Patent Publication Number: US-10330594-B2

Title: Non-linear frequency scan optical frequency-domain reflectometry having a processor to estimate a backscattering profile of an optical fiber by applying a predefined function to a beat signal

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to fiber-optic reflectometry, and particularly to methods and systems for fiber-optic reflectometry using non-linear frequency scanning. 
     BACKGROUND OF THE INVENTION 
     Fiber-optic reflectometry techniques are used for detecting and analyzing impairments and events that affect the optical properties of an optical fiber. Various fiber-optic reflectometry techniques are known in the art. 
     Some fiber-optic reflectometry techniques are based on Optical Frequency-Domain Reflectometry (OFDR). OFDR-based schemes are described, for example, by Zhou et al., in “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Optical Express, volume 20, issue 12, 2012, pages 13138-13145; by Arbel and Eyal, in “Dynamic optical frequency domain reflectometry,” Optics Express, volume 22, issue 8, 2014, pages 8823-8830; and by Bar-Am et al., in “OFDR with double interrogation for dynamic and quasi-distributed sensing,” Optics Express, volume 22, issue 3, 2014, pages 2299-2308, which are incorporated herein by reference. 
     Additional OFDR schemes are suggested by Eickhoff and Ulrich, in “Optical frequency domain reflectometry in single mode fiber,” Applied Physics Letters, volume 39, issue 9, 1981, pages 693-695; by Soller et al., in “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” IEEE Conference on Avionics, Fiber Optics and Photonics, 2006, pages 38-39; and by Barfuss and Brinkmeyer, in “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” Journal of Lightwave Technology, volume 7, issue 1, 1989, pages 3-10, which are incorporated herein by reference. 
     Yet additional OFDR techniques are described by Soller et al., in “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Optics Express, volume 13, issue 2, 2005, pages 666-674; and by Mussi et al., in “−152.5 dB sensitivity high dynamic-range optical frequency domain reflectometry,” Electronics Letters, issue 32, volume 10, 1996, pages 926-927, which are incorporated herein by reference. 
     Various techniques have been suggested for generating frequency-scanning optical signals used in OFDR. One approach uses an electro-optical modulator that is external to the laser. Such techniques are described, for example, by Tsuji et al., in “Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator,” IEEE Photonics Technology Letters, volume 7, issue 7, 1995, pages 804-806; by Fan et al., in “Centimeter-level spatial resolution over 40 km realized by bandwidth-division phase-noise-compensated OFDR,” Optics Express, volume 19, 2011, pages 19122-19128; by Fan et al., in “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Optics Letters, volume 32, issue 22, 2007, pages 3227-3229; and by Ito et al., in “Long-range coherent OFDR with light source phase noise compensation,” Journal of Lightwave Technology, volume 30, issue 8, 2012, pages 1015-1024, which are incorporated herein by reference. 
     A different approach for generating frequency-scanning optical signals is to directly modulate one of the laser parameters. Techniques of this sort are suggested, for example, by Passy et al., in “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” Journal of Lightwave Technology, volume 12, issue 9, 1994, pages 1622-1630; by Geng et al., in “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photonics Technology Letters, volume 17, issue 9, 2005, pages 1827-1829; and by Li et al, in “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Physics Letters, volume 10, issue 7, 2013, which are incorporated herein by reference. 
     SUMMARY OF THE INVENTION 
     An embodiment that is described herein provides a system for fiber-optic reflectometry. The system includes an optical source, a beat detection module and a processor. The optical source is configured to generate a non-linearly-scanning optical interrogation signal having an instantaneous optical frequency that is a non-linear function of time. The beat detection module is configured to transmit the optical interrogation signal into an optical fiber, to receive from the optical fiber an optical backscattering signal in response to the optical interrogation signal, and to mix the optical backscattering signal with a reference replica of the optical interrogation signal, so as to produce a beat signal. The processor is configured (i) to hold a predefined function that is indicative of an expected phase of the beat signal resulting from the non-linearly-scanning optical interrogation signal as a function of position along the optical fiber and time, (ii) to estimate a backscattering profile of the optical fiber by applying the predefined function to the beat signal, and (iii) to sense one or more events affecting the optical fiber by analyzing the backscattering profile. 
     In some embodiments, the instantaneous optical frequency of the optical interrogation signal is a sinusoidal function of time. In an embodiment, the predefined function specifies a complex conjugate of an exponential phase factor of the beat signal, which is expected to result from the non-linearly-scanning optical interrogation signal, as a function of the position and the time. In a disclosed embodiment, the processor is configured to hold a matrix of discrete values of the predefined function, and to apply the predefined function to the beat signal by multiplying the matrix by a vector of samples of the beat signal. 
     In some embodiments, the processor is configured to calculate multiple successive estimates of the backscattering profile, by applying the predefined function to multiple respective time periods of the beat signal, and to sense the events by analyzing the multiple successive estimates of the backscattering profile. In an example embodiment, the optical source is configured to generate the non-linearly-scanning optical interrogation signal with a given bandwidth and a given modulation frequency, and wherein the predefined function depends on the given bandwidth and the given modulation frequency. In an embodiment, the beat detection module is configured to mix the optical backscattering signal with the reference replica of the optical interrogation signal using In-phase/Quadrature (I/Q) mixing, such that the beat signal is complex-valued. 
     In some embodiments, the optical fiber is part of an optical communication system, and the one or more events include a fault in the optical fiber. In other embodiments, the optical fiber is part of a perimeter security system, and the one or more events include a breach of the perimeter security system. In yet other embodiments, the optical fiber is installed in a utility infrastructure, and the one or more events include a fault in the utility infrastructure. 
     There is additionally provided, in accordance with an embodiment of the present invention, a method for fiber-optic reflectometry. The method includes generating a non-linearly-scanning optical interrogation signal having an instantaneous optical frequency that is a non-linear function of time. The optical interrogation signal is transmitted into an optical fiber, and an optical backscattering signal is received from the optical fiber in response to the optical interrogation signal. The optical backscattering signal is mixed with a reference replica of the optical interrogation signal, so as to produce a beat signal. A backscattering profile of the optical fiber is estimated, by applying to the beat signal a predefined function that is indicative of an expected phase of the beat signal resulting from the non-linearly-scanning optical interrogation signal as a function of position along the optical fiber and time. One or more events affecting the optical fiber are sensed by analyzing the backscattering profile. 
     The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram that schematically illustrates a fiber-optic reflectometry system that uses sinusoidal frequency scanning, in accordance with an embodiment of the present invention; 
         FIG. 2  is a diagram that schematically illustrates a pre-computed matrix of expected fiber profiles under sinusoidal frequency scanning, in accordance with an embodiment of the present invention; 
         FIG. 3  is a flow chart that schematically illustrates a method for fiber-optic reflectometry using sinusoidal frequency scanning, in accordance with an embodiment of the present invention; and 
         FIGS. 4A-4C  are graphs showing example experimental results of a fiber-optic reflectometry system that uses sinusoidal frequency scanning, in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Overview 
     Optical Frequency-Domain Reflectometry (OFDR) may be implemented by generating an optical signal whose instantaneous optical frequency varies linearly with time. In such an implementation, the optical signal is transmitted through an optical fiber, the backscattered optical signal received from the fiber is mixed with a replica of the original optical signal, and the resulting beat signal is analyzed in the frequency domain. 
     In the above naïve implementation, it is possible to derive spatial information from the beat signal with relatively simple frequency-domain analysis, because of the linear dependence of the instantaneous optical frequency of the optical signal on time. In practice, however, it is highly challenging to generate, with a sufficiently high repetition rate, an optical signal whose instantaneous frequency varies linearly with time. 
     When using external modulation, for example, the specification of the external Radio Frequency (RF) generator is extremely difficult to meet. Direct modulation of the laser is no less challenging, because lasers tend to distort the linear modulation. The implementation challenges are particularly severe in dynamic sensing applications, in which the optical signal is required to scan over a large bandwidth with fast scan repetition rate. 
     Embodiments of the present invention that are described herein provide improved methods and systems for fiber-optic reflectometry. The methods and systems described herein use a non-linearly-scanning optical interrogation signal, i.e., an optical interrogation signal whose instantaneous optical frequency is a non-linear function of time. The resulting beat signal is analyzed using a novel signal processing technique that compensates for the effects of the non-linear scanning. The embodiments described below refer mainly to sinusoidally-scanning optical interrogation signals, by way of example. The disclosed techniques, however, are in no way limited to sinusoidal scanning and may be implemented using various other types of non-linearly scanning optical interrogation signals. 
     In some embodiments of the present invention, an OFDR system comprises an optical source, a beat detection module and a processor. The optical source is configured to generate a sinusoidally-scanning optical interrogation signal having an instantaneous optical frequency that is a sinusoidal function of time. The beat detection module is configured to transmit this optical interrogation signal into an optical fiber, to receive the resulting optical backscattering signal from the optical fiber, and to mix the optical backscattering signal with a reference replica of the optical interrogation signal, so as to produce a beat signal. 
     The processor is configured to analyze the beat signal so as to sense one or more events affecting the optical fiber. The analysis is based on a predefined function, stored in the processor, which is indicative of the expected phase of the beat signal resulting from the sinusoidally-scanning optical interrogation signal as a function of position z along the optical fiber and time t. The predefined function typically depends on the bandwidth and modulating frequency of the sinusoidally-scanning optical interrogation signal, and on the group velocity of light in the fiber. 
     In an embodiment, the predefined function gives the complex conjugate of the exponential phase factor of the beat signal, which is expected to result from the sinusoidally-scanning optical interrogation signal. Other suitable predefined functions can also be used. Typically, the processor holds a matrix  R  of discrete values of the predefined function, over discrete ranges of z and t. 
     The processor calculates an estimate of the backscattering profile of the optical fiber, i.e., the complex-valued backscattering coefficient of the fiber as a function of position z, by applying the predefined function to the beat signal. In a typical implementation, the processor multiplies matrix  R  by a vector of discrete-time samples of the beat signal. The processor then analyzes the backscattering profile so as to sense events of interest. 
     In some embodiments, the above process is repeated continually in multiple scanning periods of the optical interrogation signal. In each period, the processor applies the predefined function to a respective time interval of the beat signal. The processor analyzes the resulting sequence of backscattering profiles, so as to detect dynamic changes in the fiber. 
     The methods and systems described herein exploit the implementation benefits of using a sinusoidally-scanning or other non-linearly scanning optical interrogation signal, without compromising performance measures such as resolution and update rate. Example experimental results are provided further below. Additional experimental results and performance data of such a system can be found in U.S. Provisional Patent Application 62/133,392, cited above, and in an article by Leviatan and Eyal, entitled “High resolution DAS via sinusoidal frequency scan OFDR (SFS-OFDR),” Optics Express, volume 23, issue 26, December, 2015, pages 33318-33334, which is incorporated herein by reference. 
     The disclosed techniques can be used for implementing various types of sensors for use in a wide variety of Dynamic Acoustic Sensing (DAS) applications. Example applications include optical network monitoring, perimeter security, as well as monitoring of infrastructure such as pipelines, railways and roads, to name just a few. 
     System Description 
       FIG. 1  is a block diagram that schematically illustrates a fiber-optic reflectometry system  20  that uses sinusoidal frequency scanning, in accordance with an embodiment of the present invention. System  20  transmits an optical signal through an optical fiber  24 , referred to as a sensing fiber, and analyzes the optical signal reflected from the fiber. In particular, system  20  detects backscattering from various reflectors at various points along fiber  24 , and estimates the locations along the fiber at which such backscattering occur. 
     Backscattering may be caused by distributed elastic scattering in the fiber (Rayleigh scattering), by permanent or transient mechanical faults or deformations in the fiber, or by any other suitable phenomenon or event that affects the fiber&#39;s optical properties at certain points. Detection and analysis of backscattering may serve as a basis for a wide variety of sensing applications, as will be elaborated below. 
     In the present example, system  20  comprises a waveform generator  28 , an optical interrogation unit  32 , and an analysis processor  36 . Optical interrogation unit comprises a scanning laser  40 , an optical splitter  44 , a circulator  48 , a 90° optical hybrid  52 , and a pair of balanced optical detectors  56 A and  56 B (also referred to as optical receivers). Hybrid  52  may also be referred to as an I/Q or quadrature hybrid, mixer, demodulator or downconverter. 
     Waveform generator  28  generates an electrical signal having a time-varying waveform that modulates the optical frequency (the wavelength) of laser  40 . As a result, laser  40  generates an optical signal whose instantaneous optical frequency varies as a function of time. In the present example waveform generator  28  generates an electrical signal having a sinusoidal waveform, which cause laser  40  to produce an optical signal whose instantaneous optical frequency is a sinusoidal function of time. 
     The optical signal produced by laser  40  is split using splitter  44  into an interrogation signal and a reference signal. The interrogation signal is launched into sensing fiber  24 , and a backscattering signal is received from the fiber in response. The received backscattering signal is mixed with the reference signal to produce a beat signal that is in turn analyzed. 
     In the example of  FIG. 1 , the interrogation signal is transmitted via circulator  48  (via ports  1     2  of the circulator) into fiber  24 . The reference signal (a reference replica of the interrogation signal) is applied to the Local Oscillator (LO) port of hybrid  52 . The interrogation signal is reflected (e.g., backscattered) from various points along fiber  24 . The superposition of these reflections, which returns from fiber  24  to interrogation unit  32 , is an optical signal referred to herein as the backscattered signal. The backscattered signal passes through circulator  48  (via ports  2     3  of the circulator) and is applied to the signal port of hybrid  52 . 
     Hybrid  52  has two pairs of output fibers that are connected respectively to balanced optical detectors  56 A and  56 B. Detectors  56 A and  56 B produce respective electrical signals that represent the In-phase (I) and Quadrature (Q) components of the beat signal (the backscattered signal after it has been down-converted by mixing with the reference signal). In other words, detectors  56 A and  56 B produce a complex-valued signal representation of the light backscattered in fiber  24 . 
     The pair of electrical signals (i.e., the complex-valued beat signal) produced by detectors  56 A and  56 B is provided to analysis processor  36 . Processor  36  digitizes the complex-valued beat signal and analyzes it in the frequency domain, so as to detect and localize the points along fiber  24  at which backscattering occurs. Typically, processor  36  transforms the beat signal into the frequency domain, e.g., by applying a Fourier transform, so as to produce a frequency-domain backscattering profile of the fiber. Generally speaking, each beat frequency (and thus each frequency bin of the Fourier transform) is mapped to a respective location along the fiber. The functions of processor  36  are addressed in greater detail further below. 
     The configuration of system  20  shown in  FIG. 1  is an example configuration, which is chosen purely for the sake of conceptual clarity. In alternative embodiments, any other suitable system configuration can be used. For example, the configuration of  FIG. 1  uses direct modulation of laser  40 . Alternatively, the disclosed techniques can be used in systems that externally modulate the wavelength of the optical signal produced by the laser, or in systems that generate a scanning optical signal in any other suitable manner. 
     In the present context, waveform generator  28  and laser  40  are referred to jointly as an optical source. Splitter  44 , circulator  48 , hybrid  52  and detectors  56 A and  56 B are referred to jointly as a beat detection module. In alternative embodiments, system  20  may be implemented using any other suitable configuration of the optical source and/or beat detection module. 
     The different elements of system  20  may be implemented using various suitable optical and/or electronic hardware components, integrated or discrete. System elements that are not mandatory for understanding of the disclosed techniques have been omitted from the figure for the sake of clarity. Further aspects of this system configuration are also described in PCT Application PCT/IB2015/058819, entitled “Spectrally Efficient Optical Frequency-Domain Reflectometry using I/Q Detection,” which is assigned to the assignee of the present patent application and whose disclosure is incorporated herein by reference. 
     In one example embodiment, fiber  24  comprises a Corning SMF-28 fiber, laser  40  comprises a tunable laser by Koheras Adjustik of NKT Photonics having a central wavelength of 1550 nm. Waveform generator  28  modulates the instantaneous optical frequency of laser  40  by applying the sinusoidal electrical signal to an internal piezo-electric actuator (PZT) in the laser. Splitter  44  comprises a TW1550R5A2 device provided by Thorlabs, circulator  48  comprises a 6015-3-APC device provided by Thorlabs, hybrid  52  comprises a COH24-X device provided by Kylia, detectors  56 A and  56 B comprise PDB470C-AC devices provided by Thorlabs. In alternative embodiments, however, any other suitable components can be used. 
     Some system elements, e.g., waveform generator  28 , may be implemented using off-the-shelf or modified test equipment. Some system elements, e.g., analysis processor  36 , may be implemented using hardware, e.g., using one or more Application-Specific Integrated Circuits (ASICs) or Field-Programmable Gate Arrays (FPGAs), using software, or using a combination of hardware and software elements. 
     In some embodiments, processor  36  may be implemented using one or more general-purpose processors, which are programmed in software to carry out the functions described herein. The software may be downloaded to the processors in electronic form, over a network, for example, or it may, alternatively or additionally, be provided and/or stored on non-transitory tangible media, such as magnetic, optical, or electronic memory. 
     OFDR Analysis Based on Sinusoidal Frequency Scanning Interrogation Signal 
     As noted above, in some embodiments the instantaneous optical frequency of laser  40  is a sinusoidal function of time. The instantaneous optical frequency of the laser in these embodiments can be written as 
                     f   inst     =       f   0     +         Δ   ⁢           ⁢   F     2     ⁢     sin   ⁡     (       ω   r     ⁢   t     )                   [   1   ]               
wherein f 0  denotes the nominal center frequency of the laser at t=0, ΔF denotes the bandwidth scanned by the optical interrogation signal, and ω r =2πf r  denotes the angular frequency with which the laser is modulated. In other words, f r  denotes the frequency of the sinusoidal modulating signal generated by waveform generator  28 .
 
     The electrical field of the optical interrogation signal is thus given by 
     
       
         
           
             
               
                 
                   
                     
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     Sensing fiber  24  can be modeled as a distributed reflector along the z-dimension, having a complex-valued z-dependent backscatter coefficient denoted ρ(z). The backscattered field is given by 
                       E   B     ⁡     (   t   )       =       ∫   0   L     ⁢       ρ   ⁡     (     z   ′     )       ⁢       E   in     ⁡     (     t   -               ⁢     2   ⁢     z   ′           v   g         )       ⁢     exp   ⁡     [     i   ⁢           ⁢     Φ   ⁡     (     z   ′     )         ]       ⁢     dz   ′                 [   3   ]               
wherein L denotes the length of fiber  24 , ν g  denotes the group velocity of light in fiber  24 , and Φ(z) denotes the accumulated round-trip phase of the field that was backscattered from position z along fiber  24 .
 
     When using the sinusoidally-scanning interrogation signal defined above, the complex-valued beat signal V(t)=l(t)+iQ(t) at the output of detectors  56 A and  56 B can be written as 
                     V   ⁡     (   t   )       =     A   ⁢       ∫   0   L     ⁢         ρ   ~     ⁡     (     z   ′     )       ⁢   exp   ⁢           ⁢     {     i   ⁢         πΔ   ⁢           ⁢   F       ω   r       ⁡     [       cos   ⁢           ⁢     (       ω   r     ⁢           ⁢     (     t   -               ⁢     2   ⁢     z   ′           v   g         )       )       -     cos   ⁡     (       ω   r     ⁢   t     )         ]         }     ⁢           ⁢     dz   ′                   [   4   ]               
wherein A is a constant describing the responsivity and gain of the I/Q demodulator and detectors, and {tilde over (ρ)}(z) denotes the complex-valued backscatter coefficient at position z. The backscatter coefficient {tilde over (ρ)}(z) is defined as
 
     
       
         
           
             
               
                 
                   
                     
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     (As can be seen in Equation [4], the instantaneous optical frequency can have both positive and negative values. Therefore, to fully exploit the information conveyed in the beat signal V(t), Quadrature (I/Q) detection is used. In alternative embodiments, however, system  20  may nevertheless be implemented using real-valued detection, with somewhat reduced performance.) 
     An estimate of the complex-valued backscatter coefficient can be written as 
                         ρ   ~     ^     ⁡     (   z   )       =       ∫       -   T     /   2       T   /   2       ⁢       V   ⁡     (   t   )       ⁢   exp   ⁢           ⁢     {       -   i     ⁢         πΔ   ⁢           ⁢   F       ω   r       ⁡     [       cos   ⁢           ⁢     (       ω   r     ⁢           ⁢     (     t   -               ⁢     2   ⁢   z         v   g         )       )       -     cos   ⁡     (       ω   r     ⁢   t     )         ]         }     ⁢           ⁢   dz               [   6   ]               
wherein T is the interrogation time interval over which the beat signal V(t) is sampled.
 
     Equation [6] can be viewed as a projection of the beat signal V(t) onto the function 
     
       
         
           
             
               
                 
                   
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     The function R(z,t) in [7] is indicative of the expected backscattering profile of fiber  24 , when interrogated by a sinusoidal interrogation signal having an angular frequency ω r  and bandwidth ΔF. 
     For given values of z, t, R(z,t) gives the complex conjugate of the exponential phase factor of the beat signal, which is expected to result from backscattering of the sinusoidally-scanning optical interrogation signal from position z, after t seconds from the beginning of the current scanning period. 
     In other words, for a given z, R(z,t) is indicative of the expected phase of the signal that is backscattered from position z, as a function of time. Note that R(z,t) depends only on the scan parameters (ω r  and ΔF), and on the light velocity in the fiber (ν g ). Function R(z,t) is predefined in the sense that it does not depend on the actual real-time values of the interrogation or backscattering signals. As such, function R(z,t) can therefore be computed and stored in advance, before actual interrogation of the fiber is initiated. 
     In some embodiments, analysis processor  36  estimates the complex-valued backscatter coefficient {tilde over ({circumflex over (ρ)})}(z) by calculating the integral in Equation [6], using the actual received beat signal V(t) and the known function R(z,t). 
     Typically, however, processor  36  evaluates a discrete-time version of Equation [6]. In these embodiments, processor  36  pre-computes a matrix  R , whose vertical dimension corresponds to position z along the fiber, and whose horizontal dimension corresponds to time. 
       FIG. 2  is a diagram that schematically illustrates the pre-computed matrix  R , in accordance with an embodiment of the present invention. The matrix element on the z th  row and i th  column of matrix  R  (with z and t being discrete values) gives the complex conjugate of the exponential phase factor of the beat signal, which is expected to result from backscattering of the sinusoidally-scanning optical interrogation signal from position z, after t seconds from the beginning of the current scanning period. In other words, the z th  row of matrix  R  gives the expected conjugate phase factor of the signal that is backscattered from position z, as a function of time. 
     In these embodiments, processor  36  digitizes the complex-valued beat signal V(t), e.g., using a pair of Analog to Digital Converters (ADCs), over the interrogation time interval. Processor  36  then multiplies matrix  R  by the vector of the sampled beat signal. The resulting vector gives the backscattering profile of fiber  24 —The estimated complex-valued backscattering coefficient {tilde over ({circumflex over (ρ)})}(z) as a function of z. 
     The row size (the number of columns) of matrix  R  is the number of samples in the interrogation time interval. For a sampling frequency of 1 G samples per second and a time interval of 10 μS, the number of samples is 10,000. The column size (the number of rows) of matrix  R  depends on the length of fiber  24  and on the spatial resolution used. For a 10 km fiber and a spatial resolution of 1 meter, the column size is 10,000. Alternatively, any other suitable row and column sizes can be used. 
     The embodiments described herein refer to a sinusoidally-scanning optical interrogation signal, whose instantaneous frequency as a function of time is a sinusoid. The disclosed techniques, however, are in no way limited to sinusoidally-scanning optical interrogation signals, or to the specific predefined function of Equation [7]. In alternative embodiments, the optical source (generator  28  and laser  40 ) may generate any other suitable type of periodic optical interrogation signal whose instantaneous frequency, within each scanning period, is a non-linear function of time. Processor  36  may use any suitable predefined function that is indicative of the expected phase of the beat signal resulting from such a periodic, non-linearly-scanning optical interrogation signal as a function of z and t. 
     For example, the instantaneous frequency of the optical interrogation signal may be a sum of two or more sinusoidal harmonics or any other periodic function of time. In this case the expected phase of the beat signal will be pre-computed accordingly. Note that the predefined function does not account for the (slowly-varying frequency-independent) phase that the optical signal acquires in its round-trip along the fiber. 
       FIG. 3  is a flow chart that schematically illustrates a method for fiber-optic reflectometry using sinusoidal frequency scanning, in accordance with an embodiment of the present invention. The method begins with processor  36  of system  20  pre-computing and storing the predefined matrix  R  shown in  FIG. 2 , at a pre-computation step  70 . Alternatively, matrix  R  may be computed by some other processor and provided to processor  20  in advance. 
     At a signal generation step  74 , the optical source of system  20  generates a sinusoidally-scanning interrogation signal. The parameters of the interrogation signal (ω r  and ΔF) should match the parameters for which matrix  R  was pre-computed. 
     At a beat-signal generation step  78 , the beat detection module of system  20  sends the interrogation signal through fiber  24 , and mixes the resulting backscattered signal with a reference replica of the interrogation signal, so as to produce the complex-valued beat signal V(t). 
     At a projection step  82 , processor  36  of system  20  multiplies matrix  R  by a vector of samples of the beat signal V(t). The vector of samples is typically acquired over a single scan period of the interrogation signal, or over a portion of such a period. This multiplication essentially performs a discrete version of Equation [6], which produces an estimate of the complex-valued backscatter coefficient {tilde over ({circumflex over (ρ)})}(z) as a function of z. The method then loops back to step  74  above, for processing another scan period. 
     Processor  36  thus obtains a sequence of estimates {tilde over ({circumflex over (ρ)})}(z) of the fiber backscattering profile, corresponding to a respective sequence of time intervals. Processor  36  typically generates a two dimensional matrix of the acquired profiles as a function of time. 
     By analyzing the time dependent fiber profile, processor  36  is able to identify temporal variations in the backscattering profile, which are indicative of transient events that affect the backscattering coefficient of the fiber. The actual events being detected depend on the application of system  20 . Several example applications are described further below. 
     Example Experimental Results 
     In an example experimental setup of system  20 , the length of sensing fiber  24  was ˜780 m. Laser  40  was modulated with an electrical signal having a frequency of 21 KHz and an amplitude of 10V. This electrical signal was applied to the internal piezo-electric actuator (PZT) of laser  40  with a conversion efficiency of K(21 KHz)=18.7 MHz/V. The peak-to-peak scan bandwidth (Δf) of the resulting interrogation signal was ˜373.5 MHz. The beat signal V(t) was sampled over 12 μS intervals (25% of the modulation period), and a total of 5000 such intervals were acquired, spanning a total time of ˜238 mS. 
     Various tests were conducted using this setup. Comprehensive test results are given in U.S. Provisional Patent Application 62/133,392, and in the article “High resolution DAS via sinusoidal frequency scan OFDR (SFS-OFDR),” cited above. 
       FIGS. 4A-4C  are graphs showing example experimental results of system  20 , in accordance with an embodiment of the present invention. In this particular experiment, a section of fiber  24  was buried under ˜1 cm of sand, and a paperclip was dropped on the sand from a height of ˜5 cm. 
       FIG. 4A  shows the measured time-dependent backscattering profile of the fiber. 
       FIG. 4B  shows the variance of the backscattering profile as a function of time and position. The variance was calculated for each position along the fiber using a sliding window of 100 modulation periods (a total time of ˜4.76 mS). A burst  90  of high variance can be seen clearly in the top-right inset in the figure. Burst  90  indicates the time and position at which the paperclip was dropped. The width of burst  90  indicates a dynamic spatial resolution of ˜0.6 m. 
       FIG. 4C  shows the time dependence of the backscattering profile of the fiber at the position of burst  90  (z≈671.5 m). The paperclip drop event can be seen very clearly in the figure. 
     Example Applications 
     In various embodiments, systems such as system  20  of  FIG. 1  can be used in a wide variety of applications that involve detecting various kinds of events that affect an optical-fiber. Typically, although not necessarily, system  20  is used in dynamic sensing applications that benefit from fast update rate. 
     In some embodiments, system  20  is used for monitoring optical fibers in an optical communication network, for example in order to detect and locate faults in the fibers. In this application, the sensed events are typically faults in the optical fiber that impact the communication performance of the network. 
     In other embodiments, sensing fiber  24  is installed as part of a perimeter security system for protecting a certain area or structure. In such applications, the sensed events typically relate to illegitimate entry, i.e., illegitimate breach of the perimeter security system. 
     In other embodiments, sensing fiber  24  is installed in some utility infrastructure element, in order to detect fatigue-related faults or other faults in the infrastructure. The fiber may be installed, for example, in an oil or water pipeline, in a railway line or in a road or bridge. In this sort of application, the sensed events are typically related to faults in the infrastructure element. 
     The applications listed above are depicted purely by way of example. In alternative embodiments, the disclosed techniques can be used as part of any other suitable system and for any other suitable application. 
     Although the embodiments described herein mainly address sensing of direct static or dynamic mechanical perturbations to the sensing fiber, the methods and systems described herein can also be used in other applications where other measurands, such as temperature, current, magnetic field, electric field or pressure, are transformed by suitable transduction mechanism to mechanical perturbations in the sensing fiber. 
     It will thus be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and sub-combinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art. Documents incorporated by reference in the present patent application are to be considered an integral part of the application except that to the extent any terms are defined in these incorporated documents in a manner that conflicts with the definitions made explicitly or implicitly in the present specification, only the definitions in the present specification should be considered.