KAGRA Logbook

VIS (BS)

terrence.tsang - 21:19 Monday 08 November 2021 (18794)

BS QPD calibration

Yasui, Terrence

Before we've done anything to the QPDs, we've moved the tower of the BS close to the setpoint (using stepper moters for IP and Coil-magnet actuation offset for GAS filters) and recorded all displacement and actuation values.
The temperature was 23.7 C.
The QPD segments have non-zero gains (K1:VIS-BS_TM_OPLEV_{LEN, TILT}_{SEG1, SEG2, SEG3, SEG4}_GAIN) for some reason and I've reset them to -1.
These numbers were close to -1 anyway so I hope it doesn't matter and I don't know why they were not -1 in the first place.

We recorded the position of the QPD stages but it turned out that I was looking at the wrong markings so there's no way to return the QPDs to the exact position that they were.
We have recorded the readings and the displacements of the suspension.
So we might be able to return the QPDs close to where they were by moving the suspension back to the old positions and matching the QPD outputs.
We haven't done this because it was too late.

Nevertheless, we've recorded calibration data. The data was measured by moving the micrometer stage in 5 micrometer counts increments (equivalent to 0.05 mm displacement) and recording 20 seconds time-averaged values of K1:VIS-BS_TM_OPLEV_{LEN, TILT}_{HOR, VER}_INMON.
The measurements will be posted in a comment later.

Comments to this report:

terrence.tsang - 14:38 Tuesday 09 November 2021 (18806)

Yasui, Terrence

We tried to move the QPDs back to their original positions.
Before the calibration yesterday, we recorded the displacements of the BS and we tried to restore these displacements.
After that, we moved the QPDs such that the vertical and horizontal readings matches the original values.
Below are the displacements before calibration and after we adjusted the QPDs today.

Before calibration

IP_BLEND_LVDTL_INMON: 9.740666680907855
IP_BLEND_LVDTT_INMON: -72.2980225410355
IP_BLEND_LVDTY_INMON: -96.07249629685207
F0_DAMP_GAS_INMON: 8.051098675818544
F1_DAMP_GAS_INMON: -26.602439172286005
BF_DAMP_GAS_INMON: -3.1979734011072956
IM_DAMP_L_INMON: -38.28655840762599
IM_DAMP_T_INMON: -171.0849966741211
IM_DAMP_V_INMON: 109.89149843608632
IM_DAMP_R_INMON: -23.811413896371327
IM_DAMP_P_INMON: -676.9358121479949
IM_DAMP_Y_INMON: 45.61175951371729
TM_OPLEV_TILT_VER_INMON: 0.05137297104357774
TM_OPLEV_TILT_HOR_INMON: 0.6794230377258089
TM_OPLEV_LEN_VER_INMON: -0.07909311440687275
TM_OPLEV_LEN_HOR_INMON: 0.3713014587369544

Today's restoration:

IP_BLEND_LVDTL_INMON: 49.58961826664278
IP_BLEND_LVDTT_INMON: -87.78210591217461
IP_BLEND_LVDTY_INMON: -127.39989541265899
F0_DAMP_GAS_INMON: 8.363662941982948
F1_DAMP_GAS_INMON: -65.45176687600019
BF_DAMP_GAS_INMON: -1.5500116465954394
IM_DAMP_L_INMON: -38.349006197339364
IM_DAMP_T_INMON: -171.13256701213317
IM_DAMP_V_INMON: 111.47262403342617
IM_DAMP_R_INMON: -24.081545740836006
IM_DAMP_P_INMON: -677.507097411423
IM_DAMP_Y_INMON: 44.58334723137367
TM_OPLEV_TILT_VER_INMON: 0.12568046262169258
TM_OPLEV_TILT_HOR_INMON: 0.604868855742415
TM_OPLEV_LEN_VER_INMON: -0.08916940953537525
TM_OPLEV_LEN_HOR_INMON: 0.3718941931125822

terrence.tsang - 22:57 Wednesday 10 November 2021 (18834)

Data avaliable at /kagra/Dropbox/Subsystems/VIS/vis_commissioning/bs/calibration/
Jupyter notebook used to generate the plot available at /kagra/Dropbox/Subsystems/VIS/vis_commissioning/bs/notebook/calibration/

Undoubtedly, there're infinitely many ways to reasonably calibrate the QPDs and I struggled to settle on one. Here, I compared two methods and for the sake of unification, I will use the first one.

Method 1 (by Miyo-san): Fit an error function
$f(x; a,b,c,d) = a\,\mathrm{erf}(b(x-c))+d$
and use slope the first-order approximation of this model,
i.e. $\frac{2ab}{\sqrt{\pi}}$ to derive the calibration factor.
The benefit of this method is that the model fits the data very well because the calibration curve of the QPD behaves exactly like an error function.
However, the calibration factor is only accurate when the beam is exactly at the center and will start to degrade as the beam is offset.

Method 2: Starting with data points at the center, 1) fit a straight line, 2) select points that are within certain linearity specification of this line, 3) include them to the dataset, 4) repeat until no points can be added.
This method is better at retaining the scale of readout at a larger range. And, we can specify a target nonlinearity as well, which was chosen to be 5% randomly.

Please see the results from the figures.

A summary from the error function fit:

LEN_HOR:
calibration factor: -221.677 µm/d.u.
linear range (5% nonlinearity): $\pm$ 114.441 µm

LEN_VER:
calibration factor: -215.790 µm/d.u.
linear range (5% nonlinearity): $\pm$ 112.330 µm

TILT_HOR:
calibration factor: -346.329 µm/d.u.
linear range (5% nonlinearity): $\pm$ 194.239 µm

TILT_VER:
calibration factor: -444.266 µm/d.u.
linear range (5% nonlinearity): $\pm$ 247.32 µm

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