Calculation of sensor array induced phase angle independent from demodulation phase offset of phase generated carrier

A sensor array employs a parameter to induce a time-varying phase angle φ on an optical signal that comprises a phase generated carrier with a demodulation phase offset β. The phase angle φ is calculated independently of the demodulation phase offset β.

TECHNICAL FIELD

The invention relates generally to signal processing and more particularly to demodulation of signals from fiber optic sensor arrays.

BACKGROUND

Fiber optic sensor arrays of a time division multiplexed (“TDM”) system are often used to measure a change in a parameter, for example, acoustic vibration, fluid pressure variations, acceleration, and magnetic field intensity. The fiber optic sensor array employs a phase generated carrier with a period T to measure the change in the parameter at a given sampling rate. The fiber optic sensor array converts a phase angle associated with the parameter to an amplitude variation on an output pulse of light.

The phase angle is measured through various demodulation techniques of the output pulse. Typical demodulation techniques employ a quadrature component Q and an in-phase component I of the output pulse. The quadrature component Q corresponds to a sine of the phase angle, and the in-phase component I corresponds to a cosine of the phase angle. An arctangent of the ratio Q/I is equal to the phase angle. The magnitude of the change in the parameter can then be calculated from the change in the phase angle.

Calculation of the quadrature component Q and the in-phase component I requires multiple samples of the output pulse at specific intervals of the phase generated carrier. A period of the phase generated carrier is significantly longer than a period of the output pulse. The longer period of the phase generated carrier requires the samples to span several output pulses to obtain each required interval of the phase generated carrier. The longer period of the phase generated carrier reduces the sampling rate of the demodulation technique.

High-speed phase generated carriers (e.g., a frequency greater than 1 MHz, or a period less than 1000 nanoseconds) do not permit the precise control of a demodulation phase offset β associated with the phase generated carrier. One shortcoming of the demodulation techniques is that a variation in the demodulation phase offset β from a fixed value reduces the accuracy of the demodulation techniques.

Thus, a need exists for reduced dependency on demodulation phase offsets for demodulation techniques of fiber optic sensor arrays that employ phase generated carriers.

SUMMARY

The invention in one embodiment encompasses a method. A sensor array employs a parameter to induce a time-varying phase angle φ on an optical signal that comprises a phase generated carrier with a demodulation phase offset β. The phase angle φ is calculated independently of the demodulation phase offset β.

Another embodiment of the invention encompasses an apparatus. A sensor array employs a parameter to induce a time-varying phase angle φ on an optical signal that comprises a phase generated carrier with a demodulation phase offset β. The apparatus comprises a processor component that calculates the phase angle φ independent from the demodulation phase offset β.

A further embodiment of the invention encompasses an article. A sensor array employs a parameter to induce a time-varying phase angle φ on an optical signal that comprises a phase generated carrier with a demodulation phase offset β. The article includes one or more computer-readable signal-bearing media. The article includes means in the one or more media for calculating the phase angle φ independently of the demodulation phase offset β.

DETAILED DESCRIPTION

Turning toFIG. 1, an apparatus100in one example comprises a plurality of components such as computer software and/or hardware components. A number of such components can be combined or divided in the apparatus100. An exemplary component of the apparatus100employs and/or comprises a set and/or series of computer instructions written in or implemented with any of a number of programming languages, as will be appreciated by those skilled in the art.

Referring toFIG. 1, the apparatus100in one example comprises one or more lasers102, one or more optical switches104, one or more phase modulators106, one or more sensor arrays108, one or more optical receivers110, and one or more processor components112. In one example, the apparatus100demodulates an optical signal to measure a change in a parameter, as described herein. The laser102in one example comprises a continuous wave laser. The laser102generates and sends an optical signal through the optical switch104and the phase modulator106to the sensor array108.

The optical switch104in one example comprises a time division multiplexed (“TDM”) switch. The optical switch104gates the optical signal such that the optical signal comprises a stream of optical pulses. The phase modulator106impresses a phase generated carrier (“PGC”)114on the stream of optical pulses. For example, the laser102, the optical switch104, and the phase modulator106cooperate to create one or more optical pulses116that comprise the phase generated carrier114, as will be understood by those skilled in the art. The optical pulse116comprises a period Tpulse. The period Tpulsein one example is approximately between 100 nanoseconds and 1000 nanoseconds. The phase generated carrier114in one example comprises a period Tpgcand a modulation depth of M. The period Tpgccomprises a relationship with a frequency fpgc=1/Tpgc, as will be understood by those skilled in the art. The frequency fpgcin one example is approximately between 2 MHz and 20 MHz. The phase generated carrier114is associated with a demodulation phase offset β. The phase generated carrier114creates a time-varying phase angle equal to

The sensor array108in one example comprises one or more sensors124,126, and128, for example, mismatched path interferometers. The sensor array108splits the optical pulse116into one or more optical pulses118,120, and122, for example, one pulse per sensor. The optical pulses116,118,120, and122in one example are substantially the same. The sensors124,126, and128of the sensor array108receive the optical pulses118,120, and122, respectively. The sensors124,126, and128of the sensor array108in one example employ one or more parameters and the optical pulses118,120, and122to create one or more respective interference pulses130,132, and134. Exemplary parameters comprise acoustic vibration, fluid pressure variations, acceleration, and magnetic field intensity. For example, the sensor124splits the optical pulse118into a first portion and a second portion. The sensor124employs the parameter to induce a time-varying phase angle φ on the first portion of the optical pulse118, relative to the second portion of the optical pulse118. The sensor124recombines the first portion of the optical pulse118with the second portion of the optical pulse124to create the interference pulse130. A time-varying amplitude variation of the interference pulse130represents the time-varying phase angle φ between the first portion and the second portion of the optical pulse118.

The optical pulses116comprise an intermediary spacing such that the interference pulses130,132, and134comprise a relatively small spacing, for example, a high duty cycle, as described herein. The interference pulses130,132, and134comprise a period substantially equal to the period Tpulseof the optical pulse116. The sensor array108sends the interference pulses130,132, and134to the optical receiver110in a pulse train136, for example, in a serial fashion. For example, the optical pulse train136comprises the interference pulses130,132, and134.

The optical receiver110in one example comprises one or more photodiodes138. In a further example, the optical receiver110comprises a transimpedance amplifier140. The optical receiver110in one example comprises a polarization diversity receiver system (not shown), as defined in U.S. Pat. No. 5,852,507, assigned to the assignee of the present invention. The optical receiver110receives the optical pulse train136. The optical receiver110then creates one or more respective analog electrical signals that represent the interference pulses130,132, and134from the optical pulse train136. For example, the optical receiver110converts a magnitude of power of the optical pulse train136to a voltage signal.

The processor component112in one example comprises a digital signal processor. In a further example, the processor component112comprises an analog-to-digital converter component142. The processor component112in one example comprises an instance of a computer-readable signal-bearing media144, as described herein. The analog-to-digital converter component142converts the analog electrical signal from the optical receiver110into a digital signal. The processor component112in one example serves to sense a change in the parameters by employing the time-varying amplitude variation of the interference pulses130,132, and134to calculate the time-varying phase angle φ.

An illustrative description of exemplary operation of the apparatus100is presented, for explanatory purposes. The laser102, the optical switch104, and the phase modulator106cooperate to create the one or more optical pulses116. The sensor array108splits the optical pulse116into the optical pulses118,120, and122. The sensors124,126, and128employ the parameters and the optical pulses118,120, and122to create the interference pulses130,132, and134. The sensor array108sends the interference pulses130,132, and134as the optical pulse train136to the optical receiver110.

The optical receiver110creates an analog electrical signal that represent the one or more interference pulses130,132, and134. For example, the analog electrical signal is defined as s(t, M, β, φ):

s⁡(t,M,β,φ)=A+B·cos⁡(M·sin⁡(2⁢π·tTpgc+β)+φ),
where A is an average signal level, B is an interference term signal level, M is the modulation depth, Tpgcis the period of the phase generated carrier, β is the demodulation phase offset, and φ is the phase angle. The phase angle of s(t, M, β, φ) comprises a first portion due to the phase generated carrier,

M·sin⁡(2⁢π·tTpgc+β),
and a second portion due to the parameter, φ, as will be understood by those skilled in the art.

The analog-to-digital converter component142in one example converts the analog electrical signal from the optical receiver110into a digital signal that represents the interference pulse130. The processor component112obtains a plurality of samples Sn, n=0 to x, of the interference pulse130from the digital signal. The processor component112obtains the plurality of samples Snat time intervals Δt over a period Ts. The period Tsin one example is substantially equal to the period Tpgcof the phase generated carrier114. The period Tsin one example serves to promote an increase in sampling rate, as will be appreciated by those skilled in the art. In one example, the period Tsis less than or equal to 1.125×Tpulse. In a further example, the period Tsis less than or equal to Tpulse.

The time interval Δt in one example is equal to an even fraction of the period Tpgc, (e.g. Tpgc/8 or Tpgc/16). In one example, the processor component112obtains the plurality of samples Snstarting at a time t0, with a time interval Δt of Tpgc/8. For example, the plurality of samples Sncomprise eight samples at t0, t0+Δt, t0+2Δt, t0+3Δt, t0+4Δt, t0+5Δt, t0+6Δt, and t0+7Δt. In another example, the processor component112obtains the plurality of samples Snstarting at a time t0with a time interval Δt of Tpgc/16. For example, the plurality of samples Sncomprise sixteen samples at t0, t0+Δt, t0+2Δt, t0+3Δt, t0+4Δt, t0+5Δt, t0+6Δt, t0+7Δt, t0+8Δt, t0+9Δt, t0+10Δt, t0+11Δt, t0+12Δt, t0+13Δt, t0+14Δt, and t0+15Δt.

The processor component112employs one or more of the plurality of samples Snto calculate one or more quadrature terms and one or more in-phase terms. The processor component112in one example calculates a set of quadrature terms Qj, j=0 to y. For example, the set of quadrature terms Qjcomprises a number of quadrature terms equal to ½ a number of samples of the plurality of samples Sn. In one example where the plurality of samples Sncomprises eight samples, y is equal to three, and the processor component112calculates the set of quadrature terms Qjas:
Q0=S0−S4, Q1=S1−S5, Q2=S2−S6, andQ3=S3−S7(FIG. 3).
In another example where the plurality of samples Sncomprises sixteen samples, y is equal to seven, and the processor component112calculates the set of quadrature terms Qjas:
Q0=S0−S8, Q1=S1−S9, Q2=S2−S10, Q3=S3−S11,
Q4=S4−S12, Q5=S5−S13, Q6=S6−S14, andQ7=S7−S15(FIG. 4).

The processor component112in one example calculates a set of in-phase terms Ik, k=0 to z. For example, the set of in-phase terms Ikcomprises a number of in-phase terms equal to ¼ the number of samples of the plurality of samples Sn. In one example where the plurality of samples Sncomprises eight samples, z is equal to one, and the processor component112calculates the set of in-phase terms Ikas:
I0=(S0+S4)−(S2+S6), and
I1=(S1+S5)−(S3+S7)  (FIG. 3).
In another example where the plurality of samples Sncomprises sixteen samples, z is equal to three, and the processor component112calculates the set of in-phase terms Ikas:
I0=(S0+S8)−(S4+S12),Ii=(S1+S9)−(S5+S13),
I2=(S2+S10)−(S6+S14), andI3=(S3+S11)−(S7+S15)  (FIG. 4).

The processor component112employs the set of quadrature terms Qjto calculate a quadrature term Qaband a quadrature term Qs. The processor component112in one example calculates the quadrature term Qabto be equal to a maximum value of absolute values of the set of quadrature terms Qj:
Qab=max(|Qj|).
The quadrature term Qabis independent from the demodulation phase offset β, as will be appreciated by those skilled in the art. The processor component112calculates a constant C1as described herein. The processor component112in one example calculates the quadrature term Qsas:

Qs=C1×∑j=0j=y⁢⁢Qj2.
The quadrature term Qsis independent from the demodulation phase offset β, as will be appreciated by those skilled in the art.

The processor component112employs the set of in-phase terms Ikto calculate an in-phase term Is. The processor component112calculates a constant C2as described herein. The processor component112in one example calculates the in-phase term Isas:

Is=C2×∑k=0k=z⁢⁢Ik2.
The in-phase term Isis independent from the demodulation phase offset β, as will be appreciated by those skilled in the art. The processor component112in one example calculates the constant C1and the constant C2such that respective absolute values of the quadrature term Qs, the quadrature term Qab, and the in-phase term Isare substantially equal at a modulation depth M of an operating range.

The processor component112employs the quadrature terms Qsand Qabto calculate a quadrature term Qm. The processor component112in one example employs the quadrature terms Qsand Qabto calculate a correction term ΔQ, for example:
ΔQ=Qs−Qab.
The processor component112employs a linear combination of the quadrature term Qsand the correction term ΔQ to calculate the quadrature term Qm. The processor component112in one example calculates a constant C3and calculates Qmaccording to a first order linear equation:
Qm=Qs+(C3×ΔQ).

The processor component112calculates the constant C3to promote an increase in a maximum variation of the modulation depth M. The quadrature terms Qaband Qsand the in-phase term Ischange with respect to the modulation depth M at different respective rates. The changes with respect to the modulation depth M reduce the accuracy of the calculation of the phase angle φ, as will be understood by those skilled in the art. The correction term ΔQ serves to create the quadrature term Qmsuch that the quadrature term Qmand the in-phase term Iscomprise a substantially equal rate of change with respect to the modulation depth M over an operating range for the phase generated carrier. The substantially equal rates of change with respect to the modulation depth M of the quadrature term Qmand the in-phase term Isreduces a sensitivity to a change in the modulation depth M of the calculation of the phase angle φ, as will be appreciated by those skilled in the art.

For example, at a modulation depth M of an operating range for the phase generated carrier, Qab, Qs, and Isare substantially equal and ΔQ is equal to zero. As the modulation depth M deviates from the operating point within the operating range, Qsand Qabchange with respect to the modulation depth M with different rates. The change in Qsand Qabcause a deviation in ΔQ, and subsequently a change in Qm. A rate of change of Qmand a rate of change of Iswith respect to the modulation depth M are substantially equal within the operating range, as will be appreciated by those skilled in the art.

The modulation depth M in one example is between 1.0 and 1.7 radians. For example, the modulation depth M is sufficiently large to promote an increase in signal strength of the phase generated carrier114. The modulation depth M in a further example is sufficiently small to promote stability of the quadrature term Qsand the in-phase term Iswith respect to a change in the modulation depth M. For example, the modulation depth M is approximately equal to π/2.

The processor component112employs one or more of the set of quadrature terms Qjand the quadrature term Qmto calculate a quadrature term Q. The processor component112in one example employs a magnitude of the quadrature term Qmand a sign of one of the quadrature terms of the set of quadrature terms Qjto calculate Q. For example, the processor component112chooses the quadrature term Q1that comprises a relatively large magnitude to avoid a zero crossing of the magnitude. The processor component112chooses a different quadrature term with a larger magnitude, for example, the quadrature term Q0, when the magnitude of the quadrature term Q1approaches zero. The quadrature term Q is independent from the demodulation phase offset β, as will be appreciated by those skilled in the art.

The processor component112employs one or more of the set of in-phase terms Ikand the in-phase term Isto calculate an in-phase term I. The processor component112in one example employs a magnitude of the in-phase term Isand a sign of one of the in-phase terms of the set of in-phase terms Isto calculate I. For example, the processor component112chooses an in-phase term I1that comprises a relatively large magnitude to avoid a zero crossing of the magnitude. The processor component112chooses a different in-phase term, for example, the in-phase term I0, when the magnitude of the in-phase term I1approaches zero. The in-phase term I is independent from the demodulation phase offset β, as will be appreciated by those skilled in the art.

A change in the demodulation phase offset β in one example changes the sign of the quadrature term Q and/or the in-phase term I. Four bands of operation of width π/2 in one example exist across a total range of 0 to 2π for the demodulation phase offset β. Where the magnitude of the demodulation phase offset β is near a border of a band of operation, the magnitude of the in-phase term Ikchosen to determine the sign of I and/or the magnitude of the quadrature term Qjchosen to determine the sign of Q may approach zero. When the magnitude of the in-phase term Ikchosen to determine the sign of I and/or the magnitude of the quadrature term Qjchosen to determine the sign of Q approaches zero, the processor component112chooses a different quadrature term Qjand/or in-phase term Ik. The processor component112chooses a different quadrature term Qjand/or in-phase term Ikto promote the calculation of the phase angle φ independent from the demodulation phase offset β. The phase modulator106in one example maintains the demodulation phase offset β within a range significantly smaller than 0 to π/2, therefore the demodulation phase offset β does not need to be known, as will be appreciated by those skilled in the art.

The processor component112employs the quadrature term Q and the in-phase term I to calculate the phase angle φ independently of the demodulation phase offset β. Since the quadrature term Q and the in-phase term I are independent from the demodulation phase offset β, the calculation of the phase angle φ is independent from the demodulation phase offset β. The processor component112in one example calculates the phase angle:
φ=arctangent (Q/I).
The processor component112in one example employs the change in the phase angle φ between multiple instances of the interference pulses130,132, and134to determine the change in the parameters employed by the sensors124,126, and128.

Turning toFIG. 2, the plot202comprises an exemplary representation of the interference pulses130,132, and134and appropriate sampling times for the processor component112with respect to time t. The interference pulses130,132, and134are represented by the analog electrical signal s(t, M, β, φ). The quadrature and in-phase components of the interference pulses are represented by s(t, M, β, π/2) and s(t, M, β, 0), respectively. One or more square pulses230,232, and234represent the period Tpulseof the interference pulses130,132, and134, respectively. The square pulses230,232, and234comprise a spacing period of Tspace. The square pulses230,232, and234in one example comprise a high duty cycle, for example, the sampling period Tsis substantially longer than the spacing period Tspace.

The processor component112in one example obtains eight samples from the respective interference pulses130,132, and134. The processor component112in one example obtains the samples at a constant rate over the period Ts. For example, the processor component112obtains eight samples, S0through S7, for the interference pulse130, discards the next three samples Sdiscard, obtains the next eight samples, S0through S7, for the interference pulse132, discards the next three samples Sdiscard, and so forth.

Turning toFIG. 3, a plot302comprises a representation of a set of calculations for the quadrature terms Qjand the in-phase terms Ikfor eight samples of the interference pulse130. Where eight samples are taken, x=7, y=3 and z=1. The processor component112calculates a given term by adding and subtracting a plurality of the samples Snin a respective row of the given term. The processor component112adds or subtracts a sample according to a sign designated in the row/column pair for the given term and the sample. If a sign is not listed for a sample, the sample is not used for the given term. For example, the processor component112calculates Q0as +S0−S4, Q2as +S2−S6, and I0as +S0−S2+S4−S6.

Turning toFIG. 4, a plot402comprises a representation of a set of calculations for the quadrature terms Qjand the in-phase terms Ikfor sixteen samples of the interference pulse130. Where sixteen samples are taken, x=15, y=7, and z=3. For example, the processor component112calculates Q0as +S0−S8, Q1as +S2−S9, and I0as +S0−S4+S8−S12. Turning toFIGS. 3 and 4, patterns of the + and the − signs in one example can be seen for the quadrature terms Qjand the in-phase terms Ik, respectively. For example, similar patterns can be used to calculate a set of quadrature terms Qjand Ikfor a plurality of samples with a different number of samples.

Turning to FIGS,5,6, and7, plots502,602, and702comprise a representation of the accuracy of the calculation of the phase angle φ for various methods. The accuracy of the calculation of the phase angle φ is measured by calculating a value Δφ. For example, an output phase angle φoutof the phase generated carrier114and an input phase angle φinof the phase generated carrier114are used to calculate:
Δφ=φout−φin.
The accuracy Δφ is shown as a function of the input phase angle φ, with plots for various values of the demodulation phase offset β and the modulation depth M. The accuracy was calculated using MathCAD (Mathsoft Engineering & Education, Inc., Cambridge, Mass. 02142, http://www.mathcad.com) using a pseudo-random number generator to add a variable amplitude noise to the analog electrical signal s(t, M, β, φ). The variable amplitude noise comprises a peak 0.1% fluctuation with a uniform probability density. For comparison, plots502,602, and702comprise a same scale with an input phase angle φ between −1.5 radians and 1.5 radians and an accuracy Δφ within 0.01 radians and −0.01 radians.

Referring toFIG. 5, plot502represents the accuracy of a prior art demodulation technique that is dependent on the demodulation phase offset β and the modulation depth M. A mean value of Δφ for the prior art demodulation technique ofFIG. 5is approximately 2.5 milliradians, where β is varied within 0.00175 radians about an operating point of 0.29 radians, and M is varied within 0.05 radians about an operating point of π radians.

Referring toFIG. 6, plot602represents an exemplary accuracy of calculation of the phase offset φ where eight samples are taken (e.g. x=7, y=3, z=1). A mean value of Δφ for the plot602is approximately 4 milliradians, where β is varied between 0.1 and 1.1, and the modulation depth M is varied within 0.05 radians about an operating point of 1.63 radians.

Referring toFIG. 7, plot702represents an exemplary accuracy of calculation of the phase offset φ where sixteen samples are taken (e.g. x=15, y=7, z=3). A mean value of Δφ for the plot702is approximately 2.5 milliradians, where β is varied between 0.2 and 1.3, and M is varied within 0.07 radians about an operating point of 1.6 radians. The plots602and702comprise a similar accuracy to the prior art demodulation technique ofFIG. 5with a reduced restraint on the demodulation phase offset.

The apparatus100in one example employs one or more computer-readable signal-bearing media. One example of a computer-readable signal-bearing media for the apparatus100comprises the recordable data storage media144of the processor component112. For example, the computer-readable signal-bearing media for the apparatus100comprises one or more of a magnetic, electrical, optical, biological, and atomic data storage media. In one example, the computer-readable signal-bearing media comprises a modulated carrier signal transmitted over a network comprising or coupled with the apparatus100, for instance, one or more of a telephone network, a local area network (“LAN”), the internet, and a wireless network.

The steps or operations described herein are just exemplary. There may be many variations to these steps or operations without departing from the spirit of the invention. For instance, the steps may be performed in a differing order, or steps may be added, deleted, or modified.