I engaged a control loop on the S1FC1310PM laser.

I used the modulation input of the laser controller. I used the SR560 as a servo. I set the low pass filter at 30Hz and gain 2000.

First I measured the noise of a 50 Ohm terminator to check the spectrum analyzer noise floor.
Then I measured the spectra of the 2 PDs (in-loop and out-of-loop), without laser (dark noise) and with the laser on.
The other day there were some structures on the out-of-loop PD that we didn't understand at the time, then I found that the beam was not well centered on the PD, so after I centered (maximizing the DC) the structures disappeared.
Then I closed the loop and measured the spectra again. The signal at 380Hz in the out of loop PD reduces by 10dB (about a factor of 3).

I confirmed the noise reduction by checking the lockin output with and without control loop. The 2 plots have the same axis scale, so the reduction is more clear.
The noise now is 1.3 ppm*W

I measured the actuator TF (plant) and fitted it with a zpk model: 2 single poles at 7kHz and 30kHz.
Then I modeled a servo TF and plotted the measured open loop TF. There is a factor of 2 of discrepancy with the model because the oscilloscope was connected to the modulation input, since they have the same input inpedance, the measured TF dropped by a factor of 2. But when I closed the loop the oscilloscope was not connected, so the actual OLTF is the dashed blue line on the plot.