Ring Laser Gyro: Noise Improves Performance

We present a systematic formulation of the performance of a ring laser gyro (RLG) under the influence of a randomized sinusoidal dither. We develop the Fokker Planck equation of such a system and find its steady state solution that we use to find exact equations for the average output rate and its variance. The former determines the RLG's scale factor and the latter its angular random walk. We find a key parameter, called the residual lock-in rate, which affects both the scale factor and the random walk of the gyro. We show that when the noise amplitude is much larger than the residual lock-in rate the gyro rate output approaches that of an ideal gyro. However, this is at the expense of generating an angular random walk that is proportional to the residual lock-in rate. We present a formulation of the statistics of gyro output count and relate the average count and its standard deviation to gyro parameters. For example, we show that the angular random walk, in addition to being proportional to the residual lock-in rate, is also proportional to the inverse square root of the dither frequency.
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