Abstract:
A device and a method for suppressing 2nd order harmonic distortion in a Resonator Fiber Optic Gyroscope includes driving a laser to generate at least one of a plurality of counter propagating laser beams traveling through a fiber optic resonator according to a modulated signal. The modulated signal can be represented by a polynomial having two terms, and each of the two terms is suitably multiplied by a coefficient and a constant. A modulation amplitude adjuster amplifies the modulation signal by an amplification factor as it is used to drive the laser. When the amplification factor is suitably chosen to represent a square root of a ratio of the constants, the total harmonic distortion in the RFOG is minimized.

Description:
FIELD OF THE INVENTION 
     This invention relates generally to electronic gyroscopes and, more specifically, to instrumentation for implementing electronic gyroscopes. 
     BACKGROUND OF THE INVENTION 
     Gyros have been used to measure rotation rates or changes in angular velocity about an axis of rotation. 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 closed optical path, and the difference in the two pathlengths is proportional to the rotational rate that is normal to the enclosed area. 
     In a resonator fiber optic gyro (RFOG), the counter-propagating light beams are desirably monochromatic (e.g., in a single frequency) and circulate through multiple turns of the fiber optic coil and for multiple passes through the coil using a device that redirects light that has passed through the coil back into the coil again (i.e., circulates the light) such as a fiber coupler. The beam generating device modulates 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 condition such that all light-waves having traversed the coil a different number of times interfere constructively at any point in the coil. As a result of this constructive interference, an optical wave having a wavelength is referred to as “on resonance” when the round trip resonator pathlength is equal to an integral number of wavelengths. A rotation about the axis of the coil produces a different pathlength for clockwise and counterclockwise propagation, thus producing a shift between the respective resonance frequencies of the resonator, 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 closed optical path due to rotation, indicates the rotation rate. 
     The CW Laser inputs light into the resonator and the CW photodetector detects the CW output of the resonator. The electronics after the CW photodetector controls the CW laser frequency to a resonance frequency of the resonator. The resonance frequency is detected by modulating the laser frequency at f 1  and then demodulation the photodetector output at f 1 . At the resonance frequency the photodetector signal at f 1  passes through zero amplitude. The CW integrator controls the laser frequency via the CW laser driver to the resonance frequency by adjusting the laser frequency until the output of the demodulator is zero. The modulation at f 1  is electronically summed with the CW integrator output by a summer. The CCW laser is controlled to the CCW resonance frequency in a similar manner, except it is common that the modulation frequency f 2  is different than f 1  to eliminate errors that arise with light from one direction of propagation in the resonator inadvertently couples into the other direction. 
     Rotation rate is proportional to the difference between the CW resonance frequency and the CCW resonance frequency. It is common practice that the amplitude of the outputs of the modulation generators are set to maximize the sensitivity of the resonator output to laser frequency deviations from resonance frequency. Most rotation sensing errors are minimized when the modulation amplitude is set at or near the maximum sensitivity. However, rotation sensing errors associated with harmonic distortion most prevalent in 2 nd  order harmonics of the resonance frequency are simply amplified at the greater sensitivity, doing little to improve the performance of the RFOG. 
     An example of the interfering effects of the presence of a 2 nd  order harmonic is evident in  FIG. 1 . In a plot  3  of the modulation as a function of phase, a pure sine fundamental  5  is added to its 2 nd  order harmonic  7  to yield a new composite wave  9  that exhibits an apparent asymmetry about the x axis. This asymmetry appears as lower positive excursion in amplitude during the first half cycle and a higher negative excursion in amplitude during the second half cycle. This apparent asymmetry diminishes the accuracy of the RFOG by shifting the measured center frequency of the resonator. Because the difference between the clockwise and counter-clockwise resonance frequencies are the measure of the rotational acceleration in an RFOG, the presence of the 2 nd  order harmonic degrades the performance of the RFOG. 
     What is needed in the art is an RFOG that is configured to eliminate or minimize the interfering effects of 2 nd  order harmonics producing rotational errors. 
     SUMMARY OF THE INVENTION 
     A device and a method for suppressing 2nd order harmonic distortion in a Resonator Fiber Optic Gyroscope includes driving a laser to generate at least one of a plurality of counter propagating laser beams traveling through a fiber optic resonator according to a modulated signal. The modulated signal can be represented by a polynomial having two terms, and each of the two terms is suitably multiplied by a coefficient and a constant. A modulation amplitude adjuster amplifies the modulation signal by an amplification factor as it is used to drive the laser. When the amplification factor is suitably chosen to represent a square root of a ratio of the constants, the total harmonic distortion in the RFOG is minimized. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Preferred and alternative examples of the present invention are described in detail below with reference to the following drawings: 
         FIG. 1  is a graph to show the effect of harmonic distortion arising from the 2 nd  order harmonic; and 
         FIG. 2  is a schematic diagram of a RFOG exploiting the modulation amplitude adjuster to minimize 2 nd  order harmonic distortion. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The following detailed description of the invention is merely exemplary in nature and is not 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. 2  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  includes each of a pair of lasers  12   cw  and  12   ccw  assigned respectively as the clockwise and counter clockwise light sources respectively, assigned thus to indicate the direction which the beam each generates will enter and travel through a fiber optic ring resonator  18 . Each light beam emanates from the lasers  12   cw  and  12   ccw , each has a frequency, and each is modulated at a frequency in accord with signals originating at each of a pair of laser drivers  15   cw  and  15   ccw.    
     Optical ring resonators  18  include a waveguide in a closed loop coupled to one or more input and output waveguides. Most often, the resonator  18  is a single fiber optic strand wound to form a spiral, and then back on itself forming a tube. 
     having first and second ends. When light of the appropriate frequency is coupled to the loop by the input waveguide, it builds up in intensity over multiple round-trips due to constructive interference. The light can then be picked up by a detector. Since only some wavelengths resonate in the loop, the resonator also functions as a filter. 
     Thus the light beams each enter opposite ends to travel around the resonator in their respective directions, clockwise and counter clockwise. At each of the first and second ends, a photodetector  21   cw ,  21   ccw  detects the light wave traveling out of the resonator  18  in each of the two noted directions. 
     As earlier noted, the lasers  12   cw  and  12   ccw , each produce a light beam that is modulated at a frequency in accord with signals originating at each of a pair of laser drivers  15   cw  and  15   ccw . In turn, the laser drivers receive a signal that generates a modulating sine wave for purposes of modulating the frequency of the laser beams. For each direction, the signal is sinusoidally frequency-modulated according to a modulation generator  27   cw ,  27   ccw , the output at each photodetector  21   cw ,  21   ccw  must likewise be demodulated at a demodulator  24   cw ,  24   ccw  at the same frequency of the modulating sine wave. Thus, the demodulator  24   cw ,  24   ccw  coupled to the photodetector  21   cw ,  21   ccw  demodulates the outputs of the photodetector  21   cw ,  21   ccw  at the demodulator  24   cw ,  24   ccw  to measure resonance centers indicated by the light outputs of the CW and CCW beams. 
     The demodulated signal is approximately proportional to the frequency difference between the laser frequency and the resonance center. When the average laser frequency is on resonance center the demodulated signal will be zero. An integrator  30   cw ,  30   ccw  configures the signal to provide, in real time, an output signal that is the time integral of the input signal. Among many other applications, integrators today form the basis for extracting information from digital signals corrupted by noise. 
     One advantage of using this technique of two (or in some instances three) lasers is that it is straightforward to have the CW beam frequency adjusted to a different resonance of the resonator than the CCW beam frequency is adjusted to. Since the resonance frequencies of the ring optical resonator appear periodically every time an integer number of wavelengths fits into the optical pathlength of the resonator, the CW and CCW beam frequencies can be tuned to, for example, the frequencies where n and (n+1) wavelengths fit into the CW and CCW paths respectively, where n represents the integer number of wavelengths of light traversed in a round trip of the optical pathlength of the resonator. This alleviates rotation rate errors that can arise due to the backscattering of light from one beam into another. However, using a different number of wavelengths that form the different beams does introduce the optical pathlength of the ring resonator into the rotation rate measurement. Errors arising from the backscattering can be alleviated by incorporating a third laser beam (e.g., in the CCW direction at a frequency where n−1 wavelengths fit into the CCW optical pathlength of the resonator). 
     In either of the two or three laser configurations, rotation sensing errors can occur due to harmonic distortion. Harmonic distortion is nonlinear distortion characterized by the output of harmonics in a signal waveform that do not correspond with the input signal waveform. Harmonic distortion may be introduced at several components within the system but generally occur at modulation of the signal. 
     Rotational sensing errors are often associated with harmonic distortion of the modulation and most perniciously by the 2nd harmonic. The inventor has noted that the effects of harmonic distortion by introduction of the 2nd harmonic can be greatly reduced or eliminated when using a designated modulation amplitude. The inventive device, therefore injects a suitably amplified modulation sinusoid into the signal at the modulation amplitude adjuster  36   cw ,  36   ccw  by allowing some increase in various rotation sensing errors the error due harmonic modulation distortion can be minimized. 
     The amplification, either positive or negative of the signal emitted by the modulation generator  27   cw ,  27   ccw  occurs at the Modulation Amplitude Adjuster  36   cw ,  36   ccw  and is according to constant amplification factor derived prior to construction. 
     To understand the nature of the modulation, the modulation process is modeled using a resonance function with a polynomial. Assuming a perfectly symmetric resonance function, the distortion in question is only introduced at even orders in a selected polynomial. Therefore, the polynomial must be selected such that to have be a 4th order polynomial with minus sign to approximate resonance function such that its second derivative changes its sign. A function that satisfies this condition is:
 
 y=k   2   x   2   −k   4   x   4   (Equation 1a)
 
     Because the polynomial will be based upon at least one sinusoid, the function can be so expressed. The resulting function represents the modulation signal at a fundamental frequency and a second harmonic component due to harmonic distortion with coefficients a 1  and a 2  which represent the relative magnitude of the modulation signal at the fundamental frequency and second harmonic component respectively.
 
 x=a   1  sin(ω t )+ a   2  cos(2ω t )  (Equation 1b)
 
     Using the polynomial to model the modulation and solving for the resulting wavelength at the frequency and at the 2nd harmonic yields:
 
 y|   ω   =−k   2   a   1   a   2  sin(ω t )+2 k   4   a   1   3   a   2  sin(ω t )  (Equation 2)
 
     This polynomial expressed in Equation 2 models the distortion in the resonator output signal at the fundamental frequency (assuming sine wave demodulation). Examining the equation indicates that this distortion signal is that of an existing bias error since the modulation was set to be centered with the resonance function. The bias error goes to zero when the amplitude of the modulation is selected to be: 
     
       
         
           
             
               
                 
                   
                     a 
                     1 
                   
                   = 
                   
                     
                       
                         k 
                         2 
                       
                       
                         2 
                         ⁢ 
                         
                           k 
                           4 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     Designing the circuit to exploit this fact is aided by the fact that the coefficient of the amplification is a constant and independent of the 2nd harmonic modulation amplitude. For that reason, the simple amplification at the fixed amplitude will adequately suppress 2nd order harmonic distortion. 
     Returning, then, to  FIG. 2 , the output of the modulation generators  27   cw ,  27   ccw  is then amplified at the modulation amplification adjuster  36   cw ,  36   ccw  by a factor such that the amplitude of the modulation signal is 
               a   1     =         k   2       2   ⁢     k   4                 
provided to the summer  33   cw ,  33   ccw  for suitable addition to the output of an integrator  30   cw ,  30   ccw , which integrates the output of the demodulator  24   cw ,  24   ccw  as that signal is demodulated as described above. By means of adding the amplified modulation signal at the summer  36   cw ,  36   ccw , the 2nd harmonic distortion is driven to near zero levels within the feedback loop.
 
     While the preferred embodiment of the invention has been illustrated and described, as noted above, many changes can be made without departing from the spirit and scope of the invention. For example, a second clockwise or counterclockwise circuit might be added with its own modification amplitude adjuster for suppressing harmonics in that third circuit. Accordingly, the scope of the invention is not limited by the disclosure of the preferred embodiment. Instead, the invention should be determined entirely by reference to the claims that follow.