(12) United States Patent
`Fredin et al.
`
`I lllll llllllll Ill lllll lllll lllll lllll lllll 111111111111111111111111111111111
`
`US006606148B2
`
`(10) Patent No.:
`(45) Date of Patent:
`
`US 6,606,148 B2
`Aug. 12, 2003
`
`(54) METHOD AND SYSTEM FOR MEASURING
`OPTICAL SCATTERING
`CHARACTERISTICS
`
`(75)
`
`Inventors: Leif Fredin, Austin, TX (US); Robert
`Chin, Austin, TX (US); William
`Hallidy, Austin, TX (US)
`
`(73) Assignee: Systems and Processes Engineering
`Corp., Austin, TX (US)
`
`( *) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 75 days.
`
`(21) Appl. No.: 09/840,060
`
`(22) Filed:
`
`Apr. 23, 2001
`
`( 65)
`
`Prior Publication Data
`
`US 2003/0021528 Al Jan. 30, 2003
`
`(51)
`
`Int. Cl.7 ................................................ GOlN 21/00
`
`(52) U.S. Cl. ...................................................... 356/73.1
`
`(58) Field of Search ......................................... 356/73.1
`
`(56)
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`
`4,355,898 A
`4,495,586 A *
`4,673,299 A
`4,708,471 A
`4,794,249 A
`4,823,166 A
`5,102,232 A
`5,113,277 A
`5,196,709 A
`5,272,334 A
`5,292,196 A
`5,329,392 A
`5,449,233 A
`5,818,240 A
`5,981,957 A
`
`10/1982
`1/1985
`6/1987
`* 11/1987
`12/1988
`4/1989
`4/1992
`5/1992
`3/1993
`12/1993
`3/1994
`7/1994
`9/1995
`* 10/1998
`11/1999
`
`Dakin ........................ 356/346
`Andrews . . . . . . . . . . . . . . . . . . . . . 702/66
`Dakin ........................ 374/131
`Beckmann et al.
`........ 356/73.1
`Beckmann et al.
`. . . . . . . . . 250/227
`Hartog et al. ................. 356/44
`Tanabe et al.
`.............. 374/131
`Ozawa et al. ............... 359/127
`Berndt et al. ............ 250/458.1
`Sai ........................ 250/227.21
`Iida et al. ................... 374/131
`Cohen ........................ 359/124
`Sai et al. .................... 374/161
`Cabot ......................... 324/626
`Cruce et al. .. .. ... ... ... 250/458.1
`
`OTHER PUBLICATIONS
`F.L. Galeener, et al., "The Relative Raman Cross Sections of
`Vitreous SI02 , GE0 2 , B2 0 3 , and P2 0 5 ,'' Appl. Phys. Lett.,
`vol. 32, No. 1, pp. 34--36, Jan. 1978.
`P. Di Vita, et al., "The Backscattering Technique: Its Field of
`Applicability in Fibre Diagnostics and Attenuation Measure(cid:173)
`ments," Optical and Quantum Electronics, vol. 11, pp.
`17-22, 1980.
`P. Healey, "Optical Time Domain Refiectomertry-A Per(cid:173)
`formance Comparsion of the Analogue and Photon Counting
`Techniques," Optical and Quantum Electronics, vol. 16, pp.
`267-276, 1984.
`G.W. Bibby, et al., "Raman Thermometry Using Optical
`Fibres," Analytical Proceedings, vol. 22, No. 7, pp.
`213-214, Jul. 1985.
`A.H. Hartog, et al., "Distributed Temperature Sensing in
`Solid-Core Fibres," Elec Letters, vol. 21, pp. 1061-1062,
`Nov. 1985.
`J.P. Dakin, et al., "Temperature Distribution Measurement
`Using Raman Ratio Thermometry," SPIE Fiber Optic and
`Laser Sensors III, vol. 566, pp. 249-256, 1985.
`(List continued on next page.)
`Primary Examiner-Audrey Chang
`Assistant Examiner-Denise S. Allen
`(74) Attorney, Agent, or Firm-Baker Botts L.L.P.
`(57)
`ABSTRACT
`
`A method and system for measuring optical scattering
`characteristics includes coupling a continuous wave laser
`excitation signal to an optical fiber. Radiation backscattered
`by the optical fiber in response to the coupled excitation
`signal is detected to produce a backscattered radiation
`signal. The backscattered radiation signal is mixed with the
`excitation signal to produce a mixed signal. The mixed
`signal is filtered to reduce the magnitude of frequencies
`other than conjugate mixing frequencies relative to the
`conjugate mixing frequencies. The filtered signal is digitized
`and the magnitude of backscattered radiation from a specific
`portion of the fiber is calculated based on the digitized
`signal. The temperature of a specific portion of the fiber can
`be determined from the magnitude of the backscattered
`radiation.
`
`11 Claims, 6 Drawing Sheets
`
`75
`./
`
`80
`
`72
`
`90
`
`80
`
`HALLIBURTON, Exh. 1008, p. 0001
`
`

`

`US 6,606,148 B2
`Page 2
`
`OIBER PUBLICATIONS
`
`R. Stierlin, et al., "Distributed Fiber-Optic Temperature
`Sensor Using Single Photon Counting Detection," Applied
`Optics, vol. 26, No. 8, pp. 1368-1370, Apr. 15, 1987.
`J.K.A. Everard, et al., "Distributed Optical Fibre Tempera(cid:173)
`ture Sensor Using Spread-Spectrum Techniques," Electron(cid:173)
`ics Letters, vol. 25, No. 2, pp. 140-142, Jan. 19, 1989.
`B.K. Garside, et al., "A Photon Counting Optical Time-Do(cid:173)
`main Refiectometer for Distributed Sensing Applications,"
`SPIE Fiber Optic and Laser Sensors VII, vol. 1169, pp.
`89-97, 1989.
`M.A. Marcus, et al., "Real-Time Distributed Fiber-Optic
`Temperature Sensing in the Process Environment," SPIE
`Chemical, Biochemical, and Environmental Sensors, vol.
`1172, pp. 194-205, 1989.
`Hewlett-Packard, "HP 8703A Lightwave Component Ana(cid:173)
`lyzer: Technical Specifications," Hewlett-Packard, pp.
`1-16, 1990.
`Z. Zhang, et al., "A Novel Signal Processing Scheme for a
`Fluorescence Based Fiber-Optic Temperature Sensor," Rev.
`Sci. Instrum., vol. 62(7), pp. 1735-1742, Jul. 1991.
`P.R. Orrell, et al., "Fiber Optic Distributed Temperature
`Sensing," First European Conference on Smart Structures
`and Materials, pp. 151-154, 1992.
`Agilent Technologies, "High-Speed Lightwave Component
`Analysis: Application Note 1550-6," Agilent Technologies,
`pp. 1-23, 1992.
`Hewlett-Packard, "High-Speed Lightwave Component
`Analysis: Application Note 1550-6," Hewlett-Packard, pp.
`1-23, Date Unavailable.
`J. Zou, et al., "Distributed Fiber Optical Temperature Sensor
`Using Digital Boxcar Integrator," SPIE Measurement Tech(cid:173)
`nology and Intelligent Instruments, vol. 2101, pp. 412-414,
`1993.
`
`J.S. Namkung, et al., "Fiber Optic Distributed Temperature
`Sensor Using Raman Backscattering," SPIE, vol. 1819, pp.
`82-88, 1993.
`
`J.R. Alcala, et al., "Real Time Frequency Domain Fiberoptic
`Temperature Sensor," IEEE Transactions on Biomedical
`Engineering, vol. 42, No. 5, pp. 471-476, May 1995.
`
`M. Hobel, et al., "High-Resolution Distributed Temperature
`Sensing with the Multiphoton-Timing Technique," Applied
`Optics, vol. 34, No. 16, pp. 2955-2967, Jun. 1995.
`
`J.P. Dakin, et al., "Distributed Optical Fibre Raman Tem(cid:173)
`perature Sensor Using a Semiconductor Light Source and
`Detector," Electronics Letters, vol. 21, No. 10, pp. 569-570,
`1995.
`
`Hewlett-Packard, "Fiber Optic Test Solutions for Network
`Installation and Maintenance," Hewlett-Packard, pp. 1-12,
`1997.
`
`Lutes, et al., "Swept-Frequency Fiber-Optic Readout From
`Multiple Sensors and Technical Support Package," NASA
`Tech Briefs, vol. 21, No. 10, Item #192, pp. 35, andJPLNew
`Technology Report NP0-19725, pp. I, 1-2, and 1A-6A,
`Oct. 1997.
`
`Hitachi Cable, Ltd., "FTR: Hitachi Fiber Optic Temperature
`Laser Radar," Hitachi Cable, Ltd., pp. 1-6, 1999.
`
`Hitachi Cable, Ltd., "FTR Applications Data Sheet
`TD-462C," Hitachi Cable, Ltd., pp. 1-14, Date Unavailable.
`
`B. Huttner, et al., "Optical Frequency Domain Refiectometer
`for Characterization of Optical Networks and Devices,"
`COMTEC, vol. 3-99, pp. 20-23, 1999.
`
`* cited by examiner
`
`HALLIBURTON, Exh. 1008, p. 0002
`
`

`

`U.S. Patent
`
`Aug. 12, 2003
`
`Sheet 1 of 6
`
`US 6,606,148 B2
`
`Fig 1
`
`HALLIBURTON, Exh. 1008, p. 0003
`
`

`

`U.S. Patent
`
`Aug. 12, 2003
`
`Sheet 2 of 6
`
`US 6,606,148 B2
`
`20
`,/
`
`24
`
`22
`
`~30~
`
`Fig2
`
`HALLIBURTON, Exh. 1008, p. 0004
`
`

`

`U.S. Patent
`
`Aug. 12, 2003
`
`Sheet 3 of 6
`
`US 6,606,148 B2
`
`72
`
`90
`
`80
`
`75
`
`/
`
`86
`
`84
`
`Fig3
`
`HALLIBURTON, Exh. 1008, p. 0005
`
`

`

`U.S. Patent
`
`Aug. 12, 2003
`
`Sheet 4 of 6
`
`US 6,606,148 B2
`
`24
`
`+-- 30~
`
`Fig4
`
`HALLIBURTON, Exh. 1008, p. 0006
`
`

`

`U.S. Patent
`
`Aug. 12, 2003
`
`Sheet 5 of 6
`
`US 6,606,148 B2
`
`44
`
`40
`
`~
`
`42-+-----
`
`f-46~
`
`Fig 5
`
`HALLIBURTON, Exh. 1008, p. 0007
`
`

`

`U.S. Patent
`
`Aug. 12, 2003
`
`Sheet 6 of 6
`
`US 6,606,148 B2
`
`Fig6
`
`HALLIBURTON, Exh. 1008, p. 0008
`
`

`

`US 6,606,148 B2
`
`1
`METHOD AND SYSTEM FOR MEASURING
`OPTICAL SCATTERING
`CHARACTERISTICS
`
`TECHNICAL FIELD OF THE DISCLOSURE
`
`The present disclosure relates in general to optical system
`monitoring, and, more particularly, to a method and system
`for measuring optical scattering characteristics.
`
`BACKGROUND
`
`Optical fibers increasingly constitute the chief means for
`transmitting information through the world's telecommuni(cid:173)
`cations network. Certain characteristics of an optical fiber
`can also be used to generate information rather than just
`transmit it. Specifically, the temperature of an optical fiber
`affects the amount and wavelength of light that will be
`scattered in response to a transmitted pulse. Careful mea(cid:173)
`surements of scattered light can therefore be used to deter(cid:173)
`mine the temperature at points along an optical fiber. As
`another example, mechanical stresses on the fiber affect the
`amount of certain wavelengths of light that will be scattered
`in response to a transmitted pulse. Once again, measure(cid:173)
`ments of scattered light can yield useful information.
`Other optical systems also scatter light in correlation with
`characteristics of interest. For example, an air-filled region
`may scatter light in proportion to the density of pollutants or
`another constituent element of interest. Accurately measur(cid:173)
`ing the extent to which certain wavelengths or ranges of
`wavelengths of light are scattered provides information
`about other characteristics of the system.
`In a conventional method a time-limited pulse of light
`with an electromagnetic spectrum of average wavelength A
`is produced at an excitation source and sent through an 35
`optical fiber. When the excitation source is a laser, the
`electromagnetic spectrum is often very narrow and is
`referred to in shorthand as a single wavelength. As the pulse
`traverses the fiber, backward scattered light is produced.
`Three types of backward scattered light, among others, are 40
`of interest: Stokes light, anti-Stokes light, and Rayleigh
`light. Stokes and anti-Stokes light are collectively referred to
`as Raman light. Stokes light constitutes an electromagnetic
`spectrum having an average wavelength greater than A.
`Anti-Stokes light constitutes an electromagnetic spectrum 45
`having an average wavelength less than A. Rayleigh light has
`the same wavelength A as the excitation source. The width
`of the Stokes and anti-Stokes spectra, as measured by the
`difference in wavelength between the points of 50%
`intensity, is often much greater than the width of the 50
`time-limited pulse spectra and the Rayleigh light spectra,
`especially if that pulse is produced by a laser.
`Some of the Rayleigh, Stokes, and anti-Stokes light
`travels to the end of the fiber at which the pulse was
`introduced, while some is scattered at an angle such that it 55
`is absorbed by the cladding of the fiber or escapes. The
`location from which the backward scattered light originated
`can be determined by the time between the introduction of
`the pulse and the receipt of the light. After a pulse is
`introduced into the fiber, backward scattered light is con- 60
`tinuously received and time functions of the total intensity
`across the Stokes and anti-Stokes spectra can be determined.
`Under particular circumstances, the temperature of a point in
`the fiber has a known relationship to the ratio of the
`anti-Stokes light produced at that point to the Stokes light 65
`produced at that point. If, however, the intensity of the
`excitation per area of the fiber core is too high, non-linear
`
`15
`
`2
`distortions eliminate the temperature proportionality.
`Increasing the measurement accuracy of Stokes and anti(cid:173)
`Stokes intensity as a function of time without introducing
`non-linear distortion, increases the accuracy of the resulting
`5 calculation of temperature as a function of position in the
`fiber.
`U.S. Pat. No. 5,113,277 discloses a Fiber Optic Distrib(cid:173)
`uted Temperature Sensor System. The '277 patent contem(cid:173)
`plates introducing a light pulse from a light source into a
`10 fiber. The scattered light is then divided by wavelength
`spectra with detectors positioned to receive the Stokes light
`and anti-Stokes light, respectively. The measurements made
`by the detectors are then introduced into an equation to
`determine the temperature at each measured distance.
`The use of timed pulses of light to detect temperature or
`mechanical stress can require expensive components. For
`example, a light source that has sufficient power and pro(cid:173)
`duces light of a wavelength that has scattering characteris(cid:173)
`tics allowing for measurements of scattering over a long
`20 distance of fiber can be very expensive. Additionally, the
`electronics necessary to convert the received intensity of
`back scattered radiation into a digital representation become
`more expensive as their processing speed increases. Increas(cid:173)
`ing the spatial resolution of the temperature measurements
`25 using timed light pulses requires digital representations of
`back scattered radiation intensity for smaller periods of time.
`Such representations are only available with the use of
`faster, and consequently, more expensive electronics.
`Additionally, high power pulses can cause stimulated emis-
`30 sion of Raman light. Such stimulated emission cannot be
`distinguished from backscattered radiation and renders cal(cid:173)
`culations inaccurate.
`The time pulse method disclosed in the '277 patent also
`uses optical components to screen Rayleigh scattered light
`from the sensors. Analyzing the characteristics of Rayleigh
`scattered light can result in useful information indicating
`possible mechanical stresses in the optical fiber. This infor(cid:173)
`mation is not available when the wavelengths comprising
`the Rayleigh scattering are blocked from the sensors.
`
`SUMMARY OF THE INVENTION
`
`A method and system of measuring optical scattering
`characteristics is disclosed. None of the advantages
`disclosed, by itself, is critical or necessary to the disclosure.
`A system is disclosed for measuring optical scattering
`characteristics that includes a laser that produces an excita(cid:173)
`tion signal. An optical fiber is coupled to the laser. At least
`a portion of the excitation signal enters the optical fiber as
`a coupled excitation signal with a continuous waveform and
`an amplitude modulated at variable frequencies. A first
`detector receives radiation backscattered from the coupled
`excitation signal by the optical fiber. In a more specific
`embodiment, the coupled excitation signal has a power less
`than 500 mW. In another more specific embodiment, the
`optical fiber is a single mode optical fiber.
`A method is disclosed for measuring optical fiber char(cid:173)
`acteristics that includes coupling a continuous wave laser
`excitation signal to an optical fiber. Radiation backscattered
`by the optical fiber in response to the coupled excitation
`signal is detected to produce a backscattered radiation
`signal. The backscattered radiation signal is mixed with the
`excitation signal to produce a mixed signal. The mixed
`signal is filtered to reduce the magnitude of frequencies
`other than conjugate mixing frequencies relative to the
`conjugate mixing frequencies. The filtered signal is digitized
`and the magnitude of backscattered radiation from a specific
`
`HALLIBURTON, Exh. 1008, p. 0009
`
`

`

`US 6,606,148 B2
`
`3
`portion of the fiber is calculated based on the digitized
`signal. In a more specific embodiment, the temperature of a
`specific portion of the fiber is determined from the magni(cid:173)
`tude of the backscattered radiation.
`It is a technical advantage of the disclosed methods and
`systems that backscattered radiation from an optical target
`receiving a variable frequency interrogation signal is
`detected.
`It is also a technical advantage of the disclosed methods
`and systems that less expensive electronics can be used to
`monitor variable frequency backscattering.
`Another technical advantage of the system and method
`disclosed is that lower cost excitation sources producing less
`power can be used to produce accurate results.
`Another technical advantage of the system and method 15
`disclosed is that a lower power excitation signal can be
`coupled to a fiber to reduce non-linear distortion.
`Another technical advantage of the system and method
`disclosed is that the temperature at a specific point of the
`optical target can be determined.
`Another technical advantage of the system and method
`disclosed is that mechanical stresses of an optical fiber can
`be determined.
`Another technical advantage of the system and method
`disclosed is that the particle density of an air-filled region
`can be determined.
`Another technical advantage of the system and method
`disclosed is that the frequency difference between the
`detected reference signal and the detected backscattered
`radiation can be used to determine the origin of the back-
`scattered radiation.
`Another technical advantage of the system and method
`disclosed is that the backscattering characteristics of single
`mode fiber can be determined.
`Other technical advantages of the present disclosure will
`be readily apparent to one skilled in the art from the
`following figures, descriptions, and claims. Various embodi(cid:173)
`ments of the invention obtain only a subset of the advantages
`set forth. No one advantage is critical to the invention. For
`example, one embodiment of the present invention may only
`provide the advantage of detecting backscattered radiation,
`while other embodiments may provide several of the advan(cid:173)
`tages.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`A more complete understanding of the present disclosure
`and advantages thereof may be acquired by referring to the
`following description taken in conjunction with the accom(cid:173)
`panying drawings, in which like reference numbers indicate
`like features, and wherein:
`FIG. 1 is a graph of electromagnetic spectra;
`FIG. 2 is a graph of a chirped, variable frequency,
`modulating signal;
`FIG. 3 is a diagram of a system for measuring optical
`scattering characteristics in accordance with one embodi(cid:173)
`ment of the present invention;
`FIG. 4 is a graph of amplitude modulation frequencies of
`backscattered radiation;
`FIG. 5 is a graph of a stepped, variable frequency,
`modulating signal; and
`FIG. 6 is a diagram of a system for measuring character- 60
`istics of optical fiber in accordance with one embodiment of
`the present invention.
`
`DETAILED DESCRIPTION OF THE
`DISCLOSURE
`FIG. 1 is a graph of electromagnetic spectra. One point in
`the fiber will reflect some light of the same optical frequency
`
`20
`
`25
`
`30
`
`4
`as the light being transmitted, known as Rayleigh scattering
`10. Of less intensity are reflections of light at optical
`wavelengths both longer and shorter than the incident light.
`The shorter wavelength light 12 is known as anti-Stokes
`5 scattering. The longer wavelength light 14, is known as
`Stokes scattering. The Stokes and anti-Stokes light are
`collectively known as Raman light. The intensity of each
`type of scattered light is a function of the intensity of the
`incident light. If the incident light is amplitude modulated,
`10 the amplitude of the backscattered radiation will also be
`affected. The different types of backscattered radiation are
`also affected by different characteristics of the fiber. For
`example, the amount of Rayleigh light scattered at a point in
`the fiber is related to the mechanical stress of the fiber at that
`point. The ratio of anti-Stokes light to Stokes light scattered
`at a point in the fiber is related to the temperature of the fiber
`at that point.
`FIG. 2 is a graph of a chirped, variable frequency,
`modulating signal. The graph shows the frequency of the
`signal as a function of time. The modulating signal 20
`progresses linearly from a minimum frequency 22 to a
`maximum frequency 24 during a chirp period 30. The slope
`of the chirp 26 can be determined by dividing the change in
`frequency (the difference between the maximum 24 and the
`minimum 22) by the chirp period 30 or duration. The
`duration of the chirp 30 is preferably longer than the amount
`of time it takes for light to make a round trip through the
`fiber or optical target to be interrogated. The greater the
`proportion of the chirp period 30 to the round-trip time, the
`greater the proportion of the detected radiation that can be
`used to measure optical backscattering characteristics.
`FIG. 3 is a diagram of a system for measuring optical
`scattering characteristics in accordance with one embodi(cid:173)
`ment of the present invention. A first frequency generator 52
`35 provides a frequency chirped signal in accordance with FIG.
`2. The signal is amplified by an amplifier 80 and controls the
`output amplitude of a laser 50. In alternative embodiments
`the output of the laser can be directed to an external
`modulator that is driven by the first signal. The output of
`40 laser 50 is a laser excitation signal. A low power laser
`excitation signal can be used to decrease nonlinear back(cid:173)
`scattered radiation responses. For example, a power of less
`than 500 mW allows for use of a 1541 nm laser source while
`reducing nonlinear response. Alternatively, a higher power
`45 laser excitation signal could be reduced to less than 500 mW
`by an external modulator or other optical device. The
`amplitude modulated light is directed to an optical target 75.
`In one embodiment, an optical fiber 74 is used to direct the
`amplitude modulated light to the optical target 75. The
`50 optical fiber 74 has first end 72 and second end 76. In one
`embodiment, an optical fiber is the optical target. The optical
`fiber can be multi-mode fiber or single-mode fiber. A portion
`of the backscattered light from the optical target traverses
`filter 90 and is received by a avalanche photodiode 58. The
`55 filter 90 determines the type of backscattered radiation
`received by the avalanche photodiode 58. For example, the
`filter 90 may allow only Rayleigh radiation or Stokes
`radiation depending on the wavelengths that the filter 90
`transfers and blocks.
`The avalanche photodiode 58 outputs a signal correspond-
`ing to the energy of photons received. That signal is ampli(cid:173)
`fied by an amplifier 80. A mixer 84 receives the amplified
`signal together with the modulating signal from the first
`frequency generator 52. The mixer 84 is a device that
`65 produces output signals at the sum and difference frequen(cid:173)
`cies of the input signals. The mixer output signal is provided
`to a low pass filter 60, an analog-to-digital converter (ADC)
`
`HALLIBURTON, Exh. 1008, p. 0010
`
`

`

`US 6,606,148 B2
`
`5
`
`5
`62, and a fast fourier transform (FF1) circuit 64. In an
`alternate embodiment, the FFT circuit 64 could be replaced
`by a software-implemented fast fourier operation. The digi(cid:173)
`tized frequency information is then received by a processor
`86.
`FIG. 4 is a graph of amplitude modulation frequencies of
`backscattered radiation. A range of backscattered radiation
`frequencies are received at any particular time. The frequen(cid:173)
`cies range from the minimum chirp frequency 22 to the
`maximum chirp frequency 24. The received frequencies are 10
`periodic over the chirp period 30. For example, at a time t1
`a range of frequencies 23 are received. The highest fre(cid:173)
`quency was reflected by the nearest point in the optical target
`and is essentially identical to the current frequency of laser
`modulation. The lowest frequency was reflected by the 15
`furthest point in the optical target and is equal to the laser
`modulation frequency at a previous time. The time differ(cid:173)
`ence in modulation is equal to the time required for the light
`to traverse the optical target twice. For example, if the
`optical target is an optical fiber of length L and light travels 20
`through the optical fiber at speed c, the lowest frequency of
`received radiation will be the frequency at which the laser
`was modulated at a time
`
`6
`as a function of time from a fiber of length, L, and absorption
`coefficient, a(l), can be expressed as an integral over the
`length of the fiber, after an initial transient period of one
`round trip time on the fiber, 2L/c:
`
`r(t) = ~mPof exp[-2fo'a:(l')dl']cos[\O(r-¥)]cr(l)dl
`
`Eqn. 5
`
`2L
`fort> -
`c
`
`where a(l) measures the returned strength, from position 1,
`of the backscattered signal that is trapped in the fiber and c
`is the speed of light in the fiber. In one embodiment, a(l) is
`assumed to be a constant, independent of 1, so that the
`interior integral of Eqn. 5 is equal to al. With that assump(cid:173)
`tion the complex return, R(t) can be defined as
`
`LL
`
`0
`
`1
`R(t) = -mPo
`2
`
`so that:
`
`Eqn. 6
`
`Eqn. 7
`
`2L
`
`25
`
`r(t)=Re[R(t)].
`
`previous.
`An expression for the instantaneous frequency of the 30
`chirp is:
`
`f(t)=f 0+ymod(t;t)
`where f 0 is the minimum frequency, y is the chirp rate, and
`i: is the chirp period. The laser's output power waveform 35
`then has the form:
`
`Eqn. 1
`
`P(t)=O, t<O
`
`P(t)=P0{1-msin2[<P(t)/2]}, O~t
`
`with
`
`<P(t)=2Jt ff(t)dt
`
`Eqn. 3
`
`where <I>(t) is the phase of the waveform. The excitation 45
`shown in Eqn. 2 can be rewritten as:
`
`P(t) =Po{ 1 - ~m + ~mcos[\O(tJJ}.
`
`Eqn. 4
`
`The time span of the dashed regions in FIG. 4 is just
`
`2L
`
`In one embodiment, only data from outside the dashed
`regions is considered for determining optical backscattering
`characteristics. In that embodiment, data is available if
`
`50
`
`55
`
`FIG. 3 illustrates that the real return signal is mixed with
`the real excitation signal at mixer 84. Because these signals
`each consist of both an AC and a DC component and
`because the AC part of each real signal is half the sum of the
`corresponding complex signal with its conjugate, the real
`mixed signal contains four types of terms: DC terms from
`the DC/DC mixing, terms at the original chirp frequencies
`from the AC/DC mixing, terms at twice the original chirp
`frequencies from the direct AC mixing (e;e; and e-ie-i) and
`low frequency terms from the conjugate mixing (eie-i and
`
`In one embodiment, the DC terms are eliminated by
`coupling only AC from the frequency generator 52 and
`avalanche photodiode 58 to the mixer 84, for example using
`a capacitor. The low pass filter 60 eliminates the AC/DC
`mixing terms and the direct AC mixing terms. The only
`terms passed in this embodiment to the ADC 62 are the low
`frequency terms that result from conjugate mixing.
`The result of the mixing and filtering may then be written
`as:
`
`Thus
`
`Eqn. 8
`
`Eqn. 9
`
`2L
`- <r.
`c
`
`60 where K and A are constants that depend on circuit param(cid:173)
`eters.
`In one embodiment we restrict the acquisition time to
`
`Eqn. 4 shows that the intensity modulation of the back(cid:173)
`scattered radiation received from the optical target will have 65
`both a DC and an AC component. The AC component of the
`modulation of the received backscattered radiation intensity
`
`2L
`-::;r::;r,
`c
`
`HALLIBURTON, Exh. 1008, p. 0011
`
`

`

`US 6,606,148 B2
`
`resulting in:
`
`7
`
`I
`f(t')dt' =[Jo +yt] -
`t ¥
`.
`c
`
`(21)
`
`2
`.
`
`- -r -
`1 (21)
`2
`c
`
`Eqn. 10
`
`Writing f(t)=f 0 +yt and substituting
`
`k(t) = 2f(t),
`c
`
`we have
`
`8
`which we call bookmatching, to include negative k. This will
`permit us to set (k)=O in Eqn. 14. The remaining terms will
`then vary much more slowly than the sine function. If we
`also choose k 1 =0, Eqn. 14 takes the approximate form
`
`m(l, k1) = r" 2
`M(kJe'2rrkl dk
`J_k2
`"2Ak2 LL e-2a1cr(l)sinc [2k2(l - t)] di
`
`Eqn. 16
`
`5
`
`10
`
`where we have approximated
`
`Eqn. 11
`
`15
`
`,,1
`
`where the dependence of k on t is implicit. Performing a
`Fourier transform of M(k) yields an expression that can be
`solved for a(i).
`
`M(/)= 1:
`
`dk
`
`Eqn. 12
`
`However, data is available only over the finite range of time,
`
`2L
`-::;r::;r,
`c
`
`and over corresponding ranges of f(t) and k(t), where
`O~k1 ~k~k2. Thus, for a continuous range of k, we have
`
`Eqn. 13
`
`and
`2~ sine [2kil-l)],.,o(i-l).
`The first approximation becomes exact when y=O.
`20 When backscattering from the fiber occurs from both
`discrete and continuous scatterers, the received signal from
`different locations on the fiber may include a wide dynamic
`range. In that instance, the contribution in Eqn. 16 from the
`sidelobes of the sine function for a discrete scatterer may
`25 swamp the distributed scattering signal from nearby loca(cid:173)
`tions. In order to reduce this effect, we multiply the mixed
`signal of Eqn. 11 by a low pass window function, W(k), to
`produce
`
`30
`
`Mw(k)=W(k)·M(k)
`
`Eqn. 17
`
`By defining W(k) as a real, symmetric function of k, the
`function Mw(k) will satisfy the condition for bookmatching
`if M(k) does.
`After bookmatching, we follow the procedures for Mw(k)
`35 which led to Eqn. 16 for M(k) to obtain
`
`nlw(l, k1) = ('2 Mw(kJe•2rrkl dk
`J_k2
`
`Eqn. 18
`
`which, after some manipulation, yields
`
`nl(l, k1, k1) = A(k2 -k1)
`
`40
`
`Eqn. 14
`
`where
`
`45 where W(l) is the Fourier transform of a suitably normalized
`window function, W(k), chosen to ensure that W(l) approxi(cid:173)
`mates the Dirac function.
`Typical, non-normalized window functions that we have
`used include the offset Gauss type
`
`If the remaining terms under the integral were slowly
`varying, the sine function could be approximated by a Dirac
`delta function. However, for positive k, we note that
`
`1
`(k) > 2(k2 -k1),
`
`50
`
`55
`
`so that this condition is not met in practice.
`We are only able to collect data for positive frequencies, 60
`f(t), so we only have experimental data for positive values
`of k(t). However, if we examine Eqn. 11 for M(k), we see
`that if the condition
`
`ny(2L!c)2«1
`Eqn. 15 65
`is met, then M(-k),.,M*(k), where * indicates complex
`conjugation. Thus, M(k) may be extended by this process,
`
`Wc(k)= 1,
`
`Eqn. 19
`
`( k-ko )2
`= e -a k~kQ , ko ::; k ::; k1
`
`= 0,
`
`elsewhere
`
`and a generalized raised cosine function
`
`Wc(k) = 1,
`
`O:o;k <ko
`
`Eqn. 20
`
`= 0,
`
`elsewhere
`
`where ko and a are parameters that determine the width and
`rate of decay of the window.
`
`HALLIBURTON, Exh. 1008, p. 0012
`
`

`

`9
`For zero offset, the normalized, bookmatched, Gauss type
`window function, W G, may be written
`
`10
`If these constraints are satisfied, we find
`
`M(l,kN)=Ae-2 aia(fJ, o~1~L
`
`Eqn. 26
`
`US 6,606,148 B2
`
`Wc(k) = G(k) · n (k)
`
`k2
`
`where G(k) is a Gaussian function and
`
`Eqn. 21
`
`5
`
`in agreement with our earlier result from Eqn. 16, where the
`right hand side Eqn. 26 is independent of kN. If we relax the
`assumption that a(l) is a constant, independent of 1, that was
`made in simplifying Eqn. 5 to Eqn. 6, we find
`
`Eqn. 27
`
`n(k)
`k2
`
`10
`
`is the unit step function with support -ls~k~ls- The
`Fourier transform of this widow is given by
`
`Eqn. 22 15
`Wc(l)=G(l)®2~·sinc (2k2l)
`where G(l) is also a Gaussian function and ® denotes a
`convolution.
`The central peak of a sine function is twice as wide as
`each of its sidelobes. We can choose G(k) in Eqn. 21 so that
`the width of G(l) matches that of the sine's central peak.
`From Eqn. 22, this allows us to significantly reduce the
`sidelobes of W G(l) in comparison with those of the sine
`function while minimizing the spread of its central peak.
`Data will normally be collected in discrete samples at
`equal intervals rather than continuously. Furthermore, it is
`also desirable to avoid taking zero frequency (DC) data. By
`choosing sample times so that the least sample frequency is
`half the frequency interval between samples, we arrive, after
`bookmatching, with a set of equally spaced samples,
`
`{M(kn):-N~n~N-1 },
`
`where
`
`with
`
`2bf
`bk=-,
`c
`frequency interval of =yllt and sample time interval llt.
`Discrete Fourier transform of the data yields
`
`N-!
`rfl(l,kN)= ~
`n=-N
`
`Eqn. 23
`
`LL_,,,,
`
`= Abk
`
`e
`
`o
`
`{sin[rr2kN(1-t)]}
`di!
`CF(/)
`sin[rrbk(I -1)]
`
`A
`
`where
`
`The function in curly brackets is called the array factor. It
`will approximate a Dirac delta function over the region of
`integration provided the following conditions are met:
`
`and
`
`nokL<<l
`
`Eqn. 24
`
`Eqn. 25
`
`Thus, we see that if the constraints of Eqn. 15, Eqn. 24 and
`Eqn. 25 are satisfied, the transformed, low pass part of the
`mixed signal allows us to determine the signal backscattered
`from fiber as a function of position, i, along the fiber. We also
`observe the expected exponential decay of the return signal
`with i.
`FIG. 5 is a graph of a stepped, variable frequency,
`20 modulating signal. Like the chirped signal 20, the frequency
`