Abstract:
Methods and apparatus are provided for attenuating polarization errors in ring resonators of fiber optic gyros. A ring resonator is provided having first and second resonance frequencies and comprising an optical fiber coil having a hollow core and first and second ends, a light beam generator coupled to the optical fiber coil and configured to generate first and second counter-propagating beams in the hollow core, and a light recirculator coupled to the first and second ends of the optical fiber coil and configured to direct a first light beam exiting the first end of the optical fiber coil into the second end of the optical fiber coil. The first light beam is based on one of the first and second counter-propagating beams. The light recirculator comprises a first polarizing unit configured to reflect a first polarized component of the first light beam and further configured to extract a second polarized component of the first light beam.

Description:
FIELD OF THE INVENTION 
   The present invention generally relates to gyro systems, and more particularly relates to rotational sensors for use in a fiber optic gyro. 
   BACKGROUND OF THE INVENTION 
   Gyros have been used to measure rotation rates or changes in angular velocity about an axis. A basic conventional fiber optic gyro (FOG) includes a light source, a beam generating device, and a coil of optical fiber coupled to the beam generating device that encircles an area. The beam generating device transmits light beams into the coil that propagate in a clockwise (CW) direction and a counter-clockwise (CCW) direction along the core of the optical fiber. Many FOGs utilize glass-based optical fibers that conduct light along a solid glass core of the fiber. The two counter-propagating (e.g., CW and CCW) beams experience different pathlengths while propagating around a rotating path, and the difference in the two pathlengths is proportional to the rotational rate. 
   In a resonator fiber optic gyro (RFOG), the counter-propagating light beams are desirably monochromatic (e.g., in a single frequency) and recirculate through multiple turns of the fiber optic coil and for multiple passes through the coil using a recirculating device such as a fiber coupler. The beam generating device modulates and/or shifts the frequencies of each of the counter-propagating light beams so that the resonance frequencies of the resonant coil may be observed. The resonance frequencies for each of the CW and CCW paths through the coil are based on a constructive interference of successively recirculated beams in each optical path. A rotation of the coil produces a shift between in the respective resonance frequencies of the resonant coil and the frequency difference, such as may be measured by tuning the CW beam and CCW beam frequencies to match the resonance frequency shift of the coil due to rotation, indicates the rotation rate. 
   The RFOG may encounter a variety of anomalies that decrease the accuracy of the rotational rate measurement. Polarization-induced errors are initiated by light coupling from one polarization state to another within the fiber resonator. For instance, such light coupling may result from fiber couplers that incidentally couple light into a second polarization mode, either from one optical fiber to an adjacent optical fiber or within the same fiber. As a result, the second polarization mode has a resonance that may produce an asymmetry in the resonance lineshape of the first polarization mode used to measure a rotation. Even though the resonance frequency of the second polarization mode may be the same for the CW and CCW beams, the amplitude of light in such mode may be different, thus causing different observations, beyond the effect of rotation, of the resonance frequencies of the CW and CCW beams. Polarization-induced errors may severely limit the accuracy of the RFOG because determination of the resonance centers for each of the resonance frequencies of the CW and CCW beams directly affects the rotational rate measurement. The errors in the gyro generally depend on the magnitude of light propagating in the second polarization state. 
   Several mechanisms may couple light into the undesired polarization state of the fiber optic resonator. In general, light traveling in the undesired polarization state results from a combination of these mechanisms. As previously mentioned, light may be cross-coupled inside the re-circulating device, such as a fiber coupler. Light may also excite the second polarization state, or couple into the second polarization state, of the resonator when undesirably injected into the optical fiber with a component of the light in the undesired polarization state. This may be exacerbated by possible variances in the states of polarization of the fiber inside the resonator due to temperature or stress variation, thereby making repeated light launches into one polarization state of the resonator more difficult. Even if the lights beams are originally introduced to the coil of the RFOG in the first polarization mode, the optical fiber may have one or more imperfections that couple light into the second polarization mode. One way of limiting such cross-talk between polarization modes of the fiber resonator is to employ polarization preserving fiber. Polarization preserving fiber incorporates stresses defining different speeds of light (i.e., birefringence) that attenuate the cross-coupling of light from one polarization axis of the fiber to the other. This feature of polarization preserving fiber stabilizes the polarization mode of the ring resonator, thereby assisting the task of stably launching a fraction of light into a desired mode. 
   Using conventional optical fibers, particularly in polarization preserving fibers, the difference in the speed of light between light traveling on the two principle axes of polarization in the fiber typically varies with temperature. This variation can cause the relative resonance frequencies of the two polarization states to vary with temperature. In some instances, the resonance frequency of the undesired polarization state may coincide with the resonance frequency of the desired polarization state under some environmental conditions. 
   Polarization-induced errors may severely limit the accuracy of the RFOG because the accuracy of the determination of the resonance centers, and thus the resonance frequencies in the CW and CCW directions, directly affects the rotational rate measurement. Additionally, these errors in the measurement may change radically with respect to the temperature in conventional optical fibers due to the sensitivity of the associated birefringence to temperature. 
   Consequently, the gyro output may drift without influence from a variation in rotation rate. Thus, two primary error mechanisms are the excitation of light in the undesired polarization state, and the environmental instability of the resonance frequency of the undesired polarization state relative to that of the desired polarization state. Additional error mechanisms in an RFOG employing conventional glass fibers that are attributable to the propagation of light in the solid glass medium of the optical fiber include optical Kerr Effect, Stimulated Brillouin Scattering, and Raleigh back-scattering. 
   Accordingly, it is desirable to provide a fiber optic gyro that attenuates polarization errors in rotational rate measurements. In addition, it is desirable to provide a method for attenuating polarization errors in rotational rate measurements of a fiber optic gyro. Furthermore, other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description of the invention and the appended claims, taken in conjunction with the accompanying drawings and this background of the invention. 
   BRIEF SUMMARY OF THE INVENTION 
   Methods and apparatus are provided for sensing a rotational rate of a ring resonator about an axis. In an exemplary embodiment, a ring resonator is provided having first and second resonance frequencies and comprising an optical fiber coil having a hollow core and first and second ends, a light beam generator coupled to the optical fiber coil and configured to generate first and second counter-propagating beams in the hollow core, and a light recirculator coupled to the first and second ends of the optical fiber coil and configured to direct a first light beam into the second end of the optical fiber coil. The first light beam is based on one of the first and second counter-propagating beams. The light recirculator comprises a first polarizing unit configured to direct with a low loss a first polarized component of the first light beam into the second end and further configured to impart a high loss to a second polarized component of the first light beam. 
   In another exemplary embodiment, a resonator fiber optic gyro (RFOG) assembly is provided comprising a beam generator, an optical fiber coil having first and second ends coupled to the beam generator and having a hollow core, a polarizing unit coupled to said first and second ends of said optical fiber coil, a first photodetector configured to determine a resonance center of the first light beam based on the first polarized light component, a second photodetector configured to determine a resonance center of the second light beam based on the first polarized light component, and a frequency shifter coupled to the second photodetector. The beam generator is configured to produce first and second counter-propagating light beams in the optical fiber coil, and each of the first and second counter-propagating light beams has a frequency. The polarizing unit is configured to reflect a first polarized light component of the first and second counter-propagating light beams, pass a second polarized light component of the first and second counter-propagating light beams, and recirculate the first and second counter-propagating light beams through the optical fiber coil. The frequency shifter is configured to shift the frequency of the second light beam by a frequency Δf to the resonance center of the second light beam. The frequency Δf indicates a rotational rate of the RFOG. 
   In another exemplary embodiment, a method for sensing a rotation rate of a ring resonator having a hollow core optical fiber is provided comprising the steps of transmitting first and second counter-propagating light beams into the hollow core optical fiber, recirculating the first and second counter-propagating light beams through the hollow core optical fiber while substantially removing a first polarized light component out of each of the first and second counter-propagating light beams, and measuring a frequency shift between a resonance frequency of the first counter-propagating light beam and a resonance frequency of the second counter-propagating light beam. The frequency shift indicates the rotation rate. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will hereinafter be described in conjunction with the following drawing figures, wherein like numerals denote like elements, and 
       FIG. 1  is a schematic diagram of a resonator fiber optic gyro in accordance with an exemplary embodiment of the present invention; 
       FIG. 2  is a schematic diagram of a resonator fiber optic gyro in accordance with another exemplary embodiment of the present invention; and 
       FIG. 3  is a flow diagram of a method for sensing a rotation rate of a ring resonator in accordance with an exemplary embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The following detailed description of the invention is merely exemplary in nature and is not intended to limit the invention or the application and uses of the invention. Furthermore, there is no intention to be bound by any theory presented in the preceding background of the invention or the following detailed description of the invention. 
   Referring now to the drawings,  FIG. 1  is a schematic diagram of a resonator fiber optic gyro (RFOG)  10  in accordance with an exemplary embodiment of the present invention. The RFOG  10  comprises a tunable light source  12  (e.g., a laser) configured to generate a light beam having a frequency f 0 , a beam splitter  14  configured to receive the light beam from the light source  12  and further configured divide the light beam from the light source  12  into first and second light beams, a first wave modulator  16  configured to receive the first light beam from the beam splitter  14  and further configured to modulate the first modulated light beam, a second wave modulator  18  configured to receive the second light beam from the beam splitter  14  and further configured to modulate the second light beam, a frequency shifter  20  configured to receive the first modulated light beam from the first wave modulator  16  and further configured to shift the frequency of the first modulated light beam, a recirculator  22  configured to receive the first modulated light beam from the frequency shifter  20  and the second modulated light beam from the second wave modulator  18 , a hollow core optical fiber coil  24  having first and second ends coupled to the recirculator  22 , a first photodetector  26  configured to receive a first return beam from the recirculator, and a second photodetector  28  configured to receive a second return beam from the recirculator  22 . The combination of the recirculator  22  and the fiber coil  24  is referred to as a resonator  25 . The recirculator  22  is further configured to introduce the modulated light beams to the optical fiber coil  24  and recirculate the modulated light beams through the optical fiber coil  24 . The RFOG  10  may include additional mirrors  30 ,  32  and beam splitters  34 ,  36  for directing the propagation of light beams from the light source  12  to the optical fiber coil  24  and for directing light from the recirculator  22  to the photodetectors  26 ,  28 . 
   In an exemplary embodiment, the light source  12  is a single frequency tunable laser having frequency stability, substantially narrow line width, and relatively high power capability. The wave modulators  16 ,  18  frequency-modulate the first and second light beams such as by introducing a sinusoidal waveform into the light beams, and the particular modulation may be selected to improve sensitivity of the RFOG  10  to a detected frequency shift (Δf), described in greater detail herein below. The first modulated light beam and second modulated light beam are introduced into the optical fiber coil  24  in a counter-clockwise (CCW) and a clockwise (CW) direction, respectively, such as via opposite ends of the optical fiber coil  24 . 
   The CW beam has an unshifted laser frequency (f 0 ) and is introduced into the resonator  25 . For rotation sensing, the frequency f 0  of the CW beam is tuned (e.g., by tuning the frequency of the laser  12 ) to the resonance frequency of the resonator  25  in the CW direction. The frequency shifter  20  is configured to tune the frequency Δf to align the CCW beam frequency with a resonance center relative to the resonance frequency of the resonator in CCW direction. During rotation sensing, the frequency shifter  20  frequency shifts the light from the laser  12  by an amount Δf and injects the frequency shifted light into the optical fiber coil  24  in the CCW direction. Two methods of accomplishing a frequency shift include the use of an acousto-optic frequency shifter and the use of a phase modulator with a serrodyne modulation waveform. In the latter method, the serrodyne waveform is a form of a sawtooth waveform. To apply a relatively pure frequency shift, the phase shift amplitude of the sawtooth waveform, described in greater detail hereinafter, is set to an integer multiple of 2π and the sawtooth waveform has a substantially fast flyback time when compared to its period. 
   To measure the resonance center-frequencies of the optical fiber coil  24 , in either the CW direction or CCW direction, a standard synchronous detection technique is used. Each input light beam (e.g., CW beam and CCW beam) is sinusoidally phase-modulated, and therefore frequency modulated at frequencies f m  and f n , respectively, to dither each input beam frequency across a resonance lineshape as measured by the photodetectors  26 ,  28 . For example, additional circuitry coupled to the photodetectors  26 ,  28  may demodulate the outputs of the photodetectors  26 ,  28  at frequencies f m  and f n , respectively, to measure resonance centers indicated by the light outputs of the CW and CCW beams. At a line center of the resonance lineshape, or the resonance center, the photodetectors  26 ,  28  detect a minimum output at the fundamental detection of frequencies f m  and f n , respectively. When the input beam frequency (e.g., f 0  or f 0 +Δf) is off-resonance, an error signal at frequencies f m  and f n , respectively, is sensed by the photodetectors  26 ,  28  and used to tune the respective beam frequency to the respective resonance frequency of the optical ring resonator  25 . The frequency of the CW beam is tuned by changing the frequency of the laser, f 0 , and the frequency of the CCW beam is adjusted via a feedback loop that changes the frequency shift of the frequency shifter, Δf, so that f 0 +Δf matches the CCW resonance frequency of the optical ring resonator  25 . 
   When f 0  is tuned away from the resonance frequency of the resonator  25  in the CW direction, the energy from the CW beam does not enter the optical fiber and the light is reflected off the highly reflective mirror  22  to produce a maximum intensity at the CW photodetector  26 . When f 0  is tuned at the resonance frequency of the resonator  25  in the CW direction, the CW beam enters the optical fiber coil  24 , and the light striking the CW photodetector  26  has a minimum output, i.e., a resonance dip, thereby indicating the resonance center. Similarly for the CCW light beam, the energy of the CCW beam enters the optical fiber coil  24  when the CCW beam is tuned to the resonance frequency of the resonator  25  in the CCW direction. 
   In the absence of rotation, the round-trip path-lengths of the CW and CCW beams inside the resonator  25  in the CW and CCW direction, respectively, are substantially equal. Thus, Δf is tuned to zero by the frequency shifter  20 . In the presence of rotation, the round-trip path-lengths differ between the CW and the CCW directions producing a resonance frequency difference between the two directions that is proportional to the rotation rate. By tuning the frequency f 0  to track the CCW resonance and the frequency Δf to track the CCW resonance center, the rotation rate is determined. 
   In a preferred exemplary embodiment of RFOG  10 , frequency shifting is obtained using a serrodyne method whereby a phase ramp is applied to an input light beam (e.g., CW and CCW beams). By driving a phase modulator, such as the wave modulators  16 ,  18 , with a continuous and linear phase ramp, a frequency shift may be obtained, that is proportional to the slope of the phase ramp. A sawtooth waveform of having a 2π phase height and a frequency Δf produces substantially equivalent results as the continuous ramp, and the sawtooth frequency (Δf) is adjusted to track the CCW resonance in the presence of rotation. As previously mentioned, the frequency shifter  20  may apply a relatively pure frequency shift when the sawtooth waveform flyback time is substantially fast compared to the waveform period. 
   A hollow core, band-gap, optical fiber having an extremely low bend loss is preferably used with the resonator  25 , and the coil  24  preferably has a large number of turns about a substantially small area to achieve a compact gyro which is one advantage of this invention. For example, the coil  24  may have from about 20-40 turns of the optical fiber about a one centimeter diameter. The hollow core optical fiber is typically glass-based with a plastic outer jacket and a hollow inner core. In the hollow core optical fiber, light injected from the recirculator  22  traverses mostly through free space (e.g., air or a vacuum) along the core, and only about a few percent or less of the optical energy of light is contained in the glass walls of the fiber surrounding the hollow core. Because a large majority of the light energy traverses through free space along the hollow core of optical fiber, the transition between the recirculator  22  and the hollow core optical fiber has a near-perfect index matching, and a high reflectivity laser mirror with low loss and attractive polarization properties may be used for the recirculator  22 . The hollow core fiber is suited to significantly attenuate, or eliminate altogether, the rotation measurement errors commonly associated with the properties of the glass medium in the core of conventional fibers. 
   The recirculator  22  reintroduces light emerging from one end of the optical fiber coil  24  into the other end of the fiber coil  24 , thus causing light to propagate through the fiber coil  24  many times. The recirculator  22  comprises at least one polarization unit  23  that attenuates light emerging from the optical fiber coil  24  having an undesired polarization state while minimizing losses of a desired polarization state in the light emerging from the optical fiber coil  24 . The polarization unit  23  reflects light in the desired polarization state (e.g., S-polarization) back into the optical fiber coil  24  to a substantially high degree (e.g., about 95% or more) and passes light in the undesired polarization state (e.g., P-polarization) out of the optical fiber coil  24  (e.g., removes light in the undesired polarization state from the light recirculating in the optical fiber coil  24 ) to a substantially high degree. The recirculator  22  may comprise a single polarization unit to receive/reflect light exiting from the ends of the optical fiber coil  24  or may comprise a network of two or more optical elements with multiple polarization units to separately receive/reflect light exiting from each end of the optical fiber coil  24 . 
   In an exemplary embodiment, the polarization unit has a Brewster angle of incidence (e.g., about 56°), for light impinging on the main surface (e.g., the surface receiving light exiting from the optical fiber coil  24 ) of the polarization unit  23 , at which S-polarized light is reflected at a substantially high degree and P-polarized light is passed out of resonator  25  at a substantially high degree. In this exemplary embodiment, the polarization unit  23  preferably receives light from the ends of the optical fiber coil  24  at this Brewster angle of incidence. One example of the polarizing unit  23  is a thin film polarizer that comprises a glass substrate having a coating (e.g., a stack of dielectric coatings), although a variety of other reflective devices having polarization sensitivity may be used. In conjunction with the hollow core optical fiber, light recirculating in the optical fiber coil  24  having the desired polarization may have a significantly low loss when propagating from the hollow core fiber into free space and then reflected by the polarization unit  23 . Additionally, by using hollow core fiber that substantially maintains the state of polarization of light, or high birefringence hollow core optical fiber, the polarization state of the light inside the optical fiber may be oriented and maintained relative to the polarization state of the light reflected by polarization unit  23 . Thus, losses associated with the desired polarization state are minimized, and the error in the rotation rate measurement due to the resonance magnitude of the undesired polarization state may be minimized. Further, the use of hollow core fiber significantly reduces the temperature dependence of the birefringence which allows for a stable resonance frequency separation between the desired polarization state and the residual undesired polarization state. Consequently, the use of hollow core fiber reduces errors in rotation rate over a wider variety of environmental conditions. Light guiding hollow core fiber may be realized via an optical bandgap effect in photonic crystal fiber structures and is frequently referred to as bandgap fiber. 
     FIG. 2  is a schematic diagram of a resonant fiber optic gyro  40  in accordance with another exemplary embodiment of the present invention. The RFOG  40  includes first and second tunable lasers  42 ,  44  that each synthesize the CW and CCW light beams, respectively, and introduce the light beams into the resonator  25  thereby replacing the beam splitter  14  shown in  FIG. 1 . The resonator  25  includes the recirculator unit  22  and the optical fiber coil  24 , and the recirculator unit  22  includes a polarization unit  23 . The light beam produced by the first laser  42  is tuned to a frequency f 0 , and the light beam produced by the second laser  44  is tuned to a frequency f 0 +Δf thereby replacing the frequency shifter  20  shown in  FIG. 1 . In this example, the relative frequency drift and jitter between the two laser frequencies should be substantially minimized to a level that minimizes or does not affect the accuracy and stability of the frequency shift, and thus rotational rate, measurement. This can be accomplished by laser frequency stabilization techniques, such as those that use electronic servos to lock their beat frequencies to a tunable stable offset (proportional to rotational rate). Each of the lasers  42 ,  44  sinusoidally frequency modulates the respective frequencies thereby replacing the frequency modulators  16 ,  18  shown in  FIG. 1 . 
     FIG. 3  is a flow diagram of a method for sensing a rotation rate of a ring resonator in accordance with an exemplary embodiment of the present invention. The method begins at step  100 . Referring to  FIGS. 1 and 3 , first and second counter-propagating light beams are transmitted into the hollow core optical fiber coil  24  at step  105 . The recirculator  22  recirculates the first and second counter-propagating light beams through the hollow core optical fiber coil  24  while substantially removing light having the undesired polarization out of each of the first and second counter-propagating light beams in the resonator  25 . In an exemplary embodiment, the polarization unit  23  reflects light emerging from the fiber having the desired polarization from each of the first and second counter-propagating light beams back into the hollow core optical fiber at step  110 . Additionally, the polarization unit  23  passes light having the undesired polarization from each of the first and second counter-propagating light beams away from the hollow core optical fiber at step  115 . The frequency shifter determines a frequency shift between the resonance frequency of the first counter-propagating light beam and the resonance frequency of the second counter-propagating light beam at step  120 , and this frequency shift indicates the rotation rate of the ring resonator. 
   Advantages of the RFOG  10  include, but are not limited to: a capability of providing about a 0.01 deg/hr bias and about a 0.001 deg/root-hr angle random walk (ARW) in a low-cost, small-sized package; a resonator having less than a few meters of fiber wound into tight turns with low loss; use of a high reflectivity mirror rather than a fiber optic coupler to recirculate light in the ring resonator; a compact, stable laser whose key components can be mounted on a silicon optical bench; a MEMS prism embeddable in silicon that efficiently directs light in and out of silicon; minimized non-linear effects in silica fibers that may promote gyro errors; attenuated thermally-driven polarization errors by minimizing the drift (over temperature) of a potential second resonance peak corresponding to a second polarization mode in the optical fiber; substantial reduction of light loss at transition point to optical fiber coil  24 ; a capability of winding the optical fiber coil into a very tight (e.g., pencil diameter) loops with little to no change in light transmission properties. 
   In one exemplary embodiment, the RFOG  10  is constructed on a silicon-based micro-optical bench that integrates electronics and optics and provides an efficient, expedient, and mechanically stable interface between the two. Optical functions, such as associated with the wave modulators  16 ,  18 , may be incorporated in waveguides located close to the surface of the optical bench, and miniature optical components having a feature size of as little as 10 microns may be mounted on silicon surfaces to eliminate large bulk optics, even though the light wave may be traveling in free space. Laser diodes and external elements for stabilizing their frequency may also be mounted on the top surface of the silicon optical bench. In this exemplary embodiment, the laser and related frequency tuning components may be mounted on the optical bench, and using the serrodyne method for frequency shifting enables the use of an integrated optical phase modulator in a silicon waveguide for the frequency shifter. A micro-electromechanical system (MEMS) optical prism may be used as a highly reflective laser prism capable of directing light into and out of the silicon waveguide. The use of these techniques allows the fabrication of optics in a silicon platform and thus integrated with the electronics. 
   The RFOG  10  is suited to a variety of applications including, by way of example and not of limitation, applications requiring inertial guidance such as aircraft, land vehicle, submarine, satellite, surface ship navigation, and the like., In addition, the relatively small size envisioned for the RFOG  10  would enable a practical usage on very small platforms including, by way of example and not of limitation, small robots, individual soldier footwear, and small-scale satellites. 
   While at least one exemplary embodiment has been presented in the foregoing detailed description of the invention, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or exemplary embodiments are only examples, and are not intended to limit the scope, applicability, or configuration of the invention in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing an exemplary embodiment of the invention. It being understood that various changes may be made in the function and arrangement of elements described in an exemplary embodiment without departing from the scope of the invention as set forth in the appended claims.