Here are the considerations, references, and proposed candidates for O3 calibration lines.
Goals:
1) Move SUS, PCAL, DARM lines to lower frequencies between 15Hz - 20 Hz. Now there are four lines: UIM, PUM, TST, PCAL.
2) Move optical gain cavity pole line to ~ 425 Hz
We've used the following criteria to determine what those frequencies should be: The original criteria are in 2014 aLog.
(1) Avoid SUS rigid body resonances and violin mode frequencies
(2) Avoid known pulsar frequencies
(3) Avoid 60 [Hz] power line and harmonics
(4) Avoid the most sensitive region of the IFO ~50-100 [Hz]
(5) Avoid integer number frequencies, ensure frequencies are not harmonics of each other
(6) Use different calibration line frequencies per interferometer
(7) At least 0.5Hz separation between two calibration lines
SUS rigid body resonances:
| B (Hz) | R (Hz) | |
| QUAD | (see LHO alog) | highest at 13.927 |
| BSFM | 17.54 | 25.74 |
| HLTS | 28.10 | 44.72 |
| HSTS | 27.32 | 40.369 |
Known pulsar frequencies: (see pulsar gaps veto alog, may need to rerun and update)
Violin mode frequency (see tech doc)
Proposed line frequencies:
(1) Choose 8 frequencies between 15Hz - 20Hz: (at least meet the 0.1Hz non-vetoed bands in pulsar gaps veto alog, because the 0.5Hz non-vetoed bands are not enough)
LLO - Stay with the current choices - 15.7Hz, 16.3Hz, 16.9 Hz (this one meets 0.5Hz non-vetoed bands) (see alog), and add one more 18.1Hz (this one meets 0.5Hz non-vetoed bands)
LHO - 15.5Hz (this one meets 0.5Hz non-vetoed bands), 16.7Hz (this one meets 0.5Hz non-vetoed bands), 18.3Hz, 18.9Hz
(2) Choose optical gain cavity pole line: LLO - 441.7Hz, LHO - 443.3Hz
I did a quick study to assess cross-contamination of calibration lines that are close to each other in frequency. This was in relation to criterion #7, which is primarily motivated by stochastic searches. However, the purpose of the study was to determine how close in frequency two lines can be to each other before they start to affect measurements of each other. The test I did was to generate white noise an a sinusoid with a frequency of 16.3 Hz (one of LLO's line frequencies) with a line height comparable to the calibration lines. This data was demodulated at a randomly-generated frequency between 16.3 Hz and 17.3 Hz using the same algorithm used in the gstlal calibration pipeline to demodulate the calibration lines. The RMS of the result was plotted as a function of frequency-separation (first plot). It is seen that the signal is not visible beyond a separation of 0.15 Hz. Note, the kappas are median'ed and averaged for an additional 138 seconds, which would further reduce the signal.
The second plot is similar, but without any white noise. It looks like the Fourier transform of a Blackman window, due to the fact that a 20-second Blackman window is used as a low-pass filter for demodulation. This shows that the separation between lines should be at least 3/T, where T is the length of the low-pass filter. Additionally, optimal frequency separations are given by (3 + n) / T, where n = 0, 1, 2, ...
I don't know the details of the demodulation technique used by the front-end calibration pipeline (i.e., low-pass filtering), but this result is valid for the gstlal calibration pipeline.
In case we need to choose different frequencies in the future, an added requirement will need to be avoiding the ADS lines that are used for alignment control.