Interferometric system with multiaxial optical fibre and method for processing an interferometric signal in such a system

An interferometric system with multi-axis optical fiber and a method for processing an interferometric signal in such a system, the multi-axis interferometric system includes a light source (1); a plurality of N optical-fiber coils (11, 12), a first optical separation element (3) capable of splitting the source beam (100) into a first split beam (140) and a second split beam (240); shared phase-modulation element (4); a photodetector (2) and a signal-processing system (800). The N optical-fiber coils (11, 12) are connected in parallel, the coils having respective transit times T1, T2, . . . TN that all differ from one another, and the signal-processing system (800) is capable of processing the interferometric signal (720) detected by the shared photodetector (2) as a function of the respective transit times in the various coils.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to Sagnac-ring fiber optic interferometric systems. A Sagnac-ring interferometer allows in particular a measurement of rotation about the axis of the ring forming the optical path. Such interferometric systems find applications in particular in the fiber optic gyroscopes (or FOG, see “The Fiber optic gyroscope”, H. Lefèvre, Artech house, 1993).

A multi-axis interferometric system includes several optical-fiber coils, for example three in number, integral with each other and the axis of which are arranged along different directions. Such a multi-axis interferometric system makes it possible to measure the rotations of the system about each of the axis of the different coils. Moreover, the number of optical-fiber coils may be increased to provide redundant information and to improve the performances of the system.

The simplest construction of a multi-axis interferometric system consists in arranging several interferometers operating in parallel with a single, shared light source, each interferometer comprising an optical modulator, an optical-fiber coil about an axis and a detector. The increase of the number of coils hence generally involves an increase of the number of optical and/or electronic components.

Description of the Related Art

Different architectures have been proposed for the purpose of reducing the size, the number of optoelectronic components and finally the cost of the multi-axis interferometric systems.

In particular, different architectures of multi-axis interferometric systems exist in which a single detector is connected to several optical-fiber coils.

The document U.S. Pat. No. 4,815,853 (H. Lefèvre) describes a three-axis fiber optic interferometric system implementing a shared source, three optical-fiber coils connected in series, a shared photodetector and a time multiplexing of the signals. In this series architecture, a first optical coupler connects the second fiber coil preferably to the middle of the first coil, and a second optical coupler connects the third coil preferably to the middle of the second coil. According to this document, coils of same length L are chosen and the intensity of the source is modulated with a gate function of duration τ and period of repetition 3τ, the source being switched on for the duration τ and switched off for a duration 2×τ at each period of repetition, where τ represents the transit time τ of the modulated beams in any one of the optical-fiber coils, being defined by the formula:

τ=Lvg
where vgrepresents the group velocity in the optical fiber. The photodetector receives respectively at the instant t+τ, an interferometric signal corresponding to the optical path of the first coil, at the instant t+2τ, an interferometric signal corresponding to an optical path comprising the first and the second coil, and at the instant t+3τ, an interferometric signal corresponding to the optical path of the three series coils. A time demultiplexing of the signals makes it possible to calculate the relative rotation rate about each axis, by supposing that these speeds remain constant between the instants t, t+2τ and t+3τ. The coil connection fibers make this device sensitive to the temperature gradient, liable to cause thermally induced non-reciprocities, due to the Shupe effect.

The document U.S. Pat. No. 5,033,854 (A. Matthews, G. Varty, J. Darling) describes a system of three fiber optic gyroscopes each having a distinct interferometric optical device and in which the three detectors are connected to a shared signal-processing electronic system comprising a time multiplexer, an analog-to-digital converter (or ADC) and a signal-processing system (or DSP). The multiplexer includes an electronic switch to select one of the electric signals coming from one of the different gyroscope towards the single exit (col. 4 L. 50-61 and FIG. 2a). A same modulation voltage is applied simultaneously to each of the individual phase modulators of each gyroscope (col. 4 L. 46-49). Each of the gyroscopes is sampled at a speed equal to n·Y, where Y is the transit time in a coil. This electronic system performs a time division multiplexing.

The document U.S. Pat. No. 5,719,674 (P. Martin, T. Gaiffe, J. Morisse, P. Simonpietri, H. Lefèvre) describes a three-axis ring fiber optic interferometric system, wherein three fiber optic interferometers are connected to a shared source and to a shared detector. Each interferometer comprises an optical-fiber coil, a Y-junction coupler-separator and an optical phase modulator. A 3×3 coupler separates the source beam into three beams each directed towards an interferometer. The 3×3 coupler recombines the three interferometric signals to form the detected signal. The lengths of the optical-fiber coils being identical, the transit time is identical in all the coils. Different periodic phase modulations are applied to each coil. These phase modulations have a same modulation frequency fm=1/Tmwhere Tmis equal to 2τ, i.e. twice the common transit time and are time offset with respect to each other by a time interval δt1=Tm/(2·N) for each of the N interferometers Ii. A signal processing makes it possible to demultiplex the detected signal to extract respectively from each time interval δtithe Sagnac phase-shift signal relative to one interferometer Ii. This device hence includes three independent interferometers connected to a same source, each having a specific modulation and a shared time-multiplexed detector that measures at each instant an interferometric signal coming from a single one of the different interferometers. This device requires a rated operation of the different optical modulators.

The document U.S. Pat. No. 5,294,972 describes a multiaxial rotation-rate sensor comprising several optical-fiber coils connected in parallel to a pulsed light source, an optical modulator and a photodetector, wherein the lengths of the optical-fiber coils are in ratios that are multiple from each other and wherein the signals corresponding to the different coils are distinguished either downstream from the photodetector by a time demultiplexing, or at the phase modulator, by application of a phase shift of ±π·n.

BRIEF SUMMARY OF THE INVENTION

One of the objects of the invention is to propose a multi-axis interferometric system architecture alternative to the prior architectures.

Another object of the invention is to propose a multi-axis interferometric system comprising a limited number of optoelectronic components so as to reduce the costs and the size of the system.

Still another object of the invention is to propose a signal processing method adapted to such a multi-axis interferometric system.

The invention will find a particularly advantageous application in the navigation or guidance systems on-board surface ships, underwater vehicles or spatial vehicles. More specifically, the invention will find applications in the multi-axis interferometric systems intended for applications in the spatial or nuclear fields, the cost of the procedures of qualification of the optoelectronic components leading to drastically reduce the number of electronic components by limiting the degradation of the system performances.

The invention more particularly relates to a multi-axis fiber optic interferometric system including a shared light source adapted to emit a source beam, a plurality of N optical-fiber coils, each coil forming a ring optical path about an axis; a first optical separating means adapted to spatially separate the source beam into a first split beam and a second split beam; shared phase-modulation means adapted to apply a time-modulated phase shift between the first and the second split beams and to form a first modulated beam and a second modulated beam; a shared photodetector and a shared signal-processing system.

According to the invention, the N optical-fiber coils are connected in parallel, so as to inject simultaneously a fraction of the first modulated beam at a first end of each coil and a fraction of the second modulated beam at a second end of each coil, said N optical-fiber coils having respective transit times T1, T2, . . . TN that are all different from each other; the first optical separation means being adapted to recombine said fractions of the first modulated beam and said fractions of the second modulated beam having travelled through the N coils in counter-propagating directions to form an interferometric beam, and the signal-processing system being adapted to process the interferometric signal detected by the photodetector as a function of the respective transit times T1, T2, . . . TN in the different coils.

In the present document, the notion of simultaneity of the modulation of the optical beams translates the fact that a same electro-optical modulation is applied with no phase shift at the entry of the N ring optical paths connected in parallel.

The multi-axis interferometric system of the invention advantageously makes it possible to determine, during a same period of modulation, the Sagnac phase shifts with respect to each of the axis of the different optical-fiber coils by using an extremely compact opto-electronic architecture, with no optical switch nor electronic switch.

According to a particular and advantageous embodiment, the multi-axis fiber optic interferometric system further comprises:a second optical separation means arranged between the shared light source and the shared photodetector;third optical separation means arranged on the optical path of the first modulated beam between the phase-modulation means and the first ends of each of the N optical-fiber coils;fourth optical separation means arranged on the optical path of the second modulated beam between the phase-modulation means and the second ends of each of the N optical-fiber coils;the third optical separation means and the fourth optical separation means each having at least one entry and N exits so as to transmit simultaneously and in parallel a fraction of the first modulated beam at the first end of each of the N optical-fiber coils and a fraction of the second modulated beam at the second end of each of the N optical-fiber coils and so that said fractions of the first modulated beam and said fractions of the second modulated beam propagate in opposite directions in each of said coils.

According to a particular and advantageous embodiment, the signal-processing system is adapted to record a series of at least 2*N components of the detected signal at determined instants as a function of the respective transit times T1, T2, . . . TN associated with each of the N optical-fiber coils, respectively, and to extract therefrom at least N Sagnac phase-shift measurements respectively associated with each of the N optical-fiber coils from said series of components.

According to various particular and advantageous aspects, the fiber optic interferometric system includes a planar integrated optical circuit including the first optical separation means, the shared phase-modulation means and the third and fourth optical separation means.

Advantageously, the first optical separation means includes a Y junction.

According to various particular and advantageous aspects, the fiber optic interferometric system includes a digital-to-analog converter adapted to apply a modulation voltage to the shared phase-modulation means so as to generate a modulated phase shift at a modulation frequency fm.

According to a particular and advantageous embodiment, the third optical separation means, and respectively the fourth optical separation means, comprise one or several 2×2 couplers arranged in series, a 1×N coupler or a 3×3 coupler.

The invention also relates to a method for the interferometric measurement of a plurality of phase shifts in an interferometric system comprising N optical-fiber coils optically coupled in parallel to a shared source, a shared phase modulator and a shared detector, said N optical-fiber coils having respectively transit times T1, T2, . . . TN that are all different from each other, the method comprising the following steps:spatial separation of a source beam into a first split beam and a second split beam;application of a time-modulated phase shift between the first split beam and the second split beam to form a first modulated beam and a second modulated beam;spatial separation of the first modulated beam into N fractions of the first modulated beam and spatial separation of the second modulated beam into N fractions of the second modulated beam;simultaneous and parallel injection on the plurality of optical-fiber coils, respectively, of a fraction of the first modulated beam at the first end of each optical-fiber coil and of a fraction of the second modulated beam at the second end of said optical-fiber coil, so that each of said fractions of the first modulated beam and each of said fractions of the second modulated beam respectively travel through an optical-fiber coil in counter-propagating directions with, respectively, a different transit time T1, T2, . . . TN for each of the N optical-fiber coils;recombination of the N fractions of first modulated beam having each travelled through an optical-fiber coil to form a first recombined beam;recombination of the N fractions of second modulated beam having each travelled through an optical-fiber coil to form a second recombined beam;recombination of the first recombined beam and of the second recombined beam to form a time-modulated interferometric beam as a function of the respective transit times T1, T2, . . . TN in the different optical-fiber coils;detection of the interferometric beam and generation of an interferometric electronic signal;recording of at least 2*N components of the interferometric electronic signal at a series of at least 2*N instants as a function of the respective transit times T1, T2, . . . TN in the optical-fiber coils (11,12,13);processing of the at least 2*N components of the interferometric electronic signal recorded at the previous step to deduce therefrom at least a plurality of N Sagnal phase-shift measurements respectively associated with each of the N optical-fiber coils.The method of multi-axis interferometric measurement of the invention advantageously makes it possible to determine simultaneously and in parallel the Sagnac phase shift relative to several axes of optical-fiber coils, without optical switching nor electronic switching and with a simple misalignment matrix between the different axes. In other words, the misalignment matrix, describing the relations between each of the values provided by the sensor and each of the measurements that it is desired to perform, is more easily diagonalizable, with coefficients that are less dependent on the environmental parameters (temperature, rotation, etc. . . . ).

According to various particular and advantageous aspects of the method of the invention:the step of application of a time-modulated phase shift comprises a rectangular-wave modulation at a modulation frequency fm;the modulation frequency fmis equal to the proper (or eigen) frequency fpof one of the optical-fiber coils, said coil having a transit time Ti, and the proper frequency being defined as follows: fp=1/(2·Ti);the modulation frequency fmis lower than the proper frequency of all the optical-fiber coils; orthe modulation frequency fmis higher than the proper frequency of all the optical-fiber coils, the modulation frequency being lower than:

fm≤12×(TMAX-Tmin)where TMAXrepresents the maximum of the transit times T1, T2, . . . TN of all the coils and Tminrepresents le minimum of the transit times T1, T2, . . . TN of all the coils.

Particularly advantageously, the step of detection of the interferometric beam and/or of recording of at least 2*N components of the interferometric electronic signal comprises the detection and the recording of rising and/or falling fronts at instants determined as a function of the respective transit times T1, T2, . . . TN in the different optical-fiber coils and of the modulation frequency.

In a particular embodiment, the step of processing of said at least 2*N recorded components of the interferometric electronic signal comprises operations of linear combination of said at least 2*N components to deduce therefrom at least the plurality of N Sagnac phase-shift measurements associated with each of the N optical-fiber coils, respectively.

The present invention also relates to the characteristics that will be revealed in the following description and that will have to be considered in isolation or according to any technically possible combination thereof.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

We will first detail the architecture of a single-axis interferometric system and the operation in modulation-demodulation of this interferometer in relation withFIGS. 1-3.

FIG. 1schematically shows a single-axis interferometric system according to the prior art. This interferometric system includes a light source1, an optical-fiber coil11, a first optical coupler-separator3, a second optical source separator6, a photodetector2and a signal-processing system800.

In the present document, the term beam applies to an optical wave and the term signal to an electric or electronic signal.

The light source1emits a source beam100having a decoherence length Lc. The light source1is preferably of broadband spectrum so as to limit the decoherence length to a few hundredths of micrometers. The light source1is for example a broad-spectrum laser source or laser diode (ASE source) having a decoherence length of the order of 600 micrometers. The light source1emits a continuous and not-pulsed radiation. Advantageously, the intensity of the radiation of the light source1is constant as a function of time.

The first optical coupler-separator3, called a coil separator, spatially separates the source beam100into a first beam and a second beam. An optical phase modulator4makes it possible to modulate the phase shift between the first beam150and the second beam250. The first modulated beam150is coupled to the first end A1of the optical-fiber coil11. Simultaneously, the second modulated beam250is coupled to the second end A2of the optical-fiber coil11. Hence, the first150and second250modulated beams propagate simultaneously in the optical-fiber coil11following opposite directions. The same optical coupler-separator3recombines the beams at the exit of the optical-fiber coil11to form an interferometric beam310. The second optical source separator6directs the interferometric beam310exiting from the optical-fiber coil11towards the photodetector2.

In the embodiment shown inFIG. 1, an integrated optical circuit10advantageously comprises a polarizer5, the optical coupler-separator3, which is a Y-junction coupler, and an optical modulator4. The optical modulator4makes it possible to apply a modulated optical phase shift between the two counter-propagating beams. The integrated optical circuit10is for example consisted of a lithium niobate substrate on which are manufactured optical waveguides configured to form the polarizer5and the Y-junction optical separator3. Electrodes deposited in the vicinity of the Y-junction branches make it possible to obtain a perfectly reciprocal optical phase modulator4. Each of the two ends A1, A2of the optical-fiber coil11is connected by a section of optical fiber to one end of the two waveguides at the exit of the integrated optical circuit10.

Advantageously, fiber optic links connect the light source1, the photodetector2and the integrated optical circuit10to the optical source separator6.

The optical source separator6is for example consisted by a 2×2 directional coupler that makes it possible to direct the interferometric beam exiting from the optical-fiber coil11towards the photodetector2.

The photodetector2converts the power of the interferometric beam310into an analog signal70transmitted to a signal-processing system.

The signal-processing system800comprises for example an analog-to-digital converter7, a digital processor or DSP8, for example of the FPGA type, and a digital-to-analog converter9. The digital processor8makes it possible to extract a rotation signal80in a digital output. The digital-to-analog converter9makes it possible to apply a modulation voltage90to the optical phase modulator4.

The optical intensity of the interferometric beam is a cosine function of the phase shift accumulated between the two counter-propagating waves during the propagation in the coil (FIG. 2b). In the absence of a non-reciprocal effect, this phase shift is null. Due to the Sagnac effect, the response of the interferometer depends on the non-reciprocal phase shift between the two counter-propagating waves. In particular, during a rotation of the interferometer about the axis of the optical-fiber coil12, a Sagnac phase shift φsproportional to the rotation rate appears.

The techniques, well known by the one skilled in the art, of phase modulation in fiber optic interferometers are used to improve the sensitivity and the linearity of the interferometer response to the phase shift due to the Sagnac effect.

The implementation of a phase modulation Vmodin the form of a rectangular-wave of amplitude of for example ±π/2, hence makes it possible to generate a time-modulated signal.

A time-demodulation processing of the detected signal makes it possible to extract a signal representative of the phase shift due to the Sagnac effect.

FIG. 2illustrates the effect of a rectangular-wave modulation on the measurement of the Sagnac-effect phase shift.

FIG. 2(a)shows, as a function of time t, the modulation voltage Vmodapplied to the optical phase modulator4of a ring interferometer, as shown inFIG. 1. The modulation frequency fmis herein chosen equal to the proper frequency fpof the ring interferometer, where fpis defined as follows:
fp=1/(2·τ)

where τ represents the transit time of a modulated wave propagating in the coil at the group velocity (or group transit time).

FIG. 2(b)shows the intensity of the interferometric beam as a function of the phase shift Δφ between the two counter-propagating waves.FIG. 2(c)shows the optical phase-shift at the exit of the interferometer in presence of the modulation Vmodand of a Sagnac phase shift φS: this phase shift, modulated as a function of time at the modulation frequency fm, is equal to ±π/2+φS. However, the photodetector2does not measure directly the phase shift at the exit of the interferometer, but measures the power P of the detected interferometric signal70.FIG. 2(d)shows the power P of the signal measured at the exit of the interferometer as a function of time. At each period of modulation Tm, the measured signal conventionally shows two plateaus, separated by peaks that correspond to the change of phase of the applied modulation. The difference between the two values of power is representative of the non-reciprocal phase shift due to the Sagnac effect φs.

The modulated interferometric signal detected inFIG. 2(d)shows two levels of signal that are equal to each other when the interferometer is at rest, and that are offset in presence of a Sagnac-effect phase shift. At the time of the change of sign of the modulation, the detected signal crosses zero, which produces the peaks ofFIG. 2(d). A signal processing is generally used to suppress these peaks and to measure the difference between the two levels of signal linked to the two half-periods of modulation, respectively. This difference is representative of a Sagnac-effect phase shift φs.

FIG. 3shows the implementation of a rectangular-wave phase modulation at a modulation frequency fmlower than the proper frequency fpof a single-axis ring interferometer.FIG. 3(a)shows the modulation voltage Vmodapplied as a function of time t;FIG. 3(b)shows the intensity of the interferometric beam as a function of the phase shift Δφ between the two counter-propagating waves;FIG. 3(c)shows the phase shift Δφ as a function of time t andFIG. 3(d)shows the power of the detected interferometric signal as a function of time t.

In the case ofFIG. 3, the modulation voltage Vmodapplied to the optical phase modulator4is a periodic voltage of period Tmand in the form of a rectangular-wave. In this example, the modulation frequency fmis lower than the proper frequency of the interferometer:
fm<1/(2τ)
where τ represents the transit time in the coil11.
Compared toFIG. 2(d), at each period of modulation Tm, the detected interferometric signal inFIG. 3(d)also includes two levels separated by bands broader than the peaks ofFIG. 2(d). A signal processing makes it possible, at each period of modulation Tm, to measure the difference between the two levels of signal, this difference being representative of a Sagnac-effect phase shift φs.

The techniques of modulation described in relation withFIGS. 2 and 3are applied to an interferometric system with only one optical-fiber coil.

Other types of modulation than a rectangular-wave modulation, for example a sinusal modulation, may be implemented on an interferometric system as illustrated inFIG. 1. In this case, the signal-processing system is adapted to process the detected signal as a function of the applied modulation so as to extract the Sagnac-effect phase shift of the ring interferometer.

In a conventional multi-axis interferometric system comprising several fiber optic interferometers connected to a same source and possibly a same detector, each interferometer includes an own phase modulator and a specific method of modulation-demodulation is implemented on each interferometer.

FIG. 4schematically shows a first embodiment of the invention in an interferometric system architecture comprising two optical-fiber coils11and12. The same elements appearing inFIG. 1are denoted by the same reference signs. In particular, the system ofFIG. 4includes shared optical components: a light source1, a photodetector2and an optical phase modulator4.

The system ofFIG. 4includes a first optical-fiber coil11and a second optical-fiber coil12. The first optical-fiber coil11has a first end A1and a second end A2. The second optical-fiber coil12has a first end B1and a second end B2.

Two coils11and12having different transit times, respectively T1and T2, are chosen. For example, the coils are manufactured from identical optical fibers, but have different lengths. In the preferred embodiment, the difference of length between the two coils is equal to at least 10% of the total length of the optical-fiber coil. In a variant, optical-fiber coils having different dispersion properties are chosen so that the two coils have different respective transit times.

The interest is herein about the transit time of the modulation of the signals, at the modulation frequency fm, in the different optical-fiber coils, and not about the transit time of a non-modulated optical beam in the optical-fiber coils. The transit time of the modulation is determined by the group velocity in each of the optical-fiber coils.

As in the single-axis system ofFIG. 1, the multi-axis interferometric system ofFIG. 4also includes a first optical coupler-separator3and a second optical source separator6. The first optical coupler-separator3spatially separates the source beam100into a first split beam and a second split beam.

The optical modulator4applies a time-modulated optical phase shift between the first split beam and the second split beam, so as to generate a first modulated beam150and the second modulated beam250that remain spatially separated before being injected into the optical-fiber coils.

The second optical source separator6directs towards the photodetector2an interferometric beam320exiting from the first optical separator3and propagating in the opposite direction to that of the source beam100.

The multi-axis interferometric system ofFIG. 4further includes a third optical separator21arranged on the optical path of the first modulated beam150and a fourth optical separator22arranged on the optical path of the second modulated beam250, and more particularly between the optical modulator4and the ends of the optical-fiber coils11and12.

Advantageously, for a system with two optical-fiber coils11and12, the third and/or fourth optical separator includes an optical separator with one entry and two exits. An optical separator with one entry and two exits may be consisted of a Y-junction coupler or a 2×2 evanescent-field fiber optic coupler in which only one of the two entries is used.

The path of entry of the third optical separator21is connected by optical fiber to an exit of the optical phase modulator4and the path of entry of the fourth optical separator22is connected by optical fiber to another exit of the optical phase modulator4.

One of the two optical paths of exit of the third optical separator21is connected to a first end A1of the first optical-fiber coil11. The other optical path of exit of the third optical separator21is connected to a first end B1of the second optical-fiber coil12.

Similarly, one of the two optical paths of exit of the fourth optical separator22is connected to the second end A2of the first optical-fiber coil11. The other optical path of exit of the fourth optical separator22is connected to the second end B2of the second optical-fiber coil12.

Hence, the third optical separator21spatially separates the first modulated beam150into a first fraction of the first modulated beam151and a second fraction of the first modulated beam152. The first fraction of the first modulated beam151is injected at the first end A1of first optical-fiber coil11. Simultaneously, the second fraction of the first modulated beam152is injected at the first end B1of the second optical-fiber coil12. The first fraction of the first modulated beam151and the second fraction of the first modulated beam152are hence applied simultaneously and in parallel at the first end A1, respectively B1, of each optical-fiber coil11, respectively12. Preferably, the third optical separator21is equi-distributed in power so that the first fraction of the first modulated beam151and the second fraction of the first modulated beam152have the same amplitude. However, a difference of amplitude between the modulated beams151and152does not alter noticeably the operation of the interferometric system.

Similarly, the fourth optical separator22spatially separates the second modulated beam250into a first fraction of the second modulated beam251and a second fraction of the second modulated beam252. The first fraction of the second split beam251is applied at the second end A2of the first optical-fiber coil11. Simultaneously, the second fraction of the second modulated beam252is applied at the second end B2of the second optical-fiber coil12. The first fraction of the second modulated beam251and the second fraction of the second modulated beam252are hence applied simultaneously and in parallel at the second end A2, respectively B2, of each optical-fiber coil11, respectively12. Preferably, the fourth optical separator22is equi-distributed in power so that the first fraction of the second modulated beam251and the second fraction of the second modulated beam252have the same amplitude.

Hence, the first fraction of the first split beam151and the first fraction of the second split beam251travel through the first coil11in counter-propagating directions. Simultaneously, the second fraction of the first split beam152and the second fraction of the second split beam252travel through the second coil12in counter-propagating directions.

The fourth optical separator22receives, on the one hand, from the second end A2of the first coil11, the first fraction of the first split beam161having travelled through the first coil11and, on the other hand, from the second end B2of the second coil12, the second fraction of the first split beam162having travelled through the second coil12. The fourth optical separator22recombines by superimposition these two beams161,162having travelled through the first coil11and the second coil12, respectively, and forms a first recombined beam160. Coils are chosen, which have a difference of transit time |T2−T1| corresponding to a difference of optical path in the optical fiber higher than the decoherence time of the source, so that the beams161and162do not interfere with each other during recombination by the optical separator22.

The third optical separator21receives, on the one hand, at the first end A1of the first coil11, the first fraction of the second split beam261having travelled through the first coil11and, on the other hand, at the first end B1of the second coil12, the second fraction of the second split beam262having travelled through the second coil12. The third optical separator21recombines by superimposition these two beams261,262having travelled through the first coil11and the second coil12, respectively, and forms a second recombined beam260. For the same reason as detailed in the previous paragraph, the beams261and262do not interfere with each other during recombination by the optical separator21.

The first optical coupler-separator3receives the recombined beam160and the recombined beam260. The optical coupler-separator3superimposes the recombined beams160and260. More precisely, the coupler-separator3recombines on the one hand the beams151and251having travelled through the first coil with a transit time T1in opposite directions, and on the other hand the beams152and252having travelled through the second coil12with a transit time T2in opposite directions, to form a single interferometric beam320. The second optical source separator6directs the interferometric beam320exiting from the two optical-fiber coils11and12towards the photodetector2. The interferometric beam320is hence consisted by the sum of an interferometric beam associated with the first coil11and of another interferometric beam associated with the second coil12, which do not interfere with each other, due to the difference of transit time between the two coils. The detector transmits a detected signal720to the signal processing system800. The processing system analyses and decomposes the detected signal720to extract a measurement280of the Sagnac phase shift associated with each of the optical-fiber coils.

A signal-processing system800comprises an analog-to-digital converter or ADC7, a processor of the DSP type8, for example a FGPA, and a digital-to-analog converter or DAC9. The ADC digitizes the electric signal coming from the detector2. The DSP8is adapted to process the digitized signal720as a function of the respective transit times T1and T2and to extract therefrom a series of measurements280comprising a measurement of the Sagnac phase shift associated with the first coil11and a measurement of the Sagnac phase shift associated with the second coil12. The DAC9applies a modulation voltage190to the phase modulator4.

Method of Modulation-Demodulation in a Two-Axis Interferometric System

FIG. 5shows the implementation of a method of modulation and demodulation on a multi-axis interferometric system as described in relation withFIG. 4.

FIG. 5(a)shows, as a function of time t, the modulation voltage Vmodapplied to the optical modulator4to introduce a time-modulated optical phase shift between the first modulated beam150and the second split beam250. Advantageously, the modulation is a rectangular-wave modulation having a modulation frequency fmand, equivalently, a period of modulation Tm=1/fm.

In a first embodiment, illustrated inFIG. 5, the modulation voltage Vmodhas a modulation frequency fmlower than the proper frequency fpof each of the two coils11,12and a cyclic ratio of 1/2.

Let's note T1the transit time in the first coil11and, respectively, T2the transit time in the second coil12. By way of example, the first coil11is shorter than the second coil12, so that T1<T2.

It is chosen a modulation frequency fmlower than the proper frequency of each of the two coils, defined as follows:

FIG. 5(b)shows the intensity Iiof the interferometric signal as a function of the phase shift Δφ1between two counter-propagating waves in the first coil11and the intensity I2of the interferometric signal as a function of the phase shift Δφ2between two counter-propagating waves in the second coil12. In other words, the curve I1represents the response of the fiber optic gyroscope formed of the first coil and the curve I2represents the response of the fiber optic gyroscope formed of the second coil. The first coil11is sensitive to a Sagnac phase shift φ1about its axis; the second coil12is sensitive to a Sagnac phase shift φ2about its axis. The first coil11being shorter than the second coil12, the sensitivity of the first coil11is lower than the sensitivity of the second coil12.

FIG. 5(c)shows, as a function of time t, the Sagnac phase shift φ1about the axis of the first coil11and the Sagnac phase shift φ2about the axis of the second coil12. The transit time T1in the first coil being different from the transit time T2in the second coil, for a same modulation Vmodapplied to the beams travelling through the two coils, the Sagnac phase-shift signals φ1about the first coil11and φ2about the second coil are time offset proportionally to the difference of transit time. More precisely, the first coil11being shorter than the second coil12, the Sagnac phase shift φ1of the first coil11occurs before the Sagnac phase shift φ2of the second coil12.

The invention takes advantage of the delay line operation of a Sagnac ring fiber optic interferometer. The modulation voltage applied to the shared phase modulator shows periodically rising fronts at the instants t=0, Tm, . . . , and falling fronts at t=Tm/2, 3τm/2 . . . . These rising or falling fronts of modulation are herein liken to pulses used to sound during a same modulation period and in parallel the two optical-fiber coils. The first coil11responds to a pulse of modulation with a delay time equal to the transit time T1. Similarly, the second coil12responds to a modulation pulse with a delay time equal to the transit time T2. The transit times T1and T2being distinct, the response of the first coil arrives to the detector before the response of the second coil.

Coils11and12are chosen, which have a sufficient difference of transit time |T2−T1| with respect to the maximum speed of electronic processing of the signals, which is determined by the signal detection and processing system. More precisely, the minimum difference of transit time between two optical-fiber coils is chosen so as to be higher than the response time of the signal-processing electronic system in order to make it possible to time separate the signals associated with each of the optical-fiber coils. The response time of the processing electronic system is of the order of the MHz. The phase modulation frequency fmis in general of the order of a few hundreds of kHz.

It is hence possible to detect separately in time the interferometric signal associated with the first coil and the interferometric signal associated with the second coil, although these two interferometric beams are optically superimposed in intensity and are detected by a single and same detector.

Hence,FIG. 5(g)shows the chronogram of the modulation voltage, respectivelyFIG. 5(d)the chronogram of the power P1of the interferometric signal of the first coil,FIG. 5(e)the chronogram of the power of the interferometric signal of the second coil, andFIG. 5(f)the chronogram of the power of the detected interferometric signal that is the sum of the powers P1and P2.

As illustrated inFIG. 5(g), a rectangular-wave phase modulation is applied simultaneously at the entry of the two coils with a period Tm.

Advantageously, 1+2*2 acquisitions, i.e. 5 acquisitions, per period of modulation are performed for a system with two optical-fiber coils. The time position of these acquisitions is determined by the position of the fronts and is not regularly distributed over the period of modulation. The rising and/or falling front detection mode is used to trigger the acquisitions and to record the instant of arrival and the height of each rising and/or falling front.

It is observed on the power signal P1(seeFIG. 5(d)), a first rising front at the instant t1=T1(modulo Tm) and a second rising front at the instant t2=(Tm/2+T1) (modulo Tm). The Sagnac phase shift φ1linked to the first coil11is equal to the difference between the height of the first rising front at the instant t1and of the second rising front at the instant t2.

Similarly, it is observed on the power signal P2(seeFIG. 5(e)), a first rising front at the instant t3=T2(modulo Tm) and a second rising front at the instant t4=(Tm/2+T2) (modulo Tm). The Sagnac phase shift φ2linked to the second coil12is equal to the difference between the height of the first rising front at the instant t3and of the second rising front at the instant t4.

However, the detector2receives at each instant the sum of the power P1and of the power P2.

FIG. 5(f)shows the power of the detected interferometric signal that is the superimposition of the power P1and of the power P2. The transit times T1and T2being separated, it is observed a first series of rising fronts at the instants t1=T1and t3=T2, then a falling front, and a second series of rising fronts at the instants t2=(Tm/2+T1) and t4=(Tm/2+T2). The transit times T1and T2in the coils being different, the electronic system of detection may be adapted to record in the detected signal two rising fronts at the determined instants t1, t3, then a falling front at an instant t0and finally two rising fronts t2and t4.

The detected power P changes of level at the following instants:at the instant t1, P passes from a level A to a level B;at the instant t3, P passes from a level B to a level C;at the instant t0, P passes from a level C to a level E;at the instant t2, P passes from a level E to a level F;at the instant t4, P passes from a level F to a level C.

The detected interferometric signal is not recorded at predetermined instants or a predefined frequency, but at instants t0, t1, t2, t3, t4that are triggered by the arrival of rising and/or falling fronts to the detector.

The processing system makes it possible to extract from the measurements of the levels A, B, C, D, E and F, for example via linear combinations, a measurement of the Sagnac phase shift φ1in the first coil11and a measurement of the Sagnac phase shift φ2linked to the second coil12.

For example, the signal-processing system is configured to calculate the height difference of the fronts measured at the instants t1and t2to deduce therefrom a measurement of the Sagnac phase shift φ1linked to the first coil11, and respectively the height difference of the fronts measured at the instants t3and t4to deduce therefrom a measurement of the Sagnac phase shift φ2linked to the second coil12.

It can be noticed that the measurements of the second coil are independent from the measurements of the first coil. It ensues therefrom a relatively simple misalignment matrix between the two axes respectively associated with the two coils, contrary to a configuration of a multi-axis system where the optical-fiber coils are connected in series and where the misalignment matrix proves to be complex.

The upper limit on the difference between the transit times of the two coils is such that:
T2−T1≦Tm/2.

The signal-processing method hence takes advantage of the different transit times of the different coils to separate in time the response of each optical-fiber coil.

Hence, from a single source1, a shared phase modulator4and single detector2, the device and the method of the invention make it possible to extract two measurements of Sagnac phase shift related to two optical-fiber coils11and12connected in parallel.

Complementary, the processing of the data advantageously makes it possible to measure one or several other parameters in addition to the Sagnac phase shifts, as for example the voltage Vpi applied to the phase modulator to produce a phase shift of Pi radian or the proper frequency of the optical-fiber coils.

The interferometric systems and methods of acquisition of an interferometric signal of the prior art generally operate at a fixed frequency of acquisition, for example by sampling the detected signal over the period of modulation. On the contrary, the system and the method of acquisition of the multi-axis interferometric signal described in relation withFIGS. 4 and 5is function of the transit time, in other words the delay, of each coil and not of a frequency associated with each coil.

The case illustrated inFIG. 5corresponds to a modulation frequency fmlower than the proper frequency of the two coils.

In a particular and advantageous embodiment, it is possible to apply a closed-loop control to the Sagnac phase shift of one of the optical-fiber coils.

According to another embodiment, it is chosen a modulation frequency fmhigher than the proper frequencies of the different coils. This operation makes it possible to exploit the full dynamic of the multi-axis interferometric system. The limit of modulation frequency is defined as follows:
fm1/(2·(T2−T1)).

In another embodiment, it is also possible to choose the modulation frequency fmequal to the proper frequency of one of the coils:

This embodiment is particularly advantageous because it makes it possible to limit the Kerr effect in the coil having a proper frequency corresponding to the modulation frequency fm. For that purpose, it is desirable not to deviate too much from the proper frequency of the different coils. Hence, the modulation frequency is advantageously chosen equal to the proper frequency of an optical-fiber coil, and the difference of transit time so that the frequency of the other coil is close, for example ±10%, of the modulation frequency.

In the case where it is desired to obtain an interferometric system having a sensitivity of the same order on the two optical-fiber coils, a small difference of transit time between the two optical-fiber coils is chosen.

On the contrary, in a system where a lower sensitivity is accepted on the first coil and where a maximum sensitivity is desired on the second coil, T1<<T2is chosen. Such a configuration makes it possible to favour an axis with respect to another axis from the point of view of the bias performances or of the scale factor performances.

Other types of modulation, for example a rectangular-wave modulation of cyclic ratio different from 1/2, may be implemented in an interferometric measurement system and method as illustrated inFIGS. 4-5. In this case, the signal-processing system is adapted to process the detected signal as a function of the applied modulation so as to extract the Sagnac-effect phase shift of each coil of the interferometer.

FIG. 6schematically shows another embodiment of an interferometric system architecture comprising three optical-fiber coils11,12and13. The same elements appearing inFIGS. 1 and 4are denoted by the same reference signs. In particular, the system ofFIG. 6includes a shared light source1, a shared photodetector2and a shared optical phase modulator4.

As in the two-axis system ofFIG. 4, the three-axis interferometric system ofFIG. 6also includes a first optical coupler-separator3and a second optical source separator6. The first optical coupler-separator3spatially separates the source beam100into a first split beam140and a second split beam240. The second optical source separator6directs towards the photodetector2an interferometric beam320exiting from the first optical separator3and propagating in the direction opposite to that of the source beam100.

The optical modulator4makes it possible to apply a time-modulated optical phase shift between the first split beam140and the second split beam240and to generate a first modulated beam150and a second modulated beam250.

The system ofFIG. 6includes a first optical-fiber coil11, a second optical-fiber coil12and a third optical-fiber coil13. The first optical-fiber coil11has a first end A1and a second end A2. The second optical-fiber coil12has a first end B1and a second end B2. The third optical-fiber coil13has a first end C1and a second end C2.

T1the transit time of the group velocity in the first coil11,

T2the transit time of the group velocity in the second coil12, and

T3the transit time of the group velocity in the third coil13.

The transit times T1, T2and T3are all different two by two. In an exemplary embodiment: T1≦0.9×T2and 1.1×T2≦T3. For example, the coils11,12,13are manufactured from a same optical fiber, but have different lengths.

The three-axis interferometric system ofFIG. 6further includes a third optical separator31arranged on the optical path of the first modulated beam150and a fourth optical separator32arranged on the optical path of the second modulated beam250. Advantageously, for a system with three optical-fiber coils11,12and13, the third and fourth optical separator each include a one-entry and three-exit optical separator. A one-entry and three-exit optical separator may be consisted of a 1×3 coupler or, as an alternative, of a 3×3 coupler in which only one of the three entries is used. As an alternative, the third and/or fourth optical separator may be formed of a series of 2×2 couplers arranged according to a tree structure, so as to spatially separate the modulated beams into three beams. Advantageously, the third optical separator31and the fourth optical separator32are each consisted of a 1*3 coupler and are integrated on a planar integrated optical circuit made of lithium niobate, which also includes the optical modulator4, the first optical separator3and a polarizing waveguide5.

The optical path of entry of the third optical separator31is connected by optical fiber to a path of exit of the optical modulator4and the optical path of entry of the fourth optical separator32is connected by optical fiber to another path of exit of the optical modulator4.

One of the three optical paths of exit of the third optical separator31is connected to the first end A1of the first optical-fiber coil11, the second optical path of exit of the third optical separator31is connected to the first end B1of the second optical-fiber coil12and the third optical path of exit of the third optical separator31is connected to the first end C1of the third optical-fiber coil13.

Similarly, one of the three optical paths of exit of the fourth optical separator32is connected to the second end A2of the first optical-fiber coil11; the second optical path of exit of the fourth optical separator32is connected to the second end B2of the second optical-fiber coil12and the third optical path of exit of the fourth optical separator32is connected to the second end C2of the third optical-fiber coil13.

Hence, the third optical separator31spatially separates the first modulated beam150into a first fraction of the first modulated beam151, a second fraction of the first modulated beam152and a third fraction of the first modulated beam153. The first fraction of the first modulated beam151is injected at the first end A1of the first optical-fiber coil11. Simultaneously, the second fraction of the first modulated beam152is injected at the first end B1of the second optical-fiber coil12and the third fraction of the first modulated beam153is injected at the first end C1of the third optical-fiber coil13. The first, second and third fractions of the first modulated beam151,152and153are hence applied simultaneously and in parallel at the first ends A1, respectively B1, C1, of the three optical-fiber coils11, respectively12and13. Preferably, the third optical separator31is equi-distributed in intensity so that the first, second and third fractions of the first modulated beam151,152and153have the same intensity. However, a difference of intensity between the beams151,152and153do not alter notably the operation of the interferometric system.

Similarly, the fourth optical separator32separates the second modulated beam250into a first fraction of the second modulated beam251, a second fraction of the second modulated beam252and a third fraction of the second modulated beam253. The first fraction of the second modulated beam251is applied at the second end A2of the first optical-fiber coil11. Simultaneously, the second fraction of the second modulated beam252is applied at the second end B2of the second optical-fiber coil12and the third fraction of the second modulated beam253is applied at the second end C2of the third optical-fiber coil13. The first, second and third fractions of the second modulated beam251,252,253are hence applied simultaneously and in parallel at a second end A2, respectively B2and C2, of the three optical-fiber coil11, respectively12and13. Preferably, the first, second and third fractions of the second modulated beam261,262,263have the same amplitude.

Hence, the first fraction of the first modulated beam151and the first fraction of the second modulated beam251travel through the first coil11with a transit time T1in counter-propagating directions. Simultaneously, the second fraction of the first modulated beam152and the second fraction of the second modulated beam252travel through the second coil12with at transit time T2in counter-propagating directions. Likewise, simultaneously, the third fraction of the first modulated beam153and the third fraction of the second modulated beam253travel through the third coil13with a transit time T3in counter-propagating directions.

The third optical separator31receives on the one hand, exiting from the first end A1of the first coil11, the first fraction of the second modulated beam261having travelled through the first coil11, on the other hand, from the first end B1of the second coil12, the second fraction of the second modulated beam262having travelled through the second coil12, and finally, from the first end C1of the third coil13, the third fraction of the second modulated beam263having travelled through the third coil13. The third optical separator31recombines by superimposition these three beams261,262,263having travelled through the first coil11, the second coil12and the third coil13, respectively, to form a recombined beam260. The differences of transit time between the fiber coils11,12and13are higher than the decoherence time of the source, so that these three beams261,262,263do not interfere with each other.

The fourth optical separator32receives, on the one hand, exiting from the second end A2of the first coil11, the first fraction of the first modulated beam161having travelled through the first coil11, on the other hand, from the second end B2of the second coil12, the second fraction of the first modulated beam162having travelled through the second coil12, and finally, from the second end C2of the third coil13, the third fraction of the first modulated beam163having travelled through the third coil13. The fourth optical separator32recombines by superimposition, with no interference, these three beams161,162,163having travelled through the first coil11, the second coil12and the third coil13, respectively, to form a recombined beam160.

The first optical coupler-separator3receives the recombined beam160and the recombined beam260. The optical coupler-separator3superimposes the recombined beams160and260to form a single interferometric beam330. More precisely, the interferometric beam330is formed by the superimposition of the recombinations, respectively, of the beams161and262having travelled through the first coil11with a transit time T1in opposite directions, of the beams162and262having travelled through the second coil12with a transit time T2in opposite directions, and finally of the beams163and263having travelled through the third coil13with a transit time T3in opposite directions. The second optical source separator6directs the interferometric beam330exiting from the three optical-fiber coils11,12and13towards the photodetector2. The interferometric beam330is herein a composite beam comprising an interferometric beam component associated with the first coil, another interferometric beam component associated with the second coil, and still another interferometric beam component associated with the third coil. The detector2transmits a detected signal730to the signal-processing system800. The processing system800digitizes and numerically processes the detected signal730so as to extract a measurement280of the Sagnac phase shift associated with each of the optical-fiber coils, respectively, similarly to the method of demodulation described in relation withFIG. 5.

Advantageously, a rectangular-wave modulation at a modulation frequency fmis applied, and the rising fronts are detected in the detected interferometric signal at determined instants, as a function of the respective transit times T1, T2and T3.

In the case of an interferometric system with three optical-fiber coils and a rectangular modulation signal, an interferometric signal formed of a series of steps is detected. These steps are measured at different instants. Advantageously, 1+2*3=7 acquisitions per period of modulation are performed, the time position of these acquisitions being determined by the position of the step fronts. For example, for a system with three optical-fiber coils, similarly to the method described in relation withFIG. 5, it is recorded in the detected interferometric signal three rising fronts at determined instants t1, t3, t5then a falling front at a determined instant to, and finally three rising fronts at determined instants t2, t4and t6. More particularly, the instants t0, t1, t2, t3, t4, t5and t6are determined as a function of the respective transit times T1, T2and T3in the three coils and as a function of the modulation period and cyclic ratio.

The different Sagnac phase shifts associated with the different optical-fiber coils are deduced by linear combinations of the 7 acquisitions.

Advantageously, a rising and/or falling front detection mode is used to trigger the acquisitions and to record the instant of arrival and the height of each rising and/or falling front. Hence, the acquisition of the interferometric signal is not performed at predetermined instants or at a predefined frequency, but at instants t0, t1, t2, t3, t4that are triggered by the arrival of rising and/or falling fronts to the detector.

FIG. 7schematically shows an interferometric system with three optical-fiber coils according to a preferred embodiment of the invention, wherein a multifunction integrated optical circuit16integrates the first optical separator3, the second optical separator6and the optical phase modulator4. 1×3 splitting couplers form the third optical separator31and the fourth optical separator.

Method of Modulation-Demodulation in a Three-Axis Interferometric System First Variant Tm/2>Ti

FIGS. 8(a)-8(e)show the implementation of a method of modulation and demodulation on a three-axis interferometric system as described in relation withFIG. 7.

InFIG. 8, the modulation is a rectangular-wave modulation having a modulation frequency fm and, equivalently, a period of modulation Tm=1/fm, the half-period of modulation being higher than the transit time in the three coils:
T1<T2<T3<Tm/2

FIG. 8(a)shows the intensity11, respectively,12,13, of the interferometric signal as a function of the phase shift Lip between two counter-propagating waves in the first coil11, respectively in the second coil12and in the third coil13. The first coil11is sensitive to a Sagnac phase shift φ1about its axis; the second coil12is sensitive to a Sagnac phase shift φ2about its axis; and the third coil13is sensitive to a Sagnac phase shift φ3about its axis.

FIG. 8(b)shows, as a function of time t, the Sagnac phase shift φ1, respectively φ2, φ3, about the axis of the first coil11, respectively of the second coil12and the third coil13. The respective transit times T1, T2and T3being all different, for a same modulation Vmod applied simultaneously and in parallel to the beams travelling through the three coils, the Sagnac phase-shift signals φ1, respectively φ2and φ3, arrive to the detector with time offset between each other. More precisely, the Sagnac phase shift φ1of the first coil11occurs in first, before the Sagnac phase shift φ2of the second coil12, and finally the Sagnac phase shift φ3of the third coil13.

In this example, the amplitude of the rotation viewed by the second coil12is lower than the amplitude of the rotation viewed by the third coil13, which is itself lower than the amplitude of the rotation viewed by the first coil11, so that:
φ2<φ3<φ1

FIG. 8(c)shows the chronogram of the rectangular-wave modulation voltage of cyclic ratio 1/2 applied to the optical modulator4to introduce a time-modulated optical phase shift between the first modulated beam150and the second split beam250, this modulation being applied simultaneously at the entry of the three coils.

FIG. 8(d)shows in superimposition the chronogram of the power P1, respectively P2, P3, of the interferometric signal of the first coil, respectively of the second coil and the third coil.

FIG. 8(e)shows the chronogram of the power of the detected interferometric signal that is the sum of the powers P1, P2and P3ofFIG. 8(d).

Advantageously, 1+2*3 acquisitions, i.e. 7 acquisitions, per period of modulation are performed for a system with three optical-fiber coils. The time position of these acquisitions is determined by the position of the fronts and is not regularly distributed over the period of modulation.

InFIG. 8(e), it is observed that the detected power has levels A, B, C, D, E, F, G at instants determined as a function, on the one hand, of the respective transit times, T1, T2, T3in the coils, and on the other hand, of the period of modulation and of the cyclic ratio of modulation.

It is shown that the Sagnac phase shifts in the three coils are calculated by linear combinations from the measured levels A-G.

For example, the respective Sagnac phase shifts are deduced for each coil:
φ1=A−E−B+F
φ2=B−F+C+G
φ3=C−G.

It is observed from the above equations that, in the case of a three-axis interferometer, the measurement of the phase shift of each axis is independent from the measurement of the phase shifts on the two other axes.

From the point of view of the Sagnac phase shifts, only 6 over the 7 measurements are used in the above formulas, as the measurement of the level D does not intervene in the above phase-shift calculations.

Second Variant Tm/2<Ti

FIGS. 9(a)-9(e)show the implementation of a method of modulation and demodulation on a three-axis interferometric system as described in relation withFIG. 7.

InFIG. 9, the modulation is a rectangular-wave modulation having a modulation frequency fm, hence a period of modulation Tm=1/fm, the half-period of modulation being lower than the transit time in the three coils:
Tm/2<T1<T2<T3.

FIG. 9(a)shows the intensity11, respectively12,13, of the interferometric signal as a function of the phase shift Δφ between two counter-propagating waves in the first coil11, respectively in the second coil12and in the third coil13. The first coil11is sensitive to a Sagnac phase shift φ1about its axis; the second coil12is sensitive to a Sagnac phase shift φ2about its axis; and the third coil13is sensitive to a Sagnac phase shift φ3about its axis.

FIG. 9(b)shows, as a function of time t, the Sagnac phase shift φ1, respectively φ2, φ3, about the axis of the first coil11, respectively the second coil12and the third coil13. The respective transit times T1, T2and T3being all different from each other, for a same rectangular-wave modulation Vmod applied simultaneously and in parallel to the beams travelling through the three coils, the Sagnac phase-shift signals φ1, respectively φ2and φ3, arrive on the detector with time offset between each other. More precisely, the Sagnac phase shift φ1of the first coil11occurs first, before the Sagnac phase shift φ2of the second coil12, and finally the Sagnac phase shift φ3of the third coil13.

In the example shown, the amplitude of the rotation viewed by the second coil12is lower than the amplitude of the rotation viewed by the third coil13, which is itself lower than the amplitude of the rotation viewed by the first coil11, so that: φ2<φ3<φ1.

FIG. 9(c)shows the chronogram of the rectangular-wave modulation voltage of cyclic ratio 1/2 applied on the optical modulator4to introduce a time-modulated optical phase shift between the first modulated beam150and the second split beam250, this modulation being applied simultaneously at the entry of the three coils.

FIG. 9(d)shows in superimposition the chronogram of the power P1, respectively P2, P3, of the interferometric signal of the first coil, respectively of the second coil and of the third coil.

FIG. 9(e)shows the chronogram of the power of the detected interferometric signal that is the sum of the powers P1, P2and P3ofFIG. 9(d).

Similarly toFIG. 8, it is observed inFIG. 9(e)that the detected power shows levels A, B, C, D, E, F, G at instants determined as a function, on the one hand, of the respective transit times T1, T2, T3in the three coils, and on the other hand, of the period of modulation and of the cyclic ratio of modulation. The instants of acquisition corresponding to the levels A-G are hence different from each other, on the one hand, in the case ofFIG. 8(e), where Tm/2>Ti, and on the other hand, in the case ofFIG. 9(e), where Tm/2<Ti, where Ti represents the transit time in the coils (Ti=T1, T2or T3).

Advantageously, 1+2*3 acquisitions, i.e. 7 acquisitions, per period of modulation are performed for a system with three optical-fiber coils. The time position of these acquisitions is determined by the position of the fronts and is not regularly distributed over the period of modulation.

It is shown that the Sagnac phase shifts in the three coils are calculated by linear combinations from the measured levels A-G.

The same formula as forFIG. 8(e)is applied to deduce therefrom the respective Sagnac phase-shifts for each coil:
φ1=A−E−B+F
φ2=B−F+C+G
φ3=C−G.

Indeed, the modification of the duration Tm affects only the duration of the levels A and E, but does not affect the duration of the other levels, nor the height of the levels A-G.

It is observed that, for the measurements of the Sagnac phase shifts, only 6 components are sufficient, as the measurement of D does not intervene in the above formulas.

A two- or three-axis interferometric system and the method of modulation/demodulation of an interferometric signal described in relation withFIGS. 4 to 9can be generalized to an interferometric system including more than three optical-fiber coils connected in parallel to a single source, a single detector and a single shared optical phase modulation device, provided that the different optical-fiber coils have different transit times, and that the signal-processing system is adapted to detect the components of the composite interferometric signal as a function of the respective transit times of each of the optical-fiber coils.

In the case of a system with N optical-fiber coils, 2*N acquisitions per period of modulation are performed, the time position of these acquisitions being determined, or triggered, by the position of the step fronts in the detected interferometric signal. The different Sagnac phase shifts associated with the different optical-fiber coils are deduced by linear combinations of the 2*N acquisitions.

The phase modulation frequency fmmay be chosen either:lower than the proper frequency of each of the optical-fiber coils, which makes it possible to use a slower, and less expensive, electronic system;higher than the proper frequency of each of the optical-fiber coils, which allows a better dynamic of measurement; or equal to the proper frequency of one of the optical-fiber coils.