KAGRA Logbook

MIF (General)

takafumi.ushiba - 12:54 Thursday 28 July 2022 (21630)

Calibration of ALS DARM signals

[Yamamoto, Ushiba]

Abstract:
We implemented calibration factors from feedback signals of PDH X/Y (unit of Volts) to arm length variation (unit of meter).
So, K1:LSC-ALS_DARM_IN1 signals are calibrated to displacement.

Detail:
We can calbrate frequency change of Green laser when locking GRX/Y as following formula:
$\Delta \nu = \frac{1}{H}V_{\mathrm{err}}-AV_{\mathrm{ctrl}}$

where V_err and V_ctrl are error and feedback signals of PDH loops, respectively. H and A are optical gain (including cavity pole) and actuator efficiency, respectively.
Since UGF of PDH loop is higher than 10kHz, V_err term can be negligible in this time.
So, the equation can be simplied as follows:

$\Delta \nu = -AV_{\mathrm{ctrl}}$

Here, frequency change and cavity length variation has a relation as follows:

$\frac{\mathrm{d}L}{\mathrm{d}\nu}=\frac{L\lambda}{c}$

where L, $\lambda$ , c are arm length, wavelength of green laser, and speed of light, respectively.
Thus, arm length variation can be described as following formula:

$\Delta L=\frac{\mathrm{d}L}{\mathrm{d}\nu}\Delta\nu=-\frac{L\lambda}{c}AV_{\mathrm{ctrl}}$

According to the past measurement, VOC actuator efficiencies are 0.42 and 0.43 MHz/V for PDHX and PDHY, respectively (klog6544).
So, the calibration factors for X and Y arms are:

$\small \small C_X=-\frac{L\lambda}{c}A_X=-\frac{(3\times10^{3})\times(532\times 10^{-9})}{3\times10^{8}}\times(0.42\times10^6)=-2.23\times10^{-6}\,\mathrm{m/V}\\ C_Y=-\frac{L\lambda}{c}A_Y=-\frac{(3\times10^{3})\times(532\times 10^{-9})}{3\times10^{8}}\times(0.43\times10^6)=-2.29\times10^{-6}\,\mathrm{m/V}$

These calibration factors are implemented to ALS-{X,Y}_DRIFT_SERVO (FM3), and thus current LSC-ALS_DARM_IN1 is calibrated to displacement.

Note:
During the work, we found that somehow ALS_DARM is sum of V_ctrl and ALS_CARM is subtraction of V_ctrl.
Since this worked during O3, it should DARM and CARM but we need to consider the signal signs carefully.

Comments to this report:

takafumi.ushiba - 13:37 Thursday 28 July 2022 (21632)

I asked Nakano-kun why the ALS_DARM is sum of PDH signas.
The reason is that actuator sign (frequency shift when adding RF signals to AOM) is opposite for X and Y (klog8394).
This actuator sign flip seems not accidental but intentional one for some reasons (Nakano-kun doesn't remember the detail well).

takahiro.yamamoto - 23:13 Thursday 28 July 2022 (21639)

[Ushiba, YamaT]

For confirming the calibration of current ALS DARM, calibrated spectra was compared with the past one which was measured on Sep. 11th, 2020 reported as klog#15021.
Current calibration doesn't seems to be so bad as shown in Fig.1.

-----
Nakano-kun measured DARM spectra with ALS DARM lock and unlock.
These spectra is available as K1:LSC-DARM_IN1_DQ. In correctly, Nakano-kun's measurements was done with K1:LSC-DARM2_IN1.
Because all FMs on DARM1 were turned off at this time, we were able to use DARM_IN1_DQ instead of DARM2_IN1 without any correction filters (See also Fig.2).

Red and blue curves show the latest calibrated ALS_DARM (K1:LSC-ALS_DARM_OUT) without and with FNC lock, respectively. (Thanks to FNC, ALS_DARM signal becomes slightly quiet.)
Brown one shows the Nakano-kun's measurement.
According to Fig.1, there seems to be no large mistake in current calibration factor.

Note:
Nakano-kun's measurement was done with some control filters (DammyP and ELP100) in ALS-PDH_{X,Y}_DRIFT_SERVO as show in Fig.3.
In order to compare our measurements with Nakano-kun's measurement, we applied DammyP and ELP100 to our results on diaggui.

Images attached to this comment

21639_1659017245_Screenshot from 2022-07-28 22-48-17.png

21639_1659017280_Screenshot from 2022-07-28 17-45-36.png

21639_1659017285_Screenshot from 2022-07-28 17-46-06.png

takafumi.ushiba - 10:50 Thursday 25 August 2022 (21898)

I misunderstood the VCO actuator efficiency in klog6544.
I thought VCO actuator efficiency is the efficiency of green beam frequency changes but it is the efficiency of VCO output frequencies according to the private email from Enomoto-kun.
Since green AOMs are double-pass configuration, actuator efficiency, A in original post, should be 0.84 MHz/V and 0.86 MHz/V for X and Y, respectively.
This fact changes the calibration factors of ALS_DARM by a factor of 2.

So, I corrected the calibration factors and ALS_DARM calibration was fixed.
Also, according with these changes, I changed the filter gains by a factor of 2 for compensating calibration factor correction.