Once all isolation filters are engaged on HEPIs and ISIs, the absolute motions of the optical tables are amplified by less than 10 times in the Y direction while the length of the cavity is amplified by 100 below 100mHz.

Coupling from HEPI-ISI to Test masses (figure 1)
ASDs of the pitch and the yaw of the test masses are presented in three different configurations:
- HEPI ON – ISC Y feedback (UGF: 1mHz) - ISI Damped
- HEPI ON – ISC Y feedback (UGF: 1mHz) - Sensor correction -  ISI Damped
- HEPI ON – ISC Y feedback (UGF: 1mHz) - Sensor correction - ISI Damped & Controlled (100mHz blend with T240s)

This figure 1 shows that:
- When HEPIs at BSC-6 and BSC-8 are ON, ETM & ITM are tilting in pitch and yaw by the same amounts at all frequencies. Blend filters of the IPS on HEPIs have a 800mHz corner frequency (below 100mHz, the blend filters transfer functions are close to 1). Consequently, no amplifications of the pitch and the yaw of the test masses are expected below 100mHz.
- When the STS-2 are introduced in the HEPI super sensor blend (sensor correction), the aggressive high pass filters with a 100mHz corner frequency increase the absolute motion in the X, Y and Z directions. An amplification of the pitch and the yaw of the test masse can be expected due to eventual cross couplings from longitudinal, transverse and vertical displacement of the HEPI-ISI to the test masses. But strangely, only the rotations of the ETM are increased at low frequency. ITM rotations are unchanged or reduced. In this case, the “apparent tilt" seen by the optical levers is probably due to the longitudinal displacement of the test mass in the Y direction (cf Sensitivity of the optical levers to longitudinal displacement)
- Once the ISI is controlled (with blend at 100mHz => maximum amplification at 60mHz), pitch and yaw of the ETM are increased while pitch and yaw of the ITM is moderately increased. When HEPIs (sensor correction) and ISIs are controlled, apparent pitch and yaw of the ETM are amplified by 50 while pitch and yaw of the ITM are not amplified. Remember that the length of the cavity is increased by 100 in this configuration.

Sensitivity of the optical levers to longitudinal displacement
Pitch and yaw seen by the optical levers can be due either the tilt of the mirror or the longitudinal displacement of the test mass as shown in figure 2. In the case of a pure translation of the test mass, the “apparent tilt” seen by the optical levers can express as a function of the longitudinal displacement of the test mass where:
Tilt~d1*dl/(d2^2)
ETM optical levers are about 70 times more sensitive to the longitudinal displacement than the ITM optical levers.

Transfer functions from the “apparent pitch and yaw” (translation in the case of ETM?) of the test masses to the length of the cavity (figure 3).
Transfer functions from pitch and yaw of the test masses to the length of the cavity are presented below in three configurations:
- HEPI ON – ISC Y feedback (UGF: 1mHz) - ISI Damped
- HEPI ON – ISC Y feedback (UGF: 1mHz) - Sensor correction -  ISI Damped
- HEPI ON – ISC Y feedback (UGF: 1mHz) - Sensor correction - ISI Damped & Controlled (100mHz blend with T240s)

When there is no sensor correction, coherences between the apparent tilt (signal probably dominated by actual tilt) of the test masses and the length of the arm are close to 0. But when the controllers are engaged, the contribution of the displacement of the test mass in the tilt signals is probably not negligible especially at ETM. When the sensor correction is engaged, coherences in pitch and yaw are pretty high (0.8) on the ETM around 60mHz and stay at 0 on the ITM.
It seems that the oplev are seeing the translation of the test mass at EY. Consequently, the measured transfer functions are from “translation of the test mass” to length of the cavity. Having a good coherence close to 1 on ETM and 0 on ITM is not abnormal.

Transfer functions ISI to OPLEV (figures 4, 5, 6)
Transfer functions from the ISI to the optical levers show a good coherence from the ISI drives (especially in the Y direction) to the optical levers (pitch and yaw) of ETM. The coherence is null on ETM. Oplev are not sensitive to vertical displacement of the testmass, coherences in the case of a Z-drive are low or null.