By using PReQua (Phase locking Real-time Quality factor estimator: I gonna report the detail about that system later), finally, I found a problem with our previous diagonalization. We totally forgot about the relative phase of each basis.

I measured the coupling ratio of ITMY TM oplev at 7.5 Hz and 0.6 Hz resonance. As we know, the ratio for each resonance is totally different such as:

7.5 Hz -> P:Y = 1 : 0.14

0.6 Hz -> P:Y = 1 : 0.26

However, from the PReQua measurement, I could find a relative phase of 11 degrees and 46 degrees for 7.5 Hz and 0.6 Hz resonances, respectively.

This means the oplev beam motion is not linear, but elliptical. I write the plot of that elliptic, as shown in the attached figure. Now, everybody knows what the diagonalization angle is. I also put the line corresponds to the diagonalization axis, which we did estimate only with the coupling ratio.

The ellipticity might comes from roll motion since the oplev beam does not hit the center of the mirror. This also answers for our low reproducibility of diagonalization. The coupling ratio depends on the ellipticity corresponding to roll motion.