Sheila, Sudarshan

Since sensing function measurements taken during O3A, at low frequencies, couldnot be entirely explained by the detuned signal recycling cavity, efforts were made to understand the mechanism by which the measured sensing function could be explained. There were indications that some of these effect could be a result of unmodeled cross couplings between length and angle. Details of some previous efforts can be found in LHO alog # 50511 and DCC document G1901353.

Here we have explored the deviation in measured sensing function from the simple DARM model (with a cavity pole and optical gain) in two different configurations, with A2L gain turned on and A2L gain turned off. The details about the measurment can be found in LHO alog # 54679.

The sensing function model that is considered here is shown in the block-diagram below:

This model considers length (DARM) to angle coupling through the wavefront sensor of the DHARD loops. In this model, the sensing function depends on the the DHARD loop shape  as well as the A2L gain. The resultant sensing function differs from the simple model (without cross couplings) as follows:

C_new = C_old/[1-B(L2l*A2L/A2theta+m)]

where B is:

B = GDH/(1-GDH)*(L2WFS/WFS)

and GDH is the DHARD open loop gain.

The comparison between the model and the measurement is shown in the first attached pdf. It shows a reasonable agreement between the model and measurement, although there is some discrepancies at frequencies below 10 Hz. This model only includes the length to angle coupling in pitch. Coupling in yaw, we believe it to be relatively small, has not been considered. Additionally, the model of the DAHRD loop that is considered here doesnot completely agree with the measurement as shown in the second attachment.