- Motivation

We found that we need to look into the entire end PDH loop to figure out what causes the worse noise level of the Y-arm than before.(entry)
Today, I measured in-loop noise of the end PDH loop and the ALS loop with different end PDH servo gain of Y-arm to make sure the PDH servo gain change the noise level of the ALS control loop.

- What I did

Measuring the OLTF of the end PDH loop:
1. Measured the OLTF of the PDH loop with the end PDH servo gain 6 and 7.

The UGF and  phase margine: 16 kHz and 53 degree(gain 7) 

                                             7.8 kHz and 86 degree(gain 6)

I couldn't measure the OLTF with higher servo gain than 7 because the loop was not stable enough. I guess that is because of the noise of the SR560, which I used for node of the excitation signal.

Calibration of the end PDH error signal
2. Locked the cavity using IR and turn on the notch filter at 580 Hz of the C1:LSC-XARM. Excited the ETMY using awg with sinusoidal signal at 580 Hz. Set the end PDH servo gain to 6 and measured error signal of the end PDH. The calibration factor of the end PDH error signal H is calculated by

H = abs(G + 1) / A * Verr / Vin

where G is the OLTF of the end PDH, A is the actuator response of the ETMY, Vin is the amplitude of the excitation signal and Verr is the error signal at 580 Hz. This H convert the  error signal to the fluctuation of the cavity length, so it has the unit of V/m. We can change that unit to V/Hz by multiplying f/L, where f is the laser frequency of IR and L is the length of the arm. In this case the H convert the error signal to the fluctuation of the resonant frequency of the cavity.
 The actual number was

H = 1.4e7 [V/m]  (2.0e-6 [V/Hz])

In-loop noise of the end PDH loop
3. Measured the error signal of the PDH loop with the end PDH servo gain of 6.0, 7.0, 8.0 and 9.0. I calibrated these signals with above H, so  these unit is Hz/rHz. I attached the result of these in-loop noise. When the end PDH servo gain is 9.0, the end PDH loop looks unstable. And 8.0 looks to be the optimal gain in terms of the in-loop noise of end PDH loop.

ALS in-loop noise:
4. Stabilized the Y-arm with ALS control loop with different end PDH servo gain, and measured in-loop noise of the ALS control loop. I attached these results and discussed about this results below.

- Discussion

 Now we can say that too high PDH servo gain makes ALS loop very noisy. Compare to when the PDH servo gain is 7 or 8, the ALS in-loop noise is roughly 4 times higher when the PDH servo gain is 9.0, which means the PDH loop is not stable. However between 100 Hz and the end PDH in-loop noise has no big difference between when the servo gain is 6 and 9. If this high frequency noise comes from the end PDH control and this effect is linear, these noises should be same level. Also the PDH servo gain of 7.0 looks optimal gain in terms of the in-loop noise of ALS control loop, although the 8.0 has smallest end PDH in-loop noise. Actually PDH in-loop noise are smaller than ALS in-loop noise.

 I'm wondering what causes the 60 Hz peak in black curve. When the gain become higher, the peak at 60 Hz looks to become larger. The UGF of the ALS loop is above 100Hz, so  it's not because of that. I feel there is some hint for understanding this result in this peak.

From this observation, I could make sure that the end PDH servo gain change the ALS in-loop noise, but that effect doesn't look so simple.

By the way
 We should take care about 60 Hz comb peaks.  You can see huge peaks in PDH in-loop noise and also in ALS in-loop noise.