I calculated a noise budget for the MICH using AS55 as a sensor. The calculation includes closed-loop TF calculations.
The notebook and associated files can be found on https://git.ligo.org/40m/bhd/-/blob/master/controls/compute_MICH_noisebudget.ipynb.
Attachment 1 shows the loop diagram I was using. The equation describing the steady-state of the loop is
, where G is the adjacency matrix given by
First, the adjacency matrix G is constructed by stitching the small ABCDE matrices together. Once the inverse of (I-G) is calculated we can simply propagate any noise source to and then calculate to estimate the displacement of the optics.
Attachment 2 shows the calculated noise budget together with Yuta's measurement.
All the input and output electronics are clumped together for now. Laser noise is irrelevant as this is a heterodyne measurement at 55MHz.
It seems like there is some mismatch in the calibration of the optical gain between the measurement and model. The missing noise at 3-30Hz could be due to angle-to-length coupling which I haven't included in the model. |