Brina, Sheila
The DCPD balance matrix is normally set by Jeff using the method described in 47217. Today I wanted to try setting the matrix so that the contribution of the two sensors to the DARM loop gain is set to be equal, because I think this will make it easier to correct for the imbalance of the PDs while doing the offline cross correlation. I compared pcal line heights in the DCPD_A and DCPD_B at 17.1 Hz (A/B = h = 1.0277) and at 410.3Hz (A/B = 1.0362). We chose the 17Hz value, and calculated the matrix elements for DCPD A to the SUM 2/(h+1) = 0.9863 and B to the sum 2h/(h+1) = 1.0137.
The attached text file has commands used to copy and paste into a guardian shell to swap the DARM loop to one DCPD, and change the matrix elements. After doing the swap we measured the DARM OLG, which is the live trace in the attached dtt template.
no sqz start: 1370816035 (Jun 14 2023 22:13:37 UTC). lockloss: 22:23:18 UTC, we were just sitting there collecting data with no SQZ. The matrix elements have been reset by SDF.
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Here are some plots of the cross correlation for this time.
The first is a comparison of the pyDARM model of the OLG to the measured OLG. At 24Hz, the model was predicting 2% less gain than the measurement, so here I've scaled the model up by 2% and used that for the estiamtion of the correlated noise.
The second plot is the DCPD sum ASD loop corrected compared to the cross correlation. You can see that the cross correlation is above the DCPD sum by 7% at 24Hz, which is incorrect. I thought about if this could be because of the imbalance of the DCPDs, I will attach a note here that explains how I attempted to handle this imbalance in estimating the cross correlation. (The DCPD_A and B channels are recorded before mulitplying by the balance matrix, the sum channel is after that matrix.) In the end this did not make a significant difference, the cross correlation is still nearly 7% overestimating DARM at 24Hz when I corrected for this.
The third plot shows the cross correlation compared to an estimate of the correlated noise obtained by subtracting the calculated shot noise from the DCPD SUM asd in quadrature, this mostly agrees with the cross correlation except at low frequencies.
These plots were made using the code https://git.ligo.org/sheila-dwyer/cross-corelation commit 3c60740b I will attempt to make a comparison of this code with Craig's cross correlation code to see if this problem is still present there.
Here is a note describing how I corrected for the DCPD imbalance. Once the matrix was reset as above, things become simple. I will add a diagram to this note if I have time.
Daniel raised the point that perhaps a phase difference between the two PDs could explain a discrepancy at low frequency, in the correction I did I assumed that the two paths were only imbalanced by a scalar gain. The attached png shows a transfer function between the two DCPD channels, taken at the time of one of yesterday's broadband pcal injections. The frequency dependence of this at first glance doesn't seem right to explain what we see, ie, the error in the cross correlation doesn't have a wiggle between 20-30 Hz, although the error does seem to happen around the frequency of the cross correlation problem.
