A simple optical technique to compensate for excess RIN in a fiber-optic gyroscope

As it is well-known, a fiber-optic gyroscope uses a broadband source which drastically reduces coherence-related noises and drifts, but such a source suffers from excess relative intensity noise (excess RIN) because of the random beating between all its frequency components. The power spectral density (PSDrin) of this excess RIN is simply the inverse of the frequency spectrum width (Δf_Source): PSD_RIN=1/Δf_Source. An erbium-doped fiber source used in high-performance fiber gyros has a typical width of 1 THz, i.e. a PSD_rin = 10^-12/Hz, whilst the associated theoretical photon noise limit is potentially 2 orders of magnitude below : PSD_PHot = 10^-14/Hz. However, excess RIN that limits the ARW (angular random walk) of the gyro, can be compensated for by detecting part of the input power and subtracting its associated noise from the one of the signal power which is correlated. This is classically performed with two detectors and an electronic subtraction, taking into account the delay τ between the reference input power and the noisy output signal, due to propagation through the sensing coil. As it is well-known too, the biasing modulation-demodulation of a fiber gyro is performed at the so-called proper frequency f_p = 1/2τ, i.e. τ is equal to half the period 1/f_p. The excess RIN has to be reduced only at this operating frequency and this can be performed by a simple addition of the input power and the output signal: to subtract with compensation of the delay τ is actually equivalent to add without delay compensation at this operating frequency f_p. It is just a delay line filter! Such a summation can be simply done optically with a single detector and a single demodulation chain: part of the input power is tapped out and recombined with the output signal power. We first implement this idea by combining the input refer- nce and the signal output with the same state of polarization but with a disappointing result. It was analyzed as an interference filtering process of the frequency components of the excess RIN with a theoretical improvement limited to 3 dB in PSD, i.e. only 1.4-fold in rms noise. The question being how to sum two optical powers without interference, the solution is simply to add both powers with orthogonal states of polarization! The experimental result is quite interesting since the ARW can be improved almost down to the theoretical photon noise limit : gyro axis using a coil of 1 km length and 10 cm diameter and having a usual ARW of 1400 microdegrees/root hour exhibited "with adequate tuning" an ARW of 350 microdegrees/root hour, i. e. an interferometric phase noise of 1.5 × 10^-7 rad/√Hz, whilst the excess source RIN is 10^-6/√Hz. This result is confirmed with a noise measurement using an electronic spectrum analyzer which shows clearly the periodic sine response of a delay line filter.