I was asked to calculate the lenses that we need in order to obtained a Gouy phase close to 90 degrees between the two mirrors that are in the Xend green. Yesterday, I measured the distances between the mirrors, and the distance between the mirror relative to the cavity as illustrate in the image attached below. I looked in to the 40m elog and Manasa did the last update on the length of the cavity. She measured 37.7 + 0.05m. The waist size of the beam that was measured by Annalisa in ID 8637 after the Faraday was w0=2.943e-5m @ -0.039m. I calculated the waist size inside the cavity, and I found a waist of w0=2.2 mm. My plan this week is to keep working in the calculation and finish all the calculation this week so that next week I can go inside and place the lenses. 

I had been working on the Xend table optical layout update. Since the two steering mirrors in the Xend green are too close to each, there is a very small Gouy Phase different between these two mirrors. It was suggested to place two lenses so that we can increase the Gouy Phase. I have been working with Nick on this problem, and we had found a solution by using a la mode. We had written an a la mode code that optimize the Gouy Phase and the Mode Matching at the same time. After trying different lenses, we found the following results: a mode matching of 0.9939 as it is show in the first attachment below, and we found a Gouy Phase different between the two mirrors of about 60 degrees. I took photos of the Xend Table. The first photo is the Xend table as we had it right now. In the second photo, I moved the 2nd lens, and I placed the two more lenses that we need it, with more or lenses the correct position where they will be placed. The three old lenses will be replaced by three lenses of different focal length as it can be seen in the first attachment below. The first lens and third lens will stay in the same position where the old first lens and old third lens are, and the second lens will be moved by about half of an inch. We might have one or two of the lenses that we need, but we will have to order the rest of the lenses that need. My plan is to verify the lenses that we already have. Then, I need to let Nick know with lenses we need to order. Hopefully, we will be able to update the table by the end of this week if everything turn out fine.

 Current Mode Matching and Gouy Phase Between Steering Mirrors

We found in 40m elog ID 3330 ( http://nodus.ligo.caltech.edu:8080/40m/3330) a documentation done by Kiwamu, where he measured the waist of the green. The waist of the green is about 35µm. Using a la mode, I was able to calculate the current mode matching, and the Gouy phase between the steering mirrors. In a la mode, I used the optical distances,which is just the distance measured times its index of refraction. I contacted someone from ThorLabs (which is the company that bought Optics For Research), and that person told that the Faraday IO-5-532-LP has a Terbium Gallium Garnet crystal of a length of 7mm and its index of refraction is 1.95. The current mode matching is 0.9343, and the current Gouy phase between steering mirrors is 0.2023 degrees. On Monday, Nick and I are planning to measure the actual mode matching. The attached below is the current X-arm optical layout. 

Calculation For the New Optical Layout

Since the current Gouy phase between the steering mirror is essentially zero, we need to find a way how to increase the Gouy Phase. We tried to add two more lenses after the second steering mirror, and we found that increasing the Gouy phase result in a dramatically decrease in mode matching. For instance, a Gouy phase of about 50 degrees results in a mode matching of about .2, which is awful. We removed the first lens after the faraday, and we added two more mirrors and two more lenses after the second steering mirror. I modified the photo that I took and I place where the new lenses and new mirrors should go as shown in the second pictures attached below. Using a la mode, we found the following solution:

 label                         z (m)            type                       parameters         

 -----                          -----              ----                        ----------         

 lens 1                       0.0800          lens                      focalLength: 0.1000

 First mirror              0.1550          flat mirror            none:            

 Second mirror         0.2800          flat mirror            none:            

 lens 2                      0.4275           lens                      focalLength: Inf   

 lens 3                     0.6549            lens                      focalLength: 0.3000

lens 4                      0.8968            lens                      focalLength: -0.250

Third mirror           1.0675            flat mirror            none:            

Fourth mirror         1.4183            flat mirror            none:            

lens 5                      1.6384            lens                     focalLength: -0.100

Fifth mirror            1.7351            flat mirror           none:            

Sixth mirror           2.0859            flat mirror           none:            

lens 6                     2.1621            lens                     focalLength: 0.6000

ETM                      2.7407            lens                    focalLength: -129.7

ITM                       40.5307          flat mirror          none:             

The mode matching is 0.9786. The different Gouy phase different between Third Mirror and Fourth Mirror is 69.59 degrees, Gouy Phase between Fourth and Fifth 18.80 degrees, Gouy phase between Fifth and Sixth mirrors is 1.28 degrees, Gouy phase between Third and Fifth 88.38 degrees, and the Gouy phase between Fourth and Sixth is 20.08 degrees. Bellow attached the a la Mode code and the Plots.

Plan for this week

I don't  think we have the lenses that we need for this new setup. Mostly, we will need to order the lenses on Monday. As I mention, Nick and I are going to measure the actual mode matching on Monday. If everything look good, then we will move on and do the Upgrade.

 Nick and I measured the reflected power of the green light in locked and unlocked. I'm working on the calculation of the mode matching. Tonight, I'll be posted my calculation I'm still working on it.

JCD:  Andres forgot to mention that they closed the PSL shutter, so that they could look at the green light that is reflected off the harmonic separator toward the IR trans path.  Also, the Xarm (and the Yarm) were aligned to IR using the ASS, and then ASX was used to align the green beam to the cavity.

 Nick and I with the help of Jenne scan the green light when the cavity is unlocked. Nick placed a Beam dump on the IR so that we can just scan the green, but it was removed as soon as we finished with the measurement. I'm working on the calculation, and i'll be posted solution tonight.

Data and Calculation for the Xarm Current Mode Matching

Two days ago, Nick, Jenne, and I took a measurement for the Green Transmission for the X-arm. I took the data and I analyzed it. The first figure attached below is the raw data plotted. I used the function findpeaks in Matlab, and I found all the peaks. Then, by taking close look at the plot, I chose two peaks as shown in the second figure attached below. I took the ratio of the TEM00 and the High order mode, and I average them. This gave me a Mode Matching of 0.9215, which this value is pretty close to the value that I predicted by using a la Mode in http://nodus.ligo.caltech.edu:8080/40m/10191, which is 0.9343. Nick and I measured the reflected power when the cavity is unlocked and when the cavity is locked, so we measured the P_reflUnLocked=52+1µW and P_reflOnLocked=16+2µW and the backgroundNoise=0.761µW. Using this information we calculated  P_refl/P_in=0.297. Now, since P_refl/P_in=|E_ref/E_in|², we looked at the electric fields component by using the reflectivity of the mirror we calculated 0.67. The number doesn't agree, but this is because we didn't take into account the losses when making this calculation. I'm working in the calculation that will include the losses.

Today, Nick and I ordered the lenses and the mirrors. I'm working in putting together a representation of how much improvement the new design will give us in comparison to the current setup.

We want to be able to graphically see how much better it is the new optical table setup in comparison to the current optical table setup. In other words, we want to be able to see how displacement of the beam and how much angle change can be obtained at the ETM from changing the mirrors angles independently. Depending on the spread of the mirrors' vectors we can observe whether the Gouy phase is good. In the plot below, the dotted lines correspond to the current set up, and we can see that the lines are not spread from each other, which essentially mean that changing the angles of the two mirrors just contribute to small change in angle and in the displacement of the beam at the ETM, and therefore the Gouy phase is not good. Now on the other hand. The other solid lines correspond to the new setup mirrors. We can observe that the spread of the line of mirror 1 and mirror 4 is almost 90 degrees, which just implies that there is a good Gouy phase different between these two mirrors. For the angles chosen in the plot, I looked at how much the PZT yaw the mirrors from the elog http://nodus.ligo.caltech.edu:8080/40m/8912. In this elog, they give a plot in mrad/v for the pitch and yaw, so I took the range that the PZT can yaw the mirrors, and I converted into mdegrees/v and then I plotted as shown below. I plot for the current setup and for the new setup in the same plot. The matlab code is also attached below.

 Xarm Green Steering Mirror Upgrade

Nick and I did the upgrade for the green steering mirror today. We locked in the TEM00 mode.
We placed the shutter and everything. We move the OL, but we placed it back. Tonight, I'll be doing a more complete elog with more details.

Green Steering Mirror Update

Yesterday, Nick and I completed the green steering mirrors upgrade. I attached the file that contained the procedure that we plan before we did the upgrade. We placed an iris at the input of the OL and we place another iris before the harmonic separator. We did not use the beam scanner because someone was using it, so what we did was to assume that the cavity is well align and place the iris so that we can recover the alignment. We used the measuring tape to approximate as close as we could the position where the lenses were supposed to go. I did a measurement of the derivative of the waist size in terms of the position of the lens and the derivative of the waist Position in terms of the lenses position at the optimum solution that a la mode give us. Because of this plot, we decide to mount lens 3 and lens 5 into translational stages. After mounting each lenses and mirrors we worked on the alignment of the beam into the cavity. We were able to align the green into the cavity and we were able to locked the cavity to the TEM00 mode. We started to work on the optimization of the mode matching. However, the maximum mode matching that we got was around 0.6, which we need to work a little bit more on the tuning of the mode matching. We leave the iris mounted on the table. I took a picture of the table, and I attached below. For the OL, we just make sure that the output where somehow hitting the QPD, but we didn't really I aligned it. We need to work a little bit more on the alignment of the OL and the tuning of the mirror to maximize the green mode matching.

  Calculation for the input mode cleaner

I have been working on the calculation for the input mode cleaner. I have come out with a new optical setup that will allow us increase the Gouy phase different between the WFS to 90 degrees. I use a la mode to calculate it. The a la mode solution :

   label            z (m)      type             parameters         
    -----            -----      ----             ----------         
    MC1                    0    flat mirror      none:            
    MC3               0.1753    flat mirror      none:            
    MC2              13.4587    curved mirror    ROC: 17.8700       
    Lens1            29.6300    lens             focalLength: 1.7183
    BS2              29.9475    flat mirror      none:            
    First Mirror     30.0237    flat mirror      none:            
    WFS1             30.2269    flat mirror      none:            
    Second Mirror    30.2650    flat mirror      none:            
    Third Mirror     30.5698    flat mirror      none:            
    Lens2            30.9885    lens             focalLength: 1     
    Fourth Mirror    31.0778    flat mirror      none:            
    Lens3            31.4604    lens             focalLength: 0.1000
    Fifth Mirror     31.5350    flat mirror      none:            
    Sixth Mirror     31.9414    flat mirror      none:            
    WFS2             31.9922    flat mirror      none:      

I attached a pictures how the new setup is supposed to look like. 

 I did the calculation, and I reduced the beam Path. In my calculation, I restricted the waist size at the WFSs to be between 1mm-2mm also the other parameter is that the Gouy Phase different between the WFSs have to be 90 degrees. I also try to minimize the amount of mirrors used. I found the Gouy phase to be 89.0622 degrees between the WFSs and the following table shows the solution that I got from a la mode:

  label                         z (m)                   type               parameters         
    -----                         -----                    ----                  ----------         
    MC1                    0                        flat mirror           none:            
    MC3                    0.1753               flat mirror           none:            
    MC2                   13.4587              curved mirror    ROC: 17.8700 (m)       
    Lens1                 28.8172              lens                   focalLength: 1.7183(m)
    BS2                    29.9475              flat mirror           none:            
    First Mirror         30.0237              flat mirror           none:            
    Lens3                 30.1253              lens                  focalLength: -0.100 (m)
    Lens2                 30.1635              lens                 focalLength: 0.1250(m)
    WFS1                 30.2269              flat mirror         none:            
    Second Mirror    30.2650              flat mirror         none:            
    Third Mirror       30.5698              flat mirror         none:            
    Lens4                30.8113              lens                  focalLength: -0.075 (m)
    WFS2                31.0778              flat mirror         none:            

In the first image attached below is the a la mode solution that show the waist size in the first WFS, and I used that solution to calculate the solution of the waist size for the second WFS, which is shown in figure 2. I photoshop a picture to illustrate how the new setup it supposed to look like. 

IMC Calculation and Setup

I have been working in the calculation for improving the Gouy Phase separation between the WFSs. I tried different possible setup, but the three big constrains in choosing a good optical table setup are to have a Waist size that range from 1mm-2mm, the Gouy Phase  between the WFSs have to be greater than 75 degrees and there has to be a steering mirror before each WFS. I will be showing the best calculation because that calculation complies with Rana request of having both WFSs facing west and having the shortest beam path. I approximate the distances by measuring with a tape the distance where the current optics are located and by looking at the picture that I took I approximated the distance where the lenses will be placed. I'm using a la mode for calculating the gouy phase different. I attached a picture of the current optical table setup that we have. Using a la mode, I found that the current gouy phase that we have is 49.6750 degrees.

Now, for the new setup, a run a la mode and found a Gouy phase of 89.3728 degrees. I have to create a two independent beam path: one for the WFS1 and another one for WFS2. The reason for this is that a la mode place everything in one dimension so and since the WFS1 will have a divergence lens in order to increase the waist size, and since that lens should not be interacting with the waist size in the WFS2. We need two beam path for each WFS.  A la mode give us the following solution:

For the beam path of the WFS1

    label                z (m)           type             parameters        
    -----                  -----              ----             ----------        
    MC1                   0              flat mirror          none:           
    MC3                   0.1753     flat mirror          none:           
    MC2                   13.4587   curved mirror    ROC: 17.8700 (m)     
    Lens1                 29.3705   lens                  focalLength: 1.0201 (m)
    BS2                    29.9475   flat mirror          none:           
    First Mirror         30.0237   flat mirror          none:           
    Lens3                30.2000    lens                  focalLength: -0.100 (m)
    WFS1                30.4809    flat mirror         none: 

For the beam path of the WFS2

    label                   z (m)             type             parameters        
    -----                    -----                 ----             ----------        
    MC1                    0               flat mirror          none:           
    MC3                    0.1753      flat mirror          none:           
    MC2                    13.4587    curved mirror    ROC: 17.8700 (m)     
    Lens1                  29.3705    lens                   focalLength: 1.0201 (m)
    BS2                     29.9475    flat mirror          none:           
    Second Mirror    30.2650     flat mirror          none:           
    Lens2                 30.4809     lens                  focalLength: -0.075 (m)
    Third Mirror        30.5698     flat mirror          none:           
    WFS2                30.6968      flat mirror          none:  

I attached bellow how the new setup should look like in the second picture and also I include and attachment of the a la mode code.

 I used Mist to be able to see the read out that we get in the WFSs that take the Mode Cleaner Reflection and the QPD that take the transmitted from MC2. In the following, plots I'm misaligned the each mirrors: MC1, MC2 and MC3. The misalignment are in Yaw and Pitch. I'm dividing the WFSs reading by the total power reflect power, and I'm dividing the QPD for the MC2 transmission by the total transmitted power. In my Mist model, I have a laser of 1W and my EOM is modulated at 30MHz instead of 29.5MHz and the modulation depth was calculating by measuring the applied voltage using and Spectrum analyzer. I using Kiwamu measurement of modulation depth efficiency vs the applied voltage, https://dcc.ligo.org/DocDB/0010/G1000297/001/G1000297-v1.pdf,  I got a modulation depth of 0.6 mrad. I put this modulation depth and I got the following plots: The fourth and fifth attachment are for the current optical setup that we have. The sixth and seventh attachment is for the new optical setup. The eighth attachment is showing the mode cleaner cavity resonating. The last attachment contains the plots of WFS1 vs WFS2, MC2_QPD vs WFS1, MC2_QPD vs WFS3 for each mirror misaligned. The last two attachment are the MIST code for the calculation.

We have all the lenses that we need. I checked it last Friday and if everything is good we will be ready to do the new upgrade this coming Friday. For increasing the power, I check and we have different BS so we can just switch from the current setup the BS. Can you let me know if this setup look good or if I need to chance the setup? I would really love to do this upgrade before I leave.

 Upgrade of IMC Reflection Optical Setup

Nick and I upgrade the IMC. We move both WFSs and placed them facing west. When aligning the beam into the WFS, we make sure that the beam were hitting the center of the mirrors and then we placed the lenses in their corresponding position. We used the beam scanner to measure the waist and the waist in the second WFS was bigger than 1mm, and the second WFS was a little bit below than 1mm. We center the beam in the WFSs and in the PD. We did haven't measure whether we have a good Gouy Phase. Below I attached the picture of how the new setup look like.   

We found Mon7 in control room dead today afternoon. It's front power on green light is not lighting up. All other monitors are working as normal.

This monitor was used for looking at IMC camera analog feed. It is one of the most important monitors for us, so we should replace it with a different monitor.

Yehonathan and Paco disconnected the monitor and brought it down. We put it under the back table if anyone wants to fix it. Paco has ordered a BNC to VGA/HDMI converter to put in any normal monitor up there. It will happen this Wednesday. Meanwhile, I have changed the MON4 assignment from POP to Quad2 to be used for IMC.

Rana came and helped us figure us where to inject the noise. Following are the characteristics of the test we did:

• Inject normal noise at C1:IOO-MC1_PIT_EXC using AWGGUI.
• Excitation amplitude of 54321 in band 12-37Hz with Cheby1 8th order bandpass filter with same limits.
• Look at power spectrum of C1:IOO-MC_F_DQ, C1:IOO-WFS1-PIT_OUT_DQ and the C1:IOO-MC1_PIT_EXC itself.
• Increased the gain of the noise excitation until we see some effect in MC_F.
• Diaggui also showed coherence plot in the bottom, which let's us have an estimate of how much we need to go further.

Attachment 1 shows a screenshot with awggui and diaggui screens displaying the signal in both angular and longitudinal channels.

Attachment 2 shows the analogous screenshot for MC2.

Today we went through LSC locking mechanics with Gautam and as a "Hello World" example, worked on locking michelson cavity.

MICH settings changed:

• Gautam at some point added 9 dB attenuation filters in MICH filter module in LSC to match the 9 dB pre-amplifier before digitization.
• This required changing teh trigger thresholds, C1:LSC-MICH_TRIG_THRESH_ON and C1:LSC-MICH_TRIG_THRESH_OFF.
• We looked at C1:LSC-AS55_Q_ERR_DQ and C1:LSC-ASDC_OUT_DQ on ndscope.
• The zero crossings in AS55_Q correspond to ASDC going to zero. We found the threshold values of ASDC by finding the linear region in zero crossing of AS55_Q.
• We changed the thresold values to UP: -0.3mW and DOWN -0.05mW. The thresholds were also changed in C1LSC_FM_TRIG.
• We also set FM2,3,6 and 8 to be triggered on threshold.

We characterized the loop OLTF, found the UGF to be 90 Hz and measured the noise at error and control points.

gautam: one aim of this work was to demonstrate that the "Lock Michelson (dark)" script call from the IFOconfigure screen worked - it did, reliably, after the setting changes mentioned above.

We corrected the MICH locking snap file C1configure_MI.req and saved an updated C1configure_MI.snap. Now the 'Restore MICH' script in IFO_CONFIGURE>!MICH>Restore MICH works. The corrections included adding the correct rows of PD_DOF matrices to be at the right settings (use AS55 as error signal). The MICH_A_GAIN and MICH_B_GAIN needed to be saved as well.

We also were able to get to PRMI SB resonance. PRM was misalgined earlier from optimal position and after some manual aligning, we were able to get it to lock just by hitting IFO_CONFIGURE>!PRMI>Restore PRMI SB (3f).

We found that megatron is unable to properly run scripts/MC/WFS/mcwfsoff and scripts/MC/WFS/mcwfson scripts. It fails cdsutils commands due to a library conflict. This meant that WFS loops were not turned off when IMC would get unlocked and they would keep integrating noise into offsets. The mcwfsoff script is also supposed to clear up WFS loop offsets, but that wasn't happening either. The mcwfson script was also not bringing back WFS loops on.

Gautam fixed these scripts temprorarily for running on megatron by using ezcawrite and ezcaswitch commands instead of cdsutils commands. Now these scripts are running normally. This could be the reason for wildly fluctuating WFS offsets that we have seen in teh past few months.

gautam: the problem here is that megatron is running Ubuntu18 - I'm not sure if there is any dedicated CDS group packaging for Ubuntu, and so we're using some shared install of the cdsutils (hosted on the shared chiara NFS drive), which is complaining about missing linked lib files. Depending on people's mood, it may be worth biting the bullet and make Megatron run Debian10, for which the CDS group maintains packages.

Last night Gautam walked us through the algorithm used to lock PRFPMI. We tried it several times with the PSL HEPA filter off between 10:00 pm July 7th to 1:00 am July 8th. None of our attempts were successful. In between, we tried to do the locking with old IMC settings as well, but it did not change the result for us. In most attempts, the arms would start to resonate with PRMI with about 200 times the power than without power recycling while the arms are still controlled by ALS beatnote. The handover of lock controls "CARM+DARM locked to ALS beatnote" to "Main laser + IMC locked to the CARM+DARM" would always fail. More specifically, we were seeing that as soon as we hand over the DC control of CARM from ALS beatnote to IR by feeding back to MC2, the lock would inevitably fail before the rest of the high-frequency control can be transferred over.

Nonetheless, Paco and I got a good demo of how to do PRFPMI locking if the need appears. With more practice and attempts, we should be able to achieve the lock at some point in the future. The issues in handover could be due to any of the following:

• Although it seems like ALS beatnote fed control of arms keep them within the CARM IR linewidth as we see the IR resonating, there still could be some excess noise that needs to be dealt with.
• Gautam conjectures, that the presence of high power in the arms connects the ITMs and the ETMs with an optical spring changing the transfer function of the pendula. This in turn changes the phase margin and possibly makes the CARM loop in IR PRFPMI unstable.
• We should also investigate the loop transfer functions near the handover point for the ALS beatnote loop and the IR CARM loop and calculate the crossover frequency and gain/phase margins there.

More insights or suggestions are welcome.

Note; An earthquake came around lunch time and tripped all watchdogs. Most suspensions were recovered without issues, but ITMX appeared to be stuck. We tried the shaking procedure, but after this we couldn't restore the XARM lock. From alignment, we tried optimizing the TRX but we only got up to ~0.5 and ASS wouldn't work as usual. In the end the issue was that we had forgotten to enable the LL coil output so after we did this, we managed to recover the XARM.

[Paco, Anchal]

tl;dr: Done no harm, no lasting change.

Learn burtgooey

- Use /cvs/cds/caltech/target/c1psl/autoBurt.req as input to test snapshot "/users/anchal/BURTsnaps/controls_1210301_101310_0.snap" on rossa after not succeeding in donatella

- Browse /opt/rtcds/caltech/c1/burt/autoburt/snapshots/TODAY just to know where the snapshots are living. Will store our morning work specific snapshots in local user directories (e.g. /users/anchal/BURTsnaps)

Identifying video monitors

- Switched channels around on video controls; changed C1:VID-MON7 to 16, back to 30, then C1:VID-QUAD2_4 to 16, to 18, then 20, back to 16, to 14 (which identified as PMCT), to 1 (IMC). Anyways, looks like IMC is locked.

[Yehonathan, Paco, Anchal]

Unlocking MC

- From IOO/LockMC, MC_Servo, FSS --> closed PSL shutter, reopen it and see the lock recovers almost instantly. Try MCRFL shutter, no effect. Toggled PSL shutter one more time, lock recovered.

- From IOO/LockMC, MC_Servo, toggle OPTION (after IP2A), lose and recover lock in similar fashion. MCRFL gets most of the light.

- Looked at IFO_OVERVIEW just to get familiar with the various signals.

A cross-coupling test has been set to trigger at 05:00 am on April 1st, 2021. The script is waiting on tmux session 'cB' on pianosa. /scripts/SUS/OutMatCalc/MC2crossCoupleTest.py is being used here. The script will switch on oscillator in LOCKIN1 of MC2 at 13 Hz and 200 counts and would send it along the POS, PIT and YAW vectors on output matrix one by one, each for 2 minutes. It will take data from C1:IOO-MC_F_DQ, C1:IOO-MC_TRANS_PIT_ERR and C1:IOO-MC_TRANS_YAW_ERR and use it to measure 'sensing matrix' S. Sensing matrix S is defined as the cross-coupling between excited and sensed DOF and we ideally want it to be an identity matrix. The code will use the measured S to create a guess matrix A which on being multiplied by ideal coil output matrix would give us a rotated coil output matrix O. This guess O will be applied and the measurement will be repeated. On each iteration, next, A matrix is defined by:

This recursive algorithm converges A to the inverse of initial S. The above relation is derived by noticing that in steady state . I've taken this idea from a mathematics paper I found on some more complex stuff (c.f. https://doi.org/10.31219/osf.io/yrvck).

At each iteration, all three matrices A, O and S will be stored in a text file for analysis later.

The code has the error-catching capability and would restore the optic to the status quo if an error occurs or watchdogs trip due to earthquakes.

The coil balancing attempt failed. The off-diagonal values in the measured sensing matrices either remained the same or increased.

The attempt in the morning was too slow. By the time we reached, it had reached to iteration 7 only and still nowhere near optimum sensing matrix had reached. We still needed to see if the optimum would eventually reach if more iterations happened.

<Radhika came for shadowing us and learning about 40m>

So we worked a bit on speeding up the data loading process and then ran the code again which now was running much faster. Still within 1 hr or so, we saw it had reached to iteration 7 with no sign of sensing matrix getting any better.

<Paco left for vaccination>

To determine if the method would work in principle, I decided to stop the current run and start with a 0.5 Hz bandwidth run (so about 7 averages with 8s duration data and welch method). This completed 20 iterations before Gautum came. But it was clear now that the method is not converging to a better solution. Need to find a bug in the implementation of the algorithm mentioned in last post or find a better algoritm.

Attachment 1 is the plot of how the sensing matrix's distance from the identity matrix increased over iterations in the last run.

Attachment 2 is the plot for different off-diagonal terms in the sensing matrix. It is clear that POS->PIT,YAW coupling is not being measured properly as it remains constant.

Attachment 3 Gautum told us that there is some naming error in nds and MC_TRANS_PIT/YAW can be read through C1:IOO-MC_TRANS_PIT_ERR and C1:IOO-MC_TRANS_YAW_ERR channels instead. To test if they indeed point to same values, we did a test of exciting YAW degree through LOCKIN1 and seeing if the peaks are visible in the channels. This was also done to give Radhika an opportunity to do something I could confidently mentor about. and to experience using diaggui.

After fixing a few things we felt were wrong in our implementation of the algorithm, we ran the coil balancing for 12 iterations with just 11s per excitation and still taking CSD with 0.1 Hz bandwidth. This time we saw the distance of sensing matrix from identity going down.

Performance Analysis

• Attachment 1 shows the trend of distance of Sensing matrix from identity matrix over iterations.
• Attachment 2 shows the trend of off-diagonal terms in sensing matrix over iterations.
• Attachment 3 shows the ASD for the different sensed DOF when excited in different DOFs with the new output matrix. This is the better truth of what happened by the end. The true sensing matrix is proportional to the peak heights in this plot. Rows are different sensed DOFs (POS, PIT, YAW) and columns are excited DOFs (POS, PIT, YAW). The black dotted curves are ASD when no excitation was present.

Next step

• We want to run it for longer, more iterations and more duration to get better averaging. Hopefully, this will do a better job. We'll try running this new code tomorrow at 5:00am.
• We'll work on using uncertainties of measured data.
• Use awg to excite all DOF together at different frequencies and make the code faster.

[Paco, Anchal]

Came in a little bit after 8 and found the MC unlocked and struggling to lock for the past 3 hours. Looking at the SUS overview, both MC1 and ITMX Watchdogs had tripped so we damped the suspensions and brought them back to a good state. The autolocker was still not able to catch lock, so we cleared the WFS filter history to remove large angular offsets in MC1 and after this the MC caught its lock again.

Looks like two EQs came in at around 4:45 AM (Pacific) suggested by a couple of spikes in the seismic rainbow, and this.

As mentioned in last post, we earlier made an error in making sure that all time series arrays go in with same sampling rate in CSD calculation. When we fixed that, our recursive method just blew out in all the efforts since then.

We suspect a major issue is how our measured sensing matrix (the cross-coupling matrix between different degrees of freedom on excitation) has significant imaginary parts in it. We discard the imaginary vaues and only use real parts for iterative method, but we think this is not the solution.

Here we present cross-spectral density of different channels representing the three sensed DOFs (normalized by ASD of no excitation data for each involved component) and the sensing matrix (TF estimate) calculated by normalizing the first cross spectral density plots column wise by the diagonal values. These are measured with existing ideal output matrix but with the new input matrix. This is to get an idea of how these elements look when we use them.

Note, that we used only 10 seconds of data in this run and used binwidth of 0.25Hz. When we used binwidth of 0.1 Hz, we found that the peaks were broad and highest at 13.1 Hz instead of 13 Hz which is the excitation frequency used in these measurements.

How should we proceed?

• We feel that we should figure out a way to use the imaginary value of the sensing matrix, either directly or as weights representing noise in that particular data point.
• Should we increase the excitation amplitude? We are currently using 500 counts of excitation on coil output.
• Are there any other iterative methods for finding the inverse of the matrix that we should be aware of? Our current method is rudimentary and converges linearly.
• Should we use the absolute value of the sensing matrix instead? In our experience, that is equivalent to simply taking ratios of the PSD of each channel and does not work as well as the TF estimate method.

Today, we finally crossed the last hurdle and got a successful converging coil balancing run.

What was the issue with POS?

• Position of the MC2 mirror is being sensed using C1:IOO-MC_F_DQ channel which is proportional to the resonant frequency of the locked IMC.
• However, this sensor is always 180 degrees out of phase of our actuator, the coils.
• When the coils push the mirror forward, the length of the cavity actually decreases.
• We added an extra option of providing a sign to the sensors such that -1 will be multiplied to sensed values for sensors which measure in opposite direction to the actuation.
• This is important, because the feedback is applied to the coil output matrix assuming a particular direction of acctuation.
• When we gave negative sign for the position sensor, it all started making sense and the algorithm started converging.

First run parameters:

• We used binwidth of 0.25 Hz and duration of excitation as 41s. This would give welch and csd averaging of 19. We used median averaging to ignore outliers.
• This iteration was run after PIT and YAW were separetly uncoupled before. We'll post a clean start to end run results in near future.
• The iteration works in following manner:
  • Define a constant coil matrix C = [[1, 1, 1], [1, 1, -1], [1, -1, 1], [1, -1, -1]] which is ideal coil output matrix.
  • In each iteration, the output matrix O_k is defined as (note @ is the matmul operator):
    O_k = C @ A_k
    where A_k is a 3x3 matrix. A_-1 is identity matrix.
  • At the end of each iteration, a sensing matrix is calculated in dimensions sensedDOF x excitedDOF, S_k
  • For next iteration, A_k+1 is calcualted by:
    A_k+1 = A_k - b * (S_k - I)
    where I is the identity matrix.
  • At convergence, the sensing matrix would become same as identity and matrix A will stop updating.
• For this run, we kept the parameter b to be 0.05. This is similar to the K_P parameter in PID loops. It should be between 0 and 1.
• Since b value was small enough to allow for convergence from the inital point, but later it slowed down the process a lot.
• Ideally, we should figure out a way to increase this paramter when the coil has been balanced somewhat, to increase the speed of the algorithm.
• Secondly, we have a code which excites all DOFs at different frequencies directly using excitation channels in coil output matrix using awg.py. But for some reason, the excitation channel for 4th row in the output matrix column only connects intermittantly. Because of this, we can't use this method reliably yet. We can investigate more into it if suggested.

Balancing characteristics:

• Attachment 1 shows how the distance of sensing matrix falls as iterations increase. We only ran for 50 iterations.
• Attachment 2 shows how different off-diagonal terms of sensing matrix decreased.
  • Note that POS -> PIT, POS -> YAW and PIT-YAW have settled down to the noise floor.
  • The noise floor can be improved by increasing the excitation amplitude and/or increasing the duration of measurement.
• Attachment 3 shows the evolution of sensing matrix as iterations move.

Final balanced output matrix:

Code features and next:

• Majority of the code is in two files: scripts/SUS/OutMatCalc/MC2crossCoupleTest.py and scripts/SUS/OutMatCalc/crossCoupleTest.py .
• The code runs from start to end without human involevement and restores the state of channels in any case (error, kyboard interrupt, end of code) using finally statement.
• Currently, each excitation is done one at a time through LockIn1. As mentioned above, this can be sped up 3 times if we get the awg.py to work reliably.
• The complete code is in python3 and currently is run through native python3 on allegra (a new debian10 workstation with latest cds-workstation installed).
• The code can be easily generalized for balancing any optic. Please let us know if we should work on making the generalized optic.
• We're also working on thinking about increasing b as iterations move forward and the error signal becomes smaller.
• We can also include the uncertainty in the Sensing matrix measurement to provide a weighted feedback. That way, we can probably increase b more.

We ran again this method but with the 'b' parameter as a matrix instead. This provides more gain on some off-diagonal terms than others. This gave us a better convergence with the code reaching to the tolerance level provided (0.01 distance of S matrix from identity) within 16 iterations (~17 mins).

Attachment 1 again shows how the off-diagonal terms go down and how the overall distance of sensing matrix from identity goes down. This is 'Cross coupling budget' of the coils as iterations move forward.

Jumping to near zero-crossing:

• Rana mentioned a ezlockin code which first makes 5 step changes in output matrix without using feedback and calculates the changes required to reach zero-crossing in the behavior of the off-diagonal terms during these steps.
• This is similar to what we did above by hand where we increased the value of b for slowly converging off-diagonal elements.
• We plan to implement this 'jump' to near zero-crossing method next. Aim is to get a coil balancing code that does the job in ~5 min.
• We have been throwing away imaginary part of sensing matrix so far. We wanted to get to some owrking solution before we try more complex stuff. We have to figure out global phases in each transfer function estimate to rotate the measured transfer function appropriately.

PMC lost lock between 21:00 and 22:00 UTC on April 11th as seen in the summary pages:

https://nodus.ligo.caltech.edu:30889/detcharsummary/day/20210411/psl/#gallery-4

That's between 2pm and 3pm on Sunday for us. We're not sure what caused it. We will attempt to lock it back.

Mon Apr 12 08:45:53 2021: we used milind's python script in scripts/PSL/PMC/pmc_autolocker.py. It locked the PMC in about a minute and then IMC catched lock succefully.

However, the PMC transmission PD shows voltage level of about 0.7V. On medm, it is set to turn red below 0.7 and yellow above. In Summary pages in the past, it seems like this value has typically been around 0.74V. Simil;arly, the reflection RFPD DC voltage is around 0.063 V right now while it is supposed to be around 0.04 nominally So the lock is not so healthy.

We tried running this script and the bashscript version too (scripts/PSL/PMC/PMCAutolocker) a couple of times but it was unable to acquire lock.

Then we manually tried to acquire lock by varying the C1:PSL-PMC_RAMP (with gain set to -10 dB) and resetting PZT position by toggling Blank. After a few attempts, we were able to find the lock with transmission PD value around 0.73V and reflection RFPD value around 0.043. PZT control voltage was 30V and shown in red in medm to begin with. So we adjusted the output ramp again to let it come to above 50V (or maybe it just drifted to that value by itself as we could se some slow drift too). At Mon Apr 12 09:50:12 2021 , the PZT voltage was around 58V and shown in green.

We assume this is a good enough point for PMC lock and move on.

We tried two sets of filters on the output matrix POS column in MC2. Both versions failed. Following are some details.

How test was done:

• PSL shutter was closed and autolocker was switch off.
• Turned off damping on POS, PIT, and YAW using C1:SUS-MC2_SUSPOS_SW2, C1:SUS-MC2_SUSPIT_SW2, and C1:SUS-MC2_SUSYAW_SW2.
• Reference data was taken with no excitation to get relative increase at excitation.
• Channels C1:SUS-MC2_SUSPIT_IN1, C1:SUS-MC2_SUSPOS_IN1, and C1:SUS-MC2_SUSYAW_IN1.
• Frist we sent an excitation through LOCKIN1 at 0.11 Hz and 500 counts amplitude.
• LOCKIN column in MC2 output matrix was kept identical to POS column, so all ones.
• This formed our reference data set when no filters were used. Attachment 1.
• Note that the peak at 0.03 Hz is due to LOCKIN2 that was left switched on due to autolocker.
• Then the calculated filters were loaded using foton. Procedure:
  • Right click on filter bank med. Got to Execute-> Foton.
  • Go to File and uncheck 'Read Only'.
  • Find the filter module name in Module drop down.
  • Select an empty module section in Sections.
  • Write a name for the filter. We used DCcoupF2A and DCcouF2A2 for the two version respectively.
  • Paste the zpk foton format in Command.
  • Check with Bode plot if these are correct filters. Then click on Save. It will take about 30s to become responsive again.
  • GO back to filter bank medm screen and click on 'Load Coefficients'. This should start displaying your new filter module.
  • To switch on the module, click on the button below its name.
• Once fitlers were loaded, we realized we can not use the LOCKIn to excite anymore as it comes as separate excitation.
• So we used awggui to excite C1:SUS-MC2_LSCEXC at 0.11 Hz and 500 counts.
• Then we retook the data and checked if the peaks are visible on PIT and YAW channels and how high they are.

Filer version 1

• This was calculated by starting from ideal output matrix elements as they are currently loaded. All 1's for POS and so on.
• The calculations were done in scripts/SUS/OutMatCalc/coilBalanceDC.py.
• This file uses a state space model of the suspension and calculated the cross-coupling. Then the cross coupling is inverted and applied to the current output matrix elements to get correction DC gains.
• These corrected DC gains are then used to create the filters as described in last post.
• Attachment 2 shows the filter transfer functions and Attachment 3 shows the test results. Failed :(.
• There was practivally no change in cross coupling that we can see.

Filter version 2:

• In this version we used the output matrix optimized at high frequencies earlier (16009).
• While testing this version, we also uploaded this optimised output amtrix at high frequency.
• In this test, we realized the LOCKIN2 was on and switched it off manually. All excitations were done through awggui.
• Attachment 4 shows the filter transfer functions and Attachment 5 shows the test results. Failed :(.
• There was again practivally no change in cross coupling that we can see.

Forgot to upload new MC2 input matrix:

• In hindsight, we should have uploaded our diagonalized suspension input matrix in MC2.
• Without it, there was cross-coupling the in the sensor data to begin with.
• But this can only be part of the reason why all our filters failed miserably.
• Because the output matrix was not diagonalized earlier but it was not so bad. Onyl a fresh test can tell if it was the culprit.

The filters were somewhat successful, how much we can see in attachment 1. The tip about difference between eigenmode basis and cartesian basis was the main thing that helped us take data properly. We still used OSEM data but rotated the output from POS, PIT, YAW to x, theta, phi (cartesian basis where x is also measured as angle projected by suspension length).

Eigenmode basis and Cartesian basis:

• It is important to understand the difference between these two and what channels/sensors read what.
• Eigenmode basis as the name suggests is the natural basis for the suspended pendulum.
  • It signifies the motion along three independent and orthogonal modes of motion: POS (longitudinal pendulum oscillation), PIT, and YAW.
  • The position of optic can be written in eigenmode basis as three numbers:
    • POS: Angle made by the center of mass of optic with verticle line from suspension point.
    • PIT: Angle made by the optic face with the suspension wires (this is important to note).
    • YAW: Angle made by optic surface with the nominal plane of suspension wires. (the yaw angle basically).
• Cartesian basis is the lab reference frame.
  • Here we define three variables that can also represent an optic positioned and orientation:
    • x: Angle made by the center of mass of optic with verticle line from suspension point. (Same as POS)
    • : Angle made by the optic surface with absolute verticle (z-axis) in lab frame.
    • : Twist of the optic around the z-axis. Same as YAW angle above.
• We want to apply the feedback gains and filters in eigenmode basis because they are a set of known independent modes. (RXA: NOOO!!!!!! read me elog entry on this topic)
• Hence, the output from input matrix of suspensions comes out at POS, PIT and YAW in the eigenmode basis.
• However, the sensors of optic positional, and orientation such at MC_F, wave front sensors and optical levers measure it in lab frame and thus in cartesian basis.
• Essentially, the measured by these sensors is different from the PIT calculated using the OSEM sensor data and is related by:
  • , where PIT and POS both are in radians as defined above.
• When we optimized the cross-coupling in output matrix at high frequencies using the MC_F and WFS data, we actually optimized it In cartesian basis.
• The three feedback filters from POS, PIT and YAW which carry data in the eigenmode basis need to be rotated into the cartesian basis in the output matrix before application to the coils.
• The so-called F2A and A2L filters are essentially doing this rotation.
• Above the resonant frequencies, the PIT and become identical. Hence we want our filters to go to unity

The two filter sets:

• The filters are named Eg2Ctv1 and Eg2Ctv2 on the POS column of MC2 output matrix.
• This is to signify that these filters convert the POS, PIT, and YAW basis data (eigenmode basis data) into the cartesian basis (x, theta, phi) in which the output matrix is already optimized at higher frequencies.
• v1 filter used an ideal output matrix during the calculation of filter as described in 16042 (script at scripts/SUS/OutMatCalc/coilBalanceDC.py).
• Attachment 2 shows these filter transfer functions.
• v2 filter use the output matrix optimized to reduce cross-coupling amount cartesian basis modes (MC_F, WFS_PIT and WFS_YAW) in 16009.
• Attachment 3 shows these filter transfer funcitons.
• Because of this, the v2 filter is different among right and left coils as well. We do see in Attachment 1 that this version of filter helps in reducing POS->YAW coupling too.

Test procedure:

• We uploaded both the diagonalized input matrix and the diagonalized output matrix as calculated earlier.
• We measured channels C1:SUS-MC2_SUSPOS_IN1_DQ, C1:SUS-MC2_SUSPIT_IN1_DQ, and C1:SUS-MC2_SUSYAW_IN1_DQ throughout this test.
• These channels give output in an eigenmode basis (POS, PIT, and YAW) and the rows of the input matrix have some arbitrary normalization.
• We normalize these channels to have same input matrix normalization as would be for ideal matrix (2 in each row).
• Then, assuming the UL_SENS, UR_SENS, LR_SENS, and LL_SENS channels that come at input of the input matrix are calibrated in units of um, we calculate the cartesian angles x, theta, phi. for this calculation, we used the distance between coils as 49.4 mm (got it from Koji) and length of suspension as 0.2489 m and offset of suspension points from COM, b = 0.9 mm.
• Now that we have true measures of angles in cartesian basis, we can use them to understand the effect on cross coupling from the filters we used.
• PSL shutter is closed and autolocker is disabled. During all data measurements, we switched of suspension damping loops. This would ensure that our low frequency excitation survives for measurement at the measurement channels.
• We first took reference data with no excitation and no filters for getting a baseline on each channel (dotted curves in Attachment 1).
• We then send excitation of 0.03 Hz with 500 counts amplitude at C1:SUS-MC2_LSC_EXC and switched on LSC output.
• One set of data is taken with no filters active (dashed curve in attachment 1).
• Then two sets of data are taken with the two filters. Each data set was of 500s in length.
• Welch function is used to take the PSD of data with bin widht of  0.01Hz and 9 averages.

Results:

• Filter v1 was the most successful in reducing  coupling by factor of 17.5.
  • The reduction in  coupling was less. By a factor of 1.4.
• Filter v2 was worse but still did a reduction of coupling by factor of 7.8.
  • The reduction in  coupling was better. By a factor of 3.3.

Next, filters in PIT columns too

• We do have filters calculated for PIT as well.
• Now that we know how to test these properly, we can test them tomorrow fairly quickly.
• For the YAW column though, the filters would probably just undo the output matrix optimization as they are derived from ideal transfer function models and ideally there is no coupling between YAW and other DOFs. So maybe, we should skip putting these on.

[Paco, Anchal]

• We adopted the following procedure to balance the coil output gains using a high-frequency (> 10 Hz) excitation on "C1:SUS-MCX_ASCPIT_EXC", "C1:SUS-MCX_ASCYAW_EXC", and "C1:SUS-MCX_LSC_EXC", where X is one of {1, 2, 3} for the three IMC optics, and the cavity sensors (MC_F, and MC_TRANS);
  1. We load the new input matrix found on March-23rd.
  2. Using awggui, we launch a single 23.17 Hz sine with 500 - 1000 counts amplitude on the aforementioned channels.
     • We are still unable to launch multiple excitations simultaneously through either API (python-awg or dtt-awggui) 
  3. Using our built-in hominid neural networks, we look at the "C1:IOO-MC_F", "C1:IOO-MC_TRANS_PIT_IN", and "C1:IOO-MC_TRANS_YAW_IN" exponentially averaging power spectra, on and about the excitation frequency, and identify the amount of cross-coupling going into angular or longitudinal motion depending on the excited degree of freedom.
  4. We step the "C1:SUS-MCX_URCOIL_GAIN", "C1:SUS-MCX_ULCOIL_GAIN", "C1:SUS-MCX_LRCOIL_GAIN", "C1:SUS-MCX_LLCOIL_GAIN" coil output gains by hand in the presence of an excitation (e.g. "LSC") along a given degree of freedom (e.g. along "PIT") to try and minimize the coupling.
  5. We iterate step (4) until we find an optimum gain set, and move on to another optic.

Results

• For MC2 the optimal gains changed from: [1.0, -1.0, 1.0, -1.0] → [1.05, -1.05, 0.995, -1.03] **
  • Here we were able to first decouple PIT and YAW from a POS excitation almost entirely (see Attachment #1), but weren't as successful in decoupling YAW and POS from PIT, or PIT and POS from YAW excitations (Attachment #2).
• For MC1 the optimal gains changed from: [1.0, 1.0, 1.0, 1.0] → [0.282, 0.035, 0.302, 2.46] **
  • Here we mostly succeeded in decoupling POS from YAW and PIT excitations (see Attachments #3 - 4).
• For MC3 the optimal gains changed from: [1.0, -1.0, 1.0, -1.0] → [0.126, -0.123, 0.298, -0.306] **
  • Here the LSC_EXC didn't show up on MC_F (??), and the PIT/YAW excitations decouple by virtue of seemingly low gains, so maybe the optimum is an artifact of the lower coil gains...
  • Plots are to follow up for this one.

** The notation here is [UL, UR, LR, LL]

We did a step response test with MC2 Suspensoin Damping Gains and optimized them to get <5 oscillations in ringdown.

Procedure:

• We uploaded the diagonalized input matrix.
• We uploaded the coil balancing gains at high frequencies found in 16054.
• We applied Eg2CtQ1 filter module for DC gain balancing foun inf 16055.
• We set TRAMP to 0 in C1:SUS-MC2_SUSPOS_TRAMP, C1:SUS-MC2_SUSPIT_TRAMP, and C1:SUS-MC2_SUSYAW_TRAMP.
• We played with offsets to get a good step height. Finally we used:
  • C1:SUS-MC2_SUSPOS_OFFSET: 3000
  • C1:SUS-MC2_SUSPIT_OFFSET: 100
  • C1:SUS-MC2_SUSYAW_OFFSET: 100
• We looked at channels C1:SUS-MC2_SUSPOS_INMON, C1:SUS-MC2_SUSPIT_INMON, and C1:SUS-MC2_SUSYAW_INMON on a striptool screen to see the step response of the switching on/off of the offsets.
• We tried to decrease/increase gain to get <5 oscillations during ringdown due to the step inputs.
• Restored everything back to old values at the end.

Results:

• Gain in POS was found to be already good. In PIT and YAW we changed the gains from 10 -> 30.
• Attachment 1 shows the striptool screen when offset was switched ON/Off in POS, PIT and YAW respectively after appling the optimized gains.
• Attachment 2 shows the same test with old gains for comparison.

In the afternoon, we'll complete doing the above steps for MC1 and MC3. Their coil balancing has not been done on DC so, it is bit non-ideal right now. We'll look into scripting this process as well.

Note: The AC gains were measured by keeping output matrix to ideal values of 1s. When optimizing DC gains, the AC gains were uploaded in coil ouput gains.

Note: The AC gains were measured by keeping output matrix to ideal values of 1s. When optimizing DC gains, the AC gains were uploaded in coil ouput gains.

Today we had some trouble launching an excitation on C1:IOO-MC_LSC_EXC from awggui. The error read:

awgSetChannel: failed getIndexAWG C1:SUS-MC2_LSC_EXC ret=-3

What solved this was the following :

1. launch the dtt command line interface
2. Anchal remembers a slot number 37008
3. We issue >> awg free 37008
4. Slot freed, launch a new instance of awggui

Today we tested the F2A filters created from the DC gain values listed in 16066.

Filters:

• For a DC gain  required for balancing the coil at DC and being the resonance frequency of the mode (POS in this case), we calculate the filter using:
  where .
• Attachment 1 shows the motivation for choosing the resonant frequency in the formula above. It makes gain at DC as while keeping AC gain as 1.
• Attachment 2 shows the transfer functions of the filters uploaded.
• Filters are named Eg2CtQ3, Eg2CtQ7 and Eg2CtQ10 for Q=3,7,10 filters respectively. (Named for Eigenmode Basis to Cartesian Basis conversion filters, aka F2A filters).

Testing procedure:

• We uploaded the new input matrix listed in 16066.
• We then uploaded the coil output gains (AC gains) that are also listed in 16066.
• Then we reduced the C1:IOO-WFS_GAIN to 0.05 (by a factor of 20).
  • Rana asked us to test the WFS sensors' impulse response to observe a minimum 10s decay to ensure that the UGF of WFS control loops is at or below 0.1 Hz.
  • We were unable to have any effect on this decay actually. We tried setting offsets without tramps in multiple places but whenever we were able to excite this loop, it will always damp down in about 5-6s regardless of the value of C1:IOO-WFS_GAIN.
  • So we moved on.
• Then, with MC locked we took reference data with no excitation or filters uploaded. (dotted curves)
• We took cross spectral density from C1:IOO-MC_F to C1:IOO-MC_TRANS_PIT_IN1, C1:IOO-MC_TRANS_YAW_IN1, C1:IOO-WFS1_PIT_IN1, C1:IOO-WFS1_PIT_IN1, C1:IOO-WFS2_PIT_IN1, and C1:IOO-WFS2_PIT_IN1.
• We were also looking at the power spectral density of these channels.
• Then using awggui (after the fix we did as in 16085), we added noise in C1:SUS-MC2_LSC_EXC as uniform noise between 0.05 Hz to 3.5 Hz with amplitude of 100 and gain of 100.
• We took a set of data without switching on the filters to have a comparison later. (Dash-dort curves)
• We then took data after switching on the filters. (Solid curves)

Next:

• Tomorrow we'll repeat this for MC1 and MC3 if we get a favourable grade in our work here.
• Even if not, we'll jsut conclude the suspension optimization work tomorrow morning and get into main interferometer.

We extended the f2a filter implementation and diagnostics as summarized in 16086 to MC1 and MC3.

MC1

Attachment 1 shows the filters with Q=3, 7, 10. We diagnosed using Q=3.

Attachment 2 shows the test summary, exciting with broadband noise on the LSC_EXC and measuring the CSD to estimate the transfer functions.

MC3

Attachment 3 shows the filters with Q=3, 7, 10. We diagnosed using Q=3.

Attachment 4 shows the test summary, exciting with broadband noise on the LSC_EXC and measuring the CSD to estimate the transfer functions.

Our main observation (and difference) with respect to MC2 is the filters have relative success for the PIT cross-coupling and not so much for YAW. We already observed this when we tuned the DC output gains to compute the filters.

Good morning!

We ran the f2a filter test for MC1, MC2, and MC3.

Filters

The new filters differ from previous versions by a adding non-unity Q factor for the pole pairs as well.

This in terms of zpk is: [ [z_r + i z_i, z_r - i z_i], [p_r + i p_i, p_r - i p_i], 1] where

• Attachment #1 shows the filters for MC1 evaluated for Q=3, 7,and 10.
• Attachment #2 shows the filters for MC2 evaluated for Q=3, 7, and 10.
• Attachment #3 shows the filters for MC3 evaluated for Q=3, 7, and 10.
• Attachment #4 shows the bode plots generated by foton after uploading for Q=3 case.

We uploaded all these filters using foton, into the three last FM slots on the POS output gain coil.

Tests

We ran tests on all suspended optics using the following (nominal) procedure:

1. Upload new input matrix
2. Lower the C1:IOO-WFS_GAIN to 0.05.
3. Upload AC coil balancing gains.
4. Take ASD for the following channels:
   • C1:IOO-MC_TRANS_PIT_IN1
   • C1:IOO-MC_TRANS_YAW_IN1
   • C1:IOO-MC_WFS1_PIT_IN1
   • C1:IOO-MC_WFS1_YAW_IN1
   • C1:IOO-MC_WFS2_PIT_IN1
   • C1:IOO-MC_WFS2_YAW_IN1
5. For the following combinations:
   • No excitation** + no filter
   • No excitation + filter
   • Excitation + no filter
   • Excitation + filter

** Excitation = 0.05 - 3.5 Hz uniform noise, 100 amplitude, 100 gain

Plots

• Attachment 5-7 give the test results for MC1, MC2 and MC3.
• In each pdf, the three pages show ASD of TRANS QPD, WFS1 and WFS2 channels' PIT and YAW, respectively.
• Red/blue correspond to data taken while F2A filters were on. Pink/Cyan correspond to data taken with filters off.
• Solid curves were taken with excitation ON and dashed curves were taken with excitation off.
• We see good suppression of POS-> PIT coupling in MC2 and MC3. POS->YAw is minimally affected in all cases.
• MC1 is clearly not doing good with the filters and probably needs readjustement. Something to do later in the future.

Lock ARMs

• Try IFO Configure ! Restore Y Arm (POY) and saw XARM lock, not YARM. Looks like YARM biases on ITMY and ETMY are not optimal, so we slide C1:SUS-ETMY_OFF from 3.0 --> -14.0 and watch Y catch its lock.
• Run ASS scripts for both arms and get TRY/TRX ~ 0.95
  • We ran X, then Y and noted that TRX dropped to ~0.8 so we ran it again and it was well after that. From now on, we will do Y, then X.

WFS1 noise injection

• Turn WFS limits off by running switchOffWFSlims.sh
• Inject broadband noise (80-90 Hz band) of varying amplitudes from 100 - 100000 counts on C1:IOO-WFS1_PIT_EXC
• After this we try to track its propagation through various channels, starting with
  • C1:LSC-XARM_IN1_DQ / C1:LSC-YARM_IN1_DQ
  • C1:SUS-ETMX_LSC_OUT_DQ / C1:SUS-ETMY_LSC_OUT_DQ
  • C1:IOO-MC_F_DQ
  • C1:SUS-MC1_**COIL_OUT / C1:SUS-MC2_**COIL_OUT / C1:SUS-MC3_**COIL_OUT
  • C1:IOO-WFS1_PIT_ERR / C1:IOO-WFS1_YAW_ERR
  • C1:IOO-WFS1_PIT_IN2

** denotes [UL, UR, LL, LR]; the output coils.

• Attachment 1 shows the power spectra with IMC unlocked
• Attachment 2 shows the power spectra with the ARMs (and IMC) locked

We redid the WFS noise injection test and have compiled some results on noise contribution in arm cavity noise and IMC frequency noise due to angular noise of IMC.

Attachment 1: Shows the calibrated noise contribution from MC1 ASCPIT OUT to ARM cavity length noise and IMC frequency noise.

• For calibrating the cavity length noise signals, we sent 100 cts 100Hz sine excitation to ITMX/Y_LSC_EXC, used actuator calibration for them as 2.44 nm/cts from 13984, and measured the peak at 100 hz in time series data. We got calibration factors: ETMX-LSC_OUT: 60.93 pm/cts , and ETMY-LSC_OUT: 205.0 pm/cts.
• For converting IMC frequency noise to length noise, we used conversion factor given by where L is 37.79m and lambda is wavelength of light.
• For converting MC1 ASCPIT OUT cts data to frequency noise contributed to IMC, we sent 100,000 amplitude bandlimited noise (see attachment 3 for awggui config) from 25 Hz to 30 Hz at C1:IOO-MC1_PIT_EXC. This noise was seen at both MC_F and ETMX/Y_LSC_OUT channels. We used the noise level at 29 Hz to get a calibration for MC1_ASCPIT_OUT to IMC Frequency in Hz/cts. See Attachment 2 for the diaggui plots.
• Once we got the calibration above, we measured MC1_ASCPIT_OUT power spectrum without any excitaiton and multiplied it with the calibration factor.
• However, something must be wrong because the MC_F noise in length units is coming to be higher than cavity length noise in most of the frequency band.
  • It can be due to the fact that control signal power spectrum is not exactly cavity length noise at all frequencies.  That should be only above the UGF of the control loop (we plan to measure that in afternoon).
  • Our calibration for ETMX/Y_LSC_OUT might be wrong.

We today measured the calibration factors for XARM_OUT and YARM_OUT in nm/cts and replotted our results from 16117 with the correct frequency dependence.

Calibration of XARM_OUT and YARM_OUT

• We took transfer function measurement between ITMX/Y_LSC_OUT and X/YARM_OUT. See attachment 1 and 2
• For ITMX/Y_LSC_OUT we took calibration factor of 3*2.44/f² nm/cts from 13984. Note that we used the factor of 3 here as Gautum has explicitly written that the calibration cts are DAC cts at COIL outputs and there is a digital gain of 3 applied at all coil output gains in ITMX and ITMY that we confirmed.
• This gave us callibration factors of XARM_OUT: 1.724/f² nm/cts , and YARM_OUT: 4.901/f² nm/cts. Note the frrequency dependence here.
• We used the region from 70-80 Hz for calculating the calibration factor as it showed the most coherence in measurement.

Inferring noise contributions to arm cavities:

• For converting IMC frequency noise to length noise, we used conversion factor given by where L is 37.79m and lambda is wavelength of light.
• For converting MC1 ASCPIT OUT cts data to frequency noise contributed to IMC, we sent 100,000 amplitude bandlimited noise  from 25 Hz to 30 Hz at C1:IOO-MC1_PIT_EXC. This noise was seen at both MC_F and ETMX/Y_LSC_OUT channels. We used the noise level at 29 Hz to get a calibration for MC1_ASCPIT_OUT to IMC Frequency in Hz/cts. This measurement was done in 16117.
• Once we got the calibration above, we measured MC1_ASCPIT_OUT power spectrum without any excitaiton and multiplied it with the calibration factor.
• Attachment 3 is our main result.
  • Page 1 shows the calculation of Angle to Length coupling by reading off noise injects in MC1_ASCPIT_OUT in MC_F. This came out to 10.906/f² kHz/cts.
  • Page 2-3 show the injected noise in X arm cavity length units. Page 3 is the zoomed version to show the matching of the 2 different routes of calibration.
  • BUT, we needed to remove that factor of 3 we incorporated earlier to make them match.
  • Page 4 shows the noise contribution of IMC angular noise in XARM cavity.
  • Page 5-6 is similar to 2-3 but for YARM. The red note above applied here too! So the factor of 3 needed to be removed in both places.
  • Page 7 shows the noise contribution of IMC angular noise in XARM cavity.

Conclusions:

• IMC Angular noise contribution to arm cavities is atleast 3 orders of magnitude lower then total armc cavity noise measured.

Edit Mon May 10 18:31:52 2021

See corrections in 16129.

Test details:

• We locked both arms and opened the shutter for Yend green laser.
• After toggling the shutter on.off, we got a TEM00 mode of green laser locked to YARM.
• We then cleared the phase Y history by clicking "CLEAR PHASE Y HISTROY" on C1LSC_ALS.adl (opened from sitemap > ALS > ALS).
• We sent excitation signal at ITMY_LSC_EXC using awggui at 43Hz, 77Hz and 57Hz.
• We measured the power spectrum and coherence of C1:ALS-BEATY_FINE_PHASE_OUT_HZ_DQ and C1:SUS-ITMY_LSC_OUT_DQ.
• The BEATY_FINE_PHASE_OUT_HZ is already calibrated in Hz. This we assume is done by multip[lying the VCO slope in Hz/cts to the error signal of the digital PLL loop that tracks the phase of beatnote.
• We calibrated C1:SUS-ITMY_LSC_OUT_DQ by multiplying with
  where f is in Hz.
  The 2.44/f² nm/cts is taken from 13984.
• We added the calibration as Poles/zeros option in diaggui using gain=54.577e3 and poles as "0, 0".
• We found that ITMY_LSC_OUT_DQ calibration matches well at 57Hz but overshoots (80 vs 40) at 43 Hz and undershoots (50 vs 80) at 77Hz.

Conclusions:

• If we had DRFPMI locked, we could have used the beatnote spectrum as independent measurement of arm lengths to calibrate the interferometer output.
• We can also use the beatnote to confirm or correct the ITM actuator calibrations. Maybe shape is not exactly 1/f² unless we did something wrong here or the PLL bandwidth is too short.