2019-01-18 With Fabian
The alignment team would like the BS to be ready by this Saturday (2019-01-19). So, we recovered the optical lever beam signal by adjusting the QPDs positions with the adjustment knobs attached to the QPD stages. The beam is now hitting the QPDs and we roughly centered the beam. We also noticed that the steering mirror was recently adjusted (see 7067). Therefore, we agreed that it is necessary to diagonalize the signals again because the rotational angle of the steering mirror might be different.
For a reference, I tried to actuate the TM from the IM actuation. However, both IM and TM seemed not responsive to IML and IMY input and are only responsive to IMP input. Therefore, I suspect that there might be no actuation from the horizontal coils. After that, I also tested the actuation at the TM level and there is no response from the optical lever as well. So, I continued diagonalizing the signals following procedures similar to Mark's (3835). Using IMP offsets, I obtained the following results:
| IM_TEST_P_OFFSET (cnts) | IM_DAMP_L_INMON (µm) | IM_DAMP_P_INMON (µrad) | IM_DAMP_Y_INMON (µrad) | TM_OPLEV_TILT_PIT_OUTMON (cnts*100) | TM_OPLEV_TILT_YAW_OUTMON (cnts*100) |
| 0 | -92.4 | 667.4 | 366.0 | -1.8 | -26.8 |
| 100 | -93.8 | 691.5 | 363.8 | 4.9 | -13.9 |
| 200 | -95.2 | 715.9 | 361.9 | 10.31 | -0.1 |
| 300 | -96.7 | 739.9 | 360.6 | 16.6 | 13.1 |
| 400 | -98.2 | 764.8 | 359.3 | 22.7 | 26.0 |
| 500 | -99.2 | 789.5 | 357.6 | 29.2 | 37.8 |
For this measurement, I measured IML to see if it has significant affection to the output of the TILT QPD. From Mark's document attached in (3835), it can be calculated that the total displacement that the beam spot at the QPD plane moved in the order of 10^2 µm while the influence of longitudinal motion from the result would cause a change in the order of 10^0 µm according to the ray transfer matrix, assuming that the longitudinal motion at the IM level is similar to that of TM. Therefore, for simplicity, I ignored this the longitudinal motion. If we trust the actuation and assumes that the TM only moved in the pitch direction, we can obtain the rotational angle from the last two columns. Plotting TILT_PIT_OUTMON againsts TILT_YAW_OUTMON gives an angle of -63.6799 º from the vertical axis (where pitch is assumed to be). With these assumptions, the diagonalization matrix is
| TILT_PIT | TILT_YAW | |
| P | 1.23101156 | 2.36704139 |
| Y | 3.15803055 | -1.48589242 |
Please note that this matrix is obtained in a slightly different way. In Mark's calculation, the expression of the diagonalization matrix is
(y,p)=(diagonalization matrix)(TILT_YAW,TILT_PIT),
where
(diagonalization matrix)=(effective beam length matrix)^(-1)(calibration matrix)(rotational transformation from QPD frame to pitch-yaw frame).
However, I suspect that the order of operation should be
(diagonalization matrix)=(effective beam length matrix)^(-1)(rotational transformation from QPD frame to pitch-yaw frame)(calibration matrix),
where the rotational transformation is swapped with the calibration matrix. In this way, multiplying both sides on the left with the inverse of effective beam length matrix and the inverse of the rotational transformation from QPD frame to pitch-yaw frame (basically turned into a rotational matrix) recovers the ray transfer matrix without the longitudinal component, i.e.
(rotational matrix)(2*effective beam length matrix)(y,p)=(calibration matrix)(TILT_YAW,TILT_PIT).
I believe this order of operation is also applied to the PRs and the calibration factors are implemented as gains right after TILT_PIT and TILT_YAW.
Moving on to another aspect, as can be seen from the previous results table, as we actuate the IM in pitch direction, it also moved in the yaw direction by a tiny little bit. That motion will transfer also to yaw motion at the TM level and thus should be taken into account. However, because of the difference in effective beam lengths, the outputs of the IMP and the IMY have to be scaled by their own beam lengths so that they are comparable with the TILT_PIT and TILT_YAW which are measured in counts. So, in this case, instead of transforming the vertical axis to the fitted TILT_PIT against TILT_YAW line, it is the fitted line of IMP against IMY that is needed to be rotated. This also assumes that pitch and yaw from the IM level transferred to the TM level with a similar scale (This depends on the MOI of the IM recoil mass). Plotting IMP against IMY yields a linear fitting line with an angle of 66.4237 º from the TILT_PIT-TILT_YAW line. So, the diagonalization matrix becomes
| TILT_PIT | TILT_YAW | |
| P | 1.11047357 | 2.4203784 |
| Y | 3.22919107 | -1.34039704 |
Comparing with the original one,
| TILT_PIT | TILT_YAW | |
| P | 1.10793 | 2.55740 |
| Y | 2.94833 | -1.60176 |
| IM_DAMP_Y_INMON | TM_OPLEV_YAW_DIAGMON calculated from (1) | TM_OPLEV_YAW_DIAGMON calculated from (2) | TM_OPLEV_YAW_DIAGMON calculated from (3) |
| 366.0 | 34.1 | 30.1 | 37.6 |
| 363.8 | 36.1 | 34.5 | 36.7 |
| 361.9 | 32.7 | 33.4 | 30.5 |
| 360.6 | 33 | 36.0 | 28.0 |
| 359.3 | 33.1 | 38.5 | 25.3 |
| 357.3 | 36.0 | 43.6 | 25.5 |
| IM_DAMP_P_INMON | TM_OPLEV_PIT_DIAGMON calculated from (1) | TM_OPLEV_PIT_DIAGMON calculated from (2) | TM_OPLEV_PIT_DIAGMON calculated from (3) |
| 667.4 | -65.7 | -66.9 | -70.5 |
| 691.5 | -26.9 | -28.2 | -30.1 |
| 715.9 | 12.4 | 11.2 | 11.2 |
| 739.9 | 51.4 | 50.1 | 51.9 |
| 764.8 | 89.5 | 88.1 | 91.6 |
| 789.5 | 125.4 | 123.9 | 129.0 |
I incline not to use the original OL2EUL (3) because 1) the steering mirror has been adjusted, and most importantly 2) the order of operation of the diagonalization is skeptical (unless I am wrong, which could the case.). But I will leave the decision on what to do to the alignment team or other experts.
Miscellaneous details:
linear range for TILT QPD: ~±40 cnts (after gain of 100, from 3835)/ ~±111 µrad (pitch) ~±134 µrad (yaw)
I was not able to obtain enough information for the length sensing optical lever because I couldn't actuate the TM in L in any way before an accident happened which will be documented by another Klog. Thanks.