Method and system for correcting random walk errors induced by rate reversals in a dithered ring laser gyroscope

Abstract

A correction to the output angle of the ring laser gyroscope is calculated as a function of the phase difference and the magnitude of coupling between the two counterpropagating beams when the dither oscillations change direction. A pair of heterodyne detectors produce heterodyne signals indicative of the interference pattern between the counterpropagating beams. A signal indicative of the sum of the separate beam intensities is demodulated with the heterodyne signals to determine the magnitude of coupling between the beams in the ring laser gyroscope.

Description

BACKGROUND OF THE INVENTION

This invention relates generally to rotation sensors and particularly to ring laser gyroscope rotation sensors. Still more particularly, this invention relates to apparatus and methods for reducing the random walk error of a ring laser gyroscope caused by the tendency of the counterpropagating beams of ring laser gyroscopes to lock to a common frequency at low rotation rates.

A ring laser gyroscope employs the Sagnac effect to detect rotation. Two counter propagating light beams in a planar closed loop will have transit times that differ in direct proportion to the rotation rate of the loop about an axis perpendicular to the plane of the loop. The loop need not be planar, but the planar ring laser gyroscope has the simplest type of optical path.

There are in general two basic techniques for utilizing the Sagnac effect to detect rotations. A first technique is the interferometric approach, which involves measuring the differential phase shift between two counterpropagating means injected from an external source, typically a laser, into a Sagnac ring. The ring may be defined by mirrors that direct the light beams around the path or by a coil of optical fiber. Beams exiting the path interfere and create a pattern of light and dark lines that is usually called a fringe pattern. Absolute changes in the fringe pattern are indicative of rotation of the ring. The primary difficulty with such devices is that the changes are very small for rotation rates of interest in guidance applications.

The ring laser gyroscope uses the resonant properties of a closed cavity to convert the Sagnac phase difference between the counter propagating beams into a frequency difference. The high optical frequencies of about 10¹5 Hz for light used in ring laser gyroscopes cause the minute phase changes to become beat frequencies that are readily measured.

A ring laser gyroscope has a sensor axis that passes through the closed paths traversed by the counterpropagating beams. When the ring laser gyroscope is not rotating about its sensor axis, the optical paths for the two counterpropagating beams have identical lengths so that the two beams have identical frequencies. Rotation of the ring laser gyroscope about its sensor axis causes the effective path length for light traveling in the direction of rotation to increase while the effective path length for the wave traveling opposite in direction to the rotation decreases.

Ring laser gyroscopes may be classified as passive or active, depending upon whether the lasing, or gain, medium is external or internal to the cavity. In the active ring laser gyroscope the cavity defined by the closed optical path becomes an oscillator, and output beams from the two directions can be combined to beat together to give a beat frequency that is a measure of the rotation rate. The oscillator approach means that the frequency filtering properties of the cavity resonator are narrowed by many oders of magnitude below the passive cavity and give very precise rotation sensing potential. To date the major ring laser gyroscope rotation sensor effort has been put into the active ring laser. Presently all commercially available optical rotation sensors are active ring laser gyroscopes.

In the active ring laser gyroscope, the length of the closed optical path is controlled by means of at least one moveable mirror to maintain an intensity signals. The signals output from the detectors 50A and 50B are referred to herein as heterodyne signal A, or het A, and heterodyne signal B, or het B, respectively. The frequency difference, or beat frequency, of the two beams is seen as motion of the interference fringes across the detectors 50A and 50B. Accordingly, the direction of the motion of the fringes identifies the direction of rotation. Each full cycle of the interference pattern corresponds to 2π radians of phase, or a cycle of the beat frequency, and, therefore corresponds to fixed angular rotation increment. Each occurrence of a full cycle of the interference pattern generates a signal called a heterodyne count. For a ring laser gyroscope 10 having a 28 cm path length, the scale factor is about 1.8 arc seconds of rotation per heterodyne count.

The frequency of the beat signal produced when the two frequencies heterodyne at the detectors 50A and 50B is directly proportional to the rotation rate of the ring laser gyroscope 10 about its longitudinal axis. Referring to FIG. 4, when the rotation rate of a simple, unbiased ring laser gyroscope 10 is reduced to the lock-in threshold rate Ω_L, the counterpropagating beams lock at the same frequency. The frequencies of the counterpropagating beams are the same for a range of rotation rates ±Ω_L, which is the lock-in deadband shown in FIG. 4. The signal output from the ring laser gyroscope 10 becomes non-linear in the vicinity of the deadband, which is a departure from the output of an ideal ring laser gyroscope.

Referring to FIG. 5, lock-in is believed to be causes caused primarily by radiation backscattered from the mirrors 32-35. Since the counterpropagating beams strike each of the mirrors 32-35 at an angle of incidence of 45°, there would be no backscattered radiation from ideal, perfectly flat mirrors. The main portion of each beam is forward reflected from the mirror 32, for example, according to the laws of reflection. However, even though the mirrors 32-35 are of very high quality, surface imperfections cause some specular reflection of each beam in all directions. Light from one beam that is backscattered into an acceptance solid angle for the oppositely directed beam couples thereto. The acceptance solid angle depends upon the wavelength of the light and the diameter of the cavity 30. For a typical square ring laser gyroscope 10 having a 45° angle of incidence, about one part in 10⁶ of the total specular reflection from any one of the mirrors 32-35 is scattered into the acceptance angle of the counterpropagating beam.

Referring to FIG. 6A, the output of the detector 50 as a function of time is sinusoidal when the rotation rate is far from the lock-in threshold. Referring to FIG. 6B, when the rotation rate is near the lock-in threshold, the output of the detector 50 is distorted from the desired sinusoidal waveform. For a typical ring laser gyroscope having a cavity length of 49 cm, the lock-in threshold is about 100°/hr. Therefore, obtaining satisfactory results from the ring laser gyroscope 10 requires avoidance not only of lock-in but also avoidance of the rotation rates near the deadband.

The different equation relating the input rate, the output rate and the lock-in error is

Ψ=ω+B_L sin (Ψ) (1)

where:

Ψ is the frequency difference between the counterpropagating beams;

Ψ is the phase difference in radians between the counterpropagating beams;

ω is the input rotation rate; and

B_L is the lock-in rate.

The above equation facilitates understanding of the lock-in phenomenon. For ω≦B_L, there is a value of Ψ such that Ψ=0, and there are no output counts from the ring laser gyroscope 10. A typical value of B_L is 0.1°/sec, which is many times the earth's rotation rate. If an oscillatory bias is applied to the ring laser gyroscope 10 by mechanically dithering the frame, the input rotation rate is

ω=ω₀ +B_m cos(ω_D t) (2)

and the phase difference is

Ψ=ω_o +B_m cos(ω_D t)+B_L sin Ψ(3)

wherein

ω₀ =non-dither input rate;

ω_D =dither angular frequency; and

B_m =dither depth rate, which is the maximum value of the dither angular velocity per cycle of dither.

Even with dither the residual effects of coupling between the counter propagating beams are not negligible. For low rotation rates an error arises in the ring laser gyroscope 10 at points of reversal of the direction of the dither oscillations. This error is cumulative and is a major source of error in ring laser rotation sensors. The nature of the residual lock-in error is a random walk in the output angle of the ring laser gyro. Output random walk is analytically described as white noise in angle rate, and is parameterized by the laser gyro random walk coefficient. The mathematical relationship between the lock-in coefficient, B_L, the dither parameters, and the random walk coefficient is derived by Hammons and Ashby, "Mechanically Dithered RLG at the Quantum Limit", IEEE NAECON 1978, which is hereby incorporated by reference into the present disclosure. Equation (3) above for the counterpropagating beam phase difference of the dithered laser gyro is used to calculate the random accumulative error of the lock-in error term B_L sin Ψ. In a similar manner it is possible to analytically calculate the contribution of the error term for each pass through the lock band which occurs twice per dither cycle. It is found that the error for each pass through the lock band may be written as

ΔΨ=B_L [2π(B_m ω_D)-1 ]^1/2 sin(Ψ_T ±π/4) (4)

where Ψ_T is the value of the phase difference of the counterpropagating beams at the instant of turnaround and the choice of sign for the π/4 term is determined by the direction of reversal at turnaround: ccw to cw or cw to ccw.

It is therefore theoretically possible to calculate the residual dither error and thereby form a correction for every turnaround. This correction is to be summed to the output counts of the gyroscope. The dither parameters ω_D and B_m are controlled variables which vary a few percent from cycle to cycle. A method of control is described in U.S. patent application No. 448,363, which is mentioned in the Background of the Invention section of this disclosure and hereby incorporated by reference into this disclosure. For the purposes of forming a correction the dither variables may be taken as their average values. The key variables to form the correction are the value of Ψ_T at each turnaround and the value of the lock-in rate, B_L, which is a measure of the coupling (backscattering) between the beams.

Since the phase difference between the beams is measured by means of optical interference at the heterodyne detector, the two deterodyne detector outputs become the basis for detecting turnarounds. A difficulty with using a turnaround phase difference, φ_H, derived from the heterodyne signals is that the heterodyne is offset from the coupling phase by a phase value, ε, that is a function of the optical placement of the heterodyne detector. This offset may be written as Ψ_T =φ_H +ε. Further, the magnitude of the correction must be properly scaled to the magnitude of the coupling coefficient, B_L, between the two beams. Both ε and B_L are functions of the time and temperature. The present invention comprises an apparatus and a method for determining the phase value ε and the magnitude of the coupling coefficient B_L from the sum of the intensity fluctuations of the individual beams using synchronous demodulation techniques with the two heterodyne signals as references.

The physical coupling of the two counterpropagating beams affects both the frequency difference of the two beams and the intensity of the two beams with the input rate as the driving factor. The laser gyro equations for the frequency and intensity modulations along with experimental results may be found in several sources, for example in Aronowitz and Lim, "Positive Scale Factor Correction in the Laser Gyro" IEEE Journal of Quantum electronics, Vol. QE-13, No. 5, May, 1977. It is the method of this article, and other similar literature articles, to rewrite the basic ring laser equations for the single beam intensities and single beam frequencies in terms of a sum of intensity variable and a difference of frequency variable. The frequency pulling effects due to lock-in can be associated with the sum intensity variable under appropriate simplifying assumptions. In the development of the present invention it was discovered that for the class of ring laser gyroscopes described herein, the physically derived sum intensity signal may be used to derive the coupling variables required to perform a turnaround correction.

FIG. 7 shows the basic concept of the present invention. The mounting block 49 shown on FIG. 2 separates the laser beams into two discrete beams rather than causing them to interfere as is the case with the prism 48. The two beams labelled CW and CCW in FIG. 7 may be processed to the control length of the cavity 30. In the present invention these separate beams are also used to monitor the phase relationship between the two counterpropagating beams in the ring laser gyroscope 10 and the heterodyne detectors 50A and 50B. These separate beam are further used in the present invention to determine the magnitude of the coupling between the two counterpropagating beams in the ring laser gyroscope 10. The electrical signals indicative of the separate light beams are added together and demodulated with the heterodyne signals from the detectors 50A and 50B. The demodulated signals are processed to determine the phase relationships between the heterodyne signals and the sum signal. The magnitudes of the demodulated signals can be used to establish the scale of the angular correction. The heterodyne signals are input to a turnaround detector 90, which produces a signal indicative of the phase φ_H at turnaround and a signal indicative of the rotation sense of each turnaround. The heterodyne signals are output from the turnaround detector 90 to an intensity demodulator 92, which also receives signals indicative of the intensities of the single beams propagating in ring laser gyroscope 10.

FIG. 8 is a block diagram of the intensity demodulator 92 of FIG. 7. Referring to FIG. 8, the two separate signals CW and CCW, which are indicative of the separate beam intensities, are transmitted by partially reflecting mirror 99, detected and input to a pair of amplifiers 100 and 102, respectively. The amplifiers have gains that are adjustable to compensate for differences in photodetector response. The outputs of the amplifiers 100 and 102 are summed and then input to a highpass filter 104 to reduce the error caused by imbalances that may still exist in the gains of the amplifiers 100 and 102. The amplified intensity sum signal is monitored with suitable monitoring means such as an oscilloscope 106 to determine whether it is necessary to adjust the gains of the amplifiers 100 and 102. The sum signal is amplified by a variable gain amplifier 108 with the gain of the amplifier 108 being adjusted to avoid clipping of the sum signal at the maximum value thereof, which is ordinarily a function of temperature. It is necessary to adjust the gains of amplifiers 100, 102, and 104 only for initial calibration. Once the gains are set no further adjustment is necessary.

The output of the amplifier 108 is input to a pair of demodulators 110 and 112 that also receive inputs from the heterodyne detectors A and B, respectively. The outputs of the demodulators 110 and 112 are input to low pass filters 114 and 116, respectively. The outputs of the low pass filters 114 and 116 are sampled to obtain a sum A signal and a sum B signal, respectively.

FIG. 9 graphically displays data taken with the ring laser gyroscope 10 to show the effect of the turnaround correction method of the invention as a function of temperature. The graphs include plots of the parameters ε and B_L of the sum signal as functions of temperature. Temperature, random walk coefficients, and sum signal parameters are plotted using appropriate units and scale factors. The graphs of FIG. 9 shows that the random walk coefficient as a function of temperature has the same general variation as the magnitude of the sum signal. Therefore, the magnitude of the sum signal may be processed to determine the random walk coefficient. The random walk coefficients were calculated every minute based upon sixty samples, each taken for a time of one second. For this gyro the optical phase of the heterodyne signal is seen to rotate a full cycle for each 3°C temperature change. The turnaround correction to the output signal was generated for each dither turnaround as

ΔΨ_correction =B_L [2π(B_m ω_d)-1 ]^1/2 sin(φ_H +ε±π/4), (5)

where the variables are previously defined. The sign of the π/4 term in the above equation depends upon whether the turnaround is ccw to cw or cw to ccw. The positive sign is used when the turnaround is cw to ccw.

The turnaround correction of the present invention is based upon the theory that the accumulating beat phase error is predictable from the beam intensity fluctuations. The turnaround correction method comprises determining the turnaround points and sampling the appropriate signals related to the beam intensity to generate a correction signal. The corrections for each turnaround are accumulated and added to the heterodyne pulse counts when the magnitude of the correction exceeds the count resolution.

The present invention provides the capability of removing all of the residual body dither error so that only the quantum limit of about 3×10-4° (hr)-0.5 contributes to the rate noise. In practice, however, the accuracy of measuring the turnaround and variations of dither motion limit the improvement.

Referring to FIG. 9, the random walk coefficient calculated for the corrected gyro samples shows that the phase error is not random, but is sinusoidally related to the turnaround point. The residual dither error may be calculated if both the phase of the beat signal at each turnaround and the lock-in coefficient B_L are known. Since the ring laser gyroscope 10 is typically dithered at a frequency of about 400 Hz and since there are two turnarounds per dither cycle, the turnaround phase must be determined at twice the dither frequency or at about 800 Hz.

The fluctuations in the beam intensities are directly related to the instantaneous beat phase and amplitude. However, the intensity modulation is only about 1% to 5% of the total intensity of each beam, and the intensities are noisy because of other electrical and mechanical effects that modulate the beams. In theory it is possible to detect the turnaround and turnaround phase in the phase of the separate beams. In practice, it is easier to detect the turnaround and turnaround phase by means of the two heterodyne signals, which provide a direct measure of the beat phase at the location of the heterodyne detectors 50A and 50B. Use of the heterodyne signals has the disadvantage that the turnaround phase of the heterodyne signals is not identical to the coupling phase of the beams, but is offset by a fixed phase amount that is determined by the geometry of the placement of the detectors 50A and 50B. This phase offset can be determined by means of feedback circuitry described subsequently. The feedback circuitry also provides a measure of the amplitude of cross beam coupling that may be used to provide a measure of the lock-in coefficient and scale the correction.

FIG. 11 graphically illustrates the analog signals representative of the output of the two heterodyne photodetectors immediately before and after a turnaround. FIG. 11 also shows the squared logic signals that may derived from the heterodyne signals for the purpose of driving the output logic counters. Typical practice is to assign a count value to each edge of the two squared signals by means of discrete hardware logic. By this means the normal 2 arc second scale factor per complete fringe motion is scaled to 0.5 arc second per count. FIG. 11 shows the reversal of lead and lag between the heterodyne A signal and the heterodyne B signal that occurs at turnaround. At the point of turnaround the rate of change (slope) of each analog signal is zero. This characteristic is used to detect the turnaround point for the purpose of sampling the heterodyne signals at turnaround.

The circuitry also generates a ready signal and a rotation sense signal. The ready signal notifies the computer that data is ready for processing. The rotation sense signal is indicative of which turnaround (ccw/cw or cw/ccw) was detected. The computer uses the track signal to return the turnaround detect circuit to the tracking mode after completing the processing of a turnaround. The magnetic pickoff signal provides the rotation sense signal and also provides means for detecting the velocity of the dither oscillations. Limiting the period of turnaround detection to the portion of the dither having the lower absolute value of the rate eliminates false detections of simultaneous zero slopes at high rates. A further advantage of the circuitry is that no turnaround is indicated when input rotation rates move the inertial turnaround away from the dither turnaround and outside a predetermined velocity range.

In the ring laser gyroscope 10, the length of the cavity is controlled by translating the mirror 33 to shorten or lengthen the cavity. The cavity changes length as the temperature of the frame changes. These changes in length change the resonant frequency of the cavity, which should be held constant, U.S. Pat. No. 4,383,763 which issued May 7, 1983 to Hutchings et al., assignees to Litton Systems Inc. describes apparatus and method for controlling the path length of the ring laser gyroscope 10 by flexing a mirror. That patent is hereby incorporated by reference into the present disclosure. Other cavity length control techniques may be used with the present invention. U.S. patent application No. 656,944, filed Oct. 2, 1984 for Pathlength Controller for Ring Laser Gyro and assigned to Litton Systems, Inc. describes a pathlength control system that may be used with the present invention. That application is incorporated by reference into this disclosure.

Referring to FIG. 10, the mirror 33 may be formed as a diaphragm. The outer edges 150 of the mirror 33 are connected to a generally cylindrical support 152. A generally cylindrical post 156 extends from the back of the central portion of the mirror 33. An annular cavity 158 is between the support 152 and the post 156. The region of the mirror 33 adjacent the cavity 158 is very thin and permits axial movement of the center of the mirror 33 and the post 156. A thin membrane 160 supports a bearing member 162 adjacent an end 164 of the post 156. A plurality of piezoelectric transducers 164 are mounted to the sides of the thin membrane 160 so that application of a voltage to them causes the membrane 160, the bearing member 162, the post 156 and the mirror 33 to move along the axis of the post 156.

FIG. 12 is a block diagram of the circuitry that may comprise turnaround detector 90 of FIG. 7. A signal representative of the rate of change of each of the heterodyne signals is formed by differentiating circuits 200 and 202. The two differentiated signals are input to an AND gate 204 to determine the instant of each turnaround. The period in which a valid simultaneous detection of zero slope of the two heterodyne signals is accepted as a valid turnaround is restricted by forming a velocity window 210 based on the magnetic pickoff 60. The magnetic pickoff 60 produces electrical signals that depend upon the angular velocity of the frame 20 relative to the support 12. The purpose is to avoid spurious detection of turnarounds. The heterodyne signals are input to sample and hold circuits 206 and 208, which latch to the values of the heterodyne signals at the sampling time. A logic value representative of the rotation sense (direction of turnaround) is also latched along with a ready signal to provide input to a computer (not shown) that a turnaround has been detected. By means of trigonometric logic using the sampled value of het A (heterodyne A) and het B, the phase of the heterodyne turnaround φ_H is determined with reference to het A. The het A and het B signals represent the sampling of a sinusoid at intervals 90° apart. This logic includes an estimation function of the peak magnitude of het A. Thus, build variation or slow time variation of the magnitude of het is not a limiting factor of the invention. The track logic signal discrete resets the turnaround detector in the state to detect the next turnaround after the computer has read the sampled signals.

Alternate methods of detecting the turnarounds and determining the phase of the turnarounds in the heterodyne signals are possible without departing from the scope of this invention. The squared heterodyne signals may also be used to detect heterodyne turnaround phase. Referring again to FIG. 11, the sense of the counts changes from +1 to -1 after the gyro reverses direction. The time intervals T_A and T_B may be recorded and used to calculate the phase value of the heterodyne turnaround based upon the known parameters of the dither motion.

The method of this invention may be applied to ring laser gyros that are not sinusoidally dithered. For example the method described may be applied to generate corrections for a rate biased gyroscope whose rate is periodically reversed. The analytic form of the correction at each reversal is then

ΔΨ=B_L [2π(kα)-1 ]^1/2 sin(φ_H +ε±π/4)

Where α is the acceleration of the gyro at turnaround, and K is the scale factor of the gyro.

Claims

1. A method for correcting random walk errors caused by coupling between two counterpropagating light beams in a ring laser gyroscope that is body dithered at a frequency ω_d about a sensor axis at a dither depth b_m, the ring laser gyroscope forming a beat signal by interference of the two counterpropagating light beams to indicate rotation by an angle Ψ about the sensor axis, comprising the steps of:

(a) producing a pair of heterodyne signals that are indicative of the phase difference between the two counterpropagating light beams;

(b) sampling the heterodyne signals to determine the phase difference Ψ_T =φ_H +ε between the two counterpropagating light beams at rate reversals of the ring laser gyroscope;

(c) adding signals indicative of the intensities of the two counterpropagating light beams to produce an intensity sum signal;

(d) demodulating the intensity sum signal with at least one of the sampled heterodyne signals from step (b);

(e) processing the demodulated intensity sum signal to determine the magnitude b_L of coupling between the two counterpropagating light beams; and

(f) calculating a correction to the angle of rotation as a function of the coupling b_L between the two beams and the phase difference Ψ_T =φ_H +ε between the two counterpropagating light beams at rate reversals of the ring laser gyroscope.

2. The method of claim 1, further including the step of determining whether the change in direction at rate reversals is counterclockwise to clockwise or clockwise to counterclockwise.

3. The method of claim 1, wherein the step of determining the magnitude of the coupling between the beams includes the steps of:

detecting changes in direction of the dither oscillations;

measuring the intensity of a first one of the beams;

measuring the intensity of the other of the beams; and

adding signals indicative of the intensities of the two beams to form a sum signal.

4. The method of claim 3, further including the step of:

forming a heterodyne signal indicative of the beat frequency produced when the counterpropagating beams interfere with one another; and

demodulating the sum signal with the heterodyne signal.

5. The method of claim 1 wherein the step of calculating a correction to the angle of rotation includes calculating a correction angle according to the equation ΔΨ_correction =B_L [2π(b_m ω_d)^{-1 ]1/2 sin (φ_H +ε±π/4).}

6. A system for correcting random walk errors caused by coupling between two counterpropagating light beams in a ring laser gyroscope that is body dithered counterpropagating light beams in a ring laser gyroscope that is body dithered at a frequency ωhd d about a sensor axis at a dither depth b_m, the ring laser gyroscope forming a beat signal by interference of the two counterpropagating light beams to indicate rotation by an angle Ψ about the sensor axis, comprising:

means for producing a pair of heterodyne signals that are indicative of the phase difference between the two counterpropagating light beams;

means for sampling the heterodyne signals to determine the phase difference Ψ_T =φ_H +ε between the two counterpropagating light beams at rate reversals of the ring laser gyroscope;

means for adding signals indicative of the intensities of the two counterpropagating light beams to produce an intensity sum signal;

means for demodulating the intensity sum signal with at least one of the heterodyne signals corresponding to the most recent rate reversal of the ring laser gyroscope;

means for processing the demodulated intensity sum signal to determine the magnitude b_L of coupling between the two counterpropagating light beams and;

means for calculating a correction to the angle of rotation as a function of the coupling b_L between the two beams and the phase difference a rate reversals of the ring laser gyroscope.

7. The system of claim 6, further including means for determining whether the change in direction at rate reversals is counterclockwise to clockwise or clockwise to counterclockwise.

8. The system of claim 6, wherein the means for determining the magnitude of the coupling between the beams includes:

means for detecting changes in direction of the dither oscillations;

means for measuring the intensity of a first one of the beams;

means for measuring the intensity of the other beams; and

means for adding signals indicative of the intensities of the two beams to form a sum signal.

9. The system of claim 8, further including:

means for forming a heterodyne signal indicative of the beat frequency produced when the counterpropagating beams interfere with one another; and

means for demodulating the sum signal with the heterodyne signal.

10. The system of claim 6 wherein the means for calculating a correction to the angle of rotation includes means for calculating a correction angle according to the equation

ΔΨ_correction =B_L [2 π(b_m ω_d) ^{-1 ]1/2 sin (φ_H +ε±π/4).}

11. A system for correcting random walk errors in a ring laser gyroscope that is body dithered at a frequency ω_d and a dither depth b_m about a sensor axis, a beat signal formed by interference of two counterpropagating light beams indicating rotation of an angle Ψ about the sensor axis, comprising:

means for producing a pair of heterodyne signals indicative of the light intensity resulting from interference of the two light beams;

a turnaround detector connected to the means for producing a plurality of heterodyne signals, the turnaround detector including means for detecting phases of the heterodyne signals when the dither oscillations change direction and including means for determining whether the change in direction of the dither oscillations is clockwise to counterclockwise or counterclockwise to clockwise;

means for producing an intensity sum signal indicative of the sum of the intensities of the two light beams; and

an intensity demodulator means for demodulating the intensity sum signal with the heterodyne signals output from the turnaround detector, the intensity demodulator including means for determining the magnitude of coupling between the two light beams and for determining the phase difference between the heterodyne signals and the intensity sum signal.

12. A method for reducing the random walk error of a ring laser gyroscope being body dithered at a frequency ω_d and having a dither depth b_m about a sensor axis with a beat signal formed by interference of two counterpropagating light beams indicating rotation of an angle Ψ about the sensor axis, comprising the steps of:

measuring the phase of optical signals input to a pair of heterodyne detectors which detect the interference of the two counterpropagating beams;

producing an intensity sum signal indicative of the sum of the intensities of the two counterpropagating light beams;

measuring temperature-induced changes in phase of the intensity sum signal; and

processing the temperature-induced changes in phase of the intensity sum signal to calibrate the output of the ring laser gyroscope to compensate for temperature-induced phase changes in the two counterpropagating beams.

13. The method of claim 12, further including the steps of:

accumulating the temperature-induced phase difference as integer multiples of 2π; and

associating each complete 2π change in the temperature-induced phase difference with a one count error in the output of the ring laser gyroscope.

14. A system for reducing the random walk error of a ring laser gyroscope being body dithered at a frequency ω_d and having a dither depth b_m about a sensor axis with a beat signal formed by interference of two counterpropagating light beams indicating rotation of an angle Ψ about the sensor axis, comprising the steps of:

means for measuring the phase of optical signals input to a pair of heterodyne detectors which detect the interference of the two counterpropagating beams;

means for producing an intensity sum signal indicative of the sum of the intensities of the two counterpropagating light beams;

means for measuring temperature-induced changes in phase of the intensity sum signal; and

processing the temperature-induced changes in phase of the intensity sum signal to calibrate the output of the ring laser gyroscope to compensate for temperature-induced phase changes in the two counterpropagating beams.

15. The method of claim 14, including:

means for accumulating the temperature-induced phase difference as integer multiples of 2π; and

means for associating each complete 2π change in the temperature-induced phase difference with a one count error in the output of the ring laser gyroscope.

16. A method for producing a signal for measuring rotation of a ring laser gyroscope about a sensing axis in which two waves propagate in opposite directions in a closed cavity and interfere to form an interference pattern that is indicative of the rotation rate of the ring laser gyroscope, comprising the steps of:

producing a pair of heterodyne signals that are indicative of the phase difference between the two counterpropagating light beams;

producing an intensity sum signal indicative of the sum of the intensities of the two waves;

high pass filtering the intensity sum signal;

demodulating the intensity sum signal with the heterodyne signals to produce a demodulated intensity sum signal; and

processing the demodulated intensity sum signal to calculate a correction term that compensates for errors in the rotation rate indicated by the interference pattern at rate reversals of the ring laser gyroscope.

17. The method of claim 16 including the steps of:

sampling the heterodyne signals at rate reversals in motion of the ring laser gyroscope about the sensing axis; and

processing the demodulated intensity sum signal to determine the magnitude of coupling between the two waves at rate reversals in motion of the ring laser gyroscope about the sensing axis. 18. The method of claim 17 including the steps of:

processing the heterodyne signals to detect rate reversals of the ring laser gyroscope;

determining the phase difference between the two counterpropagating light beams at rate reversals of the ring laser gyroscope; and

calculating a correction to the angle of rotation as a function of the coupling between the two beams and the phase difference between the two counterpropagating light beams at rate reversals of the ring laser gyroscope. 19. The method of claim 18 including the step of providing a velocity window to avoid making corrections to the angle of rotation at spurious rate reversals in the motion of the ring laser gyroscope about the sensing axis. 20. A system for producing a signal for measuring rotation of a ring laser gyroscope about a sensing axis in which two waves propagate in opposite directions in a closed cavity and interfere to form an interference pattern that is a function of the rotation rate of the ring laser gyroscope, comprising:

means for producing a pair of heterodyne signals resulting from interference of the two waves;

means for producing an intensity sum signal indicative of the sum of the intensities of the two waves;

means for high pass filtering the intensity sum signal;

means for demodulating the intensity sum signal with the heterodyne signals to produce a demodulated intensity sum signal; and

means for processing the demodulated intensity sum signal to calculate a correction term that compensates for errors in the rotation rate indicated by the interference pattern at rate reversals of the ring laser gyroscope.

21. The system of claim 20 including:

means for sampling the heterodyne signals at rate reversals in motion of the ring laser gyroscope about the sensing axis; and

means for processing the demodulated intensity sum signal to determine the magnitude of coupling between the two waves at rate reversals in motion of the ring laser gyroscope about the sensing axis. 22. The system of claim 21 including:

means for processing the heterodyne signals to detect rate reversals of the ring laser gyroscope;

means for determining the phase difference between the two counterpropagating light beams at rate reversals of the ring laser gyroscope; and

means for calculating a correction to the angle of rotation as a function of the coupling between the two beams and the phase difference between the two counterpropagating light beams at rate reversals of the ring laser gyroscope. 23. The system of claim 22 including means for providing a velocity window to avoid making corrections at spurious rate reversals in the motion of the ring laser gyroscope about the sensing axis.