Summary: The twin bumps at around 3300Hz comes from the OMC LSC loop, which has a 100Hz UGF.

Of course OMC length dither at 3300Hz should make some sidebands in the DC readout by design, but these twin bumps look really unnecessarily big.

We can reduce these by making the OMC length bandwidth much smaller.

Details:

In the attached, Red is with nominal setting (H1:OMC-LSC_SERVO_GAIN=60 and H1:OMC-LSC_OSC_CLKGAIN=6).

Blue is with 50% servo gain but with nominal dither amplitude (SERVO_GAIN=30, CLKGAIN=6), so it has half the open loop transfer function of red.

Green is is with nominal servo gain and 50% dither (SERVO_GAIN=60, CLKGAIN=3), so again it has half the OLTF of red.

IF the OMC length signal is sensing the true OMC length as opposed to just some noise that is not proportional to the dither amplitude, the OMC length control signal (middle row) for green and blue should be the same. But in reality they're 6dB apart from 8Hz and up.

Also you will expect that the OMC length error signal (bottom row) for blue and green have the same shape but different by 6dB, as the OLTF is the same but the sensing is 6dB different. That's only the case for f<8Hz.

So it's all noise for f>8Hz, and probably that's just  the noise floor of DC readout at 3300+-f Hz downcoverted by the demodulator (not dither) to f Hz, fed back to the OMC length, and upconverted by the dither back to 3300+-f. See the left column. Blue and green on the top left are the same because the sideband amplitude around 3300Hz produced by this mechanism is proportional to the product of the feed back gain and the upconversion gain (dither), the sensing part is independent of the dither amplitude.

In summary,

• OMC length signal is dominated by some noise, probably DC readout noise floor, not length fluctuation, from 8Hz and up.
• We can reduce the BW of the length control to maybe a few Hz to make the bump smaller and see if there's any ill effect on the DC signal.
• We can also filter out the feedback to make the width of the bumps smaller.

Later Dan will try some low BW filters.