We have measured the spectrum of the PZT correction signal sent to the laser when the cavity is locked, using the output PZT_mon (1/100 of the PZT correction signal). The spectrum is in the attached plot.Since in this region the gain of the loop is very high, the signal is proportional to the cavity length/frequency noise. 

The calibration is 1 MHz/V (given by the manufacturer). 

at 100 Hz we have ~ 700 nV/sqrt(Hz) corresponding to 70 Hz/sqrt(Hz), at 1 kHZ we have 100 nV/sqrt(Hz) corresponding to 10 Hz/sqrt(Hz)

The shape of the spectrum is compatible with the free running laser noise ~ 7-10 kHz /f  Hz/sqrt(Hz) up to a few kHz. According to aother measurement, after ~4 kHz the spectrum is limited by a flat noise, which is compatible with the noise of the 100 kOhm resistor at the output of the PZT_moni signal. For f<10 Hz probably the mirror control noise and the seismic noise are limiting the spectrum. 

We also see several 50 Hz harmonics. It is not clear if this harmonics can be reduced rearranging the grounds and if they have an impact on the RMS of the error signal of the filter cavity locked. To be investigated.