Here I describe the measurement of the sensing matrix.
Motivations
There were two reasons why I have been measuring the sensing matrix :
- I wanted to know how much each element in the sensing matrix drifted as a function of time because the sensing matrix didn't agree with what Optickle predicted (#6283).
- I needed to estimate the MICH responses in the 3f demodulated signals, so that I can decide which 3f signal I should use for holding MICH.
I will report #2 later because it needs another careful noise estimation.
Measurement
In order to measure the sensing matrix, the basic steps are something like this:
- Excite one of the DOF at a certain frequency, where a notch filter is applied in the LSC servos so that the servos won't suppress the excitation signal.
- Demodulate the LSC signals (e.g. C1:LSC-REFL11_I_ERR and etc.,) by the realtime LOCKINs (#6152) at the same frequency.
- Calibrate the obtained LOCKIN outputs to watts/meter.
In the actual measurement I choose the frequency of the excitation signal to be at 283.1 Hz,
at which any of the LSC servos don't have gains of more than 1 and there were no particular structures in the spectra.
For the amplitude of the excitation, I usually choose it to be 1000 - 2000 counts.
Because all the actuators have response functions of approximately 10 -9 / f^2 meter/counts ( #5637), the actual displacement in the excited DOF should be about 10 pm level. Therefore the excited displacements must be always in the linear ranges and also the amplitude in counts is reasonably smaller than the DAC range.
LOCKIN detection
The attached cartoon below shows how the LOCKIN system works for the MICH response measurement.
In the case of the PRCL response measurement, the setup is the same except that only PRM is shaken.
Here is some notes about the LOCKIN detection.
Calibration of the LOCKINs
The calibration of the LOCKIN detectors is easy because all the processes takes place in the digital land, where we know all the parameters.
In this phase the goal is to calibrate the signals into counts / meter.
To calibrate the LOCKIN output signals, the following equation is used :
[The obtained LOCKIN output in counts ] = H x ADOF x CLO x CEXC x 1/2 ,
where H is the response of a sensor (e.g. AS55_I, AS55_Q and so on) against a particular DOF in unit of counts / m and this the quantity which we want to measure here,
ADOF is the actuator efficiency of the DOF at the excitation frequency in unit of m/counts,
CLO is the amplitude of the local oscillator signal for demodulating the sensor signals in unit of counts,
CEXC is the amplitude of the excitation signal in unit of counts,
the last 1/2 term comes from the fact there is a low pass filter in each demodulation path.
Therefore once we measure the response of a sensor, dividing the obtained LOCKIN output by ADOF x CLO x CEXC x 1/2 gives the calibrated response in unit of counts/meter.
A DOF are well known as they have been measured several times ( #5637). For the MICH actuator I assumed that AMICH = 2 x (ITMY response) since they are balanced through the actuation coefficients.
Note that a confirmation of this calibration has been done
when the configuration is in the simple Michelson, where we can easily estimate the response of a sensor by letting the MICH freely swing.
Calibration of the responses to watts/meter
With the calibration process described above, we obtain the sensor responses in unit of counts/m.
Then we need to do another calibration to make them into unit of W/m.
If we think about how the RFPD signal flows, we get the following gain chain.
[raw response in counts/m ] = Hopt x CADC x Ldemod x GWF x Ztrans x RPD
Hopt is the optical gain at a sensor which we want to calibrate. It is in unit of W/m.
CADC is the conversion factor of the ADCs and the value is CADC = 1638.4 counts/m because their resolution is 16 bit and the range is +/-20 V.
L demod is the conversion efficiency of the demodulation boards in unit of V/V. I used the values which Suresh measured yesterday ( #6402). GWF is the gain of the whitening filter in unit of V/V,
Z trans is the transimpedance gain of an RFPD in unit of V/A and I used the values summarized in ( the wiki), and RPD is the responsivity of the photo diodes and I assumed RPD = 0.75 A/W for all the RFPDs.
Therefore the calibration can be done by dividing the raw response value by the entire gain chain of CADC x Ldemod x GWF x Ztrans x RPD.
Settings and parameters
- LSC RF demodulation phases
- AS55 = 17.05 deg (minimizing the PRCL sensitivity in the Q-phase)
- REFL11 = -41.05 deg (maximizing the PRCL sensitivity in the I-phase)
- REFL33 = -25.85 deg (maximizing the PRCL sensitivity in the I-phase)
- REFL55 = 4 deg (maximizing the PRCL sensitivity in the I-phase)
- REFL165 = 39 deg (random number)
- Whitening filters
- AS55 = 30 dB
- REFL11 = 0 dB
- REFL33 = 42 dB
- REFL55 = 30 dB
- REFL165 = 45 dB
- MICH servo
- AS55_Q for the sensor
- G = -5 in the digital gain
- FM2, FM3, FM5 and FM9 actiavted
- UGF ~ 100 Hz
- Feedback to ITMs differentially
- PRCL servo
- REFL33_I for the sensor
- G = 1 in the digital gain
- FM2, FM3, FM4, FM5 and FM9 activated
- UGF ~ 100 Hz
- Feedback to PRM
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Tonight I measured the sensing matrix again but this time I recorded them as a function of time using the realtime LOCKINs in the LSC front end.
I will explain some more details about how I measured and calibrated the data in another elog entry.
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