[Miyakawa, Kokeyama, Michimura]

I've made a first Michelson noise budget using Simulink NoiseBudget.
Currently, You can run NoiseBudget only on k1script machine (see wiki for usage; thanks to Kokeyama-san and Miyakawa-san!).

Result
 0. MICHNB.png is the screenshot of the current model. The model is /kagra/kagranoisebudget/iKAGRA/Michelson.slx. You can run this model with run_Michelson_NB.m in the same directory.

 1. MICHOLTF.png is the plot of openloop transfer function of Michelson lock. Blue line shows the OLTF simulated with NoiseBudget model. Red dots are the measured data by Miyakawa-sab on Mar 24. They agree pretty well, but gain differs by factor of ~1.6. This could be from the contrast difference.

 2. MICHNoiseBudget.png is the noise budget. "Intensity noise" is the measured intensity noise of IMC transmission using K1:IMC-MCL_TRANS_OUT_DQ. The intensity noise coupling factor was estimated using eyeball fitting, so the mechanism is not completely understood (see klog #1209). "Seismic noise" is the modeled Type-C seismic noise. See below for more details. "Sensor noise" is currently limited by ADC noise, and "Actuator noise" is currently limited by DAC noise.

Details of the model and discussion
 = ADC and DAC, AA and AI filters, whiteing and dewhitening filters =
  - ADC has a factor of 2^16/40 counts/V
  - DAC has a factor of 20/2^16 V/counts
  - Analog AA/AI are 3rd-order Butterworth at 10kHz
  - Digital AA/AI are also assumed to be 3rd-order Butterworth at 10kHz for now (see /opt/rtcds/rtscore/release/src/fe/controller.c).
  - Whitening and dewhitening filters are all turned off

 = PD signal chain and sensor noise =
  - REFL DC PD is Thorlabs PDA100A, and has response of 0.3 A/W, and transimpedance of 0.75e3 V/A with 0dB setting
  - PD dark noise is assumed to be zero now (TO DO).
  - ADC noise is included in "Sensor noise" and I used the measured value I had measured at LHO.
  - Intensity noise is coupled in the PD signal chain (see Result section above).

 = IFO optical responses and noises =
  - Michelson optical gain is the measured value by Ando et al (klog #1169). 2.3e10 counts/m (counts at REFL_PDA1_DC_OUT / Michelson differential length lx-ly) correspond to 6.2e4 W/m. Currently, the input power at BS is P0 = ~250 mW. Thus, theoretial optical gain should be 2*pi*nu/c*P0 = 1.4e6 W/m. So, current optical gain is more than 20 times smaller than the simplified theoretical value. Bad contrast, clipping, ETM transmissivity, etc. could be the reason.
  - K1:LSC-REFL_PDA1_DC_OUT during lock is roughly 3000 counts, which correspond to ~8 mW. The shot noise is calculated using this value
  - "Frequency noise" is a modeled frequency noise of IMC (see /kagra/kagranoisebudget/FSS/KAGRA_FSS.mdl model).

 = Suspension chain and noises =
  - TM actuation resoponse is assumed to be a simple pendulum with resonant frequency of 0.87 Hz with Q = 3.5 (see K. Arai Master Thesis). The gain was adjusted so that it matches with the measured value by Ando et al (klog #1169). The actuation efficieny at DC is 5.2e-7 m/V, at 80 Hz is 5.9e-11 m/V (this correspond to 1.8e-14 V/counts). Factor of 6 discrepancy with independent actuator efficiency measurement is still a mystery.
  - Coil driver noise is the modeled High Power Coil Driver noise calculated in LIGO-T080014, and included in "Actuator noise."
  - As for DAC noise, measured ADC noise is used with some factor to match with the measured noise level (see this report for the noise level). The DAC noise is included in "Actuator noise."
  - "Seismic noise" is a modeled Type-C noise and injected for BS, ETMX, and ETMY. The model equation is 8e-9*freq.^-2./(1+(2./freq).^-8) m/rtHz.

 = LSC filters and matrices =
  - LSC filters are made in Matlab so that it match with K1:LSC-MICH filter bank. This should be replaced with LiveParts.
  - Inpurt matrix and output matrix are set to match with current situation (use REFL_PDA1_DC, actuate on ETMX and ETMY). This should be replaced with LiveParts.

 = Calibration =
  - The calibration was done by using the measured data at K1:LSC-MICH_OUT, and this is calibrated into Michelson differential length (lx-ly).

Next:
 1. Replace filters and matrices with LiveParts
 2. Currently, NoiseBudget cannot get online data. Make it use online data (with help from Hayama-san).
 3. Add many more noises