I redid half-PRC mode scan by applying mislignment to PRM.
Half-PRC's sagittal g-factor is 0.9837 +/- 0.0006 and tangential g-factor is 0.9929 +/- 0.0005.
sagittal g-factor is 0.968 +/- 0.001 and tangential g-factor is 0.986 +/- 0.001. (Edited by YM; see elog #8056)

Method:
 1. Same as elog #8049, but with small misalignment to PRM.

 2. Algined half-PRC, and misaligned PRM in pitch to get sagittal g-factor.

 3. Restored pitch alignment and misaligned PRM in yaw to get tangential g-factor.

Result:
 Below left is the plot of POP DC and PRCL error signal (REFL11_I) when PRM is misaligned in pitch. Below left is the same plot when misaliged in yaw.
left:    right:

 By averaging 5 sets of peaks around TEM00, I get sagittal/tangential g-factors written above.

Discussion:
  The fact that tangential g-factor is larger than sagittal g-factor comes from astigmatism mainly from PR3. Effective PR3 curvature is

sagittal Re = R/cos(theta) = -930 m
tangential Re = R*cos(theta) = -530 m   (where R = -700 m , theta = 41 deg)

so, PR3 is more convex in tangential plane and this makes half-PRC close to unstable. This is opposite of Jamie's calculation(elog #8022). I'm confused.

  I first thought I don't need to misalign PRM because alignment was not so good - it was hard to align when beam motion is large. Also, this motion makes angular misalignment, so I thought free swinging is enough to make higher order modes. However, misaligning PRM intentionally made it easier to resolve higher order modes. I could even distinguish (10,01) and (20,11,02), as you can see from the plot.

Next:
  We have to compare with expected g-factor before moving on to PRMI.