[Ushiba, YamaT]
 

Abstract

We made a noise projection plot link below.
https://dac.icrr.u-tokyo.ac.jp/KAGRA/DAWG/Detchar/klog/klog23945
This plot contains MICH to DARM, CARM to DARM, PD dark noise, DAC noise of Type-A suspensions.
There is still unknown noise which is 10-times larger than DARM sensitivity in the frequency range of 100-1000Hz.
 

Details

For all noise estimation below, whitened displacement signal as CAL-CS_PROC_DARM_DISPLACEMENT was corrected to the true displacement
by applying zpk([1,1,1], [100,100,100], 1e-9).

MICH to DARM
Transfer function from BS_TM_SUMOUT_L_OUT to CAL-CS_PROC_DARM_DISPLACEMENT was measured and stored as
/users/Commissioning/data/MICH/2023/0212/TF_BSL2DARM_20230212.xml.
Because this was measured with the white gauss injection, there was no coherence in some frequency region and noisy transfer function was available as shown in Fig.1.
So I roughly fitted by using f^-2 and decided a gain factor at 1Hz to make a model transfer function from MICH control to the DARM displacement.
MICH to DARM projection was made by applying modeled transfer function for the MICH control signal.

CARM to DARM
Transfer function from REFL_PDA1_RF45_I_ERR_DQ to CAL-CS_PROC_DARM_DISPLACEMENT was measured and stored as /users/Commissioning/data/IMC/2023/0212/TF_REFL45I2DARM_20230212.xml.
This was measured with the swept sine injection. So the transfer function with enough coherence was available as shown in Fig.2.
For this reason, I directly applied the measured transfer function for the CARM error signal.

PD dark noise
We measured noise spectra of CAL-DELTAL_RESIDUAL which is (1/C) * DARM_IN1 when all laser shutters were closed.
'C' means the sensing function including optical gain, coupled cavity pole response and all circuit and digital filter responses between DARM displacement to the DARM error signal.
(Strictly speaking , effects of super-Nyquist zero/pole for 16kHz were ignored.)
And also, we know current PD dark noise is limited by ADC noise in almost all frequency.
So after whitening filter will be engaged, it will be modified.

DAC nosie
Transfer function from each test coil actuator (COILOUTF_H[1-4]) to CAL-CS_PROC_DARM_DISPLACEMENT_DQ had been measured by Tamaki-kun as shown in Fig.3.
We estimated the DAC noise contribution by used these transfer functions.
Because transfer functions from TM coil of all four Type-A suspensions have similar gain (within +/-1dB),
we estimated the total noise contirbution of TM coils as the multiplication of a factor 4 (=\sqrt{16}), nominal DAC noise level (~1uV/rHz),
and a transfer function from one coil to DARM displacement (/users/tamaki/low_noise/noise_projection/20221222/ETMY_coil_tm_H1.xml).