We tried to fit with various function the LC retardation as a function of applied voltage.

Up to now we were using R = a + b/(1+(V/c)**d)**e (1pole in attached figure) but it seemed not optimal as seen from the residual shape.

We now tried the 2 poles function : R = a + b/(1+(V/c)**d)**e + b/(1+(V/f)**g)**h and 2 different poles :  R = a + b/(1+(V/c)**d)**e + i/(1+(V/f)**g)**h.

These 2 functions improved a lot both residual rms and peak-to-peak values. We are now able to reconstruct the LC retardance better than for polarimetry.

New step is to add the temperature dependence.

I remeasured the transfer function whose resonant frequency is set around 0.5Hz.
I measured it from 2Hz to 0.1Hz.
The peak of resonant looks like 0.4Hz.

This time, peak of resonant is crushed by range of photo sensor.
When I measured it around resonant frequency, displacement is bigger than linear range of photo sensor.

What I did: measure transfer function of Roberts linkages.
 

I measured transfer function of Roberts linkages.
I attacehd two transfer function.
Resonant frequency are set at 1.5Hz(Fig 1, 2) and around 0.5Hz(Fig 3, 4) respectively.
The set up of these experiments are also attached.

The experiment whose resonant frequency is set at 1.5Hz probably have peak at 1.5Hz(Fig 1).

The peak on experiment whose resonant frequency is set around 0.5Hz is 3Hz(Fig 3). This peak is yaw motion.
The reason that I didn't measure transfer function surrounding resonant frequency is the range of photo sensor.
I realized that when I measure the transfer function, I need to measure mutiple time.
 

What I will do: I will remeasure the transfer function whose resonat frequency is set around 0.5Hz.

I tryed to check how much the shaker works.

I attached the pictures of the fransfer function from input of the shaker's power amplifiler to read out from the accelerometers' gain amplifiler.
The accelerometers are on the shaker's floor.

I didn't tune read out voltage from these accelerometers, so I only be able to refer the shapes of transfer function.

The shaker is MEE-035 made by Akashi Corporation (Fig 3).
The power amplifier for shaker is AME-100made by Akashi (Fig 4).
The accelerometer on shaker's floor are 707LFZ and 710B190 made by TEAC (Fig 5, 6). The manual says that these accelerometers have frequency response from 0.2Hz to 8000Hz and from 0.02Hz to 200Hz respectively.
The gain amplifier for accelerometer is SA-16P and SA-16U made by TEAC (Fig 7).

The input for power amplifiler is 1Vpp. The gain for accelerometer is 200 for 707LFZ and 10 for 710B190.
I set lowpass filter at 100Hz on the gain amplifiler for accelerometers.

I tuned accelerometer's resonat frequency to measure seismic noise and know the mechanics of accelerometer.
In this time, I tried to make resonant frequency be close to around 0.2Hz.

The pictured and transfer function was attached.
The weight attached accelerometer is 341.2g.

The transfer function is from actuator voltage to accelerometer's LDVT read out voltage. 

[Marc, Shalika]

We were guessing that part of the peak-to-peak uncertainty is due to the unwrapping of the ellipticity.

We decided to switch to cross-polarizer characterization as there is only 1 unwrapping compared to 2 in the direct characterization.

We tuned HWP and QWP to generate an input polarization state with ellipticity = 0.1deg and azimth = 0.05deg.

We installed a power meter to monitor a pick-off of the input beam. We measured input power of 3.6 mW and after HWP/QWP 0.8 mW.

This powermeter readout is also implemented inside our VI.

We installed a TAMA polarizer before the camera (NEWPORT 10GL08AR.33) before the camera and rotated it to minimize the transmitted power (36 nW)

We installed our LC and rotated it to maximize the transmitted power (23 uW).

We took some measurements in this configuration but it does not seem to improve our fitting uncertainty.

Maybe we should try to tweak our fitting function as it seems that most of the fitting error arises around our inflection point.

For reference I attach to this entry the retardation fit with and without taking into account the temperature of the LC.

Note that here and in previous entry I used the mean of the 3 data taken at every voltage step.

Taking into account the temperature in the fit reduce the residual rms by a factor 2 and the peak to peak by 50%.

I fit the unwrapped retardation of the LC (expressed in nm) as a function of temperature and voltage.

The peak to peak uncertainty is surely about 20 nm due to our 2.5deg azimuth angle we measured with 0V applied to the LC.

Indeed, the largest peak in the residuals appear at the folding voltages.

The rms of the residual is 2.6nm.

[Marc, Rishabh, Shalika]

After Takahashi-san opened the END gate valve, we recovered the GR beam on 2nd target.

We corrected the H3 sign issue and could realign the END reflection on 2nd target. We did some offload in pitch and yaw without issue.

We also realigned the END oplev.

Finally, we realigned INPUT by overlapping the input and reflected beam on the GR Faraday Isolator.

After some alignment tweaks, we were able to see GR fundamental mode in transmission of the FC but were not able to engage the lock.

We will investigate this issue.

[Marc, Rishabh, Shalika]

We first tried to rotate the LC while monitoring both azimuth and ellipticity.

It seems that we have a minimum azimuth angle of 2deg..

We changed the mounts of QWP and HWP for motorized ones.

By rotating the HWP we can now bring back the azimuth angle after the LC to 0deg...

It is not clear to me how this can happen..

We acquired some sweep in this condition but found similar levels of retardation.

Then, we installed and aligned a PBS before our camera to acquire data in the crossed polarizers technique.

FInally we heated the LC to about 40deg and acquire data with 0Vrms applied while letting cool down to about 25deg as shown in figure 1.

We have to add input power monitor to get more precise estimation.

I kept looking into the IRMC locking issue. I decided to start by splitting the measurement of the control loop transfer function

Figure 1 shows a model of the control loop for the electronics boards that we use in TAMA (Eleonora Capocasa thesis appendix D). We can extract the following transfer functions using noise injection and frequency response measurement:

• Servo transfer function: Noise to PERTURB IN, Frequency Response PZTmon/EPS2 - This is the transfer function of the electronics components inside the circuit board. Generically, it has an integrator response at low frequency (can set to single integrator 1/F or triple integrator 1/F^3), is flat or low slope across the UGF of the cavity in question, then rolls off at high frequency.
• "Optomechanical" transfer function: Noise to RAMP, Frequency Response EPS2/PZTmon - This is the transfer function of the light going in and out of the cavity when the piezo is excited. It should be generally flat until the cutoff frequency, i.e. low pass filter. The noise injection to the piezo will excite the mechanical resonances of the piezo and invar spacer, so it becomes a low pass filter with mechanical peaks. Actually, I don't really like this "optomechanical" terminology, to me it means 3 different things: 1) Thorlabs' terminology for moving mounts of optics such as translation stages, 2) The effect of spurious mechanical vibration of tables and housings on the amount of power going in and out of a cavity, 3) The direct interaction of quantum radiation pressure with moving mirrors (Braginsky and Khalili yellow book, etc).
• "Open loop" transfer function: Noise to PERTURB IN, Frequency Response EPS1/EPS2 - This is the open loop transfer function of the controlled cavity on lock. But again, I don't like how it is often generically called "open loop transfer function", because the above two are also open loop transfer functions

I measured the open loop transfer function for the optical cavity, as well as the electronics. The cavity transfer function looks fine (figure 2 - note that the appropriate noise excitation level is 100x lower when injecting to RAMP vs PERTURB IN). Basically the same as the reference version in the wiki. The electronics transfer function (figure 3, 4) is very low though. It has a -20dB/decade slope across the supposed UGF. I adjusted the gain of the servo and it didn't make much difference in the shape. Looking at the shape a bit more, I figured that it might be an issue with the integrator, since it is missing a lot of low frequency gain. So I tried to do the measurement again switching to 1/F^3 integrator, but the IRMC mostly refused to lock even when I tried different gain settings. I did see a bit of a flash of transmission (servo gain = 4) so I don't think it is just the 1/F^3 switch. Maybe it is something else along the chain that is badly behaved when in the presence of a triple integrator.

Some reference curves for the GRMC are shown in figure 5, from Yuhang's thesis. These are for the GRMC, but it has the exact same geometry as the IRMC. The overall unity gain frequency of the loop is 2 kHz. The servofilter has a -10 dB/dec slope across this frequency. The servofilter itself has a UGF of 200 Hz and a stronger slope at lower frequency. by comparison, the IRMC servofilter pretty much just strongly suppresses the signal even at 10 Hz.

Next, I tried looking at the RF sideband level. For the EOM used in the IRMC locking (QUBIG PM8-NIR_88), we have the following parameters:

• Resonant frequency: 88.3 MHz
• Applied signal (DDS1 channel 0): Output -8.5 dBm -> + 14.1 dB (RF amplifier board at bottom of FC cleanroom electronics) -> 5.6 dBm 
• Modulation depth at 1064 nm, 5.6 dBm: 0.2 rad (guess based one some generic datasheet, I don't have the actual one)

Using these, I estimated the amplitude of 88 MHz sidebands applied to the beam, with the following relevant parameters:

• 1064 nm photoelectric response: 0.6 A/W
• Transimpedance gain (50 Ohm load): 5.0 x 10^3 V/A
• -3 dB bandwidth: 150 MHz

If the bandwidth specification actually means a linewidth of 75 MHz, then having the 88 MHz sidebands out of the linewidth would result in an extra -2.7 dB attenuation past the 3 dB point (assuming first order rolloff for the photodiode), i.e. -5.7 dB power. Using the transimpedance gain there is 3.0 V/mW from optical power to PD signal. 

I measured the RF sidebands directly from IRMC REF RF (i.e. the cable from the PD that is filtered with a DC block) with the IRMC in scan mode, applying a T before the electronic signal goes to the mixer with the demodulation signal from DDS1. The sidebands have a level of approximately 60 mV. This implies a power level of 0.02 mW. The sideband relative intensity at 0.2 rad modulation depth is J_1(0.2) = 0.1. We start with 1.68 mW x J_1(0.2), then there is an extra -5.7 dB attenuation = x 0.27, and then divide again by 2 for 2 sidebands. This gives 0.023 mW converted by the PD into voltage for one first order sideband. So it seems consistent with us having -5.7 dB attenuation of sidebands at the PD due to being out of band.

[Marc, Shalika]

We used our new VI to characterize our LC (previously described in elog 3157 or 3155)

First, we aligned HWP and QWP to read 0+/-0.1 deg ellipticity and 90+/-0.1 deg azimuth angle with our camera.

We installed the LC and rotated it to maximize the ellipticity (-12deg). Note that we expect the LC to not affect the azimuth angle in this configuration but we measured 87.5 deg.

This could mean that our LC axis is not perfectly aligned with our input polarization/camera. We will try to further check this behavior.

In any case we then saved several sets of sweep as in figure 1.

we performed the ellitpticity unwrapping as in figure 2 by flipping twice the ellipticity compared to its maximum value (as expected as we have 2 wrapping points of the ellipticity).

Also note that we had to remove +/-5 points around the end of a sweep which exhibit strange behavior (spikes in ellipticity, azimuth and power).

This could be because the Vrms applied to the LC is quickly change from its maximum to minimum values as we do not see this feature with slow sweep by hand (if I remember correctly).

We measured retardation between 949.9 to 15.7 nm.

The descrepancy with our previous measurements and Thorlabs measurement could be due to this 2.5deg offset in azimuth that might indicate an improper alignment of the LC axis or due to long term fluctuations of the LC response.

Finally, figure 3 reports our 10 sweeps unwrapped.

All these steps are done in Python codes saved in LC-experiment folder.

As the temperature was changing during the measurement, we can see that the main effect is at really low Vrms applied to the LC only.

We plan to further characterize the temperature effect on maximum LC retardation with 0Vrms applied.

Note that one sweep (ie in future corresponding to 250 polarization states) took 25s but this is not limited by VI execution time nor LC.

[Marc, Shalika]

We merged our 3 VIs into a global one to perform LC calibration.

We followed a similar structure as for the PCI VI : a time structure where we first initialize parameters of VI, a while loop to do measurements and change LC voltage or temperature, and finally exiting all VI.

We plot and save data in a parallel while loop to the one where we set up the LC parameters.

Both these loops have different execution time. This is also because we need to be able to sweep the LC voltage at a different time interval than data acquisition or save.

Now we have one issue with LC temperature control where it stops if the target temperature is too far from the actual temperature. We have to enable/disable the temperature control few times to reach the wanted temperature.

While this can be done with one button of our front panel, we want to find a way to do it automatically.

Next steps :

- synchronize data saving and LC voltage sweep

- improve temperature control

- implement filtering

- add rotator control

We found that the issue of not being able to move END yaw is similar as in elog 2995, namely the sign of H3 is flipped...

Also, we now have about 2mm range for the pitch picomotor in one direction but it should be enough for our offload.

[Takahashi, Marc, Rishabh]

We opened the chamber to investigate the suspension in the west end.

• All actuator magnets are still on the mirror.
• There is no rubbing point.
• The pitch-yaw motion of the mirror with the picomotors looks fine.
• We found that the OpLev beam hits the cables for the actuator coils. We treated the cables so as to avoid the beam.

Using the power meter in reflection I saw that the mode matching of IRMC was > 95%.

Flipping the INV/NON INV switch makes the IRMC lock to the mode with output power up to 1.01 mW (/1.68 mW input = 60%). So that works now. Actually, I did the same thing for SHG previously when it was showing similar behaviour...

Adjusting the gain on the IRMC servo shows very little change in the transfer function. For gain increase from 1.1 to 7, the unity gain frequency increases to a rather underwhelming 15 Hz. Now that I think about it, the IRMC PD (Thorlabs PDA05CF2) is specified for a -3dB bandwidth of 150 MHz (75 MHz linewidth). 

IRMC error signal has a DC offset of 150 mV for some (probably not good) reason (figure 1). Green mode cleaner error signal suddenly went to about 60% of what it was yesterday (figure 2).

[Marc, Rishab, Shalika]

TLDR :

PR and BS are offloaded and fine ; INPUT need offload ; END can not move in yaw

cameras are fine ; can not connect to pico server or 2nd target

First we wanted to do suspension healthcheck but had again time-out issue.

It was solved by restarting the standalone pc. We found out that the BS response was really strange (eg fig 1) and that a END had a too low magnitude (fig2).

We went to tried to realign BS (even though was already good enough for the previous measurement) and went to END room where we found that the oplev gain was 10 instead of 100.

We put the proper gain and also realigned slightly the END oplev.

Before, we were not able to see camera image from 2nd target or end room in central building so we confirmed that END room cameras are working properly.

In central building, we restarted the quad camera board that solved this issue.

We could see green flash on GR transmission.

We then offloaded PR by keeping the GR beam on second target and acting on picomotors to make the coils offset go to 0.

We did the same for BS. However, at first both pitch and yaw of coils moved in diagonals in the camera. We found out that once the coils offset absolute value is below 200 this coupling is removed.

Now both PR and BS are working fine and offloaded.

We have to do the same for END (but now yaw coil offset is 0 and it seems far off good alignment and coils do not work) and INPUT.

We found that the ethernet cable that connect the picomotors pc to the switch was squash below a monitor. We replaced the cable but still are unable to connect to picomotors nor 2nd target...

Rishabh, Michael

We intended to go and tweak the IRMC control loop gain for better control bandwidth and stability, as well as measuring the GRMC/MZ transfer functions. But there were a few problems.

The IRMC seems a bit misaligned. We only have about 0.33 mW/1.66 mW = 19.9% transmission. We tried unlocking and relocking several times. Trying to view the free spectral range on the IRMC reflection PD showed some weird jagged spectrum with not very high amplitude. Power meter showed nothing, although Marc later said this is because the bandwidth of the power meter needs to be set to High. Perhaps the PLL alignment process affected the IRM alignment again. The injection and reflection power are basically the same as when it was working properly though.

On the green path after the SHG, the 90/10 green beamsplitter sends reflection to the filter cavity green AOM, which was optimised as per recent elog entries. Accordingly, due to optimisation of the 90/10 BS reflection alignment, there will be a small amount of change in the transmitted path length to the GRMC and MZ. Indeed, some change in the mode spectrum could be seen in the GRMC transmission (figure 1). We used the steering mirror after MZ and now the mode matching is (1.25/(1.25+0.40)) = 96.9% (figure 2, 3). We also tweaked a bit the PDH error signal - the phase was adjusted from 164.993 to 185 degrees (DDS2 Channel 2 GRMC Demod), so the error signal looks a bit more symmetrical (figure 4).

We couldn't lock the GRMC though. According to a previous entry from Yuhang regarding this issue, we looked at several troubleshooting points:

0. grmc has a good alignment.
97% mode matching (figure 2, 3)

1. PDH signal has 316mV pk-pk checked from EPS1.
120 mV pk-pk (figure 4)

2. grmc has loop sign of INV, which is as design.
Yes

3. The RF source phase is reloaded. The phase of RF source is 125deg. When it is changed to 35deg, the signal around resonance becomes flat. This indicates the RF signal phase is still a good one.
Due to the change of EOM the DDS phase is different, but we flipped by 90 degrees and saw that the signal around resonance became zero so indeed the error signal and DDS configuration are fine.

4. There is a switch which has +/- sign. This doesn't decide the sign of control loop. But when we use this type of servo for CC1/2 controls, we need to flip this switch. I tried to flip this switch, but it doesn't help to close loop.
I tried this but no change

5. grmc transmission is checked to have 1.13V peak. This is two times smaller than the value written by Pierre.
The main peak reads 1.25V from the PD signal (figure 3)

6. Loop gain is 3 as usually used.
Yes. Likely this will need to be changed later though due to the EOM change.

7. Threshold for peak identification is -0.55V. This is as required.
The threshold knob was set to 3.3 but I tried changing it to a few values and didn't get any lock.

8. The GR power reaching AOM is measured to be 44mW, whose nominal value is 50mW.
We have 47 mW reaching the AOM

We have good mode matching and a good error signal shape. So the alignment, transmission PD, DDS configuration and PZT are all fine. It seems like the issue is coming from the servo module, or perhaps the amplitude of the error signal. Hopefully it's just to do with the settings and not something for which we have to take the board outside of the cleanroom.

[Marc, Michael, Rishabh, Shalika]

We tweaked the last mirror on green injection into PR and recovered targets on PR tank.

We moved PR coils and recovered BS target. Actually, the gate valve between BS and INPUT is open so we could not use it to fine tune this alignment.

However, we found out that centering the beam on the 2inch mirror inside BS chamber was also a good way to have the beam centered on the first target.

We tried to control the 2nd target and look at its camera from remote but we could not connect to them. Maybe related to the on-going fiber installation in the arm?

We went to 2nd target and could recover alignment by moving BS pitch and PR yaw. It now seems that at least one of the yaw magnet of BS fall down as the beam is not moving properly.

Then we tuned END to recover the back-reflection on the 2nd target. However, it also seems that END yaw is not working properly..

We tweaked a bit INPUT and the green beam is now back to the injection FI.

We will have to offload several suspension using pico-motors as current coil offset is quite large for several dofs.

I checked the alignment to the green AOM (FC first stage length control).

Initially the following signal was applied to the AOM: 109.036 035 615 MHz, 5 dBm signal generator amplitude + 18 dB RF amp, 24V 0.5A power supply to RF amplifier

I used the " BSN10 GR 90/10" (as it is labelled) to move the beam into the AOM, then kept going to align the first order diffracted beam into the iris (figure 1). The following power levels were measured:
Power from SHG: 270 mW
Power into AOM: 47.0 mW
Power after AOM (no signal): 46.0 mW
Power after iris (23 dBm signal): 22.0 mW

(c.f. reference levels 2764: 48.6 mW in, 24.3 mW out)

I took a few different measurements of the first order power for different RF signal amplitude - not really a comprehensive characterisation, just a quick check. Seems roughly consistent with old measurements (531 1679), but I wasn't trying to be too precise for now. I didn't rotate the AOM at all though.
22 dBm -> 18.6 mW (40%)
23 dBm -> 22.0 mW (47%)
24 dBm -> 26.0 mW (55%)
25 dBm -> 30.0 mW (67%)
26 dBm -> 33.2 mW (70%)

The green beam is roughly aligned close to the PR targets (figure 2). There shouldn't be too much adjustment needed, though it is a 2 person job.

Through the time I was in the cleanroom the SHG unlocked a few times, maybe once every 45 minutes or so.