[Lee, Torrey, Daniel]

On Friday, we adjusted the loop shaping on the filter cavity to try and make the lock better. With a 1/f loop, it will lock, but goes between flickering out of lock, to oscillating as the gain is increased.

The new shaping uses the "slow" output of the "laser lock box." It shapes the fast output to have a 10Hz - 200Hz boost (pole - zero), giving 20x gain at low frequencies. The overall 1/f is then put at 1Hz in the slow path. We are able to get a UGF of 1kHz, with 30-40deg remaining. We lose 90deg by 2kHz from either the actuator or the Moku, so 1kHz is around the max UGF we can currently get.

Even with that loop, we get dropouts while talking loudly or while the fans are on. Problematic. That mean the loop can supress the peak length noise below 1.5um / 2  / (2 * finesse). Our current input coupler is 1%, so our finesse is around 2pi / 0.01 = 600 (it might be as low as 300, depending on the losses in the cavity). So our peaks/RMS are around 0.5nm - 1nm of noise.

+1 to the piezo transfer teams. both 11380 and 11373 have the transfer function data along with the plots. It looks like all of the phase we are losing in the cavity lock is from the piezo (though could still be from Moku). We'll need to fit and at least slightly invert this actuator transfer function to make a loop above 1kHz UGF. The fit can help tell us how much of the phase is from the piezo roll-off.

We are going to need it - the current loop & cavity  has marginally too much noise, with an RMS around the linewidth. That is going to be a problem once we increase the finesse of the cavity. So we'll need to reduce the noise and/or improve the loop a respectable amount.

our voices are driving 100-300Hz, so we need gain there. If we can get the UGF up as high as 3kHz, then we should also be able to move the boosts up to 600Hz or so. That should give 9x more loop gain and cover much of the need.

options:

frequency lock - good for acquiring and transitioning to aggressive lock, but not an option for operating the experiment

optimal control - we can determine how good we can do with what we have

fitting/inverting actuator - probably needed to get UGF higher. May vary with time in bad ways

sound attenuation or active noise cancellation - may be possible and should look into engineering this.

We should determine if the sound driving is from pushing the mirrors or from the index fluctuation as the pressure modulates. 11290 has calculations about the pressure pushing on a 1kg mass. My worry is that the small alignment adjust set-screws in the MKS flexture mounts are fairly compliant. Could sound drive them 1nm?
My guess is that the light going through 2m of air is the culprit.

The sound pressure of 40dB should be around 2000uP. Air pressure is 101kPa. The index of air is 1.000293

2m / (1.000293**2) * 2000e-6Pa / 101kPa * (1.000293 - 1) = 1.2e-11m

So that is a little small, but if our sound is at 80db, which would be quite loud, then it would be enough to cause this.

For the mirror motion, the mirror mounts are about 1.5in square. On the pressure level that is

(.0254m * 1.5)**2 * 2000e-6Pa = 3e-6N

of the mirror+panel is about 35g (very rough estimate). For a free mass motion that is

1 / ((2 * np.pi * 100Hz)**2 * 0.03534291735288516kg) * 3e-6N = 2e-10m which is getting in the ballpark with 60db of noise rather than 40db. The mirrors aren't free though.

and now I'm curious how that is against the spring constant of the tiny screw.