[go: up one dir, main page]

WO2025076589A1 - Détecteur de phase - Google Patents

Détecteur de phase Download PDF

Info

Publication number
WO2025076589A1
WO2025076589A1 PCT/AU2024/051068 AU2024051068W WO2025076589A1 WO 2025076589 A1 WO2025076589 A1 WO 2025076589A1 AU 2024051068 W AU2024051068 W AU 2024051068W WO 2025076589 A1 WO2025076589 A1 WO 2025076589A1
Authority
WO
WIPO (PCT)
Prior art keywords
time
phase
varying
determining
signals
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
PCT/AU2024/051068
Other languages
English (en)
Inventor
Anneshwa DEY
Chathura Priyankara BANDUTUNGA
Malcolm Bruce Gray
Justin Chak Tin WONG
Paul George SIBLEY
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Australian National University
Original Assignee
Australian National University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from AU2023903241A external-priority patent/AU2023903241A0/en
Application filed by Australian National University filed Critical Australian National University
Publication of WO2025076589A1 publication Critical patent/WO2025076589A1/fr
Pending legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/60—Receivers
    • H04B10/61—Coherent receivers
    • H04B10/616—Details of the electronic signal processing in coherent optical receivers
    • H04B10/6165—Estimation of the phase of the received optical signal, phase error estimation or phase error correction
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03D—DEMODULATION OR TRANSFERENCE OF MODULATION FROM ONE CARRIER TO ANOTHER
    • H03D3/00—Demodulation of angle-, frequency- or phase- modulated oscillations
    • H03D3/007—Demodulation of angle-, frequency- or phase- modulated oscillations by converting the oscillations into two quadrature related signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/50—Transmitters
    • H04B10/516—Details of coding or modulation
    • H04B10/548—Phase or frequency modulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J14/00—Optical multiplex systems
    • H04J14/002—Coherencemultiplexing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J14/00—Optical multiplex systems
    • H04J14/005—Optical Code Multiplex
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
    • G01J2009/0203—Phased array of beams
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
    • G01J2009/0211—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods for measuring coherence
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
    • G01J2009/0226—Fibres
    • G01J2009/023—Fibres of the integrated optical type

Definitions

  • the present disclosure relates to systems and methods for phase determination, including determining (which includes measuring and/or recovering) time-varying phase of time-varying signals.
  • the invention has been developed primarily for use in methods and systems for detecting time-varying phase of time-varying signals using an open-loop phasemeter topology for differential optical interferometric measurements and will be described hereinafter with reference to this application. However, it will be appreciated that the invention is not limited to this particular field of use.
  • interferometer configurations include, laser interferometer length measurements [1,8], fiber strain sensing [9], interferometer stability characterization [10,11], cyclic error reduction [12,13] and, dispersion spectroscopy [14].
  • phase difference measurements include, laser interferometer length measurements [1,8], fiber strain sensing [9], interferometer stability characterization [10,11], cyclic error reduction [12,13] and, dispersion spectroscopy [14].
  • common mode noise suppression through phase subtraction is integral to achieving the desired sensitivity.
  • phase subtraction techniques use two phasemeters that independently track their required phases with the subtraction computed following phase recovery. This requires each phasemeter to phase track with the required sensitivity of the final subtraction and the dynamic range of the individual signals to fully remove common noise sources.
  • each phasemeter to phase track with the required sensitivity of the final subtraction and the dynamic range of the individual signals to fully remove common noise sources.
  • the aforementioned arctangent and unwrap operations can degrade. This makes achieving the required phase fidelity on each individual phasemeter difficult. Therefore, a trade-off exists between the differential measurement sensitivity and the individual measurement dynamic range.
  • Heinzel et al [15] proposed a novel solution when using wavefront sensing to extract beam pointing errors in addition to longitudinal length sensing, for the Laser Interferometer Space Antenna mission (LISA) [16].
  • LSA Laser Interferometer Space Antenna mission
  • Heinzel et al. demonstrate; four parallel PLLs, a combination matrix, individually tailored servo controllers for each variable of interest and, a decombination matrix. This solution removes common mode dynamics from each phase-difference variable. This, in turn, allows the optimization of each controller dependent only on the dynamics of the particular variable.
  • all four PLLs must phase track without error. If the high speed, longitudinal variable PLL cycle slips, then all variables are compromised.
  • phase detection technique uses an arctan operation. This technique is used in conjunction with quadrature demodulation (also referred to as “IQ demodulation”) to return the in-phase (“I”) and quadrature (“Q”) components of a time-varying signal, e.g., representing an RF field.
  • IQ demodulation quadrature demodulation
  • I and Q quadrature components
  • IQ pair a time-varying signal
  • Arctan typically uses the “arctan2” algorithm operating on an IQ pair to produce phase ( ⁇ ) using the following operation: arctan(Q/I) modulo 2 ⁇ .
  • the arctan2 function has discontinuities at ⁇ where the Q value transits zero and the I value is negative.
  • An unwrapping algorithm the second component of this phase recovery method, is then required to recover the desired phase ( ⁇ ) using the following operation: unwrap ⁇ arctan(Q/I) ⁇ to remove the discontinuities.
  • arctan operation arises when the unwrap algorithm must make a decision to either unwrap, or not, at or near a discontinuity based on the immediate history of phase evolution. As the phase discontinuity point corresponds to a zero in Q, even a small amount of noise at this location can generate an incorrect unwrap decision. Accurate decision-making therefore requires high bandwidth and high-fidelity phase measurements that encompass all signal phase dynamics, even if the required signal bandwidth is modest. When this onerous requirement is not met, cycle slips will occur, corrupting the recovered phase signal.
  • phase detection technique uses a phase-locked loop (PLL).
  • PLL phase-locked loop
  • the PLL avoids phase unwrapping and the related cycle slip issues of the arctan-unwrap technique.
  • the PLL typically mixes down a single quadrature component (Q) and, after low pass filtering, uses this Q component to drive a numerically controlled oscillator (NCO), or a voltage-controlled oscillator (VCO) in an analog PLL.
  • NCO numerically controlled oscillator
  • VCO voltage-controlled oscillator
  • Phase recovery is obtained by integrating the control signal provided to the NCO/VCO.
  • the PLL may be understood to use negative feedback to linearize the Q component and thus recover the signal phase.
  • the PLL architecture requires that all significant signal phase dynamics are tracked and that the total phase dynamics at frequencies above the PLL unity gain frequency are sufficiently small to stay well within the linear range of the Q component mixer response.
  • the in-loop sensor noise is limited by shot noise, dark noise and ADC noise; thus, if the total sensor noise, when integrated across the PLL bandwidth, becomes sufficiently large to drive the Q component mixer response outside its linear response range, then cycle slipping may occur and phase tracking will become compromised.
  • any one of the terms “including” or “which includes” or “that includes” as used herein is also an open term that also means including at least the elements/features that follow the term, but not excluding others. Thus, “including” is synonymous with and means “comprising”. [0020] In the claims, as well as in the summary above and the description below, all transitional phrases such as “comprising”, “including”, “carrying”, “having”, “containing”, “involving”, “holding”, “composed of”, and the like are to be understood to be open-ended, i.e., to mean “including but not limited to”. Only the transitional phrases “consisting of” and “consisting essentially of” alone shall be closed or semi-closed transitional phrases, respectively.
  • the DDPR phasemeter implementation described herein eliminates common phase signals prior to phase tracking. In doing so, it dramatically reduces the dynamic range and signal bandwidth required to measure phasemeter differences.
  • DDPR operates directly in ⁇ ⁇ space, DDPR generates the ⁇ ⁇ Vector of the phase subtraction. The phase difference alone can then be recovered by implementing the arctangent of the DDPR generated ⁇ ⁇ pair, removing the need to track the full dynamic range of the individual signals.
  • an arctangent phase readout we eliminate the need for feedback resulting in complete elimination of common mode dynamics such that high fidelity phase difference signals are routinely available when common mode phase dynamics make phase tracking impossible for individual channels.
  • a method for determining a time-varying phase difference between two time- varying signals comprising: receiving or generating two independent time-varying in-phase components and two independent time-varying quadrature components from two or more demodulated time-varying signals; and determining the time-varying phase difference from the two time-varying in-phase components and two time-varying quadrature components by combining the four signals at each time point.
  • the method may further comprise the step of determining a time-varying phase difference from the combined signals, and optionally determining a time-varying phase from the time-varying phase difference.
  • the step of determining the time- varying phase difference from the combined signals may comprise determining an arctan of the combined signals.
  • the method may further comprise the steps of anti-alias filtering and/or decimating the determined time-varying phase difference.
  • the step of determining the two independent time- varying in-phase components and the two independent time-varying quadrature component may comprise: automatically generating one of the two time-varying in-phase components by delaying the other of the two time-varying in-phase components by a selected time delay such that the two signals are independent; and automatically generating one of the two time-varying quadrature components by delaying the other of two time-varying quadrature components by the selected time delay such that the two signals are independent.
  • the step of determining the time- varying phase difference from the combined signals may comprise determining an arctan of the combined signals; or, when the selected time delay is below a predetermined threshold, determining that the time-varying phase difference is linearly related to the combined signals.
  • the step of determining the time-varying phase may comprise integrating the time-varying phase difference with respect to time.
  • the method may further comprise the step of performing the delaying and/or the integrating in one or more DSP hardware components, for example in FPGAs.
  • the method may further comprise the steps of anti-alias filtering and/or decimating the determined time-varying phase.
  • the step of determining the arctan of the combined signals may comprise the step of using a coordinate rotation method or component, for example on a coordinate rotation digital computer (CORDIC).
  • the step of combining the four determined signals into the combined signals may comprise: determining products of the [I1(t), I2(t)] and the [Q1(t), Q2(t)], including according to the relationships: IA.IB, QA.QB, QA.IB, and IA.QB.; and determining a sum and a difference of the products, including according to the relationships: (IA.IB + QA.QB), and (QA.IB ? IA.QB).
  • the step of determining the time-varying phase from the combined signals may comprise determining a ratio of the difference and the sum of the products, including according to the relationship: (QA.IB ? IA.QB) / (IA.IB + QA.QB).
  • the method may further comprise the step of determining the products, the sum, the difference and/or the ratio in one or more DSP hardware components, for example in one or more FPGAs.
  • the method may further comprise the step of low-pass filtering the four determined signals and prior to determining the time-varying phase difference, optionally using a code filter.
  • the time-varying phase difference or the time-varying phase may comprise radio frequencies.
  • a system configured/built to perform the method according to the first aspect, for example in an FPGA.
  • a system for determining a time-varying phase difference between two time- varying signals comprising: means for receiving or generating two independent time-varying in-phase components and two independent time-varying quadrature components from two or more demodulated time-varying signals; and means for determining the time-varying phase difference from the two time-varying in-phase components and two time-varying quadrature components by combining the four signals at each time point.
  • the system may further comprise means for determining a time-varying phase difference from the combined signals, and optionally determining a time-varying phase from the time-varying phase difference.
  • a method for determining a time-varying phase difference between two time-varying signals or a time-varying phase of one time-varying signal comprising: receiving or generating two time-varying in-phase components and two time-varying quadrature components from one or more demodulated time-varying signals; and determining the time-varying phase difference from the two time- varying in-phase components and two time-varying quadrature components by: combining the four signals at each time point, and determining a time-varying phase difference from the combined signals; and optionally determining a time-varying phase from the time- varying phase difference.
  • the two time-varying signals are independent signals.
  • the step of determining the time-varying phase difference from the combined signals include determining an arctan of the combined signals.
  • the method further comprises the steps of anti-alias filtering and/or decimating the determined time-varying phase difference.
  • the step of determining the two time-varying in-phase components and the two time-varying quadrature component includes: automatically generating one of the two time-varying in-phase components by delaying the other of the two time-varying in-phase components by a selected time delay; and automatically generating one of the two time-varying quadrature components by delaying the other of two time-varying quadrature components by the selected time delay.
  • the step of determining the time-varying phase difference from the combined signals includes: determining an arctan of the combined signals; or when the selected time delay is below a predetermined threshold, determining that the time- varying phase difference is linearly related to the combined signals.
  • the step of determining the time-varying phase includes integrating the time-varying phase difference with respect to time.
  • the method further comprises the step of performing the delaying and/or the integrating in one or more DSP hardware components, for example in FPGAs.
  • the method further comprises the steps of anti-alias filtering and/or decimating the determined time-varying phase.
  • the step of determining the arctan of the combined signals comprises the step of using a coordinate rotation method or component, optionally on a coordinate rotation digital computer (CORDIC).
  • the step of combining the four determined signals into the combined signals comprises: determining products of the [I 1 (t), I 2 (t)] and the [Q 1 (t), Q 2 (t)], including according to the relationships: I A .I B , Q A .Q B , Q A .I B , and I A .Q B .; and determining a sum and a difference of the products, including according to the relationships: IA.IB + QA.QB, and QA.IB ⁇ IA.QB.
  • the step of determining the time-varying phase from the combined signals comprises: determining a ratio of the difference and the sum of the products, including according to the relationship: (Q A .I B ⁇ I A .Q B ) / (I A .I B + Q A .Q B ).
  • the method further comprises the step of determining the products, the sum, the difference and/or the ratio in one or more DSP hardware components, for example in one or more FPGAs.
  • the method further comprises the step of low-pass filtering the four determined signals and prior to determining the time-varying phase difference, optionally using a code filter.
  • the time-varying phase difference or the time-varying phase may include radio frequencies (RF).
  • RF radio frequencies
  • Figures 1A and 1B are flow diagrams of an exemplary method embodiment.
  • Figure 2A is a schematic diagram of an exemplary direct differential phase recovery system embodiment.
  • Figures 2B to 2C are flow diagrams of exemplary embodiments of a direct differential phase recovery method.
  • Figure 3A is a schematic diagram of an exemplary time differential phase recovery system embodiment.
  • Figure 3B to 3D are flow diagrams of exemplary embodiments of a time differential phase recovery method.
  • Figure 4 is a graph of a transfer function according to an exemplary embodiment of a time differential phase recovery system.
  • Figure 5 is a block diagram of an exemplary embodiment of a time differential phase recovery system implemented on an FPGA.
  • Figure 6 shows a flow diagram demonstrating the signal processing to extract regular post phase tracking subtraction differential phase.
  • Figure 7 shows digital signal processing to extract DDPR phase.
  • Figure 8 shows a schematic diagram showing the bidirectional Mach-Zehnder interferometer optical configuration used for the example DDPR implementation.
  • Figures 9A and 9B show the bit growth to extract the ⁇ diff, reg ( Figure 9A) and ⁇ diff, ddpr ( Figure 9B).
  • Figures 10A to 10D show the time domain phase recovery of 2 ⁇ phase ramp at a frequency of 2 Hz.
  • Figures 11A and 11B show time domain phase recovery of 2 ⁇ phase ramp at a frequency of 656 Hz
  • Figure 12 shows the phase spectral density plot of time domain plot shown in Figure 11B
  • Figure 13 shows the time domain phase recovery of a 2 ⁇ phase ramp at a frequency of 1.3 KHz.
  • Figures 14A and 14B show a detail version of the time domain phase recovery of 2 ⁇ phase ramp at a frequency of 1.3 kHz of Figure 13.
  • Figure 14B shows a plot demonstrating the CW and CCW signals contributing to the DDPR and regular differential phase signals of Figure 14A.
  • Figure 15 shows the time domain DDPR phase recovery of a 400 kHz linear frequency tuning ramp at 1.3 kHz into the AOM and thermal tuning of laser over a frequency of 20 GHz over 80 seconds. The insert shows the start of the thermal turning.
  • Figure 16 shows a plot of the same DDPR trace as shown in Figure 15 with the post processed subtraction phase.
  • Figure 17 shows a time domain DDPR and post-processed subtraction phase recovery with a CORDIC phase recovery and diode laser tracking.
  • Figure 18 shows a time domain recovery of 2 ⁇ phase ramp at 2.6kHz and 17 Hz sinusoidal signal using IQ demodulation and TDPR.
  • Figure 19 shows a plot of the RMS phase error in TDPR subtraction with respect to DDPR phase as a function of ⁇ .
  • Figures 20A and 20B show plots of diode laser tracking with DDPR and regular subtraction in both time and frequency domain with a differential 2 ⁇ phase ramp at 5 Hz and differential sinusoidal signal at 217 Hz. Definitions [0082] The following definitions are provided as general definitions and should in no way limit the scope of the present invention to those terms alone, but are put forth for a better understanding of the following description.
  • real time for example “displaying real time data” refers to the display of the data without intentional delay, given the processing limitations of the system and the time required to accurately measure the data.
  • a process occurring “in real time” refers to operation of the process without intentional delay or in which some kind of operation occurs simultaneously (or nearly simultaneously) with when it is happening.
  • any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present invention, preferred methods and materials are described. It will be appreciated that the methods, apparatus and systems described herein may be implemented in a variety of ways and for a variety of purposes. The description here is by way of example only.
  • the term “exemplary” is used in the sense of providing examples, as opposed to indicating quality. That is, an “exemplary embodiment” is an embodiment provided as an example, as opposed to necessarily being an embodiment of exceptional quality for example serving as a desirable model or representing the best of its kind.
  • the various methods or processes outlined herein may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine.
  • inventive concepts may be embodied as a computer readable storage medium (or multiple computer readable storage media) (e.g., a computer memory, one or more floppy discs, compact discs, optical discs, magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other non-transitory medium or tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments of the invention discussed above.
  • the computer readable medium or media can be transportable, such that the program or programs stored thereon can be loaded onto one or more different computers or other processors to implement various aspects of the present invention as discussed above.
  • At least one of A and B can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.
  • Example embodiments are provided so that this disclosure will be thorough, and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth such as examples of specific components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be employed, that example embodiments may be embodied in many different forms and that neither should be construed to limit the scope of the disclosure. In some example embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail. [0097] Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.
  • DDPR Direct Differential Phase Recovery
  • Embodiments of the methods described remove common mode signal dynamics prior to phase tracking, which reduces the dynamic range requirements of the phasemeter tracking optical phase difference.
  • a phase difference measurement is experimentally demonstrated with this technique, achieving a phase sensitivity of 1 ⁇ 10 ⁇ 6 rad/ ⁇ Hz with a common-mode noise rejection of 141 dB.
  • the technique is also demonstrated where individual channels are subject to numerous cycle-slips and unable to track phase.
  • Figures 1A and 1B show an exemplary method 1 for determining a time-varying phase difference [ ⁇ (t)] between two time-varying signals or a time-varying phase [ ⁇ (t)] of one time-varying signal.
  • the method includes at step 10, receiving or generating two time-varying in-phase components [I 1 (t), I 2 (t)] and two time-varying quadrature components [Q 1 (t), Q 2 (t)] from one or more demodulated time-varying signals. This may be done by demodulation using a local oscillator, for example.
  • the method includes at step 20 determining the time- varying phase difference [ ⁇ (t)] from the determined two time-varying in-phase components [I 1 (t), I 2 (t)] and two time-varying quadrature components [Q 1 (t), Q 2 (t)].
  • Step 20 includes the step of combining the four signals [I 1 (t), I 2 (t)] and [Q 1 (t), Q 2 (t)] at each time point, at step 22.
  • Step 20 also includes the step of determining a time-varying phase difference [ ⁇ (t)] from the combined signals, at step 24.
  • step 20 also includes the step of determining a time-varying phase [ ⁇ (t)] from the time-varying phase difference [ ⁇ (t)] at step 26.
  • system 100/ method 101 can be used to determine a time-varying phase difference [ ⁇ (t)] between two time-varying signals.
  • Figure 3A-3D refer to a time differential phase recovery system 200/method 201 that can be used to implement the method according to Figures 1A to 1B.
  • system 200/ method 201 can be used to determine a time-varying phase [ ⁇ (t)] of one time-varying signal (based on a determined time-varying phase difference [ ⁇ (t)]).
  • Disclosed herein is described in detail the general direct differential phase recovery system 100/ method 101 embodiment. Following this is described in detail the general time differential phase recovery system 200/ method 201 embodiment.
  • Figure 2A shows a direct differential phase recovery system 100, which may be wholly or partly implemented on one or more hardware controllers 150, the hardware controller preferably being a DSP controller such as an FPGA, for example.
  • Figures 2B-2C show possible method steps of a method 101 that the system 100 may be configured to perform. Unless context dictates otherwise, one or more of the method steps as described with respect to Figures 2B to 2C may be optional.
  • the system 100 is configured to receive or generate two time-varying in-phase components [IA, IB] and receive or generate two time-varying quadrature components [Q A , Q B ] from two demodulated time-varying signals [A(t), B(t)] that are independent of each other.
  • the four signals are decoded outputs 152.
  • the system 100 is configured to low pass filter the received or generated two time-varying in-phase components [IA, IB] and two time-varying quadrature components [QA, QB], at step 112, using a low pass filter 154 for example.
  • the system 100 is configured to determine the time-varying phase difference [ ⁇ (t)] from the two time-varying in phase components [I A , I B ] and two time-varying quadrature components [QA, QB] as follows.
  • the system 100 is configured to combine the four signals [I A , I B , Q A, QB] at each time point into two combined signals [I ⁇ , Q ⁇ ] 156 as shown in Figure 2A.
  • the step of combining the four determined signals [IA, IB, QA, QB] into the combined signals [I ⁇ , Q ⁇ ] 156 includes: • determining products of the [I A , I B ] and the [Q A , Q B ], including according to the relationships: I A .I B , Q A .Q B , Q A .I B , and I A .Q B. , at step 122a; and • determining a sum and a difference of the products, including according t o the relationships: I A .I B + Q A .Q B , and Q A .I B ⁇ I A .Q B , at step 122b.
  • the system 100 is configured to determine the time-varying phase difference [ ⁇ (t)] from the two combined signals [I ⁇ , Q ⁇ ] 156 .
  • the determination of the time-varying phase difference [ ⁇ (t)] may be done by determining an arctan of the ratio of two combined signals [I ⁇ , Q ⁇ ] 156 .
  • the ratio may be determined according to a ratio of the difference and the sum of the products, including according to the relationship: (Q A .I B ⁇ I A .Q B ) / (I A .I B + Q A .Q B ), at step 224a .
  • the arctan of the ratio of the two combined signals may be computed for example by using a coordinate rotation method or component, such as a CORDIC rectangular polar operation 158 for example.
  • the “determining” of the time-varying phase difference [ ⁇ (t)] from the two combined signals [I ⁇ , Q ⁇ ] 156 can be considered to include “generating” the time-varying phase difference [ ⁇ (t)] from the two combined signals [I ⁇ , Q ⁇ ] 156 .
  • the “determining” of an arctan of the two combined signals [I ⁇ , Q ⁇ ] 156 can be considered to include “generating” an arctan of the two combined signals [I ⁇ , Q ⁇ ] 156 .
  • the system 100 is configured to anti-alias the determined time-varying phase difference [ ⁇ (t)], at step 128, using an anti-aliasing filter 160.
  • the system 100 is configured to decimate the determined time-varying phase difference [ ⁇ (t)], at step 129, for example using a down sampler 162.
  • the system 100 is configured to read out the time-varying phase difference [ ⁇ (t)], at step 130, for example using a phase readout display 164.
  • the time-varying phase difference [ ⁇ (t)] determined by the system 100/method 101 can include radio frequencies (RF), e.g., from electrical and/or optical signals.
  • RF radio frequencies
  • the RF frequencies include one or more frequencies between 3 Hz and 300 GHz. In some embodiments, the included RF frequencies may include frequencies up to: 30 MHz, 200 MHz, or 600 MHz.
  • Figure 3A shows a time differential phase recovery system 200, which may be wholly or partly implemented on one or more hardware controllers 250, the hardware controller preferably being a DSP controller such as an FPGA for example.
  • Figures 3B-3D show possible method steps of a method 201 that the system 200 may be configured to perform. Unless context dictates otherwise, one or more of the method steps as described with respect to Figures 3B-3D may be optional.
  • the system 200 is configured to receive or generate two time-varying in-phase components [IP, ID] and receive or generate two time-varying quadrature components [Q P , Q D ] from one demodulated time-varying signal.
  • the system 200 is configured to low pass filter the received two time-varying in-phase components [IP, ID] and two time-varying quadrature components [QP, QD], at step 212, using a low pass filter for example (not shown).
  • a low pass filter for example (not shown).
  • Such low pass filtering may be carried out after receiving/generating the two time-varying in- phase components [IP, ID] and two time-varying quadrature components [QP, QD], for example if the step at 210b is omitted (in which there is low pass filtering of I P and Q P prior to generation of I D and Q D ).
  • the system 200 is configured to determine the time-varying phase difference [ ⁇ (t)] from the two time-varying in phase components [IP, ID] and two time-varying quadrature components [Q P , Q D ] as follows. [0126] At step 222, the system 200 is configured to combine the four signals [I P , I D , Q P , QD] into two combined signals [I ⁇ , Q ⁇ ] 256.
  • the step of combining the four determined signals [IP, ID, QP, QD] into the combined signals [I ⁇ , Q ⁇ ] 256 includes: • determining products of the [I P , I D ] and the [Q P , Q D ], including according to the relationships: I P .I D , Q P .Q D , Q P .I D , and I P .Q D. , at step 222a ; and • determining a sum and a difference of the products, including according t o the relationships: I P .I D + Q P .Q D , and Q P .I D – I P .Q D , at step 222b .
  • the system 200 is configured to determine the time-varying phase difference [ ⁇ (t)] from the two combined signals [I ⁇ , Q ⁇ ] 256 .
  • the determination of the time-varying phase difference [ ⁇ (t)] is done by determining an arctan of the ratio of two combined signals [I ⁇ , Q ⁇ ] 256 .
  • the ratio may be determined according to a ratio of the difference and the sum of the products, including according to the relationship: (Q P .I D – I P .Q D ) / (I P .I D + Q P .Q D ), at step 222c .
  • the arctan of the ratio of the two combined signals may be computed for example by using a coordinate rotation method or component, such as a CORDIC rectangular polar operation 258, for example.
  • the determination of the time-varying phase difference [ ⁇ (t)], when the selected time delay [ ⁇ ] is below a predetermined threshold is done by determining that the time-varying phase difference [ ⁇ (t)] is linearly related to the two combined signals [I ⁇ , Q ⁇ ] 256 , for example through a ratio of Q ⁇ /I ⁇ .
  • the ratio of Q ⁇ /I ⁇ may be determined by using a coordinate rotation method or component, such as a CORDIC rectangular polar operation 258 for example.
  • the predetermined threshold is set by a desire that the phase difference be within the linear range of arctan. So, the value of ⁇ that this corresponds to depends on the signal phase dynamics as well as the actual selected value of ⁇ . This will be discussed in more detail later with respect to the transfer function of Figure 4.
  • the “determining” of the time-varying phase difference [ ⁇ (t)] from the two combined signals [I ⁇ , Q ⁇ ] 256 can be considered to include “generating” the time time-varying phase difference [ ⁇ (t)] from the two combined signals [I ⁇ , Q ⁇ ] 256 .
  • the “determining” of an arctan of the two combined signals [I ⁇ , Q ⁇ ] 256 can be considered to include “generating” an arctan of the two combined signals [I ⁇ , Q ⁇ ] 256 .
  • the system 200 is configured to determine the time-varying phase [ ⁇ (t)] from the time-varying phase difference [ ⁇ (t)].
  • the determination of the time-varying phase [ ⁇ (t)] is done through integration 259 of the time- varying phase difference [ ⁇ (t)] with respect to time [t].
  • the “determining” of the time-varying phase [ ⁇ (t)] from the time-varying phase difference [ ⁇ (t)] can be considered to include “generating” the time-varying phase [ ⁇ (t)] from the time-varying phase difference [ ⁇ (t)], for example by integration 259 of the time-varying phase difference [ ⁇ (t)] with respect to time [t].
  • the system 200 is configured to anti-alias the determined time-varying phase [ ⁇ (t)], at step 228, using an anti-aliasing filter 260.
  • the system 200 is configured to decimate the determined time-varying phase [ ⁇ (t)], at step 229, for example using a down sampler 262.
  • the system 200 is configured to read out the time-varying phase [ ⁇ (t)], at step 230, for example using a phase readout display 264.
  • the time-varying phase difference [ ⁇ (t)] determined by the system 200/ method 201 and/or the time-varying phase [ ⁇ (t)] determined by the system 200/ method 201 can include radio frequencies (RF), e.g., the RF frequencies mentioned hereinbefore.
  • RF radio frequencies
  • the method comprises receiving or generating two time-varying in- phase components [I 1 (t), I 2 (t), I A , I B , I P , I D ] and two time-varying quadrature components [Q 1 (t), Q 2 (t), Q A , Q B , Q P , Q D ] from one or more demodulated time-varying signals (steps 10, 110, 210).
  • the method comprises determining the time-varying phase difference [ ⁇ (t)] from the two time-varying in-phase components [I 1 (t), I 2 (t), I A ,I B , I P , I D ] and two time-varying quadrature components [Q 1 (t), Q 2 (t), Q A ,Q B , Q P , Q D ] (step 20).
  • Determining the time-varying phase difference [ ⁇ (t)] comprises combining the four signals [I 1 (t), I 2 (t), I A ,I B , I P , I D ] and [Q 1 (t), Q 2 (t), Q A , Q B , Q P , Q D ] at each time point (steps 22 , 122 , 222 ). Determining the time-varying phase difference [ ⁇ (t)] also comprises determining a time- varying phase difference [ ⁇ (t)] from the combined signals [I ⁇ , Q ⁇ ] 156, 256 (steps 24 , 124, 224).
  • the step of determining the two time-varying in-phase components [I P , I D ] and the two time-varying quadrature component [Q P , Q D ] includes: automatically generating one of the two time-varying in-phase components [ID] by delaying the other of the two time-varying in-phase components [I P ] by a selected time delay [ ⁇ ] 255 (step 210c); and automatically generating one of the two time-varying quadrature components [Q D ] by delaying the other of two time-varying quadrature components [Q P ] by the selected time delay [ ⁇ ] 255 (step 210d).
  • the step of determining the time-varying phase difference [ ⁇ (t)] from the combined signals [I ⁇ , Q ⁇ ] 256 includes: determining an arctan of the combined signals [I ⁇ , Q ⁇ ] 256; or when the selected time delay [ ⁇ ] is below a predetermined threshold, determining that the time-varying phase difference [ ⁇ (t)] is linearly related to the combined signals [I ⁇ , Q ⁇ ] 256.
  • the step of determining the time-varying phase [ ⁇ (t)] includes integrating 259 the time- varying phase difference [ ⁇ (t)] with respect to time [t].
  • the method 201 further comprises the step of performing the delaying and/or the integrating in one or more DSP hardware components, for example in FPGAs 250.
  • the method 201 further comprises the steps of anti-alias filtering 260 (step 228) and/or decimating the determined time-varying phase [ ⁇ (t)] 262 (step 229).
  • the step of determining the arctan of the combined signals [I ⁇ , Q ⁇ ] 156 , 256 comprises the step of using a coordinate rotation method or component, e.g., a coordinate rotation digital computer (CORDIC) 158, 258.
  • CORDIC coordinate rotation digital computer
  • the step of combining the four determined signals [I1(t), I2(t), IA, IB, IP, ID, Q1(t), Q2(t), QA,QB, QP, QD] into the combined signals [I ⁇ , Q ⁇ ] 156, 256 comprises determining products of [I 1 (t), I 2 (t), I A , I B , I P , I D ] and [Q 1 (t), Q 2 (t), Q A ,Q B , Q P , Q D ] according to the relationships: I 1 .I 2 , Q 1 .Q 2 , Q 1 .I 2 , and I 1 .Q 2 (steps 122a, 222a).
  • the step of combining the four determined signals [I 1 (t), I 2 (t), I A , I B , I P , I D , Q 1 (t), Q 2 (t), Q A ,Q B , Q P , Q D ] into the combined signals [I ⁇ , Q ⁇ ]156, 256 comprises determining a sum and a difference of the products according to the relationships: ( I1.I2 + Q1.Q2), and ( Q1.I2 ⁇ 1A.Q2) (steps 122b, 222b).
  • the step of determining the time-varying phase [ ⁇ (t)] from the combined signals [I ⁇ , Q ⁇ ] 156, 256 comprises determining a ratio of the difference and the sum of the products according to the relationship: Q1.I2 – I1.Q2) / (I1.I2 + Q1.Q2) (steps 124a, 224a).
  • the time- varying phase difference [ ⁇ (t)] or the time-varying phase [ ⁇ (t)] may include radio frequencies.
  • a system 100, 200 configured/built to perform any described embodiment or aspect of methods 1, 101, 201, for example in an FPGA 150, 250 .
  • I 1 (t) I A
  • I 2 (t) I B
  • Q 1 (t) Q A (t)
  • Q 2 (t) Q B
  • I 1 (t) I P
  • I 2 (t) I D
  • Q 1 (t) Q P
  • Q 2 (t) Q D. 3.
  • IQ demodulation is a simple and robust method for continuous, sub-wavelength phase tracking.
  • IQ demodulation uses phase locked sine and cosine radio frequency local oscillators to mix down an input signal (step 10, 110).
  • Equation (1) which consists of a DC component and a signal ⁇ (t) at frequency ⁇ : (1)
  • Equation (1) which consists of a DC component and a signal ⁇ (t) at frequency ⁇ : (1)
  • Equation (1) which consists of a DC component and a signal ⁇ (t) at frequency ⁇ : (1)
  • the first stage of IQ demodulation is the mixing of the signal s(t) with the RF local oscillators.
  • the resultant outputs from the LPFs are the in-phase (I) and quadrature (Q) components of the signal relative to the demodulation frequency: 3.2.
  • Equation (3) the ‘reg’ subscript refers to regular, arctangent-unwrap phase determination. Subtracting these two phases then gives: which can also be represented as the difference in angle of the two complex numbers A and B.
  • both the I and Q components of each signal contribute significantly to the recovered phase information and thereby the need to track all the significant phase dynamics. Also, given these phase dynamics, it is necessary to unwrap each of these phase signals independently to attribute the arctangent discontinuities. This makes the post-phase-tracking subtraction implementation a problematic task and highly susceptible to cycle slips.
  • each signal tracks all significant dynamics with the desired precision of the desired phase difference measurement.
  • each phase measurement is independently phase unwrapped without error. In the presence of large common noise, this is an onerous requirement that can be avoided.
  • two combined signals I ⁇ and Q ⁇ can be produced as follows (step 22, 122).
  • the phase difference of signals A and B can be represented as: [0151]
  • the angle of A.B ⁇ is determined using: (7) [0153] In situations where there are significant common-mode signal dynamics the difference than be computed directly in IQ space as per Equation (7).
  • This DDPR signal processing operates on signals in the IQ stage, generating I ⁇ and Q ⁇ . From the output of the DDPR stage, the IQ components that correspond to phase subtraction of signals A and B can then be used directly to compute ⁇ without the presence of any large common-mode signal dynamics (step 24, 124, 124a).
  • TDPR Time Differential Phase Recovery
  • the purpose of TDPR is to linearise the phase measurement of a signal by measuring the phase derivative over a fixed, short, time duration, given by a delay time ⁇ .
  • standard IQ demodulation is described below.
  • the DDPR signal processing system outlined above can be modified to operate on a single IQ signal pair that is low-pass filtered (step 210, 210a-c). Initially, both I and Q are delayed by a fixed time delay ⁇ . The following assignments can then be made: where subscripts P and D designate Prompt and Delayed respectively.
  • I ⁇ and Q ⁇ are then formed (step 22, 222, 222a-b) as: [0158] As these expressions use only simple multiplications, additions, subtractions and delays, the nature of this algorithm allows for easy and efficient implementation on DSP hardware such as FPGAs. [0159]
  • Time Differential Phase Recovery may therefore circumvent the need for arctan and phase unwrapping operations, whilst providing an open loop, unconditionally stable phase readout technique.
  • both ⁇ and ⁇ are linear variables in which each frequency component is independent of all others. It is thus possible to filter these variables as desired at liberty, without damage.
  • Figure 3A presents a simplified signal processing flow diagram of an implementation of TDPR.
  • a possible implementation may include: • Filter: 84 kHz low pass filter; • Time delay of ⁇ : for example, this could be a delay Z -k , where k is an integer; • CORDIC: co-ordinate rotation algorithm used to divide Q ⁇ by I ⁇ ; • Anti-Aliasing Filter: 2nd order CIC LPF with 2.6 kHz bandwidth; • Down sampling: down sample to 5.2 kHz sample rate for uploading to host computer; and • ⁇ : phase integrator in host to form ⁇ .
  • the I and Q components are initially filtered in the Filter stage (step 210b), implemented with independent, first order, cascaded integrator-comb (CIC) filters.
  • Variable delays of ⁇ are implemented for both I and Q using FPGA memory-based delay lines (steps 210c-d ).
  • DDPR processing of I P , Q P and I D , Q D are then realised using four multipliers and sum and difference operations (steps 222a-c ) before a co-ordinate rotation transformation (CORDIC) uses Q ⁇ and I ⁇ to generate ⁇ (step 224).
  • ⁇ is recovered by integrating ⁇ (step 226).
  • ⁇ is then down sampled (step 229) before streaming to the host computer (step 230).
  • the transfer function of the input phase ⁇ (t) to ⁇ (t) can be determined by taking the Laplace Transform of Equation (12) to give: (14)
  • this transfer function reaches a maximum value of 2 at 42 kHz.
  • the TDPR processing to create ⁇ is seen in Figure 4 to suppress low frequency components of the signal spectrum, it also suppresses all input noise sources such as shot noise and photo-detector dark noise by exactly the same ratio. With careful DSP implementation (lossless), the initial signal-to-noise ratio (SNR) can be preserved when recovering ⁇ .
  • SNR signal-to-noise ratio
  • ⁇ is integrated on the FPGA prior to low pass filtering and decimation before transferring to the host. 4.1.
  • TDPR time differential phase recovery
  • RT Filter3 ⁇ 4Step 274 Low pass filtering operations, possibly with decimation, operate in parallel on both I and Q variables in order to remove non-baseband spectral components that may arise from IQ variable generation.
  • the RT low pass filter may be a code filter in systems utilising pseudo-random modulation, such as in digital interferometry (DI) systems for example.
  • this filter removes both the fundamental and second harmonic of the heterodyne frequency and other inter-modulation products.
  • TDPR processing involves firstly delaying both I P and Q P by a time delay ⁇ to form I D and Q D .
  • Integration and Bitshift3 ⁇ 4Steps 280, 282 Integration of ⁇ on the FPGA is performed immediately after the CORDIC (step 280). This integration recovers ⁇ prior to data bit depth truncation, reducing the impact of quantization noise within the integration step. A dramatic (-32 bit) bitshift is then able to be implemented after integration without compromising low frequency phase sensitivity (step 282). 5.6. 2nd Order Decimating CIC Filter3 ⁇ 4Step 284 [0179] IQ variables are, in general, non-linear and require non-linear processing (arctan and unwrap) to produce a linear output phase variable.
  • the approximation arctan(Q ⁇ /I ⁇ ) ⁇ (Q ⁇ /I ⁇ ) can be made with no need for an arctan operation or subsequent phase unwrapping. This ensures that ⁇ is a linear variable. Since integration is a linear operation, ⁇ is also a linear variable that can be arbitrarily filtered as required. Hence, a low pass anti-aliasing filter on ⁇ can be implemented prior to decimation without damage. Decimated ⁇ can then be transferred to a host computer for recording and further processing, if desired. 6.
  • DDPR operates on two IQ pairs (two independent signals), where the real time processing of IQ variables is used to implement the equivalent of phase subtraction between the two signals at the IQ stage by implementing Equation (8) prior to phase tracking (Equation (9)).
  • Equation (9) phase tracking
  • This enables the removal of common mode phase dynamics before phase tracking. This in turn, dramatically reduces the dynamic range required for many phase tracking applications.
  • the output of the DDPR real time processing is the differential phase between two independent signals, with common-mode noise removed in a robust, and cycle-slip reduced way.
  • TDPR builds on DDPR, using the same IQ algorithm to process IQ pairs and generate the IQ pair corresponding to phase subtraction. Whereas DDPR simply operates on two IQ pairs (two independent signals), TDPR generates two IQ pairs from a single IQ pair by delaying the original IQ pair and then using the prompt and delayed IQ pairs for the DDPR algorithm of Equation (7). TDPR processing thus generates the IQ pair corresponding to the time differential ( ⁇ ) of phase of the original signal. 7. DDPR Implementation Example 7.1. Differential Phase Signal Processing 7.1.1. Regular Differential Phase Readout [0182] Figure 6 shows the digital signal processing involved in the regular phase tracking.
  • FIG. 7 shows digital signal processing to extract DDPR phase. Part of this process is done in real time FPGA. The ADC input for each signal is demodulated to extract the IQ pair, followed by the DDPR operation that yields ⁇ ⁇ and ⁇ ⁇ then is low pass filtered and decimated. Finally, in post-processing, the ⁇ . The extracted ⁇ and ⁇ diff, ddpr is computed using atan2 in MATLAB. 7.1.2.
  • ⁇ diff, ddpr ⁇ ⁇ . ⁇ * unwrap ⁇ arctan (Q ⁇ /I ⁇ ) ⁇ (21)
  • the digital signal processing involved in DDPR is shown in Figure 7.
  • Equation (20) Analogous to the regular phase tracking, the ADC inputs are multiplied by ⁇ ⁇ extraction codes to give the ⁇ ⁇ pairs for the two signals. These two ⁇ ⁇ pairs are then multiplied according to Equation (20) to generate ⁇ ⁇ and ⁇ ⁇ .
  • the last step-in high-speed FPGA is the low pass filtering and decimation of ⁇ ⁇ and ⁇ ⁇ .
  • Equation (21) is implemented on MATLAB using the same “unwrap” and “atan2” in-built functions used for regular phase tracking. [0189] As this process operates on signals at the ⁇ ⁇ stage as per Equation (20) to generate ⁇ ⁇ and ⁇ ⁇ , common mode phase dynamics of signals ⁇ and ⁇ are removed prior to phase recovery.
  • FIG. 8 Notated features of Figure 8 include AOM: Acousto-Optic Modulator 805, P: Polarization Controller 807, DAC: Digital to Analog Converter 809, ADC: Analog to Digital Converter 811, I: isolator 813, and C: 3dB Coupler 815.
  • the reference path is the through-beam of the 3 dB couplers at the input 815a and output 815b of the 500m coil 817, while the signal path travels the same path with the addition of one transit through the 500 m coil.
  • this configuration enables the simultaneous readout of both clockwise (CW) and counter-clockwise (CCW) directions around the fiber loop 817.
  • DEHoI Digitally enhanced homodyne interferometry
  • QPSK quadrature phase shift key
  • Implicit in this realization of DEHoI is the integration across a full pseudo-random, maximal length, binary code.
  • a code of 12 ⁇ sec duration is used, implementing an 84 kHz first order low pass filter on all ⁇ ⁇ components and set a differential signal bandwidth requirement of 1 kHz.
  • alternative modulation techniques may be used, provided they can obtain ⁇ ⁇ pairs for each of the two signal measurements.
  • BiMZI near identical laser frequency noise is induced in each direction.
  • both common-mode and differential phase signals can be injected into the two acousto-optic modulators (AOM), allowing the phase tracking to be tested with a broad range of phase signal dynamics.
  • AOM acousto-optic modulators
  • a Koheras X15 fiber laser operating at 1550 nm is used, whilst the interferometer is composed of SMF-28 optical fiber throughout.
  • the polarization controllers 807 evident in Figure 8 maximize fringe visibility for both clockwise (CW) and counter-clockwise (CCW) interferometers.
  • the entire interferometer 800 sits inside an aluminium box to shield the BiMZI from mechanical noise and reduce temperature variation.
  • the interfered signals from each direction are detected by Insight BPD-1 balanced photo-receivers and digitized on a National Instruments (NI) 5782 transceiver before being processed using an NI 7966R Virtex 5 field programmable gate array (FPGA).
  • This FPGA demodulates the digitized signals to extract ⁇ ⁇ pairs for both CW and CCW directions and implements Equation (20) to generate the DDPR ⁇ ⁇ pair in real-time. All three ⁇ ⁇ pair components are then low pass filtered using identical second order cascaded integrator–comb (CIC) filters, each with a zero at 1.3 kHz. All ⁇ ⁇ components are then decimated down to a 2.6 kHz sample rate prior to transfer to a host computer.
  • CIC cascaded integrator–comb
  • FIG. 9A shows the bit growth in signal processing to extract ⁇ diff, ddpr and ⁇ diff, reg .
  • the extracted ⁇ ⁇ pairs 901a and 901b for each signal are 23 bits in size with a bandwidth of 84 KHz.
  • ⁇ diff, reg and ⁇ diff, ddpr are 43 bits and 61 bits in depth, respectively.
  • the difference arises from the extra DDPR operation that involves numerous multiplications thereby, increasing the size of ⁇ ⁇ and ⁇ ⁇ , and ultimately larger bit growth in ⁇ diff, ddpr .
  • the regular phase extraction ( Figure 9A) then undergoes a second order CIC filter 903a that decimates the ⁇ ⁇ pairs to a sample speed of 2.6 KHz, adding 30 extra bits and bringing the bit depth up to 43 bits.
  • MATLAB all ⁇ ⁇ components are converted into double-precision floating point variables and the phase calculated for each interferometer direction.
  • Figure 9B shows the bit growth in signal processing for DDPR. Using the same extracted ⁇ ⁇ pairs as before, 23 bits in size with a bandwidth of 84 kHz, the four products ⁇ ⁇ . ⁇ ⁇ , ⁇ ⁇ . ⁇ ⁇ , ⁇ ⁇ . ⁇ ⁇ , and ⁇ ⁇ . ⁇ ⁇ are formed by multiplication doubling the bit depth to 46 bits. Addition and subtraction, as per Equation (20), are then performed to generate ⁇ and ⁇ with a bit depth of up to 47 bits.
  • the zoomed-in windows show a full sinusoidal cycle for both ⁇ ⁇ ⁇ and ⁇ ⁇ ⁇ and a 2 ⁇ peak-to-peak linear phase ramp derived from them.
  • 2 Hz CW variables are identical to CCW as can be seen from Figure 10B which plots the CW phase (solid trace 1007) and the CCW phase (dashed trace 1009), both of which are superimposed in Figure 10B.
  • Both traces show the same 2 Hz linear ramp superimposed on the phase drift, common to both interferometers, over 60 seconds.
  • Figure 10C plots the DDPR quadrature components ⁇ ⁇ and ⁇ ⁇ and the resulting differential phase ⁇ diff, ddpr over the same time scale.
  • Figure 10D shows the post-phase-tracking subtraction of CW and CCW (solid trace 1013) phase, and DDPR phase (dashed trace 1015) Both the traces are identical, and the insert shows the rejection of the 2 ⁇ phase ramp.
  • the ramp frequency is increased to 656 Hz.
  • Figure 11A shows the recovered optical phase signals where, CW is shown by trace 1101, CCW is shown by dashed trace 1103, and the two traces are again in close agreement. The higher ramp frequency used here results in only 4 samples per ramp period from the decimated FPGA output.
  • Figure 11B shows the corresponding DDPR (trace 1105) and post-phase-tracking subtraction of CW and CCW phases (trace 1107).
  • FIG 11B DDPR common mode suppression is seen to outperform the post-phase-tracking subtraction of CW and CCW interferometer phases, yielding a suppression ratio of 76 dB compared with the 58 dB suppression obtained by post-phase-tracking subtraction.
  • DDPR yields apparently larger suppression at 656 Hz compared to the 2 Hz result of Figure 10B. This is due to higher harmonics of the 656 Hz ramp being partially removed by the low pass filter prior to down sampling.
  • Figure 12 presents the phase spectral density plots of the time domain data shown in Figure 11B.
  • DDPR solid trace 1201
  • solid trace 1203 shows post-phase- tracking subtraction
  • small phase tracking errors in the individual channels limit the post-phase-tracking subtraction to 3 ⁇ 10 ⁇ 6 rad/ ⁇ Hz over the same frequency range.
  • the fast ramp causes the individual phasemeters to undergo numerous cycle slips in the post-phase-tracking subtraction phase, effectively rendering post-phase-tracking subtraction inoperable in this regime.
  • Figure 13 demonstrates time domain post-phase-tracking subtraction phase (trace 1205) and DDPR (trace 1207) when attempting to track a common 2 ⁇ , 1.3 kHz phase ramp over 60 seconds.
  • DDPR correctly removes common mode phase dynamics while post-phase-tracking subtraction yields numerous cycle slips, producing an unusable output.
  • Figure 14 plots both the individual CW and CCW phases for the zoomed in section of Figure 13 showing a single cycle slip event at 10.82 seconds where the phase jumps by 2 ⁇ radians and CCW phase continues to track.
  • Figure 14A plots the phase for the CW interferometer (trace 1401) as well as the resulting CCW interferometer phase (trace 1403) using MATLAB atan2 and unwrap functions. With this 1.3 kHz phase ramp, the recovered phase amplitude is approximately half the amplitude expected and variable in size due to the small number of samples per ramp cycle.
  • ⁇ diff, reg contains a cycle slip event at 10.82 seconds while ⁇ diff, ddpr tracks faithfully throughout.
  • ⁇ diff, ddpr reliably tracks the differential cyclic error of the interferometer whilst ⁇ diff, reg shows numerous small tracking errors that obscure this repetitive feature.
  • a mallet was used to apply mechanical impulses to mounting hardware surrounding the interferometer whilst simultaneously tuning AOM centre frequencies by 400 kHz at 1.3 kHz repetition frequency and, thermally tuning the Koheras X-15 laser over approximately 20 GHz of optical frequency over 80 seconds.
  • the 1.3 kHz frequency ramp simulates a laser source with far greater linewidth than the 100 Hz linewidth fiber laser while thermal tuning over 20 GHz introduces a huge dynamic range phase signal of ⁇ 3 ⁇ 10 5 radians.
  • Figure 10 plots the DDPR response as mechanical impulses are applied to the optical table surface hosting the entire experiment. Impulses are applied to the top of the interferometer housing (IF box), the optical breadboard and the optical table. For each location, the impulse is repeated three times. The size of the impulse responses reflects the mechanical responsivity of the different parts of the experiment where DDPR measures the differential optical phase induced.
  • This phase response is repeatable over time scales up to tens of minutes and is caused by fiber birefringence within the interferometer in conjunction with small differences in the CW and CCW polarization states.
  • the mechanical impulse responses can be seen starting at 39 seconds. While all four locations produce measurable responses, the breadboard table edge and the interferometer housing yield the largest DDPR phase excursions of 1.4 ⁇ 10 ⁇ 2 radians peak-to-peak. For the optical table edge impulses, signals of 1 ⁇ 10 radians peak-to-peak can clearly be detected.
  • the common mode phase suppression is quantified by taking the ratio of the peak-to-peak phase excursion of DDPR shown in Figure 15 (2.7 ⁇ 10 ⁇ 2 radians) and the total laser thermal tuning signal injected (3 ⁇ 10 5 radians). This yields a common mode phase suppression of 141 dB.
  • Figure 16 plots both results for the mechanical impulse tests of Figure 15 with laser thermal tuning and linewidth broadening (injection of a 400 kHz linear frequency tuning ramp at 1.3 kHz into each AOM and thermally tuning the laser over frequency of 20 GHz over 80 seconds).
  • the DDPR (trace 1601) is a flat line at approximately zero phase while post-phase-tracking subtraction demonstrates over 400 radians of cycle slip errors.
  • the thermal tuning of the laser over approximately 80 seconds causes multiple cycle-slip events in the post-phase-subtraction readout while DDPR maintains slip-free tracking of the CW-CCW difference for the entire duration.
  • the arctan computation of both the phases is done at the down sampled rate in MATLAB. 7.3.1. Discussion [0210]
  • the correct functioning of both non-linear functions arctan( ⁇ / ⁇ ) and unwrap places stringent requirements on the processing of ⁇ ⁇ components to generate a high-fidelity phase readout.
  • the bandwidth of the ⁇ ⁇ signal pipeline must be substantially greater than all ⁇ ⁇ dynamics to avoid ⁇ ⁇ damage, irrespective of the desired phase signal bandwidth.
  • Figure 17 shows a time domain DDPR and post-processed subtraction phase recovery: Here the phase difference of a 5km arm-length armlength mismatched bi-directional Mach-Zehnder interferometer is tracked where the laser used is the DX1 laser diode by Eblana Photonics. A 217Hz differential sinusoidal signal was also injected to calibrate the measurement.
  • FIG. 18 shows a time domain recovery of 2 ⁇ phase ramp at 2.6kHz and 17 Hz sinusoidal signal using IQ demodulation and TDPR.
  • the IQ demodulation undergoes multiple cycle slips whereas the TDPR phase tracks the 17Hz sinusoidal signal without any cycle slips. It is noted that the 17 Hz signal is not visible on this scale so it’s not clear that TDPR is tracking it.
  • Figure 19 shows a plot of the RMS phase error in TDPR subtraction with respect to DDPR phase as a function of ⁇ .
  • ⁇ is varied from 744 ns to 31 ⁇ s for 1000 seconds of phase tracking data recordings.
  • Figures 20A and 20B show a plot of the time domain and frequency domain readout from a diode laser interrogating the Bi-MZI system. The system is further modulated with a 2 ⁇ phase ramp at 5 Hz and a sinusoidal differential signal at 217 Hz. Both differential signals are tracked and recovered using DDPR while regular subtraction is unable to track the signals. 9.
  • DDPR can be applied to traditional, non-DI, heterodyne IQ phase tracking. Indeed, in this application, the lack of a DI code filter enables far higher bandwidth operation. In this application, both the bandwidth and cycle slipping probability should outperform dual phase locked loop implementations.
  • • DDPR can be compatible with digital interferometric (DI) systems that utilise pseudo-random modulation for signal identification.
  • • DDPR should enable high levels of common-mode noise rejection and signal isolation, which is necessary when synthesizing compound/multiple interferometer responses or other highly multiplexed optical sensing applications measuring small differential signal dynamics on a large common noise background.
  • DI digital interferometric
  • TDPR should enable tracking of the low frequency components of broadband lasers without cycle slipping whilst avoiding the need to track all the high frequency noise present. This could be an ideal solution when phase locking two or more high power lasers together to form optical phased arrays. 10.
  • Application Areas for TDPR [0219] There are one or more applications of TDPR in optical phase metrology where TDPR provide an advantage: • TDPR can be applied to traditional, non-DI, heterodyne IQ phase tracking. Indeed, in this application, the lack of a DI code filter enables far higher bandwidth operation. In this application, both the bandwidth and cycle slipping probability should outperform phase locked loop implementations.
  • TDPR can be compatible with digital interferometric (DI) systems that utilise pseudo-random modulation for signal identification.
  • DI digital interferometric
  • TDPR should enable tracking of time-differential phase of broadband lasers without cycle slipping whilst avoiding the need to track all the high frequency noise present. This could be an ideal solution when measuring phase differences between coherent pulses to resolve time-of-flight/distance as in LiDAR and Distributed Acoustic Sensing (DAS) systems.
  • Weak light phase meter applications should benefit from the use of TDPR to reduce, or eliminate, cycle slipping when performing very low power phase measurements. Simple SNR degradation due to shot noise should dominate and obviate the need for the PLL signal bandwidth-cycle slip trade-off.
  • the term “i” is used to represent imaginary number, and is therefore interchangeable with the term “j”.
  • the terms “I1(t)”, “I2(t)”, “Q1(t)”, and “Q2(t)” refer to digital signals, and are interchangeable with “I1[t]”, “I2[t]”, “Q1[t]”, and “Q2[t]” respectively.
  • the presence of in a Figure or the text herein is understood to mean “and/or” unless otherwise indicated, for example, “X/Y” is understood to mean “X, or Y, or both X and Y”.
  • Embodiments [0226] Reference throughout this specification to “one embodiment”, “an embodiment”, “one arrangement” or “an arrangement” means that a particular feature, structure or characteristic described in connection with the embodiment/arrangement is included in at least one embodiment/arrangement of the present invention. Thus, appearances of the phrases “in one embodiment/arrangement” or “in an embodiment/arrangement” in various places throughout this specification are not necessarily all referring to the same embodiment/arrangement, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments/arrangements.

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Spectroscopy & Molecular Physics (AREA)
  • General Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Power Engineering (AREA)
  • Measuring Phase Differences (AREA)

Abstract

L'invention concerne un procédé pour déterminer une différence de phase variant dans le temps entre deux signaux variant dans le temps, le procédé consistant à : recevoir ou générer deux composantes en phase variant dans le temps indépendantes et deux composantes en quadrature variant dans le temps indépendantes à partir d'au moins deux signaux variant dans le temps démodulés ; déterminer la différence de phase variant dans le temps à partir des deux composantes en phase variant dans le temps et des deux composantes en quadrature variant dans le temps par : combinaison des quatre signaux à chaque instant ; et détermination d'une différence de phase variant dans le temps à partir des signaux combinés, et éventuellement déterminer une phase variant dans le temps à partir de la différence de phase variant dans le temps.
PCT/AU2024/051068 2023-10-10 2024-10-10 Détecteur de phase Pending WO2025076589A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
AU2023903241A AU2023903241A0 (en) 2023-10-10 Phase Detector
AU2023903241 2023-10-10

Publications (1)

Publication Number Publication Date
WO2025076589A1 true WO2025076589A1 (fr) 2025-04-17

Family

ID=95396712

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/AU2024/051068 Pending WO2025076589A1 (fr) 2023-10-10 2024-10-10 Détecteur de phase

Country Status (1)

Country Link
WO (1) WO2025076589A1 (fr)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4750214A (en) * 1986-06-11 1988-06-07 Rockwell International Corporation Digital FM demodulator using delayed signal product with arctangent
US20020071503A1 (en) * 2000-12-07 2002-06-13 Myers Michael H. Differential phase demodulator incorporating 4th order coherent phase tracking
EP1217724A1 (fr) * 2000-12-21 2002-06-26 STMicroelectronics S.r.l. Démodulateur en quadrature
US20080075198A1 (en) * 2006-09-25 2008-03-27 Chi-Tung Chang Method for I/Q signal adjustment

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4750214A (en) * 1986-06-11 1988-06-07 Rockwell International Corporation Digital FM demodulator using delayed signal product with arctangent
US20020071503A1 (en) * 2000-12-07 2002-06-13 Myers Michael H. Differential phase demodulator incorporating 4th order coherent phase tracking
EP1217724A1 (fr) * 2000-12-21 2002-06-26 STMicroelectronics S.r.l. Démodulateur en quadrature
US20080075198A1 (en) * 2006-09-25 2008-03-27 Chi-Tung Chang Method for I/Q signal adjustment

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
NGO SILVIE, MCRAE TERRY G., GRAY MALCOLM B., SHADDOCK DANIEL A.: "Homodyne digital interferometry for a sensitive fiber frequency reference", OPTICS EXPRESS, vol. 22, no. 15, 28 July 2014 (2014-07-28), US, pages 18168 - 18176, XP093304578, ISSN: 1094-4087, DOI: 10.1364/OE.22.018168 *
SUTTON ANDREW J., GERBERDING OLIVER, HEINZEL GERHARD, SHADDOCK DANIEL A.: "Digitally enhanced homodyne interferometry", OPTICS EXPRESS, vol. 20, no. 20, 24 September 2012 (2012-09-24), US , pages 22195 - 22207, XP093198706, ISSN: 2161-2072, DOI: 10.1364/OE.20.022195 *

Similar Documents

Publication Publication Date Title
EP3540401B1 (fr) Réflectométrie en domaine de fréquences optiques interférométrique haute résolution (ofdr)
US11231268B2 (en) Sinusoidal frequency sweeping interferometric absolute distance measurement apparatus and method with dynamic offset frequency locking
Köchert et al. Phase measurement of various commercial heterodyne He–Ne-laser interferometers with stability in the picometer regime
JP5285669B2 (ja) 干渉測定法における時間変化する位相の補償法
US11940276B2 (en) Inertial point-source matter-wave atom interferometer gyroscope and extracting inertial parameters
US10712407B2 (en) Device and methodology for measuring minute changes in ambient magnetic field
JP2014109481A (ja) 計測方法及び計測装置
US8767193B2 (en) Doppler tracking in presence of vehicle velocity uncertainty
US20130135623A1 (en) Digital signal processing method and device of fiber-optic gyroscope, and fiber-optic gyroscope
Santarelli et al. Switching atomic fountain clock microwave interrogation signal and high-resolution phase measurements
Kokuyama et al. Simple digital phase-measuring algorithm for low-noise heterodyne interferometry
Karki et al. Digital cavities and their potential applications
Kazda et al. Phase analysis for frequency standards in the microwave and optical domains
WO2025076589A1 (fr) Détecteur de phase
Dey et al. Common-mode phase noise suppression with an open-loop differential phasemeter
Kokuyama et al. Phase meter based on zero-crossing counting of digitized signals
Bandutunga Digitally Enhanced Interferometry for Precision Metrology
Subrahmanya et al. On the development of an RFSoC-based ultra-fast phasemeter with GHz bandwidth
JP7048870B2 (ja) 変位計測装置
Dey Optimising Signal Isolation and Phase Measurement in Digitally Enhanced Interferometry
Dovale-Álvarez Fundamental Limitations of Absolute Ranging via Deep Frequency Modulation Interferometry
Zhang et al. An undersampling phase unwrapping algorithm based on Kalman motion estimation for heterodyne interferometer
Sibley et al. Digital Interferometric Open Loop Phase Recovery in a Fiber Optic Gyroscope
US8693002B2 (en) Fourier transform spectrometer system
Zhang et al. Investigation on upper limit of dynamic range of fiber optic interferometric sensors base on the digital heterodyne demodulation scheme

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 24875819

Country of ref document: EP

Kind code of ref document: A1