I measured Q factor for a few modes of refcav's suspension system, by shadow sensing technique, and found out that

The modes with high Q are associated with spring motion.

The vertical spring mode has Q ~ 1800 at 3.45 Hz.

Q from swing modes are not so high, ~ 150.

We will try to get rid of the springs later.

The setup is posted by Frank, see below. For sensing technique, A HeNe laser is used for

a light source and adjust so that half of the power is on the PD when the cavity is still.

Then each mode is excited, as the cavity moves, the power on the PD oscillates due to

part of the beam is sinusoidally blocked by the cavity. Then the voltage is monitored and recorded.

Details about how Q and amplitude relates is in 40m wiki page here.

The results are summarized below.

 mode                                             f0                  Q

swing (along the cavity axis)       2.25 Hz          144+/- 5

Vertical (spring)                           3.45 Hz            1800

Tilt                                                3.55 Hz       ~ 1500

Swing(left/right)/roll                     2.0 Hz            150+/- 10

Yaw                                              ~ 3Hz             N/A

1) For swing mode, the Q is low, it can be seen easily when the amplitude drops by a factor of 2 in 20 second span.

 2) However, for vertical spring it took ~ 2 mins before the amplitude decays by a factor of 2, so I measured the time

(~130 sec) and calculate Q, and plot it on a 20 second time span. I tried to excite only one mode, but it seems to excite

tilt as well, we can see the beat at ~ 0.1 Hz. Tilt is @ ~3.55 Hz, and its Q is might be about the same.

This 0.1 Hz beat also presents when I measured Q for tilt.

3) Left/Right swing and roll mode are hard to distinguish, so I treat them as one mode.

4) Yaw is really hard to measure alone, every time I excite Yaw, vertical

and tilt always couple in. I cannot get nice data out of Yaw yet, but Q seems to be pretty low.

and f0 is ~ 3Hz.

So it seems that vertical motion is crucial. The peak in beatnote has a highest peak around 3.45 Hz.

I'll add the seismic from the spring mode in the nb.

 I add the effect from the suspension to the noise budget. Assuming no cross coupling among any modes, and

treat only seismic from vertical motion and horizontal motion along the cavity axis.

(vertical mode and along the axis swing mode)

In the model, seismic (acceleration) coupling to frequency noise via cavity's sagging. No

scattering is taken into account.

Originally, in the noise budeget we have

1)velocity data from the seismometer, v,

 2) times the transfer function through double stacks.

3) times (2 pi f) to convert velocity to acceleration

4) times a converting factor for acceleration -> frequency change ( obtaining from FEA)

I have to add:

5) multiplying the result with TF due to suspension = abs[ 1/ (f^2 + i*f*fo/Q +  fo^2)

6) multiplying again by (2*pi*f)^2  (since the TF is a conversion from F to mX, and we need acceleration)

I'm not sure if I did it correctly, I'll double check it.