After Hugh's HEPI-Oplev yaw decoupling, I wanted to look at HEPI Y - ISI RX/RY tilt decoupling on this chamber. I used the same approach we've used in the past on the ISIs, using the ISI T240s as a witness. I drove HEPI at low frequency, with the ISI isolated with high blends to lock the stages to HEPI. If the there is any Y to RX/RY coupling it shows up as a g/w^2 tilt in the HEPI Y IPS to ISI X/Y T240 transfer function. For the T240 X dof, I saw that pretty clearly. For Y, the low frequency component is more like 1/f-f^1.5, instead of 1/f^2.
The attached plot shows the transfer functions (before & after) from HEPI Y IPS to the ISI X/Y T240s. In order to get the coefficient for the correction, the transfer functions need to be put into tilt units (dividing by g/w^2) and the T240s are put into displacement, so the magnitude y-axis is rad/m-rthz. After getting the units right, I just got an eyeball average of the flat, low frequency component for the Y-RY transfer function. The difference between the lower blue (measured before the correction) and yellow (measured after) curves are the improvement I was able to get. I looked at the IPS Y to oplev yaw and pitch tfs to see if there was any difference, but there was no change.
These are the same transfer functions, but not in tilt units. These are the transfer functions from HEPI IPS Y to ISI T240 X/Y. Because the T240s readout in m/s, I've had to multiply by a pole at 0 to get the tfs into m/m. I've also included the g/w^2 transfer function (divided by 1000 to keep the scale sane) for comparison.
