I!
`'.9.
`
`500
`
`Ul
`
`QJ
`t7
`§ 400
`.c
`0
`11! 300
`r;; t: 200
`100
`
`0
`
`L=3.98m
`
`l , . . ..
`
`! .
`
`W'
`
`l.82m
`
`..
`
`l.02m
`
`. 0
`..
`
`0
`
`o. . •
`. e
`
`0
`
`~
`
`•
`
`0
`
`8 o•
`Om
`o•
`• oe 0•
`o__Lo----1..._o---1...a--Lo-oLo--oL____J
`
`D.2 D.4 D.6 D.B
`
`l.D 1.2 1.4 1.6
`
`Temperature change L\T (°C)
`
`(c)
`
`* Temperature
`
`rises
`
`• Temperature falls
`
`.,·
`,,.
`
`.. ·.
`
`•*
`
`..
`..
`
`* .i
`* *,,.
`
`..
`
`* .. ·'
`••
`
`..
`..
`
`* ..
`
`0
`
`100
`Temperature T (°C)
`
`150
`
`(d)
`
`200
`
`Fig. 2. Heterodyne fiber-optic temperature sensor using polarization main(cid:173)
`taining fiber. (a) Measuring system. (b) Beat signals (signal and refer(cid:173)
`ence lights; the beat frequency = .3ll0 kHz). (c) Temperature dependence
`of phasemeter output measured as a parameter of sensor fiber length L.
`(d) Thermal cycling of 1-m-long polarization maintaining fiber temperature
`sensor.
`
`HALLIBURTON, Exh. 1007, p. 0002
`
`

`

`YOSHINO: COMMON PATH HETERODYNE OPTICAL FIBER SENSORS
`
`505
`
`Strain g~uge for
`
`calibc~~fF 2
`
`I
`I
`- l 27mm 1-
`
`PMF 1
`
`Pol. 45°
`
`t
`
`STZL
`
`BS
`
`PMF 2
`
`PMF 1
`
`(a)
`
`fil'
`2
`;:...,
`
`(!)
`b1
`
`~ ..c: u
`
`(!)
`UJ
`n:J
`..c:
`0.,
`
`2500
`
`2000
`
`1500
`
`1000
`
`500
`
`0
`
`h
`
`cu 40
`
`°' ~ 20
`~
`~
`
`0.4 u
`
`0.8
`
`Force F (Kgf)
`
`(a)
`
`60
`40
`20
`Force F (grf)
`(b)
`
`~ 4000
`l
`cu 3000
`i {)
`cu 2000
`Ul m -a
`{) 1000
`() &
`
`•.-!
`4-<
`·.-!
`
`0
`
`Applied axial force
`
`F=200grf
`
`.
`
`I 0
`
`F=lOOgrf
`I
`
`..
`. ..
`
`30
`
`50
`40
`Tenperature T (°C}
`(c)
`
`60
`
`70
`
`Fig. 4. Heterodyne fiber-optic force sensors using polarization maintaining
`fiber. (a) Tension type. (b) Microbending type. (c) Temperature dependence
`of force sensitivity.
`
`Fib. 4(b) shows another type of force sensor using a mi(cid:173)
`crobender. An 130-mm-long part of PMF was sandwiched
`by two wave-form plates having a pitch of 20 mm. Various
`weights were loaded on the upper plate, causing dominantly
`axial tensile stress in the fiber. The minimum detectable force
`was about 1 grf.
`The force-induced retardation was found to depend a little
`on fiber temperature. Fig. 4( c) shows the measured de pen-
`
`I 600
`j
`'" Ul
`'" ;§;
`
`400
`
`200
`
`tJ
`
`4
`
`1ox10-'
`
`-200
`
`Strain £
`
`(b)
`
`Fig. 3. Heterodyne fiber-optic strain sensor using polarization maintaining
`fiber. (a) Measuring system. (b) Phasemeter output measured as a function
`of applied strain.
`
`from Fig. 3(b), is given as
`
`df / Ldc: = 500° /(27 mm x 10 x 10-3c:)
`= 1.9 x 1060 c:- 1m- 1.
`
`(6)
`
`the
`The mm1mum detectable strain is proportional to
`sensor length. As the fluctuation of the phasemeter output
`was about 0.1°, the strain resolution 6..c:
`is, from ( 6),
`0.1°/(1.9 X 1060c:-1m- 1L) = 5.3 x 10-8c:m/L, or 0.053 X
`10-6c: for L = 1 m for example.
`In order to see the temperature compensation effect using
`two PMF's, the two fibers were inserted in an empire tube and
`heated over a 1-m-long part by a hair dryer. When the tube
`temperature was raised by 15°C, the change in the phasemeter
`output was 100° at worst in contrast with 2500° in the case
`of a single fiber. The temperature compensation effect is thus
`better than 1 : 25.
`Various types of strain and force sensors can be constructed.
`Fig. 4(a) shows the measured result for a tension type of force
`sensor. An 170-mm-long part of PMF was cementized in a
`glass tube and axial tensile force was applied to the fiber by
`various weights. The force-induced retardation is proportional
`to the sensor length L and, from Fig. 4(a), is
`
`dr / LdF = 600° /(0.2 kgf x 170 mm)
`= 1.8 x 1040 kgf- 1m- 1.
`(7)
`From (7), using 6..f = 0.1° the minimum detectable force 6..F
`is 0.1°/(1.8x1040 kgf- 1m- 1L) = 5.6 x 10-6 kgfm/L, or
`0.0056 grf for L = 1 m for example.
`
`HALLIBURTON, Exh. 1007, p. 0003
`
`

`

`506
`
`JOURNAL OF LIGHTWAVE TECHNOLOUY. VOL. 111. NO. 4. APRIL 1992
`
`(a)
`
`SFOdeg/sec
`
`fi\
`I I
`
`dence of force-induced retardation on temperature. The force(cid:173)
`induced retardation increased with temperature. It follows from
`Fig. 4(c) that the force sensitivity of PMF increases with
`temperature in about 0.25%/°C.
`
`C. Fiber Gyro
`
`Fiber gyro is a rotation sensor using the Sagnac effect in the
`monomode fiber loop. Much work has been done to improve
`on the gyro performances [10]. Among them, an absolutely
`constant scale factor for rotation rate detection is one of the
`most desirable features for practical fiber gyros. Here we
`present a new type of fiber gyro fulfilling the requirement.
`The method is based on heterodyne detection, but, unlike the
`usual heterodyne method [ 11 ], the interfering two laser beams
`take a common path in the entire sensor system so that the gyro
`system becomes substantially stable against the environmental
`variations.
`Fig. 5(a) shows the entire gyro system. The Sagnac ring
`interferometer consists of a polarization beam splitter PBS,
`two Faraday rotators FRI and FR2, each producing -45°
`and +45° rotations of polarization plane, and a PMF coil.
`The orthogonally linearly polarized different frequency .fi and
`h components from a STZL are split by PBS into the CW
`and CCW traveling beams in the ring interferometer. The two
`beams undergo ±45° rotations of polarization plane so that
`they can travel the PMF along a common polarization axis.
`The combination of one Faraday rotator and PBS makes an
`optical isolator so that both the CW and CCW beams going
`out of the ring interferometer don't return the laser source but
`go to a photomultiplier PMl.
`The optical beat I., generated at PM 1 has a phase
`
`<fl= 27r6.fL/c+¢s
`where 6.f = Ji - h, L is the total light path length from
`the light source to the photodetector, c is the light velocity in
`vacuum, and
`
`(8)
`
`(9)
`
`is the Sagnac shift [12], where a is the radius of the fiber coil,
`L f is the fiber coil length, ,\ is the light wavelength in vacuum,
`and n is the rotation rate of the fiber coil. In the present
`experimental conditions, a = 15 cm, L ~ L 1 = 100 m, and
`,\ = 633 nm so that <Ps[deg] = l.On[deg/s]. The optical phase
`of the beat signal Is was compared with that of the reference
`beat signal IR taken from the back side of the laser. Somewhat
`phase fluctuations were observed in the phasemeter output but
`they could be reduced down to 0.1° by vibrating a short part
`of the fiber coil by means of a PZT driven at about 10 kHz.
`Three pictures of Fig. 5( b) shows the signal and reference beat
`signals observed when the fiber coil was at rest and rotated
`at n = ±38° /s, respectively; the initial phase bias involved
`in the phasemeter output was removed; Fig. 5(c) shows the
`analog output signal of the phasemeter when the fiber coil
`was rotated by hand; the time constant of the phasemeter was
`0.4 s. The minimum detectable rotation rate was then 0.1° / s.
`The phasemeter output involves a nonreciprocal phase bias due
`to the first term of (8), which depends on the amount of the
`
`\ // ·v;; \ /! .
`'· Vi
`1JJ
`
`/\
`
`(i\ \
`
`(/\ \
`
`\
`
`I
`
`I
`
`•
`
`,
`
`SF38deg/sec
`
`SF-38deg/sec
`
`(b)
`
`Fig. 5. Heterodyne fiber gyroscope. (a) Optical system. (b) Signal and ref(cid:173)
`erence optical beats (300 kHz) for different rotation rates of n. (c) Phasemeter
`output when the fiber coil was rotated hy hand; the time constant of the
`phasemeter is 0.4 s.
`
`beat frequency 6.f and hence can vary with the beat frequency
`fluctuation. The associated phase fluctuations, however, can
`
`HALLIBURTON, Exh. 1007, p. 0004
`
`

`

`YOSHINO: COMMON PATH HETERODYNE OPTICAL FIBER SENSORS
`
`507
`
`/=300kllz
`
`rotation rate
`
`r1equencystabilized
`transverse Zeeman laser
`
`I 1,,
`
`SL:
`
`;
`
`Scmo1
`
`:~·-~·J
`
`cell
`
`Fig. 6. Schematic diagram for fiber-optic differential heterodyne sensors
`using polarimetric sensor cell. PMF: polarization maintaining fiber, SL:
`self-focusing rod lens.
`
`signals:
`
`ls= As cos(21fl:if - <I> - I')
`In= An cos(21fl:if - I')
`
`(lOa)
`(lOb)
`
`is the retardation of the sensor cell, I' is the
`where <I>
`retardation of PMF, and As and An are real numbers. The
`phase difference between the two beat signals is detected by
`a phasemeter. The minimum detectable retardation l:iI' was
`about 0.1°.
`
`~~
`12 sec
`
`(c)
`(Continued)
`
`Fig. 5.
`
`be eliminated by passing the reference light through a fiber
`having a length equal to L.
`
`A. Magnetic Field
`
`III. USE OF PMF AS OPTICAL LEAD
`
`There have been developed lots of types of fiber sensors
`which use optical fibers as optical leads to connect between
`optical transducers and light sources or photodetectors in order
`to realize flexible, in-situ, remote measurements. Among many
`types of such sensors, a polarimetric method is one of the
`most useful principles. The Faraday effect is used for the
`measurement of magnetic field [13], [14], the Pockels effect
`for voltage (14], the photoelastic effect for pressure [15], the
`natural birefringence for temperature [16] and the oblique light
`incidence for refractive index or film thickness [17]. In the pre(cid:173)
`vious polarization-based fiber sensors, however, optical fiber
`leads are mostly used to carry the intensity-modulated light
`signal, therefore being sensitive to light intensity fluctuations
`associated with fiber transmission, fiber coupling, light source
`fluctuations and so on. In this paper, intensity-insensitive fiber
`sensors are developed by the use of PMF as optical leads.
`Fig. 6 shows the entire sensing setup for measuring various
`quantities such as magnetic field, voltage, pressure and tem(cid:173)
`perature. The detection principle is based on the differential
`heterodyne scheme. The laser beam from a STZL is launched
`into a PMF (typically 10 m-long) with the mutual coincidence
`of polarization axes. Some part of the fiber was vibrated at
`about 5 kHz to reduce the fluctuation of the phasemeter output.
`The output light from the PMF is collimated by a SELFOC
`rod lens SL and incident on a polarimetric sensor cell. The
`laser beam emerging from the cell is, after passing through a
`polarizer oriented at 45° to the polarization axes of the sensor
`cell, sent to a photodetector through a fiber bundle. On the
`other hand, a light beam partially reflected from the entrance
`of the cell is detected and used for a reference light. Both
`the signal and reference lights generate the following beat
`
`In the measurement system of Fig. 6, the output light from
`PMF was passed through a quarter-wave plate QW to convert
`the incident light to the left and right circularly polarized
`lights. The sensor cell is made of FR5 glass, which has a
`Verdet constant V of -0.24 min cm- 1 G- 1 at .,\ = 633 nm.
`In order to enhance the measurement sensitivity, the multiple
`reflections of the light beam within a Faraday cell [18] were
`employed. The upper and lower surfaces of a 3.1-mm-thick
`15 mm x 20 mm wide FR5 glass plate were coated with
`the multilayers of dielectric thin films having ..\/4 optical
`thicknesses for oblique incidence so that the light beam may
`perfectly reflect with polarization maintaining. The light beam
`travels a zigzag path over a lateral region of 12.8 mm in the
`cell. Under the application of magnetic field, the cell material
`becomes circularly birefringent, thereby inducing phase retar(cid:173)
`dation between the orthogonal circular polarizations, given
`by
`
`<l>H=2·2N-VHd
`
`(11)
`
`where H is the parallel component of magnetic field to the
`direction of cell thickness and 2N is the number of the multiple
`passes of light beam within the cell. Fig. 7(a) shows a typical
`pen recorder chart of the phasemeter output when H was
`±50 Oe; the time constant of the phasemeter was 0.4 s. A
`very stable and precise measurement of de magnetic field is
`achieved, which is very difficult by the conventional intensity
`modulation Faraday sensor. The minimum detectable de field
`is less than 1 Oe. Fig. 7(b) and (c) respectively shows the
`phase changes measured as a function of relatively small and
`large de magnetic fields. The cases of 2N = 40 and 80
`correspond to the angles of incidence on the cell surface 10°
`and 5°, respectively. The measured results of Fig. 7(a) and
`(b) agrees quite well with the theoretical ones, which, e.g., for
`2N = 40, <PH[deg] = 0.099H[Oe] calculated from (11). The
`present sensors can be used for ac fields too if the response
`
`HALLIBURTON, Exh. 1007, p. 0005
`
`

`

`508
`
`JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 4, APRIL 1992
`
`+50G
`
`[
`
`_., 60 sec
`
`(a)
`
`2N=40
`
`.,.::i::
`
`50
`0
`
`I 100
`[
`ti
`-50
`3l
`~ -100
`-1k
`1k
`0
`rx:: magnetic field H (Oe)
`(c)
`
`I 40
`
`.,.::i::
`
`Q)
`
`§
`.r::: u
`
`Q)
`Ul
`
`20
`0
`-20
`~ -40
`0
`-200
`200
`rx:: magnetic field H (Oe)
`
`(b)
`
`2N=80
`
`1.0
`
`~
`.µ
`
`~
`5 0.5
`~ ·rl
`.µ
`r(J
`.....
`&
`
`40 80 120 160 200
`AC magnetic field
`(Oe)
`
`(d)
`
`Fig. 7. Phasemeter output of fiber-optic differential heterodyne magnetic field sensor using the multiple reflection FR5 Faraday
`cell; 2N is the number of light passes within the Faraday cell. (a) Recorder trace of phasemeter output; the time constant of
`the phasemeter is 0.4s and 2N = 40. (b) Characteristics for small de magnetic fields. (c) Characteristics for large de magnetic
`fields. ( d) Characteristics for 50-Hz magnetic fields.
`
`time of the phasemeter is set suitably small. Fig. 7( d) shows with
`the measured results for the commercial frequency of 50 Hz,
`where 2N was made as large as 80 by setting the angle of
`incidence at as small as 5°.
`
`• [ (<)' +(29.d)
`
`2r (14)
`
`where Vtr is the half-wavelength voltage of the Pockets mate(cid:173)
`rial in the limit of infinitely small thickness, Oa is the optical
`activity per unit length, d is the cell thickness, V = Ed is the
`applied voltage and a is an eigenvalue [19]. Calculating (12)
`leads to an eigenvector
`
`[!:L
`
`-cos(¢>/2) ± Jco.'>2 (¢/2) + (2BadfcP) 2 sin2 (¢>/2)]
`-(20adfcP) sin( ¢>/2)
`
`[
`
`(lS)
`
`with an eigenvalue
`
`a-±= exp(±i<I>E)
`
`(16)
`
`(17)
`
`(13)
`
`B. Voltage
`As a Pockels material, Bi12Si020 (BSO) is used because of
`its relatively large and hardly temperature dependent Pockets
`effect. The material, however, has optical activity, i.e., circular
`birefringence, which obviously reduces the Pockels effect
`being linear birefringence. An effective technique for getting
`rid of such reduction of the Pockels effect is to use two way
`or in more general multiple light passes within the Pockels
`cell because then an optical rotary power in an optically
`active material is cancelled whereas the Pockets effect is
`accumulated.
`1) Theory: We define an eigenstate of polarization that light
`regenerates the same polarization after one round trip within
`the Pockels cell as
`
`M(-Oa)M(Oa)[!:] = cr[!:J
`
`where
`<J>E = 2
`
`tan _ 1
`
`(12)
`
`where, referring to [20]
`
`M(Oa) =
`
`[ cos(¢/2)-i(7r~ /efi)sin(¢/2)
`
`(20ad/¢)sin(¢/2)
`
`-(2Bad/¢)sin(¢/2)
`r
`cos(¢/2)+i(7r~,, / ¢)sin(¢/2)
`
`l
`
`( ( 7r V fVtr )/¢)sin( ¢/2)
`Jcos2 ( ¢/2) + (2Bad/¢> )2 sin2
`( 4>/2)
`
`HALLIBURTON, Exh. 1007, p. 0006
`
`

`

`YOSHINO: COMMON PATH HETERODYNE OPTICAL FIBER SENSORS
`
`509
`
`It follows from (15) that
`
`(Ey/Ex)+ · (Ey/Ex)_ = -1
`
`(18)
`
`implying that the eigenstate of polarization consists of or(cid:173)
`thogonal linear polarizations. Assuming the applied voltage
`is relatively low such that 7r\V\/V1r «: 2\8a\d, it then follows
`from (15) that the eigenstates of polarization are, to a good
`approximation
`
`[~:L [~J
`
`(19)
`
`independently of applied voltages, implying the azimuths
`of the principal axes of polarization of the Pockels cell is
`independent of small applied voltages. Furthermore, for small
`voltages, ¢ ~ 28ad so that (17) becomes
`
`<I>E = (7rV/V7r) · 2N · sinc(Oad)
`
`(20a)
`
`or
`
`where
`
`v; = V7r/{2Nsinc(8ad)},
`(2N: number of light pass)
`
`(20b)
`
`(21)
`
`which is an effective half-wave voltage, being in inverse
`proportion to N.
`2) Experiment: Both surfaces of a 3-mm-thick BSO crystal
`plate are dielectric coated to have perfect reflection. A 10-mm(cid:173)
`long beam-guiding region is overcoated with ITO transparent
`electrode films. As BSO has V7r = 3900 V and Ba =
`22° mm- 1 at .A = 633 nm, the effective half-wave voltage
`becomes, from (21)
`v; = 3900 V /{2Nsinc(22° x 3)}
`= 4.91 x 103 V /(2N).
`
`(22)
`
`Using the setup of Fig. 6, the voltage-induced linear bire(cid:173)
`fringence was measured as a function of applied voltages.
`Fig. 8(a) shows the measured results for de voltages; the num(cid:173)
`ber of multiple passes is 2N = 38. The experimental curve
`yields the voltage dependence of retardation as <I>E[deg)
`1.0 V[V]. Theoretically, from (22) with 2N = 38, v; =
`129 V so that, from (20b), <I>E[deg) = (180/129) V[V] =
`1.4 V[V). Both the experimental and theoretical results are
`in reasonable accordance within the possible discrepancy
`due to the field inhomogeneity in the cell. The minimum
`detectable de voltage is as small as 1 V, which is very
`difficult to achieve by the use of the conventional intensity
`modulation scheme. Fig. 8(b) shows the experimental results
`for ac (50 Hz) voltages.
`
`j
`
`o&ri1
`
`Q)
`
`~
`-5
`
`Q)
`Ul
`
`~
`
`100
`
`0
`
`2N=38
`
`-100
`-100
`
`0
`ix: voltage V (V)
`
`100
`
`(a)
`
`~ 1.t
`2:.
`
`2N=38
`
`128
`AC voltage V (Vnns)
`
`(b)
`
`Fig. 8. Phasemeter output of fiber-optic differential heterodyne voltage sen(cid:173)
`sor using the multiple reflection BSO Pockels cell; 2N is the number of
`light passes within the Pockels cell. (a) Characteristics for de voltages.
`( b) Characteristics for 50 Hz voltages.
`
`C. Pressure
`
`The multiple-reflection FR5 glass cell described in Section
`III-A is used for the sensitivity-enhanced photoelastic cell, too.
`Various weights were loaded on the top surface of the cell so
`as to generate uniform vertical pressure within the cell. The
`pressure-induced linear retardation is given by
`
`<l>p = (27r/.A) · 2N · C0 Pd,
`
`(23)
`
`where P is the applied pressure, d is the cell thickness and
`C0 is the photoelastic constant. In the measurement setup of
`Fig. 6, the polarization azimuth of each of the incident two
`frequency components was made to coincide with the parallel
`and perpendicular directions of applied force.
`Fig. 9(a) shows a typical pen recorder chart when a weight
`providing a pressure of 8.29 x 104 Pa was loaded on and off
`the cell with 2N = 54; the time constant of the phasemeter
`was 0.1 s. A rapid response and good reproducibility over a
`wide dynamic range of 0-5 KPa is observed. The minimum
`detectable pressure is 350 Pa. Fig. 9(b) shows the phasemeter
`output measured as a function of applied pressure, representing
`a pressure dependence of <I> p[deg] = 2.8 x 10-4 P[Pa]. Putting
`the experimental result into the theoretical relationship (23) of
`<l>p(deg) = 9.5 x 107C 0 P(Pa] calculated with A = 633 nm,
`d = 3.1 mm and 2N = 54, the photoelastic constant C0 of
`FR5 is determined as 2.9 x 10- 12 Pa- 1 or 2.9 Br.
`
`HALLIBURTON, Exh. 1007, p. 0007
`
`

`

`510
`
`JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 4, APRIL 1992
`
`ON
`
`OFF
`
`j
`-rs.3x104 Pa
`r - - - - -4 - - - 23.4°
`
`- 00
`
`-I 12 sec f---
`
`Time
`
`(a)
`
`Q)
`
`~ 1000
`:g
`.,,8 800
`§
`-5 400
`0
`20
`
`Q)
`Ul
`
`Jl 0..
`
`-
`
`150
`
`~
`-e-"°' 100
`
`! 50
`
`1 2 J 4 5 x10-5
`
`Pressure P (Pa)
`
`(b)
`
`Fig. 9. Phasemeter output of fiber-optic differential heterodyne pressure
`sensor using the multiple reflection FRS photoelastic cell; 2S is the number
`of light passes within the photoelastic cell. (a) Dynamic characteristics when
`a load is on and off the cell; the time constant of the phasemeter is 0.1 s.
`( b) Characteristics for static pressure.
`
`D. Temperature
`An artificial quartz having a 2.09 mm thickness and 10 mm
`x 10 mm surface area is used for the sensor material. The
`optic axis ( c axis) of the quartz is parallel to the cell surface.
`In the measurement system of Fig. 6, the dual-frequency
`dual-polarization components from STZL are incident on
`the quartz crystal at an angle of incidence of 10° with the
`mutual coincidence of their polarization axes. The laser beams
`reflected from the back and front surfaces of the quartz plate
`are used for the signal and reference lights, respectively.
`The quartz plate was inserted in a copper block placed
`on a hot plate. The temperature of the copper block was
`changed from room temperature to 400°C, monitored by a
`mercury thermometer. Fig. lO(a) shows changes in retardation
`measured as a function of the monitored temperature T[ 0 C].
`The measured retardation monotonously increased with in(cid:173)
`creasing temperature, showing a good linearity over an interval
`of about 50°C. For 24°C-84°C in particular, dif>r/dT =
`(2.39 ± 0.01) 0 /°C, as shown in Fig. lO(b). The resolution
`of temperature measurement is 0.04°C; the temperature res(cid:173)
`olution can be easily increased by the use of the multiple
`reflection scheme.
`The retardation of the quartz plate is
`
`(24)
`if>r = (27r / >..) · .6.n · 2d
`where d is the thickness of the crystal plate and .6.n = n 0
`ne is the birefringence of quartz. The classical measurement
`on the variation of .6.n with temperature T[ 0 C] for natural
`quartz [21] at >. = 633 nm gives
`103 .6.n = 9.08 - 1.09 x 10- 3 r - 1.21 x 10- 6r 2 .
`
`(25)
`
`-
`
`---Calculated
`-Experimental
`
`300
`200
`100
`Temperature T ( °C)
`
`400
`
`(a)
`
`60
`72
`36
`84
`48
`Temperature T ( °C)
`(b)
`
`150
`
`tJ,
`~ 120
`'6<8 90
`~ 60
`-5
`
`30
`
`Q)
`Ul
`
`~
`
`Fig. I 0. Phasemeter output of fiber-optic differential heterodyne tempera(cid:173)
`ture sensor using the reflection type quartz cell. (a) Comparison between
`experimental and calculated values. ( b) Measured temperature dependence of
`phasemeter output between room temperature and 84°C.
`
`The thermal expansion of quartz between 50 and 80 K is given
`by [22] as
`
`d = do(l + 1.172 x 10- 5r + 1.168 x 10-8T 2
`+ 1.633 x 10-ur3 ).
`
`(26)
`
`Putting (25) and (26) into (24) results in
`
`if>r = ( 47rdo/ >..)10- 3 (9.08 - 9.84 x 10-4 r - 1.12
`X 10- 6T 2 + 1.21 X 10- 10T 3 ).
`
`(27a)
`
`It then follows from (26) with d0 = 2.09 mm and>. = 633 nm
`that
`
`if>r = const. - 2.334
`x r(1+1.16 x 10-3r -
`
`i.23 x 10-1r 2 ).
`(27b)
`
`The experimental results are compared in Fig. lO(b) with
`the calculated values of (27b), showing a fairly good agree(cid:173)
`ment between them. Since the present temperature sensor is
`inherently insensitive to light intensity variations, the sensor
`cell does not need to be in stable contact with the fiber but can
`be in remote setting from the fiber, meeting the requirement
`for most cases of practical temperature measurements.
`
`HALLIBURTON, Exh. 1007, p. 0008
`
`

`

`YOSHINO: COMMON PATH HETERODYNE OPTICAL FIBER SENSORS
`
`511
`
`E. Ellipsometry
`
`Ellipsometry is a powerful tool for the precise measurement
`of optical constants and/or film thickness. The conventional
`ellipsometer, however, requires mechanical moving elements
`such as rotating polarizers and is bulky, thereby being poor at
`flexible setting. In order to remove such drawbacks, a fiber(cid:173)
`optic heterodyne ellipsometer is developed and applied to film
`thickness measurements.
`1) Theory: We consider the case that a transparent thin
`film of thickness d and refractive index n' is deposited on a
`substate of complex refractive index n", as shown in Fig. 11.
`A collimated light beam is incident on the thin film at an
`angle of incidence (). We let the complex amplitude reflection
`coefficients for s(j_) and p(jl) polarizations be R. and Rp,
`respectively, and define a complex parameter as
`
`p = Rp/R. = Pexp(i'lf;).
`
`(28)
`
`n=l
`
`n'
`
`n"
`
`Air
`
`El'
`
`r'
`
`d
`
`Film
`
`Substrate
`
`Fig. 11. Thin film configuration under consideration.
`
`Here P and 'If; are real ellipsometric parameters related with
`
`R. = { r. + r: exp( -i28)} / {1 + r.r: exp(-i28)}
`Rp = { r P + r~ exp( -i28)} / { 1 + r Pr~ exp( -i28)}
`
`(29a)
`(29b)
`
`polarizer oriented at 45° to the plane of incidence, then the
`photoelectric signal is proportional to
`I = 1 + u 2 P 2 + 2uP cos(27r ~ft - 'If; - r)
`
`(36)
`
`where
`
`and
`
`r 8 = - sin (B - B')/ sin(()+ B'),
`rp =tan (B - ()')/tan (B + ()')
`r: = - sin(B' - ()")/sin (B' + ()"),
`
`r~ = tan(B' - B")/ tan(B' + ()")
`
`(30a)
`
`(30b)
`
`are the Fresnel reflection coefficients at the film boundaries
`
`sin () = n' sin B' = n" sin ()"
`
`(31)
`
`and
`
`o = (27r / >..)n' d cos B'
`which is the optical phase shift due to the single pass of light
`in the film [23]. Putting (29) into (28) and solving 8 with (32),
`one obtains the well-known formulas for film thickness [24]
`- sin2 B) 112
`d = i(>../47r) · lnrt/(n'2
`
`(32)
`
`(33)
`
`with
`
`where
`
`rt= {-B ± (B2
`
`- 4AC)
`
`112
`
`} I (2A)
`
`A= (prp - r.)<r~
`B = rprs(pr~ - <)+(pr: - r~)
`C = pr8
`- Tp·
`
`(34)
`
`(35a)
`(35b)
`(35c)
`
`The ellipsometry parameter p is determined by the differ(cid:173)
`ential heterodyne method. Letting the s- and p-polarization
`components of the incident light have frequencies Ji and
`f2, respectively and detecting the reflected light through a
`
`where u is the amplitude ratio