Summary
Attached is the dark noise of REFL9Q, along with an estimate of the shot noise and a conversion of these noises into equivalent frequency noise in CARM.
The dark noise appears to be slightly below the shot noise level.
Details
I took the TNC that goes directly into the common-mode board and put it into an SR785. Also attached is the noise with the input of the SR785 terminated.
I also have tried to estimate how this compares to the shot noise on the diode. In full lock at 24 W, we see 3.6 mW of dc light on the PD (according to the calibrated REFL_A_LF channel). Off resonance and at 2.0 W, we have 13.6 mW of dc light. So the CARM visibility is about 98%.
The shot noise ASD (in W/rtHz) and the CARM optical plant (in W/Hz) are both given in Sigg's frequency response document. With a modulation index of 0.22 rad and an incident power of 24 W, the shot noise is 9.4×10−10 W/rtHz, the CARM optical gain is 11 W/Hz, and the CARM pole is 0.36 Hz. [Edit: I was missing some HAM1 attentuation when first calculating the shot noise level. Out of lock, the amount of power on REFL A should be 24 W × 0.1 × 0.5 × 0.5 × 0.5 = 300 mW. That gives a predicted shot noise level of 7.7×10−11 W/rtHz, assuming a sideband amplitude reflectivity of 0.44. On the other hand, from the measured in-lock power we can calulate 2(hνP)1/2 = 5.2×10−11 W/rtHz for P = 3.6 mW. This includes the factor of sqrt(2) from the frequency folding but does not include the slight cyclostationary enhancement in the noise from the sidebands (although this latter effect is not enough to explain the discrepancy).] Additionally, I use Kiwamu's measurement of overall REFL9 response (4.7×106 ct/W) in order to get the conversion from optical rf beat note power into demodulated voltage (2900 V/W). These numbers are enough to convert the demodulated dark noise of REFL9Q (and the shot noise) into an equivalent frequency noise. At 1 kHz, the shot noise is about 10 nHz/rtHz; as a phase noise this is 10 prad/rtHz (which is smaller than Stefan's estimate of 80 prad/rtHz). The dark noise, meanwhile, is about 5 nHz/rtHz.
Hang, Evan
We measured the input-referred voltage noise of the summing node and common-mode boards.
- We terminated the input of the SNB that receives REFL9Q (INA2). INA1 was disabled. On the CMB, IN1 was enabled with -22 dB, and IN2 was disabled. The 40 Hz / 4 kHz boost was engaged. The fast gain was 7 dB.
- We measured the noise at the output of the CMB fast output.
- We then took the TF from SNB INA2 to CMB fast out. This is sufficient to get the input referred noise.
According to this estimate, the CARM loop is not shot noise limited; rather, at 1 kHz the noise is about a factor of 3 in ASD above shot noise.
I looked back at the CARM sensing noise data I took (on 12 Aug) using the new gain distribution: 0 dB SNB gain, −13 dB CMB common gain, 0 dB CMB fast gain, and 107 ct/ct digital MCL gain.
[For comparison, the old CARM gain distribution was 0 dB SNB gain, −20 dB CMB common gain, 7 dB CMB fast gain, and 240 ct/ct digital MCL gain.]
☞ For those looking for a message in this alog: something about the current frequency noise budgeting doesn't hang together. The projection based on the CARM sensing noise and the measured CARM-to-DARM coupling TF suggests a CARM-induced DCPD sum noise which is higher than what can be supported by coherence measurements.
☞ Second attachment: As expected, the noise (referred to the input of the SNB) is lower; at 40 Hz, it is about 350 nV/Hz1/2. However, we are not really shot-noise (or dark-noise) limited anywhere.
☞ Third attachment: I am also including the CARM-to-DARM coupling TF from a few weeks ago. This TF was taken by injecting into the CARM excitation point and measuring the response in OMC DCPD sum, using the old CARM gain distribution. Then I referred this TF to the SNB input by multiplying by the SNB gain (0 dB), the CMB common gain (−20 dB), and the CMB common boost (40 Hz pole, 4 kHz zero, ac gain of 1).
This gives a coupling which is flat at 1.0×10−2 mA/V, transitioning to 1/f2 around 250 Hz. Or, to say it in some more meaningful units:
- Assuming a REFL9Q demodulation coefficient of 2900 V/W, this implies a flat power coupling of 3.4×10−6 mA/W above 250 Hz, rising like 1/f2 below that.
- Assuming a CARM optical gain of 13 W/Hz and an optical pole of 0.48 Hz, this implies a 1/f frequency coupling above 250 Hz, a 1/f3 coupling below 250 Hz, and an overall magnitude of 6.2×10−5 mA/Hz at 1 kHz.
- Stated in terms of phase coupling (Stefan's favorite), the magnitude of the CARM optical plant is 6.2 W/rad above the cavity pole, which implies a flat phase coupling of 6.2×10−2 mA/rad above 250 Hz, rising like 1/f2 below that.
☞ Synthesis of the above: based on the measurements described above, at 40 Hz we expect a coupling into the DCPD sum of 350 nV/Hz1/2 × 0.4 mA/V = 1.4×10−7 mA/Hz1/2, which is very close to the overall DCPD sum noise of 3.2×10−7 mA/Hz1/2.
But what is wrong with this picture? If 1.4/3.2 = 44 % of the DCPD sum noise comes from CARM sensing noise, we should expect a coherence of 0.442 = 0.19 between the DCPD sum and the CARM error point.
☞ First attachment: The coherence between the CARM error point and the DCPD sum is <0.01 around 40 Hz. Now, it is almost certainly the case that not all of the CARM error point noise is captured by LSC-REFL_SERVO_ERR, since this channel is picked off in the middle of the CMB rather than the end. Conservatively, if we suppose that LSC-REFL_SERVO_ERR contains only dark noise and shot noise, this amounts to 180 nV/Hz1/2 of noise at 40 Hz referred to the SNB error point, or 0.72×10−7 mA/Hz1/2 referred to the DCPD sum. This would imply a coherence of 0.05 or so.
☞ What is going on here?: Four possibilities I can think of are:
- I've overestimated the sensing noise.
- I've overestimated the CARM-to-DARM coupling TF.
- I've made an algebra mistake somewhere.
- LSC-REFL_SERVO_ERR is corrupted by noise that is not in the CARM loop.
☞ A word about noise budgeting: In my noise budget, there was a bug in my interpolating code for the CARM-to-DARM TF, making the projection too low below 100 Hz. With the corrected TF, the projected CARM noise is much higher and begins to explain the mystery noise from 30 to 150 Hz. However, given that the above measurements don't really hang together, this is highly speculative.
According to the CMB schematic and the vertex cable layout, the CARM error point monitor goes through some unity-gain op-amps and then directly into the ADC. So I don't think we have much chance of seeing the 180 nV/Hz1/2 of shot/dark noise above the 4 µV/Hz1/2 of the ADC.
According to the CMB schematic and the vertex cable layout, the CARM error point monitor goes a gain of 200 V/V and then directly into the ADC. So the 180 nV/Hz1/2 of shot/dark noise appears as 36 µV/Hz1/2 at the ADC. But as Daniel pointed out, this should be heavily suppressed by the loop. For comparison, the ADC's voltage noise is 4 µV/Hz1/2.
For the sake of curiosity, I'm attaching the latest noise budget with the corrected CARM-to-DARM coupling TF. However, I note again that this level of frequency noise coupling is not supported by the required amount of coherence in any of our digitally acquired channels. Additionally, this level of frequency noise coupling is not seen at Livingston, although they've done a better job of TCS tuning than we have. I would not be surprised to find out that this coupling is somehow an overestimate.