As a by-product of out recent investigations to understand the CHARD angular response, we measured again the angular response of all four test masses, by driving the L2 stage from the ISCINF_P and ISCINF_Y channels and reading out the motion using the optical levers. We also measured the cross coupling, i.e. yaw to pitch (Y2P) and pitch to yaw (P2Y).
Measurements
In summary: the ETMs have reasonably low P2Y and Y2P cross-coupling, but the two ITMs show quite high Y2P cross coupling. In particular, ITMX shows a 1:1 coupling of yaw to pitch around 1.5-2.0 Hz.
Cross-coupling fits
If we want to compensate for those cross-couplings in the suspension drive, we need to compute ratios like Y2P/P2P and P2Y/Y2Y for each suspension and fit them. The two plots below show all such terms for ITMs and ETMs
As already commented, the ITM yaw to pitch coupling is larger than any other cross coupling.
I fitted all the ratios above with MATLAB and vectfit, to obtain the filters listed below, in foton format. The fit plots are also attached to this entry.
Filters have been uploaded to the suspension L2 DRIVEALIGN, but not engaged. The gain in the P2Y and Y2P filter banks should be -1 for all of them.
| Filter | |
| ITMX Y2P |
zpk([-5.3229+i*18.2835;-5.3229-i*18.2835;-0.59707+i*16.3425;-0.59707-i*16.3425;-0.51745+i*8.5794;-0.51745-i*8.5794;-0.078188+i*6.2385;-0.078188-i*6.2385;-0.17768+i*2.5529;-0.17768-i*2.5529;-0.043129+i*2.9229;-0.043129-i*2.9229;-0.26585+i*3.6894;-0.26585-i*3.6894],[-0.1698+i*2.5692;-0.1698-i*2.5692;-0.091751+i*2.8733;-0.091751-i*2.8733;-0.28013+i*3.7396;-0.28013-i*3.7396;-0.075776+i*6.2775;-0.075776-i*6.2775;-0.45674+i*8.5589;-0.45674-i*8.5589;-0.57686+i*16.5756;-0.57686-i*16.5756;-5.9231+i*18.1013;-5.9231-i*18.1013],1) Gain 0.102717 (-18.772328 db) at 1.000000 Hz |
| ITMX P2Y |
zpk([-8.9695+i*10.3701;-8.9695-i*10.3701;-0.63089+i*13.3055;-0.63089-i*13.3055;-0.37947+i*12.8329;-0.37947-i*12.8329;-2.0554+i*10.679;-2.0554-i*10.679;-0.062706+i*6.2917;-0.062706-i*6.2917;-0.077033+i*2.6657;-0.077033-i*2.6657;-0.21137+i*3.4105;-0.21137-i*3.4105],[-0.096751+i*2.6734;-0.096751-i*2.6734;-0.11292+i*3.4272;-0.11292-i*3.4272;-0.071345+i*6.3081;-0.071345-i*6.3081;-1.6284+i*10.2847;-1.6284-i*10.2847;-0.40536+i*12.5843;-0.40536-i*12.5843;-0.71506+i*13.4462;-0.71506-i*13.4462;-8.5593+i*11.2668;-8.5593-i*11.2668],1) Gain 0.060268 (-24.140847 db) at 1.000000 Hz |
| ITMY Y2P |
zpk([388.7201;-0.10941+i*16.8749;-0.10941-i*16.8749;-0.20001+i*12.7684;-0.20001-i*12.7684;-0.22548+i*8.6218;-0.22548-i*8.6218;-0.050536+i*5.9432;-0.050536-i*5.9432;-1.7281;-0.065067+i*4.0201;-0.065067-i*4.0201;0.019856+i*3.156;0.019856-i*3.156;-0.19392+i*2.8299;-0.19392-i*2.8299],[-0.39321+i*16.6698;-0.39321-i*16.6698;-0.15878+i*2.7541;-0.15878-i*2.7541;-0.06782+i*2.8676;-0.06782-i*2.8676;-0.18203+i*3.8527;-0.18203-i*3.8527;-0.058+i*6.2735;-0.058-i*6.2735;-0.17162+i*8.5836;-0.17162-i*8.5836;-0.3794+i*12.7654;-0.3794-i*12.7654;-2.4661;-100.2194],1) Gain -0.045658 (-13.661215 db) at 1.000000 Hz |
| ITMY P2Y |
zpk([86.1116;2.0023+i*16.7497;2.0023-i*16.7497;2.6275+i*9.4817;2.6275-i*9.4817;5.4093;-4.9971+i*1.1709;-4.9971-i*1.1709;0.47217+i*4.1757;0.47217-i*4.1757;-0.32142+i*2.8487;-0.32142-i*2.8487],[-0.19284+i*2.7361;-0.19284-i*2.7361;-1.7198+i*2.7035;-1.7198-i*2.7035;-0.098375+i*3.4118;-0.098375-i*3.4118;-0.22943+i*9.4543;-0.22943-i*9.4543;-0.61662+i*11.6268;-0.61662-i*11.6268;-0.86734+i*16.8508;-0.86734-i*16.8508],1) Gain -0.003954 (-43.581748 db) at 1.000000 Hz |
| ETMX Y2P |
zpk([-18.2675;-0.82779+i*12.6514;-0.82779-i*12.6514;1.5007+i*8.6156;1.5007-i*8.6156;-2.0987+i*7.1924;-2.0987-i*7.1924;-2.1174;1.1736+i*4.216;1.1736-i*4.216;-0.34513+i*2.568;-0.34513-i*2.568;0.26111+i*4.5841;0.26111-i*4.5841;-0.54416+i*3.9492;-0.54416-i*3.9492],[-0.2503+i*2.3263;-0.2503-i*2.3263;-0.04334+i*2.8892;-0.04334-i*2.8892;-0.13102+i*3.8733;-0.13102-i*3.8733;-0.81627+i*4.5349;-0.81627-i*4.5349;-0.42007+i*6.5251;-0.42007-i*6.5251;-0.24996+i*8.6606;-0.24996-i*8.6606;-0.8313+i*13.142;-0.8313-i*13.142;-1.7617+i*18.4144;-1.7617-i*18.4144],1) Gain 0.011744 (-31.428269 db) at 1.000000 Hz |
| ETMX P2Y |
zpk([-2.9959+i*17.4066;-2.9959-i*17.4066;0.24399+i*16.8876;0.24399-i*16.8876;0.74797+i*9.9451;0.74797-i*9.9451;-3.1397+i*8.8362;-3.1397-i*8.8362;-0.039055+i*2.7658;-0.039055-i*2.7658;-0.16956+i*4.3284;-0.16956-i*4.3284;-1.032+i*4.1641;-1.032-i*4.1641],[-0.078526+i*2.737;-0.078526-i*2.737;-0.08389+i*3.5445;-0.08389-i*3.5445;-0.74422+i*4.4789;-0.74422-i*4.4789;-0.44597+i*9.3427;-0.44597-i*9.3427;-0.73729+i*12.0387;-0.73729-i*12.0387;-3.1449+i*12.2137;-3.1449-i*12.2137;-0.73493+i*17.5513;-0.73493-i*17.5513],1) Gain 0.021259 (-33.440821 db) at 1.000000 Hz |
| ETMX Y2P |
zpk([160.5975;3.7643+i*14.634;3.7643-i*14.634;0.21604+i*15.4741;0.21604-i*15.4741;0.82573+i*13.2127;0.82573-i*13.2127;-0.54752+i*8.1177;-0.54752-i*8.1177;-2.682+i*5.9597;-2.682-i*5.9597;-1.4634;0.49594+i*1.4111;0.49594-i*1.4111;-0.20198+i*2.4277;-0.20198-i*2.4277],[-1.449+i*18.1053;-1.449-i*18.1053;-0.106+i*2.3741;-0.106-i*2.3741;-0.14739+i*2.8351;-0.14739-i*2.8351;-0.41064+i*6.4234;-0.41064-i*6.4234;-0.3058+i*8.6157;-0.3058-i*8.6157;-0.54587+i*12.968;-0.54587-i*12.968;-0.48895+i*16.3143;-0.48895-i*16.3143;-1.02;-3.9062],1) Gain 0.053527 (-20.036136 db) at 1.000000 Hz |
| ETMX P2Y |
zpk([-0.30816+i*21.8034;-0.30816-i*21.8034;-0.54171+i*17.0654;-0.54171-i*17.0654;-1.0045+i*13.3852;-1.0045-i*13.3852;-0.24706+i*10.0314;-0.24706-i*10.0314;-1.0325+i*7.4193;-1.0325-i*7.4193;-4.5852;-0.19665;-0.12813+i*3.7513;-0.12813-i*3.7513;-0.080833+i*2.8183;-0.080833-i*2.8183],[-0.25429+i*21.6639;-0.25429-i*21.6639;-0.1032+i*2.849;-0.1032-i*2.849;-0.12771+i*3.4715;-0.12771-i*3.4715;-1.2787+i*7.1274;-1.2787-i*7.1274;-0.48506+i*9.3168;-0.48506-i*9.3168;-0.42904+i*12.7624;-0.42904-i*12.7624;-0.62721+i*16.809;-0.62721-i*16.809;-0.1506;-12.3275],1) Gain -0.042433 (-27.268564 db) at 1.000000 Hz |
