Abstract:
The fiber optics sensor includes a polarization maintaining optic fiber forming an optical loop, and a sensing medium coupled to the optic fiber and disposed generally midway in the optical loop. First and second quarter waveplates, coupled to the optic fiber and oriented at approximately 45° with one another in close proximity to the sensing medium, convert two counter-propagating linearly polarized light waves traveling in the optical loop into two counter-propagating circularly polarized light waves prior to passing through the sensing medium. The first and second quarter waveplates further convert the counter-propagating circularly polarized light waves into two linearly polarized light waves after exiting the sensing medium. The counter-propagating circularly polarized light waves passing through the sensing medium experience a differential phase shift caused by a magnetic field or current flowing in a conductor proximate to the sensing medium. A detector is coupled to the optic fiber and detects the differential phase shift and produces an output in response thereto.

Description:
RELATED PATENT APPLICATIONS 
     This patent application is a continuation-in-part, application of U.S. patent application titled Fiber Optics Apparatus and Method for Accurate Current Sensing, Ser. No. 08/691,748, and filed on Aug. 1, 1996, now allowed U.S. Pat. No. 5,696,858. 
     This patent application is related to U.S. patent application titled Fiber Optic Interferometric Current and Magnetic Field Sensor, U.S. Pat. No. 5,644,397, issued on Jul. 1, 1997 to James N. Blake, which is a continuation of application Ser. No. 08/320,734, filed Oct. 7, 1994 of the same title and inventor, now abandoned. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     This invention relates in general to the field of fiber optic sensors. More particularly, the present invention relates to fiber optics apparatus and method for accurate current sensing. 
     BACKGROUND OF THE INVENTION 
     Over the past decade, fiber optic sensors have received attention in the application of magnetic field sensing and current sensing. Fiber optic current sensors are particularly advantageous over iron-core current transformers, since fiber optic sensors are non-conductive and light weight. Furthermore, fiber optic sensors also do not exhibit hysteresis and provide a much larger dynamic range and frequency response. 
     Fiber optic current sensors work on the principle of the Faraday effect. Current flowing in a wire induces a magnetic field which, through the Faraday effect, rotates the plane of polarization of the light traveling in the optical fiber wound around the current carrying wire. Faraday&#39;s law, stated as: 
     
         I=∫oH·dL 
    
     where I is the electrical current, H is the magnetic field and the integral is taken over a closed path around the current. If the sensing fiber is wound around the current carrying wire with an integral number of turns, and each point in the sensing fiber has a constant sensitivity to the magnetic field, then the rotation of the plane of polarization of the light in the fiber depends on the current being carried in the wire and is insensitive to all externally generated magnetic fields such as those caused by currents carried in nearby wires. The angle, Δφ, through which the plane of polarization of light rotates in the presence of a magnetic field is given by: 
     
         Δφ=V∫H·dL 
    
     where V is the Verdet constant of the fiber glass. The sensing optical fiber performs the line integral of the magnetic field along its path which is proportional to the current in the wire when that path closes on itself. Thus, Δφ=VNI, where N is the number of turns of sensing fiber wound around the current carrying wire. The rotation of the state of polarization of the light due to the presence of an electrical current may be measured by injecting light with a well defined linear polarization state into the sensing region, and then analyzing the polarization state of the light after it exits the sensing region. 
     In related U.S. Pat. No. 5,644,397 entitled Fiber Optic Interferometric Current and Magnetic Field Sensor, issued on Jul. 1, 1997 to James N. Blake (Hereinafter &#34;Blake&#34;), in-line and loop fiber optic sensors for measuring current and magnetic fields are taught. Blake is incorporated herein by reference. Blake teaches splitting the light beam into light traveling on the first and second principle eigen axes, the use of a birefringence modulator to apply a waveform or waveforms to birefringent modulate the light beam, and further the use of a quarter waveplate set at 45° to the principle axes of the fiber to convert orthogonally linearly polarized light to counter-rotating circularly polarized light prior to entering the sensing region. Upon reflection at the end of the fiber, the sense of rotation of the two light waves are reversed and the light waves travel back through the sensing region, are converted back to linearly polarized light, and are propagated back to a photodetector. The two light waves therefore undergo reciprocal paths and the same polarization evolution through the optical circuit. Blake is incorporated herein by reference. 
     The fiber optic sensors taught by Blake overcame many disadvantages associated with conventional all fiber sensors. However, the sensor and sensing method still suffers from a particularly exacerbating problem which affects the accuracy of the sensor. To have a very accurate measurement, the optical components, particularly the quarter waveplate, must be perfect and not be affected by external stresses such as temperature variations and mechanical disturbances. It is well recognized that perfect or nearly perfect quarter waveplates are difficult and very costly to design and manufacture to achieve accurate sensing required by certain applications. 
     SUMMARY OF THE INVENTION 
     Accordingly, a need has arisen for apparatus and method for compensating the error introduced by the optical element that converts linearly polarized light waves to circularly polarized light waves and back such as an imperfect quarter waveplate. 
     In accordance with the present invention, a fiber optics sensor and method for accurate measurements are provided which eliminates or substantially reduces the disadvantages associated with prior optical sensors. 
     In one aspect of the invention, a fiber optics sensor comprises a polarization maintaining optic fiber forming an optical path, and first and second counter-propagating linearly polarized light waves traveling in the polarization maintaining optic fiber on the optical path. A first quarter waveplate is coupled to the optic fiber and disposed in the optical path generally adjacent to a sensing region, the first quarter waveplate operable to convert the first linearly polarized light wave into a circularly polarized light wave traveling on the optical path prior to the sensing region. A second quarter waveplate is coupled to the optic fiber and disposed in the optical path adjacent to the sensing region, the second quarter waveplate operable to convert the second linearly polarized light wave into a second circularly polarized light wave prior to the sensing region. The first and second quarter waveplates are oriented with one another at approximately 45°. The second quarter waveplate further converts the first circularly polarized light wave back to a first linearly polarized light wave after exiting the sensing region, and the first quarter waveplate further converts the second circularly polarized light wave back to a second linearly polarized light wave after exiting the sensing region. The sensing region includes a sensing medium that is coupled to the polarization maintaining optic fiber, and the first and second circularly polarized light waves passing through the sensing medium experience a differential phase shift caused by a magnetic field or current flowing in a conductor proximate to the sensing region. A detector coupled to the optic fiber detects the differential phase shift and produces an output in response thereto. 
     In another aspect of the invention, the fiber optics sensor includes a polarization maintaining optic fiber forming an optical loop, and a sensing medium coupled to the optic fiber and disposed generally midway in the optical loop. First and second quarter waveplates, coupled to the optic fiber and oriented at approximately 45° with one another in close proximity to the sensing medium, convert two counter-propagating linearly polarized light waves traveling in the optical loop into two counter-propagating circularly polarized light waves prior to passing through the sensing medium. The first and second quarter waveplates further convert the counter-propagating circularly polarized light waves into two linearly polarized light waves after exiting the sensing medium. The counter-propagating circularly polarized light waves passing through the sensing medium experience a differential phase shift caused by a magnetic field or current flowing in a conductor proximate to the sensing medium. A detector coupled to the optic fiber detects the differential phase shift and produces an output in response thereto. 
     In yet another aspect of the invention, a method for accurately measuring a magnetic field or a current flowing in a conductor using a fiber optics sensor includes the steps of forming an optical path with a polarization maintaining optic fiber, and generating and sending two counter-propagating linearly polarized light waves traveling in the polarization maintaining optic fiber on the optical path. The two linearly polarized light waves are converted into two circularly polarized light waves traveling on the optical path toward a sensing region, which pass through the sensing region and experience a differential phase shift caused by the magnetic field or current flowing in the conductor proximate to the sensing region. The two phase shifted circularly polarized light waves are converted back into two linearly polarized light waves oriented at a relative angle of approximately 45° with respect to one another. The differential phase shift in the circularly polarized light waves are detected and an output is generated in response thereto. 
     A technical advantage of the teachings of the present invention is providing an extremely economical way to compensate for errors introduced in the optical circuit by the quarter waveplates. As a result, accurate measurement can be achieved without costly or impractical circuitry or signal analysis and processing. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a better understanding of the present invention, reference may be made to the accompanying drawings, in which: 
     FIG. 1 is a schematic diagram of an embodiment of an in-line fiber optic sensor; 
     FIGS. 2A and 2B are schematic diagrams of the paths taken by the X and Y light waves along the principle and secondary axes of the fiber to illustrate the problem; 
     FIG. 3 is a schematic diagram of an exemplary signal processing circuit according to the teachings of the present invention; 
     FIG. 4 is an exemplary plot of the D.C. and harmonic signals of the detected light output; 
     FIG. 5 is a block diagram of an exemplary signal processing circuit according to the teachings of the present invention; and 
     FIGS. 6A and 6B are plots of an exemplary modulation signals and the detected light output according to the teachings of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The preferred embodiment of the present invention and its advantages are best understood by referring to FIGS. 1-6 of the drawings, like numerals being used for like and corresponding parts of the various drawings. 
     In FIG. 1, a current sensor 10 constructed according to the teachings of the present invention comprises a broadband light source 12, which introduces a broadband light having multiple optical frequency components into a optic fiber pigtail 14. Optic fiber pigtail 14 is preferably a length of polarization maintaining fiber. Polarization maintaining fiber pigtail 14, is joined to a polarization maintaining beam splitter or directional coupler 16 where a portion of the light is directed to a polarizer 18 and the remaining light is terminated at a non-reflective termination point 20. The light beam passes through polarizer 18, which linearly polarizes the light. The eigen-axes of polarization maintaining fiber pigtail 14, polarization maintaining beam splitter 16, and polarizer 18 are aligned to one another and to the principle axis of light source 12, so as to ensure maximum light input into the sensing region. Polarization cross coupling points caused by any misalignment of these axes, in combination with an imperfect polarizer, may result in the presence of small offsets in the current measurement and should be avoided as much as possible. 
     After the light passes through polarizer 18, it is divided substantially equally into X and Y light waves by a 45° splice 22 into the two eigen-axes, X and Y respectively, of a birefringence modulator pigtail 24. Birefringence modulator pigtail 24 is a section of polarization maintaining fiber of sufficient length to depolarize the light passing through it. Birefringence modulator pigtail 24 is connected to a birefringence modulator 26, the X and Y eigen axes of these two components being aligned. Birefringence modulator 26 may be an integrated optics waveguide formed on Ti-indiffused LiNbO 3  with metallic electrodes surrounding the waveguide. Alternatively, a piezo-electric modulator may also be used. A voltage applied across the electrodes alters the birefringence of the waveguide. A modulation signal generated by a waveform generator 28 is applied to the electrodes of birefringence modulator 26 to dither or phase modulate the light beams. The modulation signal may be a variety of forms including, for example, sine wave modulation, square wave modulation, triangle wave modulation, serrodyne modulation, sawtooth modulation, and other suitable periodic waveforms. The modulation signal may also be a combination of a ramp function and a periodic waveform. 
     After the light is modulated in birefringence modulator 26, it enters a predetermined length of polarization maintaining fiber bus 30. The principle axes of polarization maintaining fiber bus 30 are aligned to the principle axes of the birefringence modulator 26. Polarization maintaining fiber bus 30 serves two purposes. The first is to carry the light to a passive sensing medium or sensing fiber 32, which typically is remotely located from the active elements such as light source 12 and birefringence modulator 26. The second purpose of polarization maintaining fiber bus 30 is to provide a time delay of sufficient length that the modulation signal applied at birefringence modulator 26 substantially changes its value during the time it takes for the light to propagate from birefringence modulator 26 to sensing fiber 32 and return. Ideally, the fundamental dither frequency of the waveform applied to birefringence modulator 26 is 1/2τ or odd multiples thereof, where τ is the propagation time for the light waves to travel from birefringence modulator 26 through sensing medium 32 and back. 
     After passing through polarization maintaining fiber bus 30, the light goes through a 45° splice 38, a zero or multiple order quarter wave plate 40 set at 45° to the principle axes of the polarization maintaining fiber bus 30, and a single mode fiber splice 42. The purpose of quarter wave plate 40 is to convert the orthogonally linearly polarized light from each of the principle axes of polarization maintaining fiber bus 30 to circular states of polarization. The quarter wave plate 40 is preferably constructed from a short section of long beat length polarization maintaining fiber, ideally a quarter of a polarization beat length long. An odd multiple of quarter beat lengths of length is also acceptable. 
     Therefore, two opposingly circularly polarized light waves are generated by quarter waveplate 40. The X light wave from the first principle axis or X axis of polarization maintaining fiber bus 30 is converted to a right hand circularly polarized (RHCP) light wave. The Y light wave from the second principle axis or Y axis of polarization maintaining fiber bus 30 is converted to a left hand circularly polarized (LHCP) light wave. The two circularly polarized light waves then pass through sensing fiber 32 wrapped around a current-carrying wire 36 at different velocities, accumulating a phase difference in proportion to the magnetic field component aligned with sensing fiber 32. Sensing fiber 32 may be constructed from a single mode fiber having a low birefringence per unit length and wound an integral number of turns around current carrying wire 36. For most applications, one to five loops of sensing fiber 32 around wire 36 has been shown to be sufficient. It is known that birefringence in sensing fiber 32 changes the sensitivity of sensor 10 as well as making it sensitive to magnetic fields arising from external sources. The use of a short length of sensing fiber 32 is thus advantageous for minimizing the total birefringence. 
     A reflector 44, such as a mirror or mirrored surface, terminates sensing fiber 32. The light is reflected by mirror 44 and passes through sensing fiber 32 again. The sense of circular polarization of the light is reversed upon reflection, causing the right hand circularly polarized light wave to be converted to be left hand circularly polarized for its return trip through sensing fiber 32, and vice versa for the left hand circularly polarized light. Since the sense of polarization and the direction of the light are reversed for both light waves during their return trip through sensing fiber 32, the relative differential phase shift accumulated between them during the first pass through sensing fiber 32 is doubled during the return trip. The total phase shift, Δφ, accumulated between the two light waves in the double pass sensing region 60 is thus Δφ=4VNI, where V is the Verdet constant of the fiber glass, N is the number of turns of sensing fiber around current carry wire 36 and I is the current flowing in wire 36. 
     After the light makes its double pass through sensing fiber 32, the light wave that was originally in the first principle axis of polarization maintaining fiber bus 30 returns to bus 30 linearly polarized along its second principle axis, and the light wave that was originally in the second principle axis of polarization maintaining fiber bus 30 returns to bus 30 linearly polarized along its first principle axis. The light waves then pass through birefringence modulator 26 and its pigtail 24 a second time, and are brought together and interfered by 45° splice 22 and polarizer 18. A portion of this light is then coupled to a photodetector 46 via polarization maintaining beam splitter 16. A signal processing electronics circuit 50 coupled to photodetector 46 may be used to provide a measurement output. 
     Therefore, the two light waves underwent exactly the same polarization evolution throughout the optical circuit, only in reverse order. Because sensing medium 32 is in-line with respect to the optic fiber, it may be seen that the sensing region around wire 36 is positioned at the midpoint of the optical path traversed by both light waves. Therefore, the only phase difference between the two light waves is that generated by the presence of a magnetic field in the sensing region. 
     However, when the quarter waveplate is not perfectly constructed or operating perfectly, some light traverses the sensing region in the wrong state of circular polarization, thereby causing inaccurate measurement. In addition, an extra D.C. light is a byproduct of the imperfect quarter waveplate. The operation of the quarter waveplate is affected by its operating environment, such as temperature variations and other external stresses. In particular, the beat length, L B , varies with ambient temperature, which is typically 0.1% per ° C. Because the quarter waveplate is typically located remotely from the light source and other electronics, and is typically exposed to the external elements, it encounters large temperature variations. With a temperature differential that can reach, for example, 100° between the high temperatures in the Summer and the low temperatures in the Winter, the beat length can change by 10% or more. 
     Referring to FIGS. 2A and 2B, the paths of the two light waves are shown explicitly with the approximate relative strengths of the light components indicated as shown. Imperfect quarter waveplate (IQ) 40 converts the X light wave on the first principle axis of the fiber bus to right hand circularly polarized (R) light wave and a small left hand circularly polarized (L S ) light component due to the imperfection of quarter waveplate 40. Mirror 44 reflects the light waves and changes them to left hand circularly polarized light (L) and a small right hand circularly polarized light (R S ). The second pass through imperfect quarter waveplate 40 converts the left hand circularly polarized light (L) to a Y light wave on the second principle axis of the fiber bus and a small X light wave (X S ) on the first principle axis. The small right hand circularly polarized light R S  is converted to a small X light wave (X S ) and an even smaller Y light wave (Y SS ). The two X S  light components are incoherent with all other light components at the detector and thus do not provide an interference signal. The two X s  light components comprise one-half of the extra D.C. light detected at the photodetector. The Y SS  light component results in a scale factor error, where the scale factor is equal to the photodetector output divided by the current in the wire. The affected scale factor contributes to the computation of inaccurate value for the current. Note that the subscript S is used to denote the intensities of the light waves as compared with the main light wave, which in this case is Y, but is not intended to indicate that the small light wave components have the same intensity. 
     As shown in FIG. 2B, the Y light wave traveling on the second principle axis is similarly converted by imperfect quarter waveplate 40 into two components: left hand circularly polarized light (L) and a small right hand circularly polarized light (R S ). Mirror 44 reflects the light waves and reverses the sense of polarization of the light waves into right hand circularly polarized light (R) and a small left hand circularly polarized light (L S ). When these two light waves pass through imperfect quarter waveplate 40 the second time, the right hand circularly polarized light is converted to a main X light wave and a small Y light wave (Y S ), and the small left hand circularly polarized light (L S ) is converted to a small Y light wave (Y S ) and an even smaller X light wave (X SS ). The two Y S  light waves traveling on the second principle axis of the fiber bus comprise the other half of the extra incoherent D.C. light detected by the photodetector. The X SS  light component gives rise to an error in the scale factor and resulting in inaccurate current measurement by the sensor. 
     In both light waves, the resultant extra D.C. light provides a clue to the magnitude of the X SS  and Y SS  and thus the scale factor error. Knowing the D.C. and A.C. components and ratio or relative proportion of the modulation signals, the relative proportion of the D.C. and A.C. components of the detected light at the detector can be compared therewith to determine the magnitude of extra D.C. light or error that is introduced by the quarter waveplate. 
     There are two basic methods to compensate for the error caused by the imperfect quarter waveplate and achieve a very accurate current measurement with sensor 10. One method is to vary the wavelength of the broadband light from light source 12 (FIG. 1) to minimize or eliminate the extra D.C. light components detected by detector 46. There are several ways to vary the wavelength of the light output. For example, the wavelength of light source 12 is affected by changes in ambient temperature. Therefore, light source 12 may be ed to a heat sink (not shown) and a temperature controller (not shown) that are used to change the ambient temperature surrounding light source 12. Typically, the wavelength of light source 12 changes by several hundred parts per million per degree centigrade. However, to compensate for a 100° C. temperature change experienced by the quarter waveplate, for example, the required temperature change for the light source may be greater than 100° C. Although achievable, this range of temperature variation may not be reasonable for most applications. 
     As another example of a method for varying the source wavelength is to selectively filter very broad spectrum light. The filter is used to vary the range of wavelengths of the resulting broadband light output to compensate for the errors caused by quarter waveplate thermal variations. However, this method requires the construction of the wavelength filter, which may be costly. 
     The method by which the imperfect quarter waveplate is compensated by changing the wavelength of the incoming light is contemplated herein as described above. However, it may be seen that this method is practicable only when the temperature variation experienced by the quarter waveplate is relatively small. 
     The second method for generating accurate sensor operations is to measure the extra D.C. light and provide corrections therefor. The intensity of the light detected by photodetector 46 of FIG. 1 is related to the electric current flowing in the wire and to the modulation signal applied to the birefringence modulator 26 through the relation: ##EQU1## where I D  is the total detected power, I O  is the power falling on the photodetector 34 in the absence of electric current and birefringence modulation, φ(t) is the birefringence modulation waveform present in the birefringence modulator, and τ is the round trip delay time from the birefringence modulator 26 to the end of the sensor 10 and back. In addition to containing a periodic waveform component, φ(t) may also contain a ramp-like component, for example, so that the difference between φ(t) and φ(t-τ) is a constant plus a periodic waveform. Therefore the modulation signal has a D.C. and an A.C. component. The slope of the ramp, and thus the value of the constant may be chosen to cancel the electric current induced phase, or 4VNI. Thus, the value of the current being sensed may be determined from the slope of the ramp necessary to cause the cancellation to occur. 
     The above equation may also be written as: ##EQU2## where φ m  is a short hand for the modulation signal which may be a sine wave, for example. 
     The apparatus and method for compensating for errors introduced by the imperfect quarter waveplate is to measure the error expressed as a single number, δ, and correct the scale factor to arrive at the accurate measurement. δ is derived by defining a Jones matrix, L which describes the element that is intended to convert linearly polarized light to circularly polarized light. In the embodiment of the present invention, a quarter waveplate set at 45° to the birefringent axes of the polarization maintaining fiber bus is used for the conversion. In general, L can be expressed as: ##EQU3## where p, q, r, s are real numbers and j=√-1. This way of expressing L is a general result for optical elements having polarization independent loss. For an ideal quarter waveplate set at 45°, we obtain p=1/2, q=-1/2, r=1/2, and s=-1/2. Then, δ is defined as 2(ps+qr)+1, where ideally, δ=0 when the quarter waveplate is operating perfectly and not influenced by external stresses. 
     Analyzing the fiber optics sensor using the Jones Matrix, including L as a general element, the detected light can be expressed as: ##EQU4## Dropping δ 2 , making γ=0, and using K to represent a constant dependent on the intensity of the detected light, the detected light becomes: 
     
         I.sub.D =K{1-δ cos (φ.sub.m cos ωt)+(1-δ) cos (4VNI+φ.sub.m cos ωt)}                          (6) 
    
     which is the equation used to analyze the solutions to the inaccurate current measurement problem. 
     If the quarter waveplate error or δ is zero, then there is a fixed relationship between the D.C. component of the detected light and all the harmonic signals therein. When δ is not zero, the proportion between the D.C. and the harmonic signals are corrupted. 
     Referring to an exemplary circuit 60 shown in FIG. 3, a peak detector 62 and a lock-in demodulator 64 are both coupled to photodetector 46 to receive an input representative of the light detected thereby. The output from photodetector 46 may be voltage level or current. Peak detector 62 determines the maximum level of the photodetector output, and lock-in demodulator demodulates the signal and provides the amplitude of the signal. The output of lock-in demodulator 64 and the output of peak detector 62 are coupled to a divider 66. 
     In operation, peak detector 62 provides the maximum level of the photodetector output, which may be expressed as: 
     
         I.sub.DMAX =2K(1-δ)                                  (7) 
    
     The output of lock-in demodulator essentially provides the first harmonic signal of the output, which may be expressed as: 
     
         I.sub.1H =2KJ.sub.1 (φ.sub.m)4VNI(1-δ)           (8) 
    
     where J 1  is the Bessel function. The output from lock-in demodulator 64 divided by the output from peak detector 62 yields: ##EQU5## This equation is independent of δ and thus can be used to solve for the current, I, since all other parameters are known. It may be deduced from the foregoing that a microprocessor-based signal analysis system may also be used to accomplish the same or similar functions as the peak detector and lock-in modulator to derive the ratio and compare it with the expected ratio based on the modulation waveform inputs. 
     Referring to FIG. 4, a diagram of the D.C. component as well as some harmonic signals of the detected light is shown. It may be seen that the harmonic signals of the detected signal is on the order of (1-δ). Therefore, any one of the harmonic signals can be divided by any signal from the detected light that is also proportional to (1-δ). In the implementation described above, the numerator is the first harmonic signal and the denominator is the peak value of the detected light. However, it may be seen that any signal component that can be isolated out of the detected light can be used in a similar manner to derive the ratios. 
     Further, it may be seen from the foregoing that the teachings of the present invention provides for a comparison of the D.C. component of the detected light to the A.C. spectrum when no quarter waveplate errors are present, which is then used as the basis for comparison when errors are present. The apparatus and method described above provides for a comparison between the peak level, which is a combination of the D.C. signal and all the harmonics, and the first harmonic signal. However, the invention also contemplates other means of comparison to derive the relationship between the D.C. signals and the harmonic signals. For example, the second harmonic signal may be measured and divided by the measured D.C. signal to establish the basis for comparison for subsequent measurements that may include quarter waveplate error. 
     Referring again to the equation: 
     
         I.sub.D =K{1+cos [4VNI+φ(t)-φ(t-τ)]}           (10) 
    
     Using a ramp function in addition to a periodic waveform at the birefringence modulator, the detected light becomes: 
     
         I.sub.D =K[1+cos (4VNI+γ+φ.sub.m cos ωt)]  (11) 
    
     where γ is a constant proportional to the slope of the ramp function. If γ=-4VNI, then the detected light is: 
     
         I.sub.D =K[1+cos (φ.sub.m cos ωt)]               (12) 
    
     Therefore, by setting γ=-4VNI, the first harmonic signal of this output becomes zero. By changing the value of γ that is introduced into the system to zero out the first harmonic signal, the desired output is derived from the slope of the ramp function or saw tooth waveform. 
     Referring to FIG. 5 for a block diagram of an exemplary circuit implementation of the signal processing electronics, the slope of the ramp function or saw tooth waveform may be determined by using a counter 72 to count the number of saw tooths occurring during a specified time period. The higher the count corresponds to more steepness in the ramp slope. The counter output is thus proportional to γ. 
     Due to errors introduced by the quarter waveplate, γ≠-4VNI but will actually be proportional to (1+δ): 
     
         γ=-4VNI(1+δ)                                   (13) 
    
     To cancel out δ, we may divide γ with a term that is proportional to (1+δ). Alternatively, γ may be multiplied with a term that is proportional to (1-δ) to generate a value proportional to (1-δ 2 ), which is approximately 1 for small δ. 
     Using sine wave modulation on the birefringence modulator in addition to the saw tooth waveform so that: 
     
         φ(t)-φ(t-τ)=γ+φ.sub.m cos ωt   (14) 
    
     and choosing φ m  =π/2: ##EQU6## Alternatively, with φ m  =2.4: ##EQU7## Thus, either of these methods may be used to obtain a suitable normalizing factor that removes the δ dependence inherent in γ. 
     Referring to FIG. 6A, if square wave modulation is used on the birefringence modulator in addition to the ramp function or saw tooth waveform, then [φ(t)-φ(t-τ)] is equal to γ plus a more complicated periodic waveform. Choosing τ≠1/2 duty cycle for off-proper frequency operation, the resultant photodetector output is: 
     
         I.sub.D =K[1+cos φ.sub.m (t)]                          (17) 
    
     which is shown in FIG. 6B. Therefore, with a nonzero δ, and φ m  =π/2: ##EQU8## which may be used as the normalizing factor to remove the dependence on δ that is inherent in γ. 
     Yet another solution to the scale factor error caused by imperfect quarter waveplates in a loop configuration of the optical sensor is the subject matter of another invention. The loop fiber optic sensor is described in detail in Blake. In the loop configuration, two quarter waveplates are disposed in the optical path at either side of the sensing medium. In the teachings of this invention, the solution provides for the orientation of quarter waveplates of approximately 45° with one another. It is shown below that the orientation of the quarter waveplates is 45° plus a rotation angle caused by the circular birefringence in the sensing medium. The quarter waveplates convert the polarization state of the counter-propagating light waves from linear to circular before entering the sensing region and back to linear after exiting the sensing region. The two counter-propagating light waves follow the same path and as a result there is a non-reciprocal phase shift only in the presence of a magnetic field in the current carrying wire. In this case, the effective refractive index seen by the circularly polarized light beams going in the opposite directions along the sensing loop is different. Thus, a non-reciprocal phase shift between the two light beams is induced, which is proportional to the magnetic field, Δφ=2VNI, where I is the electric current in the wire, V is the Verdet constant of the fiber glass and N is the number of turns in the sensing loop. For simplicity, we substitute F for VNI in the equations set forth below. 
     Under ideal conditions, when the delay introduced by the quarter waveplates is 90°, the linearly polarized light wave is perfectly converted to one circular state before its trip through the sensing fiber. An imperfect quarter waveplate, on the other hand, converts the linearly polarized light into a mixture of both right and left hand circularly polarized light waves. The unwanted circularly polarized beam accumulates the wrong phase shift, but if the second quarter waveplate is ideal, the light wave in the wrong state of circular polarization is converted to the orthogonal axis with respect to the main polarization and is eventually rejected by the polarizer. So, even if one of the quarter waveplates is imperfect, there is no scale factor error. However, if both quarter waveplates are imperfect, a small portion of light with the wrong phase is converted into the pass axis of the polarizer and falls on the detector, thereby introducing a scale factor error. The magnitude and the sign of this error depends on the quality of the quarter waveplates and the relative angle between their axes. 
     The current sensor may be modeled by the Jones matrix to analyze the polarization evolution of the light within the fiber and calculate the phase difference between the two counter-propagating beams. For the wave propagating in the clockwise direction (CW), we have the following: ##EQU9## δ 1  and δ 2  are the phase delays between the two polarizations introduced by the quarter waveplates and F is the polarization rotation induced due to the Faraday effect. The angle θ, in general, includes the relative angle between the axes of the quarter waveplates, and the polarization rotation due to circular birefringence in the sensing fiber. In the absence of circular polarization, θ=0° corresponds to aligning the quarter waveplate axes fast to fast. For these calculations, an assumption is made that the axes of the quarter waveplates are aligned 45° with respect to the polarizer, which is a perfect device. Both these conditions can easily be achieved to a high accuracy in real systems. 
     To describe the propagation of the oppositely traveling light wave, the composite Jones matrix is transposed, and the sign of the off-diagonal elements is reversed, and the sign of the Faraday angle F is also reversed. This convention preserves a right handed coordinate system with light propagation always to be in the +z direction. After multiplying out the matrices and calculating the phases of the complex amplitudes representing the electric fields of the two counter-propagating waves: ##EQU10## 
     For ψ=θ-90°, where in the absence of circular birefringence ψ is the physical angle between the eigen axes of the polarization maintaining fibers adjoining the two quarter waveplates. The phase difference is: ##EQU11## 
     For imperfect quarter waveplates we express the sum and the difference of the retardation angles in terms of the sum and difference of the errors δ 1  =δ 2  =180°+ε.sub.Σ and δ 1  -δ 2  =ε.sub.Δ, where ε.sub.Σ is the sum of the quarter-wave errors and ε.sub.Δ is the difference between them. Defining ##EQU12## 
     If the fast axis of one quarter waveplate is aligned to the slow axis of the other, the physical angle between the polarizers ψ is 0°, then from Equation (35) for small deviations of the retardation angle from 90° and small Faraday rotations, the phase difference is proportional to the product of the quarter waveplate errors. ##EQU13## where ε=δ 1  -90° and ε 2  =δ 2  -90°. If we align the fast axis of one quarter waveplate to the fast axis of the other, the angle between the polarizers, ψ, is equal to 90°, and the scale factor dependence remains quadratic with respect to the quarter waveplate error, but the sign in front of the quadratic equation term changes: ##EQU14## 
     The question now is whether it is possible to find an angle between the polarizers such that the dependence of the scale factor on the quality of the quarter waveplates in the vicinity of ε 1  and ε 2  ≅0, (small errors), is minimized. In Equation (35) g is substituted with 1-h, where h is a small value, and after ignoring any h 2  terms and applying the trigonometric identities the phase difference is found to be: ##EQU15## 
     It is desirable that this phase difference is independent of h. Therefore, the condition on the optimum angle ψ between the polarizers is: ##EQU16## or ψ=45°. Unlike the quadratic dependence of the scale factor on the error of the quarter waveplate for 0° and 90° alignments shown by Equations (36) and (37), for a 45° alignment, the scale factor changes as (ε 2 ) 2 , which makes the scale factor less sensitive to changes in the retardation angle of the quarter waveplate. ##EQU17## 
     In the presence of a magnetic field in the sensing loop, the parasitic light wave accumulates a phase shift with respect to the main beam. This phase shift depends on the relative alignment of the quarter waveplate axes and results in changes in the scale factor when the light with the wrong sense of circular polarization is mixed with the main light through the imperfect quarter waveplate. At 45° between the quarter waveplate axes (fast-to-fast, slow-to-slow, and fast-to-slow axes), the effect of this parasitic wave is minimized. For example, to maintain a scale factor accuracy of approximately 0.3% without using this alignment configuration requires a quarter waveplate with a retardation of 90±4.4°; with it, the sensor can tolerate a quarter waveplate with a retardation of approximately 90±22.30°. To provide 100 ppm stability, this alignment configuration can tolerate a quarter waveplate of approximately 90±9.6°, whereas without it, a quarter waveplate must possess a retardation of about 90±0.8°. 
     Thus, when the angle between the polarizers is 45°, even large deviations from the ideal 90° retardation of the quarter waveplates can be tolerated, thus eliminating the dependence of the scale factor stability on the quality of the quarter waveplates. 
     When the optical sensor includes a sensing medium that introduces circular birefringence, the rotation caused thereby should be taken into account in the quarter waveplate orientation. For example, if the polarization of the light waves rotates by 45° due to circular birefringence in the sensing medium, then the quarter waveplates should be oriented (45°+45°) or 90° with respect to each other. Therefore, the quarter waveplate orientation is 45° plus the degree of rotation induced by circular birefringence in the fiber in order to eliminate or minimize the scale factor error. 
     Although the present invention and its advantages have been described in detail, it should be understood that various mutations, changes, substitutions and alterations can be made therein without departing from the spirit and scope of the invention as defined by the appended claims.