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Message ID: 8489     Entry time: Thu Apr 25 03:35:28 2013
Author: Jenne 
Type: Update 
Category: Locking 
Subject: Angular motion does not explain RIN 

Den made a nice elog about the PRMI RIN that we see a few weeks ago:  8464.  The RIN that we're seeing is typically about ~30%.  The question at hand is: what is causing this power fluctuation, and more specifically, is it the angular motion of the mirrors?

I find that no, the angular motion that we see does not explain the RIN that we see.

In the attached Mathematica notebook, I calculate the power lost due to angular misalignments of one or more mirrors.  (Math comes from Appendix A of Keita's thesis.)

From calibrated oplev spectra, our mirrors are moving about 1 microradian (RMS, which is dominated by low frequencies).  From a super sophisticated "draw on the TV, then measure" method (details below), I have estimated that the maximum static misalignment that we're seeing is about 2 microradians.

With all of this, I find that for a g-parameter of 0.94, the power lost due to misalignments should, at maximum, be 0.6%.  I need a g-parameter of 0.995 to get a power loss of 23%.  Alternatively, if I take the derivative of the power coupling function, to find the static misalignment at the steepest slope of the curve (and thus, the place where any AC misalignment would have the most effect), for 1urad of AC misalignment, I get 40% power loss. 

So, in order for the AC angular motion that we see to explain the RIN that we see, either our mirrors are very, very misaligned (so much so that we couldn't really be locking), or our cavity is much closer to unstable than expected from Jamie's calculations.  Since both of these cases (static misalignment or incorrect g-parameter calculation) have to be taken to extremes before they approximate the RIN that we see, I do not think that this power loss is due to angular fluctuations.

This means that we have to think of another potential cause for this RIN that we're seeing.

Details on the "draw on TV and measure" technique for determining static cavity misalignments:  Looking at the POP camera view, with the PRM significantly misaligned, I traced the straight-through beam spot.  I then restored the PRM, and during several momentary locks, I traced the beam spot, which I took to be the saturated area of the camera.  The idea here is that the straight-through beam represents the incident beam axis, while the locked beam represents the cavity axis.  I'm assuming that the camera image plane is at the face of PR2. I approximately found the center of each of my tracings, and found them to be ~1/4 inch apart.  I also measured the "spot size" of the sideband-locked PRMI, and found it to be ~3.5 inches.  So, very roughly, the ratio of (distance between spots)/(size of beam) is ~0.07. This corresponds to a static misalignment of either the ITM or the PRM of ~2urad, rounding up. (I use the Jamie's calculated g-parameters from elog 8316, the case of flipped PR2, tangential = 0.94 to calculate the effective RoC of the PRM). 

Attachment 1: RIN_estimation_from_angular_motion.nb.zip  25 kB
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