Here I explain how I estimate the contribution from the differential noise shown in the plot on my last entry (#4376) .
According to the measurement done about a week ago, there is a broadband noise in the green beatnote path when both Green and IR are locked to the X arm.
The noise can be found on the first plot on this entry (#4352) drawn in purple. We call it differential noise.
However, remember, the thing we care is the noise appearing in the IR PDH port when the ALS standard configuration is applied (i.e. taking the beatnote and feeding it back to ETMX).
So we have to somehow convert the noise to that in terms of the ALS configuration.
In the ALS configuration, since the loop topology is slightly different from that when the differential noise was measured, we have to apply a transfer function to properly estimate the contribution.
(How to estimate)
It's not so difficult to calculate the contribution from the differential noise under some reasonable assumptions.
Let us assume that the MC servo and the end PDH servo have a higher UGF than the ALS, and assume their gains are sufficiently big.
Then those assumptions allow us to simplify the control loop to like the diagram below:
Since we saw the differential noise from the beatnote path, I inject the noise after the frequency comparison in this model.
Eventually the noise is going to propagate to the f_IR_PDH port by multiplying by G/(1+G), where G is the open loop transfer function of the ALS.
The plot below shows the open loop transfer function which I used and the resultant G/(1+G).
In the curve of G/(1+G), you can see there is a broad bump with the gain of more than 1, approximately from 20 Hz to 60 Hz.
Because of this bump, the resultant contribution from the differential noise at this region is now prominent as shown in the plot on the last entry (#4376).
I made a noise budget for the ALS noise measurement that I did a week ago (see #4352).
I am going to post some details about this plot later