In the attachment please find plots comparing controller output, local damping output, and error signals.
Input noises of the simulation are seismic noise, osem noise, input power fluctuations, sensing noises of WFSs and QPD, and air turbulence noise for WFSs. There is also optical torque noise (radiation pressure effect).
The procedure to get optical gains and sensing noises:
Having the actuator response A rad/cnts @ 3 Hz. I was shaking MC1/2/3 in pitch with B cnts @ 3 Hz and getting WFS1/2 QPD signals of C cnts @ 3 Hz, which means WFS1/2 QPD optical gain is D cnts/rad = C / (A * B) cnts/rad. So, if WFS1/2 QPD IN1 has a noise spectrum (at higher freqs) of E cnts/rtHz, that corresponds to E/D rad/rtHz of sensing noise for WFS1/2 QPD.
Actuator response [rad/cts] I was getting shaking mirrors at 3 Hz and measuring amplitudes of OSEM output (knowing the geometry of the mirror). I scaled it to DC. From here I was getting ct2tau_mc (knowing the mirror's moment of inertia, Q, and natural pitch frequencies). OSEM calibration factors [cts/rad] I was getting from the input matrix and geometry of the mirror.
The flat noise at higher frequencies from the local damping and controller output channels is presumably quantization/loss of digits/numerical precision noise which I don't include in simulations for now?!
Regarding air turbulence, in KAGRA it has been reported that air turbulence introduces phase fluctuations in laser fields that propagate in air. According to Kolmogorov’s theory, the PSD of phase fluctuations caused by air turbulence scales as ∝ L*V^(5/3)*f^(−8/3). Here, L is the optical path length and V is a constant wind speed. Since it is not obvious how can one estimate typical V in the beam paths I was taking this excess noise from the error signals data between 10 Hz and 50 Hz, extrapolated it taking into account ∝ f^(−8/3) (not for frequencies below 2 Hz, where I just put constant, since it would go too high). I expect that I won't be able to get a parameterized model that also predicts the absolute value. The slope is all I can hope to match, and this I already know. QPD chamber is much smaller (and better isolated?) and there is no this excess noise.
Regarding other things in simulations (very briefly): beam-spots are calculated from angular motions, length change is calculated from beam-spots and angular motion, cavity power depends on length change and input power, and torque on the mirrors depends on beam-spots and cavity power. From other things, local-sensor basis conversion (and vice versa) is worth noting. |