We've hit a flat (white) noise floor at around 70 mHz/rtHz.  Time to tally all the unaccounted for noises.

Photo detector sensor contributions

Here the FSS resonant detector dark noises were measured using a Lv13 ZX05-1MHW+ mixer with a 4th order LP + 50 Ω terminator on a SR785.  

Frequency equivalent noise is just input referred noise divided by the PDH discriminator value. The PDH discriminator value is computer assuming gamma=0.3 rad modulation depth, visibility of 0.5, Finesse of 15000, cavity length 3.8 cm.  This gives 4.4 nV/Hz for the slope of the error signal about resonance.

BN detector input referred noise is just input referred power divided by 1/2 Vpp of the beat note.  For 0 dBm beat note, then input equivalent power is (dividing through 1.27 kΩ TI gain) works out to 0.25 mW/rad.

So the upshot  is that there is too much FSS RFPD noise to see Brownian noise clearly but is not our current dominant noise source. We are missing about 69.6 mHz/rtHz.

Also noise contributions​ at the summing stage in FSS

I'm including this because it was a question we thought about and dismissed.  There is a 100kΩ - 1 µF - 100 kΩ  LP filter from the FSS offset channel into U3 on the servo board (R8-C5-R9, in D040105-C). There is an estimated 0.4 pA/rtHz of thermal current noise there. Also the AD829 has a current noise of 1.5 pA/rtHz  (op amp U3).  These are additive and indistinguishable from sensor noise.  The mixer output equivalent voltage noise is just the equivalent voltage across R3 and R9 in the FSS RF board (LIGO-D0901894): i.e. 0.4 pA/rtHzx146 Ω = 58.4 pV/rtHz at mixer output.  Dividing back through the mixer conversion, transformer coupler and PD gains (see PSL: 2242 for values and links) we come to some input referred noises in units of optical power tabulated below.

So electronic noise, at least from the point of summing the error signal with offsets is negligible.  We might want to revisit this later, but most points of noise injection into the FSS loop will be suppressed by the closed loop function and will be small.

Laser frequency noise

The current state of the FSS loops is ~180 kHz UGF for north and ~70 kHz UGF for south (woeful).  South is worst because the RF PD has only half the TI gain and we are at maximum gain for the FSS variable gain stages.  The whole point of these loops is to suppress laser frequency noise.  Their current performance is just not good enough.

If we assume that the laser noise is modeled as

and that we need a clearance of 10 dB at the 100 Hz point where we expect to see Brownian noise (10 mHz/rtHz @ 100 Hz), then we need to get to 1 mHz/rtHz or a a factor of 1e5 1/(1+G) suppression. This means that its very likely that our current limitation is actually FSS loop bandwidth.

Here is what we need to do.

Naively if we assume 1/f loop shape, that means that we would need a UGF of 10 MHz to reach 1e5 gain by 100 Hz.  Nope.  Of course we have some loop shaping in the lower frequency reaches of the PZT path of the FSS.  There is a boost pole-zero pair installed in the common path (PZT servo path U7) that uses R29 of 5.6 kΩ and capacitors of either 4.7 µF or 6.8 µF depending on the box.  This would put the corners between 6.0Hz and 4.1 Hz, too low (don't know why so low). If we move the boost up to 1 kHz or higher then we would be able to reach 1 mHz/rtHz by 100Hz with a overall path open loop gain crossing 0dB at 1 MHz.

Right now we cannot turn up the gain of the loops much more than 200 kHz.  We can see from looking at the EOM control signals that above a certain amount of OLG the EOM is taking too much of the actuation load and rails.  Basically the the cut off frequency for the EOM servo is not aggressive enough and the EOM is working too hard in the frequency band below 10 kHz where the laser PZT should be doing the heavy lifting.  I outlined some of the changes that need to be done in PSL:1902.  This is based on Matt Evan's modifications of the MIT Squeezer FSS system. 

MIT's FSS boxes are a few versions on from our FSS boxes but the main points remain:

• R19 24.9k to 2k (lower first zero from 1.94 kHz to 24.1 kHz)
• C23 1uF to 33nF (more AC coupling, move first zero from 145 Hz to 4.38 kHz)
• C24 1uF to 100nF (more AC coupling, move second pole from 122 Hz to 1.22 kHz)

In addition to this we want to modify the boost stage by removing the ~5 µF chunkers and trying something more like 28 nF or more.  I think what we need here is a metal film cap (no ceramic) and the question is whether setting the corner so high will be an issue with it railing between locks if there is some kind of offsetting there.  Maybe this isn't an issue.

These are relatively​ strait forward changes providing we have the appropriate capacitors in stock. It seems like boosting FSS UGF by offloading EOM path LF onto the PZT and making the boost good is the most obvious way to squash this noise and make fast progress.  Lets try and hit the 1 mHz/rtHz target with a 1 MHz FSS UGF effort.

Efforts on characterizing thermal sensors need to wrapped up but we want to get to our actual noise source.  The more recent PID improvements on the cavity temperature control (PSL:2295) have gotten us to a point where we have usable 1kHz/V VCO measurements which is as good as we need for now. Maybe a shift in effort from thermal control to laser stabilization is the best use  of our time.

I've attached a block diagram of the FSS controls below.  It shows at a glance the current configuration of the EOM, PZT and slow laser controls.

Edit awade Sat Feb 2 00:44:47 2019: Revised down FSS shot noise estimates based on correct sidebands, visibility and modulation depth values (from Tara's thesis).