Abstract
In klog#34162, ~5% difference around 100Hz between online and low-latency h(t) was pointed out.
So I checked validity of this fact and it seems to come from the incompleteness of online calibration.
This fact suggests that actual sensitivity is slightly better than one shown in control room by using online h(t).
Details
Major and known factors of incompleteness of online calibration are 1) digital AAs for 65kHz->32kHz and 32kHz->16kHz 2) compensation of whitening filter on DCPD preamp board and 3) timing mismatch between error signal and feedback signal. Response of these effects are shown in Fig.1 and Fig.2 (zoom up around 0dB).
Because 1) is a super-Nyquist effect (zero/pole above Nyquist frequency), they cannot be compensated by using foton filters which are IIR filters based on bilinear transform. So this effect can be compensated only on low-latency and/or offline h(t). Only phase delay is compensated also on online h(t) as an approximant as time delay.
2) comes from the mismatch between the best estimation of circuit response of DCPD preamp whitening and digital dewhitening on FM10 of K1:OMC-TRANS_DC_{A,B}. By updating digital dewhitening filters, accuracy of online h(t) can be improved. But this update makes a change of open loop gain around UGF. So the DARM servo filter is also update at the same time. Because phase around 7-70Hz is also changed, we should check that there is no problem also on GR and RF lock.
3) comes from the accuracy of timing (phase) adjustment between error signal and feedback signals. In low-latency calibration, arbitrary time delay is compensated. On the other hand on online calibration, time delay compensation is done as a integer multiple of the sampling rate. The best estimation of timing mismatch between two signals is ~7.8 samples in 16kHz (=476us). Current timing compensation of online h(t) is 7 samples. So there is 0.8 samples mismatch. Compensation can be update as 8 sample and mismatch can be reduced 0.2 samples even online calibration. For doing it, model or foton filter updates are required.
As shown in Fig.2, total bias coming from these effect is ~0.45dB (=~5%) which is consistent with a mismatch between low-latency and online. This fact suggest low-latency h(t) is more close to the actual sensitivity and actual sensitivity is slightly better than one shown in control room.
Fig.3 and Fig.4 (just zoom up around 0dB) show the possible accuracy of online h(t) when all compensations mentioned above will be adopted. Accuracy of online h(t) can be improved from blue (current) to orange (best effort). By the way, bad accuracy above 1kHz comes from digital AA effect. In KAGRA, OMC model is running as 32kHz model. For this reason, two digital AAs which cannot be compensated on online h(t) contaminates accuracy. If we can change OMC model as 16kHz, additional improvement (orange -> black) will be available. Of course, they can be compensated in low-latency h(t). So it's not a problem on search groups.
