I measured the DARM response with DC readout.
This time, I first measured the open loop transfer function of the X single arm lock.
The open loop gain (Gx) can be represented as a product of the optical gain (Cx), the filter (Fx), and the suspension response (S), i.e. Gx = Cx*Fx*S.
We know Fx because this is the transfer function of the digital filters. Cx can be modeled as a simple cavity pole, but we need to know the finesse to calculate it.
In order to estimate the current finesse of the XARM cavity, I ran the armLoss script, which measures the ratio of the reflected light power between the locked and the unlocked state. Using this ratio and the designed transmissivity of the ITMX (0.005), I estimated the round trip loss in the XARM, which was 170 ppm. From this number, the cavity pole was estimated to be 1608Hz.
Using the measured Gx, the knowledge of Fx and the estimated Cx, I estimated the ETMX suspension response S, which is shown in the first attachment.
Note that this is not a pure suspension response. It includes the effects of the digital system time delay, the anti-imaging and anti-aliasing filters and so on.
Now the DARM open loop gain (Gd) can also be represented as a product of the optical gain (Cd), the filter (Fd) and the suspension response (S).
Since the actuations are applied again to the ETMs and we think ETMX and ETMY are quite similar, we should be able to use the same suspension response as XARM for DARM. Therefore, using the knowledge of the digital filter shape and the measured open loop gain, we can compute the DARM optical gain Cd.
The second attachment shows the estimated DARM response along with an Optickle prediction.
The DARM loop gain was measured with darm_offset_dc = 350. Since we haven't calibrated the DARM signal, I don't know how many meters of offset does this number correspond to. The Optickle prediction was calculated using a 20pm DARM offset. I chose this to make the prediction look similar to the measured one, though they look quite different around the RSE peak. The input power was set to 1.7W in the Optickle model (again this is just my guess).
It looks as if the measured DARM response is skewed by an extra low pass filter at high frequencies. I don't know why is it so. |