Stefan, Craig, Sheila
Stefan and I changed the DARM offset and looked at the noise earlier this evening. The first attached screen shot shows the resulting change in the DARM noise, there is a large difference above 1kHz, but also a small difference which was repeated in the one on/off test we did from about 90-180Hz. Craig has repeated this on off test a few more times, and the same pattern is holding.
The noise gets better for larger DARM offsets, which might suggest that we are limited by some kind of sensing noise. Our noise budget shows that the DCPD dark noise isn't as far as we'd like it to be below DARM at high frequencies. I took the dark noise measurement used in the noise budget, and scaled it for the expected change in optical gain from the change in DARM offset. The second attachment shows the noise for these different darm offsets with the dark noise estimate subtracted. The point is that the dark noise that we measure when there is no light on the DCPD's can't explain what we are seeing.
We would like to engage more whitening filters to see if that changes this noise, but ran into problems described in 45720.
Craig and I repeated this test with the OMC dither line reduced by a factor of 2, because the OMC length sensing noise should also depend on the DCPD power. The noise introduced by a small DARM offset isn't changed by reducing the dither, so it doesn't seem like it is OMC length noise.
I repeated Sheila's study with even crazier offsets, such that the OMC DCPD Power was 1.5 mA. (according to emails from Koji, the DCPD resposivity is 0.858 A/W with quantum efficiency of 0.98, so this corresponds to 1.78 mW on the DCPDs) We see the shot noise get worse with decreased DARM optical gain, some mystery hump at 5 kHz, and some 1/f noise starting at 30 Hz.
I think there are different ways that this measurement might be affected by the calibration, but assuming that the calibration is consistent and the optical gain of the fringe is properly accounted for between these measurements at different offsets, I made a simple model to determine if this can be explained by shot noise from contrast defect light.
Rai's comments on the ISC call were to check if the extra noise in the LLO model were due to fringe offset, and this measurement should be sensitive to that (I know there are other measurements of defect as well). Here is a crosscheck to see if those measurements are consistent with this data.
I don't have the original DTT files, so I eyeballed that Sheila's 10mA/38mA measurement has a ratio of 10/9.5 in shotnoise limited sensitivity from the low offset (higher noise) to high offset (lower noise). This was just by looking at the h=10^-19rtHz crossing point.
Similarly, for Craig's 1.5mA to 38mA I get a ratio of 7/5.5.
For the model, you have to solve for the implicit defect using the shotnoise and offset.
D = Y + C
D is total power, Y is fringe power, C is defect
dD/dDARM = X_1 sqrt(Y)
is the sensitivity, X_1 is some calibration that I don't care to calculate
the noise then is
N = X_2 sqrt(D) / (dD/dDARM)
which has another calibration to shot noise
using the two noise levels and fringe offsets, solve away Y and take the ratio (removing the calibration constants)
N_1/N_2 = sqrt((D_1 * (D_2 - C)) / (D_2 * (D_1 - C)))
Attached is the plot with the two measurements and models, which indicates some background shotnoise causing light (such as defect) at about 0.5mA, moderately consistent between the measurements. Perhaps more so if the actual measured ratios were used rather than my eyeballed values.
