(This is the alog for measurement proceeded at beginning of August)

Summary

We measured JAC's LSC in-loop error signal (JAC-L_SERVO_IN1) across the 2–62 W power sweep, calibrated each dataset from its own 30 Hz line, and built a residual length-noise budget (in-loop residual, sensor floor, shot floor). IMC locking reduces the equivalent laser-frequency noise by ~1.9× over 7.5–76.7 Hz (peak ~2.6× near 12 Hz); above ~30 Hz the residual is sensing-floor-limited. This budget is the input to the excess intensity- and frequency-noise coupling estimates.

Measurement

• Data:, 2 / 35 / 62 W input (plus an unlocked set), each carrying a 30 Hz JAC-L_SERVO_EXC calibration line.
• Error signal: JAC-L_SERVO_IN1
• Main comparison: 35 W IMC-on vs 62 W IMC-off — both high-power, single-FSS-stage, each with its own directly measured optical gain.

Analysis

• Open-loop gain G = A·F·H. A (actuator) and F (servo filter) imported from the OLG fit and treated as power-invariant.
• Optical plant H(f) = optical_gain / (1 + if/f_pole), with optical_gain measured fresh per dataset from its own 30 Hz line. f_pole ≈ 593.9 kHz (ring-cavity FSR).
• A is found in alog 89399
• Free-run length noise: L_free = (IN1)·|1−G|/|H|.
• In-loop residual (closed-loop, as sensed): (IN1)/|H|
• Sensor floor: current-configuration dark reference, re-scaled per dataset by PSL power and |H|. Shot floor: sqrt(2·e·I_dc), I_dc = R_PD·P_refl from each dataset's own REFL DC.
• Total residual: sqrt(in-loop² + sensor² + shot²).
• Frequency-noise equivalent: δν = L_free·ν/L_cav (ν = c/1064 nm, L_cav = 2.02 m).

Result

• IMC on vs off: reduction of ~1.9× over 7.5–76.7 Hz (peak ~2.6× near 12 Hz), extracted data-driven from R(f) = off/on (log-frequency rolling median, threshold 1.3), not an assumed band.
• Residual budget: above ~30 Hz the in-loop residual sits at the sensor / shot floor (sensing-floor-limited); below that it is above the floors.
• OOL cross-check: the WFS SUM_A out-of-loop sensor, calibrated in situ from the same 30 Hz line, was used to cross-check the residual errors. At low frequencyes, it has a higher sensor noise then residual, and it can't be good sensor for those frequencies

Next

• This residual budget (m/√Hz, per dataset) is the direct input to the excess intensity-noise (RIN) and phase/frequency-noise coupling estimates for JAC.

Figure: free-run length noise with the sensor noise

Figure: residual noise budget — in-loop residual, sensor floor, shot floor, and their quadrature sum

Figure: equivalent laser-frequency noise, IMC on vs off,