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AdV-ISC (LSC Noise Budget)
mwas - 22:06 Wednesday 20 September 2023 (61731) Print this report
RIN coupling in simulink noise budget

This entry tries to answer questions on how the input beam RIN is coupling to the sensitivity, and how it is included in the simulink noise budget, for example in the brief measurement done last Sunday.

The noise budget uses a coupling of PSTAB to DARM measured on Mar 29. The corresponding lines in the noise budget code are:

TF_PSTAB_HF = cacheFunction(@measureTF, 1364157918, 120, par.f, 'V1:PSTAB_PDd_AC_MONIT', 'V1:LSC_DARM',0.2, 'raw');
TF_PSTAB_LF = cacheFunction(@measureTF, 1364158698, 120, par.f, 'V1:PSTAB_PDd_AC_MONIT', 'V1:LSC_DARM',0.2, 'raw');

PSTAB_coupling = rms(inputPowerData(3).data)/15e-6; % RMS of V1:LSC_DARM_PSTAB2_COUPLING_100Hz

par.TF_PSTAB = frd(PSTAB_coupling*max(abs(fresp(TF_PSTAB_HF, par.f)), abs(fresp(TF_PSTAB_LF,  par.f))), par.f, 'Units', 'Hz');

these combines two measurements done in two different frequency bands, and scales them to match coupling measured at a given using the the PSTAB2 line at 1501Hz.

Figure 1 shows the noise budget check from last Sunday, which works well above 100Hz, and which below 100Hz is projecting a noise that is too small. by about a factor 8 at 30Hz.

Figure 2 shows a model of PSTAB coupling with an interferometer with a MICH offset of 0.5nm. The figure units are  RIN on B1  per RIN of input beam to (without the effect of the DARM loop). The frequency independet part at high frequency is due to the MICH offset, and the low frequency is some other effect that is present in the simulation.

Figure 3 shows this measurement (in red) compared to a scale model (in blue). The curves are in au of DARM per Volt on the  PSTAB_PDd_AC_MONIT. The model based on an optical simulation with a MICH offset of 0.5nm is scaled to match the measurement at high frequency, times the model DARM loop transfer function that creates the bumps and notches between 100Hz and 1kHz. I have chosen the model to matche the discrepency with the measurement from March. This means than last Sunday we had a residual offset/RMS on MICH of 0.5nm, while back in March the MICH offset was much larger and had a higher contribution at high frequency compared to low frequency.

Figure 4, compares the same measurement with a model with 5nm MICH offset, this matches the measurement much better at all frequencies.

Figure 5 show the 5nm MICH offset model in unites of B1 RIN / input RIN. The coupling at high frequency of ~1 is comparable to the calibrated input RIN to B1 RIN transfer function measurement done back in Mar/Apr

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mwas - 14:51 Thursday 21 September 2023 (61738) Print this report

Given how well measurements match the model coupling at high frequency. I have replaced 6 month old measurement with the model in the noise budget, which will adjust the MICH offset in the simulation to match the RIN coupling measured at 1.5kHz.

Figure 1 shows the result of the projection during the ~20s when the PSTAB loop was open. Projection is good at high frequency, but under 100Hz there is still a factor few missing. To be sure what the coupling really is below 100Hz one would need to make a controlled measurement injecting RIN noise (without affecting too much the inteferometer control). The model correspond to a 1.2nm offset/RMS on MICH.

Figure 2 shows the projection during normal calm times, with a 0.7nm offset/RMS on MICH. The black curve correspond to PSTAB sensing noise, and the magenta curve to RF sideband RAM contamination of PSTAB sensing.

Figure 3 shows the corresponding input RIN to B1 RIN coupling used with a 0.7nm offset/RMS on MICH. The coupling comes out of an optickle simulation.

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