Resonator optical gyroscope having input beam modulation optimized for high sensitivity and low bias
Systems and methods for optimizing input beam modulation for high gyro sensitivity and low bias errors. The present invention is a resonator optical gyroscope having an optimized phase-modulation amplitude (frequency) for a selected modulation frequency (amplitude) that maximizes the gyro signal-to-noise (S/N) sensitivity. For selected values of the phase modulation amplitude, the polarization cross-coupling induced intensity modulation can be nulled. By setting the phase modulation amplitudes substantially close to these nulling points (e.g. M=3.832 or 7.016 radians, which causes the first order Bessel function to be zero J 1 (M)=0) and then optimizing the modulation frequency, the intensity modulation induced bias is reduced to zero and gyro S/N sensitivity is maximized.
1. A method for reducing modulator intensity modulation-induced bias error in a resonator optical gyroscope, the method comprising:
a. determining a set of phase modulation amplitudes where a Bessel function J1(M) of a sinusoidal phase modulation of an input light beam equals approximately zero, the determination based on parameters of the resonator optical gyroscope;
b. selecting a phase modulation amplitude M from the set of phase modulation amplitudes;
c. applying the selected phase modulation amplitude to the input light, thus reducing the intensity modulation-induced bias error;
d. generating a response from a demodulated first harmonic signal of the resonator output light based on at least one of a plurality of gyro parameter values and the selected phase modulation amplitude;
e. determining a phase modulation frequency that maximizes the generated response; and
f. applying the selected phase modulation amplitude and frequency to the input light of the resonator gyro, thus reducing the intensity modulation-induced bias error and increasing the gyro rate measurement sensitivity.
2. The method of claim 1 , further comprising:
varying at least one of the plurality of gyro parameters; and
repeating (c), (d) and (e).
3. The method of claim 1 , wherein the phase modulation frequency is determined by the phase modulation frequency that maximizes the generated response.
4. The method of claim 1 , wherein the gyro parameters include at least one of resonator parameters and laser parameters.
5. A system for sensing rotation rate, comprising:
at least one light source;
at least one phase modulator configured to receive a light beam from the light source, and to operate at a phase modulation amplitude that minimizes bias offset in the demodulated first harmonic signal due to polarization cross coupling;
a resonator configured to receive a modulated light beam from the phase modulator;
a detector configured to detect resonator output light; and
a processor configured to:
determine a set of phase modulation amplitudes where a Bessel function J1(M) of a sinusoidal phase modulation of an input light beam equals approximately zero, the determination based on parameters of the resonator:
select a phase modulation amplitude M from the set of phase modulation amplitudes;
provide the selected phase modulation amplitude to the at least one phase modulator;
generate a response from a demodulated first harmonic signal of the resonator output light based on at least one of a plurality of resonator values and the selected phase modulation amplitude;
determine a phase modulation frequency that maximizes the generated response: and
provide the selected phase modulation amplitude and frequency to the at least one phase modulator.
6. The system of claim 5 , wherein the phase modulator further operates at a phase modulation frequency that substantially increases gyro measurement sensitivity.
7. The system of claim 5 , wherein the phase modulators for different input light operate at slightly different phase modulation frequencies that are substantially close to a frequency that maximize sensitivity.
8. A method for reducing modulator intensity modulation-induced bias error and increasing measurement sensitivity in a resonator optical gyroscope, the method comprising:
a. determining a set of phase modulation amplitudes where a Bessel function J1(M) of a sinusoidal phase modulation of an input light beam equals approximately zero, the determination based on parameters of the resonator optical gyroscope;
b. selecting a phase modulation amplitude M from the set of phase modulation amplitudes;
c. generating a response from a demodulated first harmonic signal of the resonator output light based on at lease one of resonator parameters and laser parameters and the selected phase modulation amplitude;
d. determining a phase modulation frequency that maximizes the generated response;
e. varying at least one of the plurality of resonator parameters and laser parameters;
f. repeating (b), (c), and (d), as desired, to further optimize the phase modulation frequency; and
g. applying the selected phase modulation amplitude and frequency to the input light, thus reducing the modulator intensity modulation-induced bias error and increasing gyro measurement sensitivity.