Systems and methods for a polarization matched resonator fiber optic gyroscope

BACKGROUND

In commercial navigation application, there is a continuing need for developing low cost, small sized navigation grade gyroscopes. The resonator fiber optic gyro (RFOG) is one gyroscope technology that can satisfy those needs. In the RFOG, a ring resonator is formed using a fiber optic coil and couplers to couple light into and out of the ring resonator in clockwise (cw) and counterclockwise (ccw) directions. At least two input light waves are frequency-tuned to the resonances of the ring resonator in the cw and ccw directions respectively. After measuring the resonance frequencies in the two directions by tuning each input beam to them, the input beam frequencies are compared, and the difference is proportional to the rotation rate of the resonator coil. In an RFOG bias instability is manifested as an indicated rotation rate output even when the gyroscope is not rotating.

Patent document number US4588296A describes a compact optical gyro is provided wherein a beam of light is split and introduced into both ends of an optic coil whose rotation is to be sensed. At least one frequency shifter is placed to affect the frequency of the beam to introduce or adjust a nonreciprocal phase shift. The beams are then mixed back together and the resultant beam is detected and analyzed by suitable circuitry to provide an output indicative of the rotation of the light path.

For the reasons stated above and for other reasons stated below which will become apparent to those skilled in the art upon reading and understanding the specification, there is a need in the art for improved systems and methods to address RFOG bias instability.

SUMMARY

The embodiments of the present invention provide methods and systems for polarization matched resonator fiber optic gyroscope and will be understood by reading and studying the following specification.

In one embodiment, a polarization matched resonator fiber optic gyroscope (RFOG) comprises: a first light source; a fiber optic ring resonator coupled to the first light source; a first photodetector coupled to an output of the fiber optic ring resonator, where the first photodetector outputs an electrical signal that varies as a function of optical intensity measured by the first photodetector; and a first input light polarization servo; wherein the fiber optic ring resonator is coupled to the first light source via the first input light polarization servo such that a light beam from the first input light polarization servo is launched into the fiber optic resonator ring in a first direction of circulation; wherein the first input polarization servo comprises a birefringence modulator that modulates a phase shift between two components of the input polarization state of the light beam at a modulating frequency ω_m, wherein the birefringence modulator is further controlled to drive towards zero a 1^st harmonic of the modulating frequency

One issue with achieving this matched condition is that there is polarization cross-coupling within the input beams paths to the resonator that keeps it from being in the exact desired polarization state at the input to the resonator. The existence of this cross-coupling in the input leads, as well as thermally induced fluctuations in the birefringence of the input leads, can cause the input light wave polarization state to fluctuate over time, causing the coupling of input light into the polarization state of the resonator to vary. The magnitude of the cross-coupling itself can vary over time. Furthermore, even if the input light state were completely stable at the entrance of the resonator, the polarization state inside the resonator at its input can vary over time, causing the overlap with the input polarization state to vary.

The various embodiments described herein provide systems and methods for very accurately launching the input light into one polarization mode within the ring resonator reducing bias instability within the RFOG. As described in detail below, one or more of these embodiments use active feedback to constantly adjust the input polarization state of the cw and ccw inputs beams to track and match the desired polarization state of the ring resonator.

Figure 1 is a flow chart illustrating a polarization matched resonator fiber optic gyroscope (RFOG) 100 of one embodiment of the present invention. RFOG 100 comprises a fiber optic resonator ring 110 coupled to a first light source 112 via a first input light polarization servo 120. Light waves (shown at 116) exit from input light polarization servo 120 through input leads 117 and are launched into the resonator ring 110 where they circulate around the ring 110 in a clockwise (CW) direction. A fraction of the circulating CW light waves can be coupled out of resonator ring 110 (shown at 118) and detected by photodetector 114.

For simplicity, only components related to the CW operation of RFOG 100 are discussed in detail below. However, as shown in Figure 1, RFOG 100 does comprise symmetrical set of counterclockwise components. That is, fiber optic resonator ring 110 is also coupled to a second light source 112' via a second input light polarization servo 120'. Light waves (shown at 116') exit from input light polarization servo 120' into an input lead 117' and are launched into the resonator ring 110. This light beam circulate around the ring 110 in a counter-clockwise (CCW) direction. A fraction of the circulating CCW light waves are coupled out of resonator ring 110 and detected by photodetector 114'. Primed (') reference indicators (i.e., x') are used to indicate elements relevant to CCW operation. Each of the primed components (e.g., 113', 116', 117', 122', 124', 126', 130', 132', 150', 171', 172', 174' and 175') associated with input light polarization servo 120' can be assumed to be functionally identical as those described for their like-named non-primed counterparts (113, 116, 117, 122, 124, 126, 130, 132, 150, 171, 172, 174 and 175' respectively) for input light polarization servo 120, except that their operation is applicable to launching the CCW circulating light beam. In some embodiments, the first and second light sources 112, 112' may actually comprise a single light source whose output is split into two beams that are separately fed into the appropriate CW and CCW components. Further, the first and second light sources 112, 112' may be implemented, for example using tunable lasers that produce monochromatic light beams.

As shown in Figure 1, input light polarization servo 120 comprises a tunable ½ waveplate 122, a birefringence modulator 124, a first demodulator 126, a second demodulator 128, a summing amplifier 130 and a sinusoidal generator 132. The eigenstate of polarization for resonator ring 110, which will be referred to herein generally as the resonator polarization state, may be defined by two components X & Y and represented by the column matrix: $$\left(\begin{array}{c}X\\ Y\end{array}\right),$$ where X and Y are complex.

The light within resonator ring 110 is already highly (but not perfectly) polarized so that the amplitude of the Y component may be defined by ε (where ε is ≪ 1) which is equal to the relative amplitude of the Y component as compared to the amplitude of the X component. Thus the resonator polarization state may be represented by the normalized matrix: $b\left(\begin{array}{c}1\\ \epsilon e^{\mathit{i\varphi }}\end{array}\right),$ where $b=\sqrt{\frac{1}{1+{\epsilon }^2}}$ and ϕ is the phase difference between the X and Y components.

The light 113 entering input light polarization servo 120 is also already polarized into a similar polarization state, but the polarization state of light beam 113 will be mismatched with respect to the resonator polarization state. That is, ε for the polarization state of light 113 is off by Δε, while ϕ is off by Δϕ. The polarization state of light 113 entering input light polarization servo 120 can therefore be characterized by the normalized matrix: $$a\left(\begin{array}{c}1\\ \left(\epsilon -\mathrm{\Delta }\epsilon \right)e^{i\left(\varphi -\mathrm{\Delta }\varphi \right)}\end{array}\right),\mathrm{}where\mathrm{}a=\sqrt{\frac{1}{1+{\left(\epsilon -\mathrm{\Delta }\epsilon \right)}^2}}$$

Thus if input light polarization servo 120 is operated to drive both Δε and Δϕ of light beam 113 to zero, the polarization state of the launch light 116 will have the same polarization state as exists inside ring resonator 110.

To address Δϕ, input light polarization servo 120 comprises a birefringence modulator 124 positioned within the path of the light beam 113 prior to the ring resonator 110. Birefringence modulator 124 modulates the phase difference between the X-component and the Y-component of the launch light 116 (which is referred to herein as the input polarization state). There are various means for implementing birefringence modulator 124. For example, in one embodiment birefringence modulator 124 comprises a lithium niobate electro-optic phase modulator positioned along a principal axis of the input fiber 117 (which may comprise a length of polarization maintaining fiber). In another embodiment, an electro-optic transparent ceramic material is used, such as those manufactured at Boston Applied Technologies Incorporated (BATI).

In the example embodiment shown in Figure 1, a voltage is applied to birefringence modulator 124 which controls birefringence modulator 124 and the modulation of the phase shift between the x-component and the y-component of the input polarization state of launch light 116. The voltage driving birefringence modulator 124 is actually the sum of two voltage components, which may be added together by a summing amplifier 130. The first voltage component, produced by a sinusoid generator 132 (which can comprise an oscillator or similar device), is characterized by the time varying function Δø_mcos(ω_mt), where Δø_m is a selected amplitude and ω_m is the modulation frequency. The second voltage component. Δø₀ is derived from a feedback signal provided by photodetector 114. The value of Δø₀ is a function of the Δϕ difference. As discussed above, a ring resonator's eigenstate of polarization at its input can change over time and with changes in temperature. Observing the overlap between the resonator polarization state and the input state from the output of the ring resonator (as opposed to attempting to estimate a polarization state upstream from the ring resonator output) is believed to provide the best representation of the overlap, between input light polarization state and the resonator's true polarization state. The overlap between input state and the resonator state is a measure of the fraction of light energy from the input light wave is coupled into the resonator polarization state when the input frequency of light is adjusted to the resonance frequency of the resonator polarization state. The closer the fraction of light energy is to unity, the more perfect the overlap, which is the intent of this invention.

More specifically, the output intensity variation from ring resonator 110 at the peak of the resonance is sensed at ω_m. It would be appreciated that signal processing methods known in the art may be used to control the cw and ccw input wave frequencies to the resonances centers of the cw and ccw resonances, respectively. Optical intensity observed by photodetector 114 is converted into an electrical signal which is fed into the first demodulator 126. The first demodulator 126 is also referred to herein as the 1^st harmonic demodulator, because it demodulates the electrical signal from photodetector at the modulation frequency ω_m. The output of the first demodulator 126 is a DC voltage or digital value proportional to Δϕ. The output of the first demodulator drives an integrator 150. In one embodiment, integrator 150 comprises a digital accumulator. The integrator 150 output ramps up in response to a non-zero output of the first demodulator 126, which results, in steady state, in a DC voltage component Δø₀ that is imparted to the birefringence modulator 124 to adjust Δϕ such that Δϕ=0. If the input polarization state misalignment angle Δϕ is equal to 0 originally, the output of the first demodulator is zero and the input to the integrator 150 is zero. Thus, the integrator 150 output is zero in steady state. If there is a change in Δϕ, such that Δϕ≠0, then there exists a phase difference between the X-component and the Y-component of the input polarization state of launch light 116 that is different than that of the resonator polarization state. Therefore, birefringence modulator 124 is driven to minimize changes in intensity (i.e., minimize Δø₀) at the phase modulation frequency ω_m so that a phase difference between the X and Y components is applied. In this case, when Aϕ≠0, in the detected output of the photodetector 114 at ω_m will be temporarily non-zero, the demodulated output of demodulator 126 will be temporarily non-zero, and the integrator 150 output will adjust the value of Δø₀ until steady state is reached. In steady state, the Δϕ=0, and therefore the detected signal at ω_m will be zero, as well as the demodulated output of the first demodulator. When Δø₀ is adjusted such that Δϕ is driven to zero, variation at ω_m will vanish, indicating that the phase shift ϕ for the input polarization state of launch light 116 and the phase shift ϕ for the resonator polarization state match and Δϕ has been driven to zero or minimized.

As mentioned above, input light polarization servo 120 is operated to drive both Δε and Δϕ of light beam 113 to zero. To ensure maximum matching of the input polarization state to the resonator polarization state, the relative amplitudes of the x-component and the y-component of the input polarization state may be adjusted to drive Δε towards zero. To minimize Δε, input light polarization servo 120 also comprises a tunable ½ waveplate 122 positioned within the path of the light beam 113 prior to the ring resonator 110.

In the example embodiment shown in Figure 1, a driving voltage may be applied to tunable ½ waveplate 122 which causes tunable ½ waveplate 122 to rotate its optical axis, thus affecting the relative amplitudes of the X-component and the Y-component of launch light 116. It would be appreciated that a ½ waveplate typically operates to take linear light and rotate the plane of linear polarization of that light. In the present case, the input state is very near linear, but does comprise an X-component and Y-component. Here rotating the axis of the ½ waveplate operates to shift part of the X-component light to the Y-component, and part of the Y-component light to the X-component. In this way, the relative amplitudes of the X and Y components are altered by the ½ waveplate 122.

This driving voltage that controls tunable ½ waveplate is derived from a feedback signal responsive the peak optical intensity of light received at photodetector 114. Optical intensity observed by photodetector 114 is sampled and converted into an electrical signal which is fed into a sampling analog-to-digital converter 171 within the input light polarization servo 120. The output of photodetector 114 as a function of time will comprise a DC component with a sinusoidal ripple riding on the DC component due to the application of modulation frequency ω_m by modulator 124. Input light polarization servo 120 is configured to capture the maximum optical intensity level observed during each cycle of modulation frequency ω_m and average that maximum optical intensity level over time to arrive at what is referred to herein as the peak optical intensity. Averaging the measured maximum optical intensity levels over time provides the benefit of averaging out random noise sources that may cause spikes observed during individual cycles.

More specifically, analog-to-digital converter (A/D) 171 generates optical intensity sample data that is stored in memory 172. Samples are captured and stored at a sufficient frequency to capture details such as the waveform peak of the electrical signal. For example, in one embodiment, samples of the electrical signal are obtained at a rate of 1000x per cycle of the modulation frequency ω_m. Memory 172 stores sample data covering a sufficient number of cycles so that averaging the cycles of sample data stored in memory 172 effectively averages out random noise captured during individual cycles. For example, in some embodiments, memory 172 stores between 10 to 100 cycles of sample data. Alternately, in other embodiments, memory 172 may store an average of previously captured cycles and a weighted average is performed with data samples for the most recently captured cycle or cycles. The averaging of sample data stored in memory 172 is performed by processor 174 in order to arrive at the value of the peak optical intensity. Processor 172 further drives tunable ½ waveplate 122 via a waveplate controller 175 to maximize the peak optical intensity of light received at photodetector 114. That is, waveplate controller 175 produces the driving voltage that controls tunable ½ waveplate 122 based on a control signal from processor 172. Maximizing peak optical intensity of light received at photodetector 114 results in driving Δε to zero.

In one embodiment, processor 172 maximizes peak optical intensity by observing the effects adjusting tunable ½ waveplate 122 has on the observed peak optical intensity. For example, if rotating the axis of tunable ½ waveplate 122 in one direction produces an increase in peak optical intensity, then peak optical intensity prior to the adjustment was not maximized. When a control point is found such that rotating the plane of linear polarization in either direction from that control point will produce a decrease in peak optical intensity, then peak optical intensity at that control point is maximized.

In one embodiment the 1^st feedback loop used for controlling Δϕ is operated at higher bandwidth than the 2^nd feedback loop used for controlling Δε. Keeping the two loops separated in frequency space can be utilized to avoid conflicts between them. For example, in one embodiment where the 1^st harmonic feedback loop operates with 100Hz bandwidth, the 2^nd harmonic feedback loop operates with 1-10Hz since variations in phase error may be expected to occur at a greater frequency that variations in the relative amplitude error.

As explained above, the two major variables in the input polarization state of launch light 116, the polarization components' relative phase and amplitude, are adjusted to match that of the resonator polarization state of ring resonator 110. By controlling these variables in the launch light to match the resonator eigenstate, maximum power is coupled into the ring resonator 110 for maximum signal to noise, bias instabilities associated with interference from excitation of the second eignestate of the resonator are minimized or eliminated, and intensity fluctuations inside the resonator that give rise to optical Kerr effect variations (another bias instability mechanism) may be minimized.

Figure 2 is a flow chart that illustrates a method 200 on one embodiment of the present disclosure for operating a polarization matched resonator fiber optic gyroscope. In one embodiment, the method 200 is performed using the elements shown in Figure 1. In other embodiments, other elements may be utilized. Accordingly, any features, alternatives and optional implementations described with respect to Figure 1 would be applicable to the method 200 of Figure 2 and vise-verse. Further, method 200 describes a process that may be applied to either the cw or ccw operation of an RFOG. Therefore, an RFOG configured to utilize method 200 can be expected to simultaneously perform two independent instances of method 200, one implemented with respect to the cw circulation of light in the ring resonator, one implemented with respect to the ccw circulation of light in the ring resonator.

The method begins at 210 with launching a polarized light beam into a fiber optic ring resonator. The polarized light may originate from a light source, such as a tunable laser that produce monochromatic light beams. The method continues to 220 with detecting an optical intensity from an output of the fiber optic ring resonator. Observing the signal from the output of the ring resonator is believed to provide the best representation of how well the input light polarization state is matched to the resonator's true polarization state. The method proceeds to 230 with modulating a phase shift between two components of the polarization state of the polarized light beam with a birefringence modulator at a modulation frequency of ω_m. In one embodiment, the birefringence modulator is driven by a voltage having two components. The first component is characterized by the time varying function Δø_mcos(ω_mt), where Δø_m is a selected amplitude and ω_m is the modulation frequency. The second voltage component is the DC offset voltage, Δø₀ derived from a feedback signal derived from the optical intensity measurements obtained in block 220. Accordingly, the method proceeds to 240 with driving the birefringence modulator to minimize a 1^st harmonic of the modulation frequency ω_m as observed from the optical intensity of the output of the fiber optic ring resonator. As discussed above in Figure 1, in one embodiment, the electrical signal produced by a photodetector measuring the optical intensity of the output of the fiber optic ring resonator can be demodulated at the modulation frequency ω_m in order to observe the 1^st harmonic. Minimizing this first harmonic will drive Δø to zero, matching the phase angle between components of the launched light input polarization state to that of the resonator polarization state.

The method proceeds to 250 with controlling a tunable ½ waveplate to adjust a relative amplitude of a first polarized component of the polarized light beam with respect to a second polarized component of the polarized light beam. To ensure maximum matching of the input polarization state to the resonator polarization state, the relative amplitudes of the x-component and the y-component of the input polarization state can be adjusted to drive Δε to zero. In the example embodiment shown in Figure 1, a voltage is applied to tunable ½ waveplate 122 which causes tunable ½ waveplate 122 to rotate its optical axis, affecting the relative amplitudes of the X-component and the Y-components of launch light 116. Accordingly the method proceeds to 260 with driving the tunable ½ waveplate to maximize a peak optical intensity as observed from the output of the fiber optic ring resonator. In one embodiment, the optical intensity observed at block 220 is converted into an electrical signal which is sampled and stored in a memory. A processor may then determine a peak optical intensity, which can be calculated by averaging or otherwise statistically analyzing data samples captured over a plurality of modulating frequency ω_m cycles. A non-maximized peak optical intensity evidenced by observing the output of the ring resonator indicates that the relative amplitudes of the input polarization state components of launch light do not match those of the resonator polarization state. Accordingly, the tunable ½ waveplate at block 260 is therefore driven to generate feedback that drives the fiber optic resonator ring 110 to maximize peak optical intensity, which results in driving Δε to zero.

Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement, which is calculated to achieve the same purpose, may be substituted for the specific embodiment shown. Therefore, it is manifestly intended that this invention be limited only by the claims.