I've created a new filter for the RH substrate lens in TCS SIM. I'm testing it in H1:TCS-SIM_ETMY_SUB_DEFOCUS_RH. The filter bank is called "realRH".
The poles and zeros are derived from a fit of a series of exponentials to HWS data for the measured RH spherical power at LLO.
The (normalized) behaviour of the HWS measurement can be reproduced with the following sum:
defocus = -1 + sum(a_i * exp(-t/tau_i) )
| a_i |
tau_i (s) |
| 0.1127 | 397 |
| -3.96937 | 1363 |
| 6.37486 | 2636 |
| -0.0666803 | 14998 |
| -1.45155 | 29306 |
Each exponential acts as a low-pass filter with a pole frequency of 1/(2*pi*tau), so the transfer function is the sum of each of these LPFs weighted by the coefficients a_i. Math then can convert that into a ZPK filter with 4 zeros and 5 poles and the desired response should ensue. That's what I'm testing at the moment: see H1:TCS-SIM_ETMY_SUB_DEFOCUS_RH_OUTPUT from 1141778267.
I think I've put the wrong sign in the filter bank ...
This didn't work. I failed to notice that Foton substituted some of the very low frequency poles and zeros (order a few microHz) with ones that were a factor of 2 or 3 different. Plots to follow.
I've just added a simpler filter with three poles and two zeros.
poles: 9.965869E-5, 6.5094046E-5, 5.5656E-6
zeros: 2.45637E-6, -2.5739E-4
# DESIGN SIM_ETMY_SUB_DEFOCUS_RH 5 zpk([2.45637e-06;-0.000257392],[9.96587e-05;6.50941e-05;5.56564e-06],1,"n")gain(0.969)
