[Yuta, Evan]
Michelson signal challenge (alog #9857) was solved.
MICHELSON REFLAIR PATH POWER BUDGET
Tabulated by Kiwamu and Lisa in alog #9954.
MICHELSON SIGNAL CHAIN
Michelson length change: dl=lx-ly [m]
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Optical gain: dPmod/dl = 2*4*pi/lambda*Peff*J0(beta)*J1(beta)*sin(2*pi*fmod/c*lsch)*Ritm = 1.86 W/m (Confirmed with Optickle; Note that Optickle gives half of this since it gives demodulated signal with demod gain of 0.5)
| Effective input power: Peff=7.3uW (measured), Modulation depth beta=0.07 (alog #9395), Modulation frequency: fmod=5*9099471 Hz (alog #9695), Schnupp asymmetry: lsch=0.08 m (alog #9776)
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PD responce of REFLAIR_A: eta1064 = 0.76 A/W (Perkin Elmer C30642)
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Trans impedance: Z = 341 Ohm (LIGO-S1203919)
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Cable loss: Closs = 0.81 (measured; alog #9630)
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Demodulator gain: Gdmd = 11 (measured; nominally 10.9 according to LIGO-F1100004)
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Whitening gain: Gwtt = 45 dB (set by H1:LSC-REFLAIR_A_RF45_WHITEN_GAIN) (Anti/Whitening filters and AA filters are ignored here since they have DC gain of 1; see LIGO-D070081 and /opt/rtcds/rtscore/release/src/fe/controller.c)
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ADC conversion: V2C= 2**16/40 counts/V
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H1:LSC-REFLAIR_A_RF45_(I|Q)_IN1
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H1:LSC-REFLAIR_A_RF45_(I|Q)_GAIN = 5
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MICH error signal (H1:LSC-REFLAIR_A_RF45_Q_ERR) [counts]
Muliplying these numbers gives dPmod/dl * eta1064 * Z * Closs * Gdmd * Gwtt * V2C * 5 = 6.2e9 counts/m (with error of ~10%)
The measured value using Michelson fringe was 7.6e9 counts/m on Feb 17 (alog #10127), and 6.8e9 counts/m on Jan 30 (alog #9698). So, the expected value and the measurements agree within ~20%.
MEASUREMENT DETAILS
In the process of constructing the calibration chain, we ended up repeating some measurements that were done previously.
We re-measured the power in front of REFLAIR_A. With the PRM aligned, the DC output was 2.35(1) V, and with the PRM misaligned (so that the beam is predominantly the reflection from ITMX), the DC output was −1.30(3) mV. The dark voltage was −1.84(5) mV. The net voltage with the PRM misaligned is then 0.54(6) mV. Using the DC transimpedance (98 Ω) and responsivity of the PD, this gives a power of 7.3(7) μW. Additionally, the ratio of aligned to misaligned is 4.4(4) × 103, and the expected ratio is Ritm/(Tprm^2)*4 = 4.4 × 103, so we have good agreement.
We also used the Ophir power meter to measure the power with the PRM aligned; it was 33.9(1) mW. The power with the PRM misaligned was too small to see with the meter (we couldn't figure out how to remove the filter on the head).
We measured the demodulator gain by driving the RF input of the demodulator with a −10.0 dBm sine slightly offset from fMod, and then watching the Q monitor on a 50-Ω impedance scope. The ratio of pp voltage on the scope to pp voltage of the input sine was found to be 0.51(2). The output impedance of the monitor is 499 Ω, and after the monitor there is a symmetric drive (giving an extra factor of 2), so the gain is actually 11.2(4).