This entry is meant to survey the sensing noises of the OMC DCPDs before the EOM driver swap. However, other than the 45 MHz RFAM coupling, we have no reason to expect the couplings to change dramatically after the swap.
The DCPD sum and null data (and ISS intensity noise data) were collected from an undisturbed lock stretch on 2015-07-31.
Noise terms as follows:
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Shot noise
- For 20.0 mA dc on the DCPD sum, we expect a shot noise of 8.0×10−8 mA/Hz1/2.
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Dark noise
- Dan and I measured this a few months ago. In full lock we use one stage of whitening, which amounts to a dark noise of 1.5×10−8 mA/Hz1/2 or so above 100 Hz. We have at times experimented with two stages of whitening, but it requires some vigilance regarding the violin modes.
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Intensity noise
- Coupling was measured à la Kiwamu by leaving the outer loop off and driving the inner-loop excitation point. For the noise estimation, I used the outer loop out-of-loop sensor. Since Sudarshan et al. previously found that this is artificially high, this estimation is an upper limit (though probably no more than a factor of 3, given Sudarshan's plot).
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Frequency noise [CARM sensing noise only]
- Previously (i.e., when we locked CARM using the in-air REFL sensor), I estimated the coupling by looking at the TF in-vac REFL to DARM, and for the frequency noise estimation I used the noise of in-vac REFL as an upper limit for the frequency noise. Since we now lock with in-vac REFL, which has more light on it than in-air REFL does, I do not expect that the noise of in-air REFL is a particularly useful upper limit for the frequency noise.
- Therefore, I have tried to instead estimate the sensing noise in CARM (from in-vac REFL, the summing-node board, the common-mode board, and PDH shot noise) in V/Hz1/2 and propagate it (using the Izumi/Sigg expression) into a frequency noise in Hz/Hz1/2. For the CARM optical TF I use 12.7 W/Hz at dc, with a pole at 0.48 Hz.
- Then I have injected noise into CARM and looked at the TF from the residual of the excitation into DARM. This is the coupling TF needed to propagate the estimated sensing noise to DARM, assuming the CARM gain is high (this isn't quite true at high frequencies; the ugf is 17 kHz or so, and the gain does not exceed 20 dB until 3 kHz).
- Since this includes sensing noise only (and not, for example, FSS noise), I have labeled it as a lower limit. In fact, the coherence between REFL 9Q and the DCPD sum is about 0.04 around 7 kHz, perhaps suggesting a frequency noise contribution of 2×10−8 mA/Hz1/2 or so. More investigation required.
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Oscillator phase noise [not included here]
- Stefan and I measured the coupling of the 9 MHz RF source into DARM, and using the expected performance of the OCXO estimated the noise in DARM should be 2.8×10−10 mA/Hz1/2 at 1 kHz. This is quite low (and not shown on the plot).
- This number should be replaced with Alexa's and Daniel's measurements of the phase noise. An even more satisfying number could be made by trying to measure the 9 MHz and 45 MHz phase noises in situ, closer to the EOM (e.g., at the output of the distribution system on the ISC rack).
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Oscillator amplitude noise [45 MHz only]
- In this case we know that the 45 MHz RFAM is the dominant contributor (other than shot noise) to the DARM noise above a few hundred hertz. Here I use Stefan's estimate of the RFAM-induced photocurrent (1.8×10−8 mA/Hz1/2), which (as he notes) is not enough to explain the excess between sum and null.
- However, based on tonight's measurements using the new EOM driver readback, it seems that 45 MHz RFAM is enough to explain the excess. Perhaps Stefan's measurement is an underestimate, since it was done at the output of the distribution system and did not include the final rf amplifier before the EOM.
- As for 9 MHz RFAM, Stefan and I made an estimate of the coupling from the 9 MHz source into DARM. Based on the specified performance of the OCXO, the expected noise in DARM is quite small. However, it would be better to look somewhere further downstream, as Stefan did (although I think he said the measurement was not that clean). This noise is not estimated in the plot.
The downward slope in the null at high frequencies is almost certainly some imperfect inversion of the AA filter, the uncompensated premap poles, or the downsampling filter.
* What is the reasoning behind the updated suspension thermal noise plot?
* Its weird that cHard doesn't show up. At LLO, cHard is the dominant noise from 10-15 Hz. Its coupling is 10x less than dHard, but its sensing noise is a lot worse.
I remade this plot for a more recent spectrum. This includes the new EOM driver, a second stage of whitening, and dc-lowpassing on the ISS outer loop PDs.
This time I also included some displacement noises; namely, the couplings from the PRCL, MICH, and SRCL controls. Somewhat surprising is that the PRCL control noise seems to be close to the total DCPD noise from 10 to 20 Hz. [I vaguely recall that the Wipfian noise budget predicted an unexpectedly high PRCL coupling at one point, but I cannot find an alog entry supporting this.]
Here is the above plot referred to test mass displacement, along with some of our usual anticipated displacement noises. Evidently the budgeting doesn't really add up below 100 Hz, but there are still some more displacement noises that need to be added (ASC, gas, BS DAC, etc.).
Since we weren't actually in the lowest-noise quad PUM state for this measurement, the DAC noise from the PUM is higher than what is shown in the plot above.
If the updated buget (attached) is right, this means that actually there are low-frequency gains to be had from 20 to 70 Hz. There is still evidently some excess from 50 to 200 Hz.
Here is a budget for a more recent lock, with the PUM drivers in the low-noise state. The control noise couplings (PRCL, MICH, SRCL, dHard) were all remeasured for this lock configuration.
As for other ASC loops, there is some contribution from the BS loops around 30 Hz (not included in this budget). I have also looked at cHard, but I have to drive more than 100 times above the quiescient control noise in order to even begin to see anything in the DARM spectrum, so these loops do not seem to contribute in a significant way.
Also included is a plot of sensing noises (and some displacement noises from LSC) in the OMC DCPDs, along with the sum/null residual. At high frequencies, the residual seems to approach the projected 45 MHz oscillator noise (except for the high-frequency excess, which we've seen before seems to be coherent with REFL9).
Evidently there is a bit of explaining to do in the bucket...
Some corrections/modifications/additions to the above:
- I updated the optical gain and DARM pole using the pcal like at 331.9 Hz; from this line I find the transfer function from the TX PD into DCPD sum is (1.69 − 1.59i) mA/pm, which works out to an optical gain of 3.19 mA and a DARM pole of 353 Hz. I think Kiwamu may have a different number from his pcal sweep, so there might be some reconciliation to do.
- I now compensate the extra 10 kHz pole that Kiwamu found in the readout chain of the DCPDs.
- I remade the quantum noise curve for 23 W, and with a more realistic estimate of the losses. In addition to the 87 % quantum efficiency, I include 14 % readout losses that Lisa has already tabulated: we expect 96.5 % transmission through the OFI, 93 % transmission through the OMC, 99% reflection from OM3, and (according to Dan) 97 % mode matching into the OMC. This results in a quantum noise curve that is 6.6×10−20 m/Hz1/2 at 1 kHz. The DARM pole predicted by GWINC is 360 Hz or so (slightly higher than what I extracted from pcal).
- Previously, I had tuned the arm losses in GWINC to give a recycling gain of 40 W/W. In light of Sheila's analysis, this is too optimistic; usually our recycling gains are more like 36 to 37 W/W. In GWINC, this amounts to tuning the arm losses to 90 ppm (per arm), which gives a gain slightly in excess of 37 W/W.
- The null stream is 5 % – 7 % higher than the GWINC curve, so either some parameter is mistuned or we need to be looking for some extra readout loss.
- I replaced the GWINC suspension thermal noise curve with a (hopefully) more accurate curve that I got from Sheila.
- I replaced the oscillator noise trace (which was flat in DCPD photocurrent) with a trace based on the TF that Stefan and I took. I still assume the underlying noise contribution is flat in RIN, at a level of 3.5×10−8 mA/Hz1/2. This trace will become less relevant since the excess oscillator noise now appears to be gone.
- I added gas noises. Squeeze film damping was calculated after T0900582 using the nominal parameters (our end station gauges read 1×10−8 torr, and I've assumed the dominant species is molecular hydrogen). For residual gas, I again assume the species is molecular hydrogen, and the arm pressure is taken to be 5×10−9 torr (which is a rough average of the arm gauges).
- The ASC trace contains only the dHard and BS loops. I drove in cHard, but even after driving far, far above the ambient noise floor I could not make excess noise appear in DARM.
Of course, the budgeted noises don't at all add up from 20 Hz to 200 Hz, so we are missing something big. Next we want to look at upconversion and jitter noises, as well as control noise from other ASC loops.