Let's assume the additional flat noise in the ~100 Hz region that might be limiting now (w.r.t. to O4a) is due to OMC length noise. Either the OMC lenght noise is larger than before, and coupling through the residual OMC length RMS noise, or the OMC lock has an offset.

Let's assume that the OMC was locked at the top of the resonance (no offset, to be confirmed with the new demodulation phase).

According to 76137, the two PZT responses are PZT1 = 11.3 nm/V, and PZT2 = 12.7 nm/V.

Following Sheila's note in 30510, the normalized OMC transmission (RIN) is given by [after correcting for a mistake in the coefficient multipling F]

RIN = 1 / (1 + (2 F (x0 + dx)/ lambda)^2 )

where F = 400 is the OMC finesse (76386), x0 is a static lock offset (or equivalent RMS fluctuation) and dx is OMC lenght noise (form example due to dither).

The amplitude of the dither line is 0.23 V peak, corresponding to a dither amplitude (peak) of A = 2.6e-9 m, using the PZT1 calibration above.

The locking error signal is obtained using a length modulation dx = A sin(wt) that gives a RIN = (2F/lambda)^2 A sin(wt) x0, where x0 is the offsetf from resonance of the OMC length. Once demodulated, this gives

OMC-LSC_I = (2F/lambda)^2 A/2 x0 = 7.3e8 error_signal_demodulated_RIN / m (note that 30510 seems to be wrong and missing some factors, thank you Elenna for checking)

This allows me to calibrate the OMC-LSC input signal. The RMS with the OMC locked is 4.7e-5 RIN, corresponding to 6.4e-14 m RMS of residual OMC fluctuation around the lock point.

The flat noise in DARM is about 7e-21 m/rHz. Using the optical gain from the calibration measurement (3.4e6 LSC-DARM_IN cts/m) and the ratio LSC-DARM_IN / OMC_DCPD_NORM = 1.6e-5, I find an optical gain of 2.1e11 RIN/m for OMC-DCPD_NORM

Therefore the noise in DARM corresponds to a OMC-DCPD RIN of 1.5e-9 RIN/rHz

Noise coupling due to the residual OMC length RMS goes like (2F/lambda)^2 x_RMS dx_noise, where x_RMS is now the residual RMS motion computed above. Using this conversion, I found that the excess noise in DARM would correspond to a OMC length noise of 4e-14 m/rHz at 100 Hz. This still seems higher than the expected noise that should be in the 3e-16 m/rHz range (see for example section 8 of T1000276)

Tests to do:

1. check if the new demodulation phase improves anything in DARM
2. scan the OMC lock offset around 0, looking at DARM noise and at the optical gain (for example amplitude of the 410.3 Hz calibration line)
3. change the locking gain to reduce / increase RMS and check DARM