Anamaria took some time with me today to help me calibrate the sideband PRGs the same way she calculated them here for Livingston (LLO:69872). This is mostly with the intention of providing calibrated data for the finesse modeling effort that can help us better understand IFO behavior during TCS changes/powering up.
Reminder: I ran a check of the carrier PRG calibration this week (81752), which is based on the IM4 trans and end transmission values, which confirms that at 2W, our PRG is about 55.
Method:
Measure the power in the PRC at DRMI lock and compare it to the power in the PRC at 2W lock. Knowing the gamma of the 9 and 45 MHz sideband, estimate how much of the input power is sideband power. Use the predicted sideband PRG from an IFO model with perfect mode matching, and scale the expected sideband power in the PRC by those PRGs. Compare this expected value to the actual PRC power, and then scale the sideband PRGs accordingly.
Data:
DRMI lock values (measured after DRMI ASC converges):
| Channel | Value |
| POP A LF INMON | 12.5 ct |
| POPAIR RF18 | 151 ct |
| POPAIR RF90 | 27.25 ct |
| IM4 TRANS NSUM | 1.98 W |
2W full lock values (measured after full IFO ASC converges, including ADS):
| Channel | Value |
| POP A LF INMON | 283.8 ct |
| POPAIR RF18 | 154.5 ct |
| POPAIR RF90 | 28.5 ct |
| IM4 TRANS NSUM | 1.98 W |
Other useful numbers:
| Parameter | Value | Notes |
| Gamma 9 | 0.213 | 22.7 mW 9 MHz per W of input power, 62883 |
| Gamma 45 | 0.275 | 37.8 mW 45 MHz per W of input power, 62883 |
| PRM Transmission | 0.031 | https://galaxy.ligo.caltech.edu/optics/ |
| PR2 Transmission | 229 ppm | https://galaxy.ligo.caltech.edu/optics/ |
| M12 Transmission | 0.054 | Splitter on POP path, 63625 |
| 2W lock carrier PRG | 55 | Original measurement, checked again recently |
| PRG9 from model | 119 | Anamaria's Optickle model |
| PRG45 from model | 13 | Anamaria's Optickle model |
The work:
At 2 W lock, POP LF INMON measures 283.8 counts (this accounts for the dark offset). With an input power of 1.98 W and a PRG of 55, this should be 109 W. So we set a scale that 283.8 ct POP diode == 109 W PRC power.
At DRMI lock, we measure 12.5 counts in the POP diode (this accounts for the dark offset), so this gives us 4.8 W PRC power in DRMI lock.
At 1.98 W input power, 44.9 mW is 9 MHz power and 74.84 mW is 45 MHz power. We multiply by the perfect mode matching sideband PRGs and get that 5.3 W should be 9 MHz and 0.972 W should be 45 MHz in DRMI lock, so a total of 6.3 W expected PRC power in DRMI.
4.8 W / 6.3 W = 0.76, so 0.76 * 119 = 90.6 and 0.76 * 13 = 9.9, so we can say that our 2W PRG9 = 91 and PRG45 = 10.
Notice that this method ties the sideband PRGs to the measured carrier PRG. The method is perhaps not so good for the 45 MHz sideband, since we know there is so much less 45 MHz power than 9 MHz power. But these values are sensible.
Why did we do it this way?
You might notice we used the POP LF inmon value instead of the POP LF out value. There is a calibration in the POP A LF filter bank labeled "to_uW", which I assume means "microwatts of power on the POP diode". We started by using this calibrated value, and putting it into Watts of PRC power using the known transmission of the M12 splitter and PR2 (LLO calibrates POP A LF into Watts in the PRC). This resulted in a lower sideband PRG, (76.7 and 8.4 respectively). However, it also predicted that the carrier PRG should be 46. The carrier PRG calibration Craig and I performed does not rely on the POP diode at all, which is good because there is enough sideband power in the PRC to confuse the measurement. So, Anamaria and I decided to trust the independent carrier PRG measurement based on the arm transmission. Furthermore, we looked at how the H1:LSC-PR_GAIN_OUT16 channel is calibrated, and noticed that it ratios the H1:LSC-POP_A_LF_INMON value with IM4 trans. This motivated us to ignore the uW calibration filter (which then motivated us to correct for the dark offset of 3.8 ct).
Comparisons to mod depth method
If you have a good enough alog memory you might know that Craig and Jennie W have done a sideband PRG calibration in the past, using the modulation depth step test such as here: 70865 and 76358. Upon further inspection of the results, I am not sure they are so good. Mainly, the 45 MHz sideband PRG that results from this test is around 27-30, which is huge. I looked at these measurements again to try to understand why the values are so different. I noticed that when Craig steps down the 45 MHz sideband, the POP A LF value actually increases. Anamaria and I think this is because with lower 45 MHz modulation, the carrier input power increases, and the high carrier PRG (compared to the 45 MHz PRG) amplifies this excess power further. I can't find anywhere in Craig's code that accounts for this. For now, I am going to trust the method described in this alog over the mod depth step method.
Channel calibration factor
These values will calibrate the POPAIR B RF18 I ERR and RF90 I ERR channels into sideband PRGs accordingly.
calibration factor = (2W sideband PRG value) / ( 2W POPAIR count value / IM4 trans)
POPAIR18 > PRG9 calibration factor = 91 / ( 154.5 / 1.98) = 1.17, and normalize by input power
POPAIR45 > PRG45 calibration factor = 10 / (28.5 / 1.98) = 0.7, and normalize by input power
Note that if you use the POPAIR B RF18/90 I NORM MON channels instead of the ERR channels, these are already normalized by input power.