Abstract: Based on the phase modulation theory in M - Z interferometer, we have researched the phase modulation theory in a fiber optic gyroscope system, including phase bias theory, open loop and closed loop phase modulated theory, etc. A general theoretic phase modulation result is given with results suitable for all kinds of phase modulated designs in FOG. At last, in a FOG system, we have done a lot of phase modulated experiments using a Ti:LiNbO$-3$/ electro-optic crystal wave guide phase modulator. The consequences correspond with the phase modulated theory we obtained. !5
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