Detail:
For estimating coupling from OMC length fluctuation to DARM, I measured the spectrum of OMC error signals with dither CLK of 30000 and found that there is a large peak at dither frequency (fig1).
The reason of this very high peak when dither amplitude is large is the non-zero gain of band-pass filter at OMC-TRANS_DC_AC filter banks (fig2), so I tested the high-pass filter.
Gree and brown line shows the spectrum of OMC error signals when engaging 1Hz and 100 Hz HPF at OMC-TRANS_DC_AC filter bank.
Since the phase delay around 5kHz is 1 degrees or so even with 100 Hz HPF, I kept engaging 100Hz HPF at FM4 of OMC-TRANS_DC_AC filter bank.
After that, I measured time-series data of OMC error signals (dither CLK=500 and CLK=30000) and OMC feedback signals (dither CLK=500) to estimate the realistic residual OMC length fluctuation.
Figure 3 shows the spectrum calculated from time-series data.
Blue lines show the spectrum of OMC error signals with CLK gain of 30000 cnts, which can monitor the OMC length fluctuation above 1e-15 m/rtHz and basically the best estimation of free-running OMC length fluctuation at high frequency.
Orange lines show the spectrum of OMC error signals with CLK gain of 500 cnts, which tells us the sensing noise level of OMC error signals during OBSERVATION state (~8e-14 m/rtHz).
Green lines show the spectrum of OMC feedback signals multiplied by OMC PZT actuator efficiency with CLK gain of 500 cnts, which represents OMC length fluctuation inuced by feedback above UGF.
So, followings are the current best estimation of OMC length fluctuation:
1. OMC length fluctuation is summation of OMC error signals with CLK gain of 30000 and sensing noise of 8e-14 m/rtHz below UGF.
2. OMC length fluctuation is summation of OMC error signals with CLK gain of 30000 and OMC feedback signals multiplied by PZT AE with CLK gain of 500 above UGF.
To achieve above calculaion in time-series, I generated white noise and multiplied model transfer function, which reproduced seninsing noise + feedback * PZT AE as shown in fig4.
By using time-series data of OMC error signals with CLK gain of 30000 and iFFT signals of modeled noise with CLK gain of 500 shown in fig4, I calculated the OMC transmission spectrum due to OMC length fluctuation (fig5).
Orange lines show the OMC trans spectrum measured during OBSERVATION state with compensation filters for DARM loop to convert it to out-of-loop equivalent spectrum.
Green lines show the estimated OMC transmission spectrum only from OMC error signals with CLK gain of 30000, which means the lowest limit of the current configuration.
Blue lines show the estimated OMC transmission by using best estimated OMC length fluctuation.
According to the results, OMC length fluctuation dowsn't seem to contaminate the current sensitivity but not so far.
Note:
Since CLK gain of 30000cnts were saturated at DAC as reported in klog33605, I used a calibration factor of 1.5e-11 m/cnt in stead of 2e-11 m/cnt.
Since current OMC calibration is just scaled from the previous measurement, so for further precise estimation, OMC calibration is necessary.