POLARIZATION OPTICAL DETECTION WITH ENHANCED ACCURACY IN THE HIGH-SIGNAL REGIME

Abstract

In order to carry out the polarimetric detection of a measurand, light of two polarization states is passed through a sensing element, where the two states suffer a differential phase shift depending on the value of the measurand. In order to compensate for only imperfections of the device, a method is proposed that is based on calibration values obtained in a low-value regime of the measurand only. Yet the method can still be used for accurately determining higher values of the measurand.

Claims

1. A method for measuring a value Z of an alternating measurand by means of a sensing device, said method comprising: sending two different polarization states of a light beam through a sensing element, where the two different polarization states experience a measurand-dependent differential phase shift , splitting light having passed at least once through said sensing element into at least two channels and carrying out different polarimetric measurements in the two channels, thereby generating two raw signals S.sub.1,raw, S.sub.2,raw depending on the phase shift as follows
S.sub.1,raw=(S.sub.o1/2).Math.[1+K.sub.1 sin(+.sub.1)],
S.sub.2,raw=(S.sub.o2/2).Math.[1+K.sub.2 sin(+.sub.2)], wherein S.sub.o1, S.sub.o2 are parameters depending at least on a light source power and optical losses in the sensing device, K.sub.1, K.sub.2 are parameters of the sensing device, .sub.1, .sub.2 are parameters depending at least on the sensing device and having absolute values much smaller than /2, normalizing the two raw signals S.sub.1,raw, S.sub.2,raw, to two sensor signals S.sub.1, S.sub.2 of equal amplitudes Y.sub.o/2
S.sub.1=(Y.sub.o/2).Math.[1+K.sub.1 sin(+.sub.1)],
S.sub.2=(Y.sub.o/2).Math.[1+K.sub.2 sin(+.sub.2)], calculating a normalized combined signal S using a normalization value C as
S=(S.sub.1S.sub.2)/C wherein the normalization value C is calculated from previous values S.sub.1, S.sub.2 of the sensor signals S.sub.1, S.sub.2, near zero crossings of the alternating measurand, by C=S.sub.1+S.sub.2, or wherein C is calculated in an iterative approach, further calculating said value Z using an arcsine function, using K.sub.1, K.sub.2, .sub.1, and/or .sub.2

2. The method of claim 1, wherein .sub.10, .sub.20, .sub.1.sub.20, K.sub.11, and/or K.sub.21 at at least one temperature in an operating temperature range of the sensing device and/or wherein the absolute phase shift || reaches values larger than 0.1 rad, larger than 0.5 rad, and larger than 1 rad.

3. The method of claim 1, wherein the correction value C is given by a sum of S.sub.1 and S.sub.2 with S.sub.1, S.sub.2 being the previous values of S.sub.1, S.sub.2 corresponding to phase shifts having absolute values smaller than a threshold, the threshold being below 0.1 rad.

4. The method of claim 3 wherein S.sub.1 and S.sub.2 are determined as time-averaged values of S.sub.1 and S.sub.2 during time periods where || is below said threshold and over at least one half-cycle of the alternating measurand.

5. The method of claim 3 wherein, for determining said normalization value C, an extremum of a sum of S.sub.1+S.sub.2 within at least one half-cycle of the alternating measurand is determined by averaging the obtained extrema over more than one half-cycle.

6. The method of claim 1, wherein the normalization value C is calculated in an iterative approach, wherein in an iteration n with n=0, . . . , N1: C is derived from C(n), with C(n) being a function of (n), wherein (n) is an iterative value for the phase shift , and (n+1) is calculated from C(n) by calculating iterative values S(n) for S and Z(n) for Z from C(n).

7. The method of claim 6 wherein C(n)=(S.sub.1+S.sub.2).Math.k.sub.0/k(n) with k.sub.0=1/[1+k.Math.cos().Math.sin(/2)] and k(n)=1/[1+K.Math.cos(+(n).Math.sin(/2)], with K being an effective fringe contrast and =(.sub.1+.sub.2)/2 and =.sub.1.sub.2.

8. The method of claim 7, wherein N=1 or larger, and in a first iteration (0) is set to a starting value comprising zero.

9. The method of claim 8, wherein the value Z is calculated as $Z=\frac{1}{A}.Math.f\left({}_1.Math.{}_2,K_1,K_2\right).Math.\arcsin \left[\frac{1}{f\left({}_1.Math.{}_2,K_1,K_2\right)}\right]+H$ with A being a scale factor; f being a function of at least one of the parameters .sub.1 .sub.2, K.sub.1, K.sub.2; and H is an offset value comprising a value of Z near zero-crossings of said measurand.

10. The method of claim 9, wherein the value Z is calculated with f(.sub.1.sub.2, K.sub.1, K.sub.2)=koK cos [/2], with
ko=1/[1+K.Math.cos(+(n).Math.sin(/2)] K being an effective fringe contrast of S, =(.sub.1+.sub.2)/2, =.sub.1.sub.2; and wherein the offset value H is given as
h=So/A with So being a signal offset at a zero value Z, and said scale factor A is given as
A=A/cos with A being a scale factor determined by calibration in a regime of shift ||<</2, including ||<<0.1, and A being obtained from calibration data as a function of a temperature (T) of at least part of said sensing device.

11. The method of claim 9, wherein said parameters .sub.1, .sub.2, =(.sub.1+.sub.2)/2, =.sub.1.sub.2, K.sub.1 and/or K.sub.2, or parameters dependent on at least one of them, are calculated from calibration data as a function of a temperature of at least part of said sensing device or of a value indicative of the temperature of at least part of said sensing device.

12. The method of claim 11 wherein said parameters K.sub.1 and K.sub.2 are assumed to be 1 or are calculated from further parameters of the sensing device.

13. The method of claim 1 wherein, for normalizing the raw signals S.sub.1,raw, S.sub.2,raw, time-averaged amplitudes S.sub.o1,ac, and S.sub.o2,ac at an alternating frequency of said measurand are calculated and said signals S.sub.1, S.sub.2 are calculated as
S.sub.1=S.sub.1,raw.Math.S.sub.o2,ac
S.sub.2=S.sub.2,raw.Math.S.sub.o1,ac.

14. A sensing device for measuring a value Z of an alternating measurand, the sensing device comprising: a beam-splitter comprising an integrated-optic beam splitter connecting at least three downstream terminals to at least one upstream terminal, a light source connected to a first downstream terminal of the at least three downstream terminals, a first polarizer and a first light detector arranged to measure a first raw signal S.sub.1,raw from light returning from said a sensing element at a second downstream terminal of the at least three downstream terminals, and a second polarizer and a second light detector arranged to measure a second raw signal S.sub.2,raw from light returning from said sensing element at a third downstream terminal, wherein said first polarizer and said second polarizer are orthogonally polarized, and wherein said upstream terminal is connected to said sensing element; and a signal processing unit, wherein during operation, the signal processing unit causes the sensing device to perform operations comprising: sending two different polarization states of a light beam through the sensing element, where the two different polarization states experience a measurand-dependent differential phase shift , splitting light having passed at least once through said sensing element into at least two channels and carrying out different polarimetric measurements in the two channels, thereby generating two raw signals S.sub.1,raw, S.sub.2,raw depending on the phase shift as follows
S.sub.1,raw=(S.sub.o1/2).Math.[1+K.sub.1 sin(p+.sub.1)],
S.sub.2,raw=(S.sub.o2/2).Math.[1+K.sub.2 sin(+.sub.2)], wherein S.sub.o1, S.sub.o2 are parameters depending at least on a light source power and optical losses in the sensing device, K.sub.1, K.sub.2 are parameters of the sensing device, .sub.1, .sub.2 are parameters depending at least on the sensing device and having absolute values much smaller than /2, normalizing the two raw signals S.sub.1,raw S.sub.2,raw to two sensor signals S.sub.1, S.sub.2 of equal amplitudes Y.sub.o/2
S.sub.1=(Y.sub.o/2).Math.[1+K.sub.1 sin(+.sub.1)],
S.sub.2=(Y.sub.o/2).Math.[1+K.sub.2 sin(+.sub.2)], calculating a normalized combined signal S using a normalization value C as
S=(S.sub.1S.sub.2)/C wherein the normalization value C is calculated from previous values S.sub.1, S.sub.2 of the sensor signals S.sub.1, S.sub.2, near zero crossings of the alternating measurand, by C=S.sub.1+S.sub.2, or wherein C is calculated in an iterative approach, further calculating said value Z using an arcsine function, using K.sub.1, K.sub.2, .sub.1, and/or .sub.2.

15. The sensing device of claim 14, wherein a quarter-wave retarder is arranged either between said first polarizer and said first downstream terminal or between said first polarizer and second polarizer and said second and third downstream terminals.

16. The sensing device of claim 15, wherein during operation, the signal processing unit causes the sensing device to perform further operations comprising measuring a temperature (T) of said beam-splitter, and calculating said parameters K.sub.1, K.sub.2, .sub.1, and/or .sub.2 as a function of said temperature (T) using calibration data obtained in calibration measurements on said beam-splitter, wherein said calibration data describe a temperature dependence of said parameters, and wherein a temperature (T) of said beam-splitter, is determined from an accordingly calibrated signal-offset So at Z=0 or by means of a temperature sensor.

17. The sensing device of claim 16, wherein during operation, the signal processing unit causes the sensing device to perform further operations comprising: calculating a refined value Z of the value Z of the measurand Z from
Z=g(z).Math.Z, wherein g(z) is a normalized correction function.

18. The sensing device of claim 14 wherein said alternating measurand is an electrical current in a conductor and said sensing element is a fiber wound at least once around said conductor, or wherein the alternating measurand is an electrical field or voltage, and the sensing element is an element exhibiting an electro-optic Pockels effect and is placed in said field or in a field proportional to the voltage.

19. (canceled)

20. The sensing device of claim 18, wherein during operation, the signal processing unit causes the sensing device to perform further operations comprising calculating the value Z as $Z=\frac{1}{A}.Math.f\left({}_1.Math.{}_2,K_1,K_2\right).Math.\arcsin \left[\frac{1}{f\left({}_1.Math.{}_2,K_1,K_2\right)}\right]+H$ with A being a scale factor; f being a function of at least one of the parameters .sub.1, .sub.2, K.sub.1, K.sub.2; and H is an offset value comprising a value of Z near zero-crossings of said measurand.

21. The sensing device of claim 20, wherein during operation, the signal processing unit causes the sensing device to perform further operations comprising calculating the value Z with f(.sub.1.sub.2, K.sub.1, K.sub.2)=koK cos [/2], with
ko=1/[1+K.Math.cos(+(n).Math.sin(/2)] K being an effective fringe contrast of S, =(.sub.1+.sub.2)/2, =.sub.1.sub.2; and wherein the offset value His given as
h=So/A with So being a signal offset at a zero value Z, and said scale factor A is given as
A=A/cos with A being a scale factor determined by calibration in a regime of shift ||<</2, including ||<<0.1, and A being obtained from calibration data as a function of a temperature (T) of at least part of said sensing device.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0067] The invention will be better understood and objects other than those set forth above will become apparent in view of the following detailed description thereof. This description makes reference to the annexed drawings, wherein:

[0068] FIG. 1 shows an embodiment of a sensing device,

[0069] FIG. 2 shows the normalized scale factor of a fiber optic current sensor as a function of the retardation of a quarter-wave retarder for different bend-induced birefringence of the sensing fiber coil (.sub.1=0, .sub.D=16 and three different orientations of the slow axis of the retarder with respect to the slow axis of the coil (=0, =45, =90).

[0070] FIG. 3 shows the term 1/k as a function of the phase shift for various deviations .sub.1, .sub.2 from perfect 90 phase bias,

[0071] FIG. 4 shows the current versus the signal S,

[0072] FIG. 5 shows the relative signal error vs. the normalized signal S for various deviations K from a nominal contrast K=0.985,

[0073] FIG. 6 shows the relative signal error vs. the magneto-optic phase shift for various deviations K from a nominal contrast K=0.985, and

[0074] FIG. 7 is a block diagram representing the computation of S and S.sub.o from photo-detector raw signals S.sub.1,raw, S.sub.2,raw. PD=photodiode, FFT=fast Fourier transform, LPF=low pass filter, C=module for computation of normalization value C.

DETAILED DESCRIPTION

[0075] 1. Sensor Configuration

[0076] FIG. 1 shows a polarimetric fiber-optic measuring device according to prior art (Refs. 3, 4). Light from a broad-band light source 1, e.g. a superluminescent diode, is depolarized by a fiber Lyot depolarizer (not shown) and transmitted via a single-mode optical fiber SMF1 to an integrated-optic 13 splitter 2 (PLC splitter, planar lightwave guide circuit).

[0077] At the source-side facet, the splitter 2 has at least three downstream terminals D1-D3, which are connected to at least one upstream terminal U1 at the coil-side facet.

[0078] The light from light source 1 passes a polarizer P1 and a quarter-wave retarder QWR, and then it enters downstream terminal D1. At the coil-side facet, the light couples from upstream terminal U1 into a polarization-maintaining (PM) fiber 3.

[0079] The polarizer P1 is oriented at 45 to the principal axes of the PM fiber 3. Preferably, the fiber axes of fiber 3 are parallel and orthogonal to the normal of the splitter chip of beam splitter 2, i.e. polarizer P1 is aligned at 45 to the splitter normal.

[0080] The principal axes of quarter-wave retarder QWR are at 45 to polarizer P1 and parallel to the axes of fiber 3. Hence, the retarder introduces a phase delay of (2m+1)/2 between the two orthogonal linearly polarized light waves that enter the PM fiber 3. Here, m is the order of the retarder, m=0, 1, 2 . . . .

[0081] A fiber-optic quarter-wave retarder 4 converts the orthogonal light waves from fiber 3 into left and right circularly polarized waves before the light enters a sensing fiber 5 (or, more general, a sensing element). Sensing fiber 5 forms a coil with an integer number of fiber loops around the current conductor 6.

[0082] The light reflects off a reflective coating or reflector 7 at the far end of sensing fiber 5 and then passes the sensing fiber a second time. Upon reflection, the polarization states of the two light waves or modes are swapped, i.e. left circular light becomes right circular and vice versa.

[0083] Retarder 4 converts the reflected circular waves back to orthogonal linear waves. The polarization directions of the returning linear waves are also swapped compared to the forward propagating waves. The returning orthogonal waves have a differential magneto-optic phase shift as a result of the Faraday effect.

[0084] They return through fiber 3 and upstream terminal U1 into splitter 2.

[0085] Splitter 2 splits the returning light into two detection channels 8a, 8b, which end at the downstream terminals D2 and D3. The orthogonal waves of each channel 8a, 8b interfere at polarizers P1, P2. The polarizers are at +45 and 45 to the splitter normal.

[0086] Note that polarizer P1 is in the present embodiment common to the light source channel and detector channel.

[0087] Two further single mode fibers (SMF2, SMF3) guide the light transmitted through the polarizers to two photodetectors PD1, PD2. The detection channels 8a, 8b may comprise depolarizers (not shown) in order to avoid or reduce polarization dependent loss.

[0088] Typically, sensing fiber 5 is a low-birefringent fiber or a spun highly birefringent fiber.

[0089] Preferably, the waveguides of splitter 2 are of low birefringence, and retarder QWR resides in a stress-free manner in a recess of the splitter facet (Ref. 4). The waveguides may be fabricated in a glass substrate by electric-field-assisted ion exchange (Ref. 8).

[0090] The sensing device further comprises a signal processing unit 9 adapted and structured to carry out the steps of the method described here. Signal processing unit 9 may e.g. comprise a microcontroller, data and program memory, and the software and hardware required to execute the necessary steps. It further comprises interface elements for interfacing with the other components of the sensing device and with secondary electronic devices, e.g. protection relays. Furthermore, the signal processing unit may be configured to interrogate more than one, in particular three sensing elements.

[0091] Sensor Signal

[0092] The two raw detector signals measured by the photodetectors PD1, PD2 can be written as

S.sub.1,raw=(S.sub.o1/2).Math.[1+K.sub.1.Math.sin(+.sub.1)](1)

S.sub.2,raw=(S.sub.o2/2).Math.[1K.sub.2.Math.sin(+.sub.2)](2)

[0093] The magneto-optic phase shift is given as

=4NVI(3)

[0094] N, V, I are the number of windings of the fiber coil, the Verdet constant of fiber (1 mrad/A at 1310 nm for fused silica fiber), and the current, respectively. Eq. (3) assumes an ideal fiber coil (free of linear birefringence) and a perfect fiber quarter-wave retarder. Deviations from the ideal case are discussed further below. The fringe contrast terms K.sub.1 (i=1, 2) are also explained in more detail below.

[0095] The phase terms .sub.1, .sub.2 are the deviations of the phase bias from a perfect 90-bias of the returning waves at the polarizers P1 and P2 for zero current (zero measurand). They are mainly determined by properties of the splitter 2 and the quarter-wave retarder QWR. Possible contributions to these phase offsets are a deviation of the splitter quarter-wave retarder QWR from perfect 90-retardation (e.g. in case of retarder tilt relative to the beam direction; for example, the retarder is tilted, if the splitter facets are polished at an angle to suppress back reflections) and contributions from the splitter waveguides.

[0096] Under ideal conditions, differential phase shifts due to waveguide birefringence cancel out over a full roundtrip of the light due to the swapped polarization directions of the light waves on the return path. However, if the birefringence in the three waveguide branches of the splitter is not identical, non-zero net phase shifts will remain. For example, the birefringent phase retardation of the splitter may correspond to a few hundred degrees for a single pass, and the remaining (uncompensated) retardation after a roundtrip of the light may be up to a few degrees. (Note that the principal axes of the waveguide birefringence, if present, are commonly oriented parallel and orthogonal to the splitter substrate).

[0097] Due to the temperature dependence of the retarder, the phase offsets .sub.1, .sub.2 vary with temperature, at rates of 0.91 degrees/100 C. and 2.73 degree/100 C. for zero-order and first order quartz retarders, respectively.

[0098] A further contribution to the temperature dependence is due to an unbalanced waveguide birefringence. For adequately designed splitters, this contribution is small or negligible, however. If it is non-negligible, not only the individual offsets .sub.1, .sub.2 are temperature dependent, but also their difference may change with temperature. The resulting implications are discussed further below.

[0099] .sub.1, .sub.2 can be obtained from calibration measurements on beam-splitter 2 as a function of its temperature.

[0100] The fringe contrast terms K.sub.1 in Eq. (1) and (2) are composed of contributions from the splitter and the fiber coil:

K.sub.1K.sub.i,sK.sub.c(4)

[0101] The coil contribution K.sub.c is the same for both signals S.sub.1,raw, S.sub.2,raw whereas the contributions K.sub.i,s from the splitter may somewhat differ. For an ideal sensor, K.sub.i,s and K.sub.c are equal to unity. In practice, K.sub.i,s may be reduced, e.g. due to an imperfect angular orientation of the polarizers, splitter retarder, and the PM fiber.

[0102] The coil contrast K.sub.c can be expressed as:

K.sub.c=K.sub.(T)cos [(T)](5)

[0103] The term K.sub. is a function of the bend-induced birefringent phase retardation of the sensing fiber. The phase term is represented by

(T)=90+(T)(T).(6)

[0104] Here, p is the retardation of the fiber retarder 4, and is a phase angle depending on the coil retardation and the angle between the slow fiber retarder axis and the coil normal (slow axis of the coil birefringence). For the special cases of =0, 45, 90, the term corresponds to =, 0, and , respectively. For other values of , is between and +.

[0105] In preferred embodiments the contrast K for the combined detector signal S (see below), i.e. the effective fringe contrast, can be calculated from K.sub.1 and K.sub.2, e.g. as arithmetic average (K.sub.1+K.sub.2)/2, geometric average (K.sub.1.Math.K.sub.2).sup.1/2, or as 2K.sub.1.Math.K.sub.2/(K.sub.1+K.sub.2).

[0106] As mentioned further above, the /2-phase-bias between the interfering light waves may be introduced by means other than a quarterwave retarder, in particular a Faraday rotator crystal (Ref. 6).

[0107] Imperfections

[0108] Imperfections of the analyzer optics (e.g. due to undesired birefringence) or of the rotator crystal give rise to deviations from a perfect 90-phase-bias. Furthermore, the extra phase offsets (.sub.1, .sub.2) may be different in the two (anti-phase) detector channels and vary with temperature. As a consequence, the combined signal of the two channels is no longer a perfect sine-function but distorted. The distortions increase with increasing difference of .sub.1, .sub.2. Hence, the linearization of the signal by an arcsine-function is no longer fully adequate and leads to errors, which become the larger the closer the magneto-optic phase shift gets to /2. As a result, the usable measurement range may be substantially smaller than /2.

[0109] Another phenomenon that causes errors is that the fringe contrast of the two detector signals and thus the amplitude of the normalized combined signal is smaller than unity (ideal case) and changes with temperature due to temperature dependent birefringent phase shifts at the fiber coil (fiber retarder, bend-induced fiber birefringence).

[0110] All adverse effects can theoretically be taken into account by a two-dimensional calibration of the sensor, i.e. a calibration over the entire /2-range of magneto-optic phase shifts and operating temperatures, for example from 40 to 85 C. However, such a calibration represents a substantial extra effort and complication, and currents as high as 100 kA and beyond may be required in some cases. The present invention provides a more efficient approach that does not necessarily require calibrations over a large range of currents.

[0111] 2. Temperature Compensated Fiber Coil

[0112] In a preferred embodiment, the retardation .sub.o at a reference temperature (commonly room temperature) is chosen such that, at small phase shifts , the term cos [(T)] in the beam splitter contrast K.sub.3 compensates the variation of Verdet constant in the argument of the sine-functions of Eq. (1) and (2). (For simplicity, we assume that the variation of K.sub. (see Eq. 5, 6) with temperature is small compared to the variation in cos ). The compensation technique has been disclosed in Ref. 3 for polarimetric sensors with a fiber coil of negligible linear birefringence (=0) and in Ref. 9 for the case of spun, highly birefringent fiber.

[0113] For completeness, FIG. 2 illustrates the situation for a low-birefringent sensing fiber coil with bend-induced birefringence. Here we assume we have a coil with a birefringent phase retardation of =16. (This corresponds, for example, to a coil with four fiber loops with a diameter of 170 mm, a fiber diameter of 80 mm, and a wavelength of 1310 nm). FIG. 2 depicts the small current sensor scale factor (i.e. for ||1) (defined as signal change per infinitesimal current change) in normalized units as a function of the retardation for three different fiber retarder orientations) (0, 45, 90) and =0 and 16; derived by describing the light propagation by means of the Jones matrix formalism (Ref. 10). The curves represent the term K.sub. cos []. If we assume that the retarder has a temperature dependence of (1/ /T=2.410.sup.4 C..sup.1, the room temperature retardation .sub.o must be chosen according to the vertical dashed lines for the three indicated cases in order to achieve temperature compensation. The decrease of the scale factor along the corresponding heavy curve segments at rising temperature largely balances the increase in the Verdet constant V; (1/V) V/T=0.710.sup.4 C..sup.1.

[0114] It should be noted that, for a fiber retarder that deviates from perfect quarter-wave retardation, a sensing fiber with bend-induced birefringence, or a spun birefringent sensing fiber, the magneto-optic phase shift is no longer perfectly proportional to the current I and may exhibit a certain degree of non-linearity (Refs. 9, 12).

[0115] 3. Combined Normalized Sensor Signal

[0116] The amplitudes S.sub.o1, S.sub.o2 in Eq. (1) and (2) are proportional to the light source power. Different insertion loss in the sensing device is taken into account by normalizing the two channels to equal power with procedures as disclosed in Ref. 4.

[0117] A preferred procedure is to filter out, in each channel, the AC signal component (component at the current frequency) and to multiply the signal of the respective other channel with a time-averaged amplitude of this component. That is, channel 1 is multiplied with a term proportional to (S.sub.o2,raw/2).Math.K.Math.cos .sub.2 and channel 2 is multiplied with a term proportional to (S.sub.o1,raw/2).Math.K.Math.cos .sub.1 (with K as given further above), i.e. the amplitudes after normalization are given by (S.sub.o1/2).Math.(S.sub.o2/2).Math.K.Math.cos .sub.2 and (S.sub.o1/2).Math.(S.sub.o2/2).Math.K.Math.cos .sub.1. Note that unequal phase offsets .sub.1, .sub.2 result in a slight asymmetry in the amplitudes of the normalized signals corresponding to a factor cos(.sub.1)/cos(.sub.2. Since, commonly, the individual values and the difference of .sub.1, .sub.2 are small (e.g. =.sub.1.sub.2<2), we neglect the effect for the further considerations.

[0118] Further, it is noted that (S.sub.o1/2).Math.K.Math.cos .sub.1 and (S.sub.o2/2).Math.K.Math.cos .sub.2 can e.g. be obtained by the methods of Ref. 4.

[0119] (Note: In order to prevent erroneous normalization in case of very small or vanishing current signals or during large transient signals, updating of the normalization factors is interrupted, if the signal amplitudes fall below or exceed preset thresholds, e.g. during transient measurand peaks.)

[0120] According to prior art, the difference of the two power-normalized signals S.sub.1, S.sub.2 divided by their sum results in combined normalized signal S independent of S.sub.o1, S.sub.o2 and hence independent of variations in light source power or insertion losses. If we assume .sub.1=.sub.2=0, one obtains:

S=K.Math.sin ,(7)

and for ||1:

S=K.Math.(8)

[0121] A number of modifications occur, if the phase offsets .sub.1, .sub.2 have non-zero values. The sensor signal becomes erroneous, particularly at large magneto-optic phase shifts, if the offsets are not properly taken into account. The following discloses modified signal processing methods and corresponding sensor calibration procedures that avoid such errors.

[0122] We rewrite Eq. (1, 2) as

S.sub.1=()Y.sub.o[1+K sin(+.sub.1)](9)

S.sub.2=()Y.sub.o[1K sin(+.sub.2)](10)

[0123] Here, ()Y.sub.0 is the amplitude of the two raw signals after they have been normalized to equal power. The difference and the sum of the two signals is then given as

S.sub.1S.sub.2=Y.sub.o.Math.sin[+(.sub.1+.sub.2)/2].Math.cos[(.sub.1.sub.2)/2](11)

S.sub.1+S.sub.2=Y.sub.o.Math.{1+K cos[+(.sub.1+.sub.2)/2].Math.sin[(.sub.1.sub.2)/2]}(12)

[0124] The combined normalized signal S=(S.sub.1S.sub.2)/(S.sub.1+S.sub.2) can then be written as:

S=k.Math.K.Math.cos(/2).Math.sin(+)(13)

with

k=1/[1+K.Math.cos(+).Math.sin(/2)](14)

=.sub.1.sub.2(15)

=(.sub.1+.sub.2)/2(16)

[0125] The dependence of k on the phase shift is a measure for the deviation of signal S from a pure sinusoidal dependence of .

[0126] It is apparent that, if 0, the signal S is no longer a perfect sine-function of the magneto-optic phase shift , but is distorted by the current (phase shift)-dependent term k in the amplitude. For illustration, FIG. 3 shows 1/k as function of for various combinations .sub.1, .sub.2.

[0127] At small currents (||1), Eq. (13) can be approximated as

S=k.Math.K.Math.cos(/2).Math.[(cos ).Math.R.Math.I+sin ](17)

[0128] Here, has been replaced by the current I and a proportionality factor R. R is essentially given by the product of the Verdet constant of the sensing fiber and the number N of fiber loops. As mentioned above, the parameters of the fiber retarder (in case of a non-90-retarder) and bend-induced fiber birefringence also affect the value of R and may introduce some current dependence: R=R(I). Similarly, in case of a spun highly birefringent sensing fiber, the spin pitch and embedded linear birefringence play a role.

[0129] At small , , and , the term k is approximately given by k=k.sub.o1K.Math.sin(/2).

[0130] The signal offset S.sub.o at zero current is given as

S.sub.o=k.Math.K.Math.[cos(/2)].Math.sin (18)

[0131] Sensor calibration at small AC current (||1) as a function of temperature gives the small current scale factor A (T)=S/I at small values of I:

A(T)=k.Math.K.Math.R.Math.cos(/2).Math.cos (19)

[0132] Inverse Signal

[0133] The signal processor of the sensor determines the current from the signal S by means of the inverse of Equation (13), FIG. 4:

[00002]$\begin{array}{cc}I=\frac{1}{R}.Math.\arcsin \left[\frac{S}{k.Math.K.Math.\cos \left[.Math./2\right]}\right]-\frac{}{R}& \left(20\right)\end{array}$

[0134] Inserting the low-current scale factor A from Eq. (19) and S.sub.o from Eq. (18) yields

[00003]$\begin{array}{cc}I=\frac{\cos .Math..Math.}{A^{}}.Math.k.Math.K.Math.\cos \left[.Math./2\right].Math.\arcsin \left[\frac{S}{k.Math.K.Math.\cos \left(.Math./2\right)}\right]-\frac{S_0}{A^{}}.Math.\cos .Math..Math.& \left(21\right)\end{array}$

[0135] The cos term in Eq. (21) can be approximated by

cos cos S.sub.o(22)

[0136] This follows from =arcsin {S.sub.o/[k.sub.o.Math.K.Math.cos (/2)]}, Eq. (18), with the assumptions that k.sub.o, K are near unity and S.sub.o and are small.

[0137] Eq. (21) can then be rewritten as:

[00004]$\begin{array}{cc}I=\frac{\cos \left(S_0\right)}{A^{}}.Math.k.Math.K.Math.\cos \left[.Math./2\right].Math.\arcsin \left[\frac{S}{k.Math.K.Math.\cos \left(.Math./2\right)}\right]-\frac{S_0}{A^{}}.Math.\cos .Math..Math.S_0& \left(23\right)\end{array}$

[0138] .sub.1, .sub.2 (and hence ), and K can be obtained from corresponding calibration measurements on the device. A can be obtained by calibration the sensing device at low AC current (<<1). Preferably, all calibration measurements are done as a function of temperature within the foreseen operating temperature range.

[0139] The signal offset S.sub.o at zero current (zero measurand) can e.g. be obtained by low pass-filtering the signal S (preferred) or by low-pass filtering the two individual detector signals (after they have been normalized to equal power) and dividing their difference S.sub.1,DC and S.sub.2,DC by their sum:

[00005]$\begin{array}{cc}{S}_o=\frac{S_{1,D.Math.C}-S_{2,D.Math.C}}{S_{1,D.Math.C}+S_{2,D.Math.C}}& \left(24\right)\end{array}$

[0140] (In this context, low-pass filtering is understood as a filtering or averaging over a time typically much larger than the cycle time of the current (measurand)).

[0141] Note that at small signals (|S|1) the terms k K.Math.cos(/2) in the amplitude and argument of the arcsine-function of Eq. (21) cancel each other. The terms are important, though, for correct linearization of the current signal at higher values of S. Errors in the term k.Math.K.Math.cos(/2) will lead to signal errors in the high-current regime. The signal S in Eq. (21, 22) is the complete signal including AC terms and the DC offset S.sub.o. The cos -term in the amplitude of the arcsine-function of Eq. (21) and, equivalently, the cos(S.sub.o)-term in Eq. (23) take into account that the working point (signal at zero current) is not at S=0 but at S=S.sub.o. (Note: As an alternative, one can work with the high-pass filtered signal in the argument of the arcsine-function and omit the cos -term in the amplitude, which, however, will lead to errors at large signals).

[0142] 4. Signal Errors in the High Current Regime and their Elimination

[0143] From the above equations, it is obvious that there can be substantial signal errors in the high current regime (phase shifts approaching /2) in case of non-zero phase offsets .sub.1, .sub.2 and uncertain fringe contrast of the splitter and fiber coil, K.sub.s and K.sub.c, if these parameters and their variation with temperature are not properly taken into account.

[0144] 4.1 Errors Due to Phase Offset Difference

[0145] The errors in the signal S versus current I (magneto-optic phase shift ) as a result of the current-dependence of the term k, Eq. (14), amount to about sin(/2) at =/2, assuming that the sensor is calibrated in the low current regime and therefore the error is zero at small . Hence, at =2, the error in S at =/2 corresponds to about 1.7%. However, the error in the inverse signal (current signal) is substantially larger since, due to the high slope of the arcsine-function of S near S=1, any uncertainty in the function translates into a correspondingly large error in the sensor output. The effect is illustrated in the next section in context of the fringe contrast.

[0146] 4.2 Errors Due to Uncertain Fringe Contrast

[0147] Similar errors result from uncertainty in the contrast K=K.sub.s.Math.K.sub.c. For illustration, FIGS. 5, 6 show the signal error defined as E=[(K+K)(K)]/(K), which occurs if the actual fringe contrast K deviates from its nominal value (here with K.sub.nominal=0.985) by an amount K.

[0148] For example, if the contrast uncertainty is within K=0.01 and the maximum allowed signal error is 2.5%, the maximum measurement range corresponds to a magneto-optic phase shift of 76.4, as indicated in FIG. 6 (rather than the theoretical maximum of 90). Likewise, for maximum errors of 1% and 5% the corresponding ranges are 65.4, 80.6, respectively.

[0149] 4.3 Calibration Procedures

[0150] As a matter of principle, the above errors can be taken into account by a two-dimensional calibration of the sensor, i.e. a calibration over the entire /2-range of magneto-optic phase shifts and the full range of operating temperatures, for example from 40 to 85 C. However, such a calibration would represent a substantial extra effort and complication. Also, currents as high as 100 kA and beyond may be required in some cases.

[0151] Here, we disclose a calibration and signal processing procedure that reduces the calibration effort to a minimum and still gives high signal accuracy at high magneto-optic phase shifts (phase shifts approaching /2).

[0152] The calibration procedure advantageously comprises the following steps:

[0153] A) The low current AC scale factor A and the DC offset S.sub.o of the signal S are measured as a function of temperature (common temperature of polarization splitter and fiber coil). An inverse T(S.sub.o) of the function S.sub.o(T) is determined such that signal processing enables extraction of the splitter temperature T. The extracted temperature is used to compensate any residual temperature dependence of the sensor (Ref. 4). The two functions A(T) and T(S.sub.o) can be represented by polynomials or the like, such as a spline-function or look-up table. In this context, it is preferred to work with a first-order retarder (and not a zero-order retarder). A first order retarder triples the slope of S.sub.o=S.sub.o(T) and hence the accuracy of the extracted temperature.

[0154] Besides for temperature compensation, the DC offset S.sub.o(T) is also useful for correct linearization of the sensor output as expressed by Eq. (23).

[0155] Note: Alternatively, A (and other parameters such as K) can be represented as function A(S.sub.o(T)), i.e. the compensation of the temperature dependence of A (and other parameters if desired) is done more directly via S.sub.o(T).

[0156] B) The splitters are pre-characterized separately. This characterization gives the phase bias offsets of the two detector channels, .sub.1(T) and .sub.2(T), and the splitter contrast K.sub.s(T) as a function of splitter temperature. Preferably, the phase offsets versus temperature are represented by a first-order polynomial or stored in a look-up table. In general, the contrast K.sub.s can be represented as a temperature-independent parameter.

[0157] For characterization, the splitter is attached to an accordingly prepared test fiber coil. Preferably, the coil has a fringe contrast K.sub.c close to unity. A high contrast can be achieved by a sensing fiber with small or negligible bend-induced birefringence (large loop diameter) and a perfect 90-fiber retarder. Alternatively, the actual contrast can be measured in an independent experiment. The test coil remains at room temperature and generates alternating magneto-optic phases shifts, e.g. at a frequency of 10 Hz, of amplitude somewhat larger than /2. The required current can be kept reasonably small by an adequate number of cable windings. The phase offsets .sub.1, .sub.2 can be extracted in a straightforward manner from the two detected signals, Eq. (9) and (10). The contrast K is calculated from the individual channel contrast terms K.sub.i as described further above; i=1, 2. The K.sub.i-terms are given as K.sub.i=(S.sub.i,maxS.sub.i,min)/(S.sub.i,maxS.sub.i,min) where S.sub.i,max and S.sub.i,min are the signal maxima and minima (after subtraction of electronics offsets, if any). The splitter contrast is then given as K.sub.s(T)=K(T)/K.sub.c.

[0158] As alternatives to a test fiber coil, other means such as electro-optic or piezo-electric modulators may be used to generate the phase modulation.

[0159] 4.4 Signal Computation Adapted for Error Correction

[0160] 4.4.1 Non-Zero Phase Offset Difference

[0161] As noted above, at a non-zero phase offset difference , the sum of the signals S.sub.1, S.sub.2 becomes a function of current, i.e. (see Eq. 12), which causes current-dependent distortions of the (ideally sinusoidal) sensor response S (described by the parameter k in Eq. (13)). In case of alternating and transient magneto-optic phase shifts (such as caused by fault currents), such distortions are avoided, if S is calculated from the two (power-normalized) detector signals S.sub.1, S.sub.2 according to

S=(S.sub.1S.sub.2)/C(25)

[0162] Here, the normalization value C is calculated from previous values S.sub.1, S.sub.2 of the sensor signals S.sub.1, S.sub.2, at small currents (||1, in particular at ||<0.1 rad), i.e. near zero crossings of the measurand.

[0163] Advantageously, C=S.sub.1+S.sub.2.

[0164] In this case, C corresponds to the vertices of the parabolas depicted in FIG. 3 and is given by:

C=Y.sub.o[1+K.Math.cos sin(/2)](26)

[0165] Hence, the parameter k of Eq. (14) becomes k=k.sub.o:

k.sub.o=1/[1+K.Math.cos .Math.sin(/2)](27)

[0166] Eq. (23) is thus replaced by

[00006]$\begin{array}{cc}I=\frac{\cos \left(S_0\right)}{A^{}}.Math.k_0.Math.K.Math.\cos \left[.Math./2\right].Math.\arcsin \left[\frac{S}{k_0.Math.K.Math.\cos \left(.Math./2\right)}\right]-\frac{S_0}{A^{}}.Math..Math.\cos \left(S_0\right)& \left(28\right)\end{array}$

wherein now, in the scale factor A, the term k is also replaced by k.sub.o:

A(T)=k.sub.o.Math.K.Math.R.Math.cos(/2).Math.cos (29)

[0167] In more general terms the measurand Z is computed according to

[00007]$\begin{array}{cc}Z=\frac{1}{A}.Math.f\left({}_1,{}_2,K_1,K_2\right).Math.\arcsin \left[\frac{S}{f\left({}_1,{}_2,K_1,K_2\right)}\right]+H& \left(30\right)\end{array}$

with

[0168] A being a scale factor;

[0169] f being a function of at least one of the parameters .sub.1, .sub.2, K.sub.1, K.sub.2; and

[0170] H is an offset value, in particular a value of Z near zero-crossings of said measurand,

[0171] and in particular wherein

f(.sub.1,.sub.2,K.sub.1,K.sub.2)=ko K cos[/2],(31)

with

k.sub.0=1/[1+K.Math.cos().Math.sin(/2],(32)

[0172] K being an effective fringe contrast of S, =(.sub.1+.sub.2)/2, =.sub.1.sub.2, and [0173] with the offset value H given as

H=S.sub.o/A(33)

[0174] with S.sub.0 being a signal offset at a zero value Z, and wherein said scale factor A is given as

A=A/cos (34)

with A being a scale factor determined by calibration as a function of the sensing device temperature T in a regime of ||<</2, in particular |<<0.1.

[0175] There are several possibilities to extract C from previous values S.sub.1, S.sub.2. The following Procedures 1 and 2 correspond to the first class of embodiments as outlined above, while procedure 3 corresponds to the second class of embodiments.

[0176] Procedure 1 Commonly the normal operating regime of the sensor corresponds to |1, where the current-dependent distortions do not occur. In case of transient fault currents with large , the sum S.sub.1+S.sub.2 is no longer updated with the instantaneous values, but the signal processor continues to use earlier small-current value of S.sub.1+S.sub.2 as long as || is above a preset threshold, e.g. above 0.1 rad. To this end, the low current value of S.sub.1+S.sub.2 is continuously stored as a moving average as long as || is below the preset threshold (or the last sample of C=S.sub.1+S.sub.2 is used that was recorded before passed the threshold).

[0177] Procedure 2

[0178] During each cycle, or at least during some of the cycles, of an AC measurand value, the signal processor determines the vertex of the parabola that represent S.sub.1+S.sub.2, i.e. by determining the extremum of the sum S.sub.1+S.sub.2. (The sum S.sub.1+S.sub.2 passes the vertex twice within a full cycle). The value of C=S.sub.1+S.sub.2 may be updated for each half cycle of the measurand or the value of C may be recorded as a moving average over a preset time period, i.e. averaged over more than one half cycle. The normalization works not only for the large || of transient nature, but for any alternating independent of its amplitude (preferred procedure).

[0179] Procedure 3

[0180] A further alternative is an iterative procedure in iterations n with n=0, . . . , N1: In a first step (n=0), a first estimate I(0) of the current I and thus a first estimate (0)=I(0).Math.R of the magneto-optic phase shift are determined according to Eq. (28), i.e. with k=k.sub.0, and by using a first value S(0) of signal S computed from the current-dependent sum, i.e. S.sub.1+S.sub.2, i.e. S(0)=(S.sub.1S.sub.2)/(S.sub.1+S.sub.2).

[0181] Then, using the first estimate (0), a first estimate k(0) of the parameter k is computed according to Eq. (14). Now, a second value S(1) is then recalculated by multiplying the first value S(0) of S with the ratio k.sub.0/k(0), i.e. S(1)=S(0).Math.k.sub.0/k(0) with k.sub.0 calculated according to Eq. (27). The second step can be repeated several times to increase the accuracy. Finally, the current I (or more generally the measurand value Z) is recalculated according to Eq. (28) using the last recalculated signal value S(N1) and corresponding offset S.sub.0(N1) with N1 being the final iteration number.

[0182] In more general terms, the value C to be used in Eq. (25) is calculated in an iterative approach in N iterations, with n=0, . . . , N1:

[0183] C is derived from C(n), with C (n) being a function of (n). (n) is an iterative value for the phase shift , and (n+1) is calculated from C(n), in particular by calculating iterative values S(n) for S and Z(n) for (Z) from C(n).

[0184] In particular, C(n)=(S1+S2).Math.k.sub.0/k(n) with k.sub.0=1/[1+K.Math.cos ().Math.sin(/2)] and k(n)=1/[1+K.Math.cos {+(n)}.Math.sin(/2)]. K is the effective fringe contrast, =.sub.1.sub.2, and =(.sub.1+.sub.2)/2.

[0185] The number of iterations N is advantageously at least one or more.

[0186] At the end of the iteration process, the current I (or measurand Z) can be calculated according to Eq. (28), (30).

[0187] 4.4.2 Nonlinearity in R

[0188] If desired, S can be further corrected for the mentioned non-linearity between the magneto-optic phase shift and current I, i.e. for the current dependence of R. To this purpose, R(I) is either computed by means of a theoretical model or determined experimentally for a given coil type in an independent experiment. The current I obtained from Eq. (30) is then recalculated according to

I=g(I).Math.I(35)

wherein g(I) is a normalized correction function:

g(I)=R.sub.o/R(I)(36)

[0189] Here, R.sub.o is the value of R at ||1.

[0190] 4.4.3 Processing

[0191] The block diagram of FIG. 7 schematically shows how the signal S and DC offset S.sub.o are determined from the two photo-detector signals S.sub.1,raw, S.sub.2,raw. The signals S.sub.o1,ac=(S.sub.o1/2) K.Math.cos .sub.1 and S.sub.o2,ac=(S.sub.o2/2).Math.K cos .sub.2 are the filtered AC components of the two channels, and they are used to equalize the two detector channels to equal power. (The diagram only shows the basic concept and leaves out, e.g., amplification and digitalization of the detected signals).

[0192] In the embodiment shown, S.sub.o1,ac and S.sub.o2,ac are filtered out by means of a fast Fourier transform of the detector signals (FFT) with subsequent low pass filtering (LPF) for time-averaging with a time-constant much larger than the cycle time of the current or measurand (Ref. 4). Various alternative filtering methods may be applied also, e.g. via signal demodulation or bandpass filtering.

[0193] The rescaled signals S.sub.1, S.sub.2 are added and further processed according to one of the procedures 1-3 described above for generating C, preferably with C=S.sub.1+S.sub.2. Further, they are subtracted for generating S.sub.1S.sub.2. A divider is used for calculating S=(S.sub.1S.sub.2)/C.

[0194] A low-pass filter LPF with a time-constant typically much larger than the cycle time of the current or measurand is applied to S for calculating S.sub.o.

[0195] 4.4.4 Fringe Contrast K

[0196] The splitter contrast terms K.sub.i,s in the term K=K.sub.i,s.Math.K.sub.c are taken as unity, or their value is determined experimentally as explained further above (by means of a test coil).

[0197] The temperature dependence of K is given by K.sub.c=K.sub.(T)cos [(T)] and possibly a contribution K.sub.s(T). For a given coil type (coil diameter, number of fiber loops, retarder orientation and retardation), K.sub.c is measured once as a function of temperature. The procedure is the same as for measuring the splitter contrast K.sub.s and phase offsets .sub.1, .sub.2 with the difference that the coil is temperature-cycled, whereas the splitter is kept at constant temperature.

[0198] Alternatively, K.sub.c(T) may be simply calculated from the retarder and coil parameters and their temperature coefficients.

[0199] Again, K.sub.i,s(T) and K.sub.c(T) may be described by polynomials, spline functions, or stored in look-up tables.

[0200] The signal processor extracts the temperature from the measured value of S.sub.o according to the known temperature dependence S.sub.o(T).

[0201] K can then be determined according to the stored temperature dependence K(T); alternatively, K is represented as a function of S.sub.o and is accordingly determined from the measurement of S.sub.o.

[0202] Alternatively, the complete term K(T), or equivalently K(S.sub.o), may be calibrated for each completed sensor (but this is less preferred since a large number of current windings must be applied to each individual sensor rather than just once to a permanently configured test coil).

[0203] In case of a low-birefringent sensing fiber with a retarder deviation from 90-retardation and/or non-negligible bend-induced birefringence, the relationship between the current and magneto-optic phase shift is slightly nonlinear as noted further above. This is also true for spun highly birefringent sensing fiber. This effect also gives rise to deviation of the signal-vs-current from a perfectly sinusoidal relationship. This can be taken into account by calibrating the current dependence of the parameter R in an independent measurement and correcting the final current signal accordingly (see above).

[0204] 5. Further Remarks

[0205] Instead of glass-based waveguide devices, integrated optic splitters based on other materials such as for example Si, SiN, SiP, or InP may be used.

[0206] The sensor of FIG. 1 is implemented with an integrated-optic splitter chip. It should be noted, that all inventive features of the disclosure also apply to polarimetric current sensors of this kind that use bulk-optic beam splitters or polarimetric sensors that introduce the phase bias not by a quarter-wave retarder but by a Faraday rotator (Ref. 6). At bulk-optic beam splitters, phase shifts that occur at the splitter(s) may contribute to the phase offsets .sub.1, .sub.2. Similarly, deviations of a Faraday rotator from perfect 45-rotation also cause phase offsets of this kind.

[0207] It should further be noted that the invention also applies to other types of sensing fibers, in particular spun highly birefringent sensing fibers (Ref. 4). In that case, the parameters of the spun fiber determine the fringe contrast K.sub.c.

[0208] Furthermore, instead of a fiber a bulk magneto-optic transducer, e.g. of glass or of another magneto-optic material such as an iron garnet, may be used as a sensing element.

[0209] In FIG. 1, the sensing fiber coil is operated in reflective mode. However, the invention may also be applied to coils or bulk magneto-optic materials operated in transmission.

[0210] Furthermore, the invention may not only be applied to polarimetric current and magnetic field sensors, but also to other types of polarimetric sensors, in particular electric field sensors based on the Pockels effect in an electro-optic crystal (Ref. 11). In this case, the value Z of the measurand is a value other than the current I. For example, the measurand can be a voltage to be measured, in which case the sensing element is a Pockels-type device placed in the electrical field of the voltage.

[0211] In particular, any of the above is also valid for a voltage or electric field sensor using the Pockels effect, if the Verdet-constant is replaced by a suitable electro-optic coefficient and the current by the electrical field.

[0212] In other words and in complete generality, the current I mentioned herein can be any measurand value Z that can be detected with the sensing element. Hence, in all equations disclosed herein, I can be replaced by Z (and I by Z).

[0213] Typically, the unambiguous measurement range of a polarimetric sensor is limited to phase shifts of 90. It should be noted, however, that depending on the allowed error, the usable measurement range can be extended beyond 90. For example, if the allowed error at high phase shifts, e.g. for fault current measurement, corresponds to 10%, the actual measurement range can be extended to about 116 (where the sine-function again reaches a value of 0.9). It can be advantageous to set the value Z at high phase shifts , above phase shifts corresponding to 80, 85, or 90, to a constant value, e.g. a value corresponding to a phase shift of 85.

[0214] While there are shown and described presently preferred embodiments of the invention, it is to be distinctly understood that the invention is not limited thereto, but may be otherwise variously embodied and practiced within the scope of the following claims.

REFERENCES CITED

[0215] 1. K. Bohnert, P. Gabus, J. Nehring, and H. Brandle, Temperature and vibration insensitive fiber-optic current sensor, Journal of Lightwave Technology, Vol. 20, pp. 267-276, 2002. [0216] 2. The fiber-optic gyroscope, Herve Lefevre, Artech House, Boston, London, 1993. [0217] 3. K. Bohnert, A. Frank, H. Brandle, Fiber-optic current sensor with polarimetric detection scheme, WO2007/121592A1. [0218] 4. K. Bohnert, A. Frank, G. Mller, L. Yang, Optical Sensor, WO2015/090448. [0219] 5. K. Kurosawa et al., Polarization properties of flint glass fiber, J. Lightwave Technology 13, 1378, 1995. [0220] 6. R. Kondo, K. Kurosawa, Optical fiber electric current sensor e.g. reflection type optical fiber electric current sensor, has signal processing unit that converts separated polarized components into signals by photoelectric conversion, WO2011/125564A1. [0221] 7. Standard of the International Electrotechnical Commission (IEC), IEC60044-8, Instrument transformersPart 8: Electronic current transformers. [0222] 8. K. Forrest et al., Channel waveguides in glass via silversodium field assisted ion exchange, J. Lightwave Technology LT-4 (2), 140, 1986. [0223] 9. WO2014/006121 A1 [0224] 10. R. C. Jones, A new calculus for the treatment of optical systems. I. Description and discussion of the calculus, J. Opt. Soc. Am., vol. 31, pp. 488-493, 1941. [0225] 11. K. Kurosawa et al., Development of an optical instrument transformer for DC voltage measurement, IEEE Transactions on Power Delivery, Vol. 8, 1771, 1993. [0226] 12. K. Bohnert, P. Gabus, J. Nehring, H. Brandle, M. Brunzel, Fiber-optic current sensor for electrowinning of metals, J. Lightwave Technology 25, 3602, 2007. [0227] 13. J. Hafner, B. Jacobson, Proactive HVDC breakersA key innovation for hybrid HVDC grids, Proceedings of Cigre International Symposium on The electric power system of the futureIntegrating supergrids and microgrids, pp 264-271, Bologna, Italy, 13-15 Sep. 2011.

LIST OF REFERENCE NUMBERS AND LETTERS

[0228] 1: light source [0229] 2: beam splitter [0230] 3: polarization-maintaining fiber [0231] 4: fiber-optic quarter-wave retarder [0232] 5: sensing element (sensing fiber) [0233] 6: current conductor [0234] 7: reflector [0235] 8a, 8b: detection channels [0236] 9: signal processing unit [0237] D1-D3: Downstream terminals [0238] LPF: Low-pass filter [0239] P1, P2: polarizers [0240] PD1, PD2: photodetectors [0241] QWR: quarter-wave retarder [0242] SMF1, SMF2, SMF3: single-mode fibers [0243] U1: Upstream terminal