[Elenna, Sheila]
Continuing work on the ASC AS and REFL WFS from alog 62262 (where I showed the WFS are not ADC noise limited), I calculated the shot noise present on the AS and REFL A and B WFS. Marie Kasprzack did a similar ASC noise budget for LLO, presentation here (DCC G2100751), and slide 16 shows a comparison between dark, shot, and adc noise similar to my plots.
To calculate shot noise I am using the formula S = sqrt(2*h*f*P_DC), h is Planck's constant, f is the laser frequency, and P_DC is the DC power on the photodiodes. I am using data from May 4th 2021 when the IFO was locked to find the DC power in counts, and the cts/rtHz spectrum from DTT. The circulating power in the X arm was 254 kW and in the Y arm was 268 kW. For the dark noise spectrum I used data from a maintenance day when the IFO was down.
DC Counts:
- REFL A DC = 20,200 cts
- REFL B DC = 20,400 cts
- AS A DC = 60,500 cts
- AS B DC = 64,500 cts
To calibrate the counts to Watts I used the ADC conversion of 6.103e-4 V/ct (16 bit with +-20V), transimpedance of 1 kOhm, and photodiode responsivity of 1.25 W/A. The resulting calibration factor is 7.63e-7 W/ct. I then used this power value in the shot noise formula above to calculate the W/rtHz.
The resulting power on the PDs is
- REFL A DC = 15.4 mW
- REFL B DC = 15.5 mW
- AS A DC = 46.1 mW
- AS B DC = 49.1 mW
For the RF chain I used the same ADC conversion (6.103e-4 V/ct) and PD responsivity (1.25A/W). Sheila and I found the ASC AS and REFL datasheets on the DCC to get the transimpedance for each channel (AS datasheet and REFL datasheet).
- REFL 9 = 900 Ohms
- REFL 45 = 650 Ohms
- AS 45 = 800 Ohms
- AS 36 = 900 Ohms
Each channel also has a whitening gain applied
- REFL 9 = 21 dB
- REFL 45 15 dB
- AS 45 = 3 dB
- AS 36 = 15 dB
and each channel has an additional gain factor when the IFO is locked
- REFL 9 = 1
- REFL 45 = 1.41
- AS 45 = 1.41
- AS 36 = 3.95
I used this calibration to convert the cts/rtHz output from DTT into W/rtHz for the locked data and dark noise data.
The calibration factor for each channel:
- REFL 9 = 7.55e-8 W/ct
- REFL 45 = 1.48e-7 W/ct
- AS 45 = 4.78e-7 W/ct
- AS 36 = 3.82e-8 W/ct
My matlab script which I attached also inlcudes this process and all the values I used if you want to follow my calculation.
I understand these plots to show that we are not shot noise limited for the ASC AS and REFL WFS.
In case someone stumbles across this alog and is either confused, or tries to use my values here, I made some errors. (Although the person most likely to look back at this is me).
For DC calibration, the AS WFS calibration needs to be divided by an additional 20 dB. See alog 46482 where Daniel discusses the WFS DC calibration. This means that DC power on the AS WFS should be 4.6 mW, which lines up much better with the power we actually expect there (you can do the calculation based on OM3 transmission, AS_C power, etc).