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Message ID: 1340     Entry time: Sun Mar 6 15:38:15 2011
Author: Zach  
Type: Laser 
Category: GYRO 
Subject: more noise analysis -- optical gain problem 

I have been saying things like "the new PD is lower-noise than the PDA255". This is not true; the output noise is actually a bit higher even. The way we win is thus because the transimpedance is a little bit better and more importantly because the dynamic range is much higher. Here is the demod noise analysis akin to that from this post for the PDA255.


In my post about the shot-noise-limited locking scheme, I claimed that the input-referred noise of the RFPD was well below our requirement curve. This is not true at the moment because of (still) poor optical gain. I calculated that based on the theoretical maximum optical gain in V/Hz we could obtain, assuming that we could at least do as well as a sizable fraction of that. More on this later, but it appears that the purely optical component ([W/Hz]) is orders of magnitude lower than it could be, despite the fact that we are getting ~50% transmission through the cavity.

Since residual common mode noise ("spillover noise") has been our main obstacle to date, I decided to do some analysis of the primary loop error signal before bothering to put together the rest of the gyro. Here is a busy plot, followed by a wordy explanation:


Note: all traces are calibrated to units of (rad/s)/rHz by dividing the error signal noise level by the appropriate optical gain in V/Hz and then multiplying by (lambda S / 4 A) to get rad/s. Also note that the overall OLTF of the primary loop is roughly the same for all the plots (not entirely true, as I was only able to get our UGF up to about 10 kHz as opposed to the ~15 kHz we had before).

  • Blue trace: this is the error signal noise of the last working state of the gyro, as found in the noise budget. Check that to jog your memory, but otherwise just remember that it accounted for all the gyro noise above 30 Hz, and that we think given the new vacuum system and IOO enclosure it will account for it all below this frequency, as well. The broadband floor at around 6 x 10-7 (rad/s)/rHz was discovered to have been caused by the PDA255 we were using as the REFL PD.
  • Green trace: this was the same error signal as of yesterday morning, with the new PD and the PDH #1437 box modified to have lower gain to accommodate the higher optical gain (from simple power increase on the PD). You can see that the noise is lower below about 100-200 Hz. It is not as much better as we'd hoped because of the increase in output noise level and slight decrease in open-loop gain (that is, since our OL gain went down slightly, the optical gain did not increase exactly as much as our PDH gain decreased). Above this frequency, the noise is dominated by mechanical vibrations and will require a real increase in OL gain to reduce. Barring down-conversion, though, we don't really care what is happening at these frequencies since we don't plan to operate in this band.
  • Red trace: This is the measured, bright output noise of the demod setup calibrated to rotation sensing noise in the same way as the error signal. It accounts for the new low-frequency noise level of the error signal in green.
  • Cyan trace: I realized that since the output noise of the PD is higher than the input noise of the PDH box or of the mixer, and since at this point I didn't have that much light on the PD, I could improve the low-frequency noise simply by redistributing the gain: attenuate signal between the PD and the mixer while increasing the optical power proportionately. I did this to the tune of 13 dB (which made the optical power ~100 mW---we don't want it any higher on the PD), and you can see the direct improvement from the green trace to the cyan trace.
  • Magenta trace: this is the same as the red trace but minus 13 dB from the improvement explained in the last bullet. It is higher than the actual error signal below ~8 Hz because I also did an EOM RFAM minimization in the time between when the two error signal spectra were taken. I think a new measurement of the PD/demod noise would show that it is right were the cyan trace is at low frequencies.

So, the low-frequency spillover noise is now ~30x better than it was in the previous setup. I would put on a party hat and dance in a circle, but this is shit: we are still something like a factor of 200 away from the sensing requirement from 200 mHz - 1 Hz, and worse at 100 mHz since the requirement drops down there. We cannot fix this by adding servo gain as we were planning to do for noise here caused by mirror motion, etc; this is sensor noise, so we need to improve SNR up front.

This is why, in my last post, I suggested we do away with the Cougar---it takes away SNR where we are dying for it, while in the current case we are just attenuating the signal downstream. We also need to improve our modulation depth. Right now, we are at < 0.3 rad, whereas we want something like 1 rad for best signal.

Here's the confusing thing: right now, we have a pure optical gain (cavity response) of ~4 nW/Hz, whereas the theoretical maximum is something like 1 uW/Hz for our power level and cavity parameters. Why is our cavity response so piss-poor? Increasing the modulation depth could improve this by a factor of 4 or so, but that still leaves us at around 1% of the available response. This would seem to fit with my observation that coupling our astigmatic beam to a non-astigmatic-but-elliptical cavity mode should lead to ~1% overlap with the solution that gives 99% coupling for an ideal input beam, but the fact remains that we are still coupling ~50% through the cavity! It is as though this light is not contributing to the error signal but still fits in the cavity mode at the same frequency and just comes along for the ride! What?!

Yes, I have considered that there could be something going on with the demodulation (mixer starvation, non-optimized phase angle, etc.), but this won't account for it because any attenuation there should also attenuate the noise level out of the PD, which appears in the error signal exactly as predicted.

Any ideas?

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