Summary

• We compared the new output matrix with old one by the step response test.
• We focused on the off-diagonal components of the step response result to compare the output matrix.
• We found that the old one is relatively good to WFS1/2 and MC2_TRANS whereas the new one is useful only to WFS1.
• Also we found that the new output matrix made from the sensing matrix was not significantly better than the original one.

Purpose

Alex, Anchal, and I did the experiment to find out the better output matrix. We got the new output matrix from the step response test in 40m/17500, so we checked whether the output matrix is good or not.

Theory

We used the following method to check the output matrix. In the previous step response test, we applied the step offset to ``ExciteIn'' points, and measure the step response at ``SensOut'' points. These points are defined in Attatchment 4. From the test, we got the matrix . Thus, we derived the new output matrix  from taking the inverse of , . If the new output matrix is well derived, the matrix can diagonalize the product of  and , , where  is the identity matrix.  can be measured by the step response test from ``SensIn'' to ``SensOut.'' Therefore we checked the output matrix by measuring . We call the measured matrix  as a sensing matrix.

To evaluate that  is diagonalized, we computed the sum of the absolute values of the off-diagonal components in 

Note that each column of the matrix was normalized by its diagonal component.

We tried to find out the better output matrix as the following method. We created new output matrix  from , and did the same step response test with . Then we got the new sensing matrix . We computed the sum of the absolute values of the off-diagonal components in , . We can get the relation  if  is better than . Therefore we compared  with .

Note: If  and  have the relation , the output matrix  will get better and better.

We also did the step response test with , which is defined as the output matrix now used. Then we compare  with .

Method

Before doing each step response test, we did the following processes:

• MC WFS relief for 60 secs with closed loops,
• turn off the WFS servo,
• turn off all the filters (WFS1/2: FM3, 4, 6; MC2-TRANS: FM1, 3, 4, 6),
• change the output matrix,
• set all the gain as unity,
• adjust each step offset.

We used the python script, toggleWFSoffsets.py, for testing the step response. The script is stored in /opt/rtcds/caltech/c1/Git/40m/scripts/MC/WFS/. The time appling each step offset is set as 120 secs.  are specifically the following matrix:

Note:  is different from [-0.188, -0.009, ...] in 40m/17500 because the previous calculation had a mistake.

The step response data is analyzed for making plot and calculating  and  by the python script, /opt/rtcds/caltech/c1/Git/40m/scripts/MC/WFS/IOO_WFS_YAW_RESPONSE_TEST_100323.ipynb. 

Result

The step response results for  are represented in Attachment 1, 2, 3, respectively. In each plot, upper left shows all the data for WFS1 (solid green), WFS2 (solid blue), and MC2_TRANS (solid brown). Also upper right, lower left, and lower right shows the result of WFS1, WFS2, and MC2_TRANS, respectively. The plots except for the upper left have the applied step offset drawed by dashed line. The three step offsets were applied in the order of WFS1 (dashed green in the upper right), WFS2 (dashed blue in the lower left), and MC2_TRANS (dashed brown in the lower right). The high-frequency components of all the plots are removed with a second-order Butterworth low-pass filter and then plotted. Dotted line and its surrounding area show the mean value for each step response or existing offset without the step offset, and its standard deviation, respectively.

We summarize each plot:

The matrix of  is written from Attachment 1:

Focusing on each column in  and the plot, only the step response for WFS1 is well diagonalized. The result of  is . Note that all the sign of the step offset in Attachment 1 is negative because we set each gain of the filter as -1.

The matrix of  is written from Attachment 2:

The output matrix  has worse normalization to WFS1 than  from comparing  with .  also gets worse value than : .

The matrix of  is written from Attachment 3:

Although  has relatively better normalization to WFS1 and 2 than , it is characterized by a large overall error.  has minimum value with relatively large uncertainty: .

Discussion

We compare each value , which is plotted in the left of Attachment 5. From the figure, we can find  and  agree within the margin of error, and  is significantly smaller than  and . Also we compare  focusing on WFS1 column shown in the right of Attachment 5.  have almost the same value, and  has slightly larger value than other. This result shows  is relatively good to WFS1/2 and MC2_TRANS whereas  is useful only to WFS1.

I tried a different method today to see if it works. Following are the steps:

• Run WFS relief.
• Turn off the WFS loops.
• Calculate the effective current YAW matrix by transferring C1:IOO-MC#_YAW_GAIN to respective rows of the matrix read from C1:IOO-OUTMATRIX_Y. No need to change the matrix itself.
  • This step should not be required. We should move these gains to the matrices as soon as we can.
• Put in the first column (corresponds to WFS1_YAW controller output) of this effective current YAW matrix to C1:IOO-LKIN_OUT_MTRX_4_1, C1:IOO-LKIN_OUT_MTRX_5_1, C1:IOO-LKIN_OUT_MTRX_6_1.
  • This is the output matrix of LOCKIN in WFS screens.
  • We are trying to actuate on what we think only affects WFS1_YAW and see if it is crosscoupled to WFS2_YAW or MC2_TRANS.
  • Then we can cancel coupling to the other two sensors by changing our couple vector.
• Turn on locking at 0.5 Hz with gain 1.
• Turn on BLP0.3 filter module. This is a 8th order 0.3 Hz butterworth filter.
• Adjust phases to get all signal in the I quadratures.
• Using ratio of C1:IOO-WFS_LKIN_I5_OUT16 to C1:IOO-WFS_LKIN_I4_OUTPUT, subtract or add this much factor of the WFS2_YAW column (the second column) of the effective YAW matrix to the column that is put in the LOCKIN output matrix.
  • I was able to subtract to less than 10% cross coupling with the intial matrix I started with.
• Repeat until no cross-coupling is seen between WFS1_YAW and WFS2_YAW.
• Repeat the above steps for WFS2_YAW column by putting that into the LOCKIN output matrix. Use the column calculated in last step for adding or subtracting WFS1 actuation.
  • I was able to make WFS2 column very clean with less than 1% measurable crosscoupling to other sensors.
• I repeated the step for WFS1 column again to remove the cross coupling to WFS2 further to less than 1%.
• For doing the above steps for MC2_TRANS column, the initial effective matrix column was very bad. The outputs were higher in WFS1 and WFS2 then MC2_TRANS output itself.
• So I made the first guess by taking a cross-product between the obtained WFS1_YAW and WFS2_YAW columns estimated earleir.
• Then I repeated the above steps to minimize coupling to WFS1 or WFS2 sensors to less than 10% of MC2_TRANS.
• THe three column vectors obtained represent the new outpute YAW matrix. I removed the normalization that would be applied by C1:IOO-MC#_YAW filter gains from the rows of this amtrix to get the output matrix that can be put into C1:IOO-OUTMATRIX_Y

Once this matrix was in, I quickly tested it by closing the loop and making gain sign flips if required. Then I took quick swept sine transfer functions to estimate UGFs and scaled the columns of the output matrix to get UGF of 2.5 Hs for WFS1_YAW and WFS2_YAW loops and 0.1 Hz for MC2_TRANS YAW loop when all filter gains are 1 and overall gain C1:IOO-WFS_GAIN is 4. See attached plots.

Old matrix:

-4.094  ,  -3.0383 ,  34.0917
-0.1259 ,   0.27008, -16.081  
-7.1811 ,   0.74271,  28.9458

This was used with gains: 0.5 for WFS1_YAW loop, 0.6 for WFS2_YAW loop and 0.3 for MC2_TRANS_YAW loop.

New matrix:

-1.48948, -1.3029 , -4.93096
-0.05839,  0.15206, -3.66245
-2.82285,  0.92391, -4.68009

All loop gains 1.

Alex and Tomohiro are characterizing this matrix with step response and UGF measurements.

From the work that Anchal has completed for diagnolizing the YAW ouput matrix, a step response was taken of this new matrix using our previous methodolgies and the following results:

The step response can be seen plotted in attachment 1. The off diagonal terms of this new matrix sum to 1.24, which is a large decrease from the current matrix and the matrices that were tested from our previous step responses. 

Tomohiro and I are now currently working futher to configure the UGF's for YAW given this new output matrix.

UPDATE:

Tomohiro and I have completed testing the YAW Sensor outputs with broadband noise injection and have confirmed that gains currently set on each filter module (which is 1.0 for WFS1, WFS2, and MC Trans) provides us with adequate UGF's. As seen bellow in attachment 2-3, WFS1 and WFS2 have UGF's between 2 and 3 Hz. MC Trans can be seen in attachment 4 and has been confirmed to have a UGF around 0.1 Hz.

Finally, attachment 5 displays the off diagnolized sums and uncertainties for each of our previous step response results and the newest result (labeled "new") for Anchal's OUTPUT YAW matrix. The first graph in blue displays the overall sum and uncertainty related to each step response taken. Then in the following 3 plots, the sum's and uncertaintes for each sensor are displayed individually for each step response test.

For reference:

New: corresponds to Anchal's YAW OUPUT MATRIX

D0: refers to the previously implemented matrix, prior to any testint or updates

D1: refers to the matrix that was computed based off of the first test Tomohiro and I performed

D2: refers to the matrix computed as a secondary result from D1. This matrix was thought to provide a lower off diagonal sum, but did not.

This thoroughly displays our results such that the newly computed matrix from Anchal is much more diagnolized then that of the step response matrices Tomohiro and I have computed.

I realized that for more phase margin, rana added 6:3lead filter on WFS PIT loops. Since we have increased the UGF on YAW loops too, I turned these on the YAW loops as well. The loops remain stable unlike with the previous matrix. Attachment 1 is the repeat of teh emasurement done by rana earlier but with the new matrix and updated gains in PIT loops. The dark green traces are the references from last measurment with higher gain and HEPA off. The remainging colored traces were measured today.

The WFS loops were not maximizing the IMC transmission. The transmission counts remained stuck at around 12500 counts. The reflection DCMON from IMC had reached above 0.35 while nominally it had been around 0.2. So today, I manuaaly aligned the IMC to best transmission and lowest reflection, then unlocked IMC and reset the offsets on WFS1 and WFS2 RF readouts. After the offsets were changed, the error singals were fluctuating around 0 in best algined state. Then turning on the WFS loops made the transmissions slighlty higher to 13250 counts.

Alex, Anchal, and I adjusted the number of the MC2-TRANS column in the YAW output matrix. We used the same method in 40m/17504 but the amplitude of oscillator for Lock In Amplifier is increased from 1 to 4.

The corrected numbers of the column in the output matrix is as follows:

We did the step response test for the corrected output matrix. The sum of off-diagonal terms was 0.62, which is the minimum value. Attachment 1 is the step response test result. From the figure, the reduction of the sum is because the column MC2_TRANS can diagonalize better. We can find out the property from Attachment 2.

Purpose

• To adjust the components of the WFS2 column in the YAW output matrix.
• To check the value of the off-diagonal components of the WFS1 column.

Method

Alex, Anchal, and I used the same method in 40m/17504 to adjust the components of the WFS2 column. And we did the same step response test to check the value of the off-diagonal components in the YAW output matrix.

Used script & file

All the scripts & files are stored in /opt/rtcds/caltech/c1/Git/40m/scripts/MC/WFS/ directory.

• DiagnoalizatingMethod.ipynb: for adjusting the components and replacing the new output matrix,
• toggleWFSoffsets.py: for doing the step response test,
• IOO_WFS_YAW_STEP_RESPONSE_TEST.py: for analyzing the step response result.

Result

We changed the WFS2 column as follows

We can successfully diagonalize the WFS2 column. The sum of the off-diagonal components is slightly reduced. However, WFS1 has worse diagonalization.

The same step response test should be performed on a different day to see if the results change. It is because the multiple causes could exist: the influence of the changed other columns, the long time drift, the day to day change, and so on.

Tomohiro and I performed some tests under Rana's guidance to find cross corelations between WFS1 and WFS2 output signals in both pitch and yaw. We performed this test to further understand the degree to which our output matrices have been diagonolized.

Seen in attachment 1 is our base level with no injected noise source. In each figure, we also have inlcuded the coherence plot which compares each control signal to the overalll YARM power signal.

Attachments 2-5 display our results for injecting noise into each control signal individually.

We found the following corelations for each respective test:

We judged our corelated signals by the peaks seen from out noise injection on the power spectrum as well as by their coherence at the same frequencies of our noise (20Hz-30Hz) compared to the overall power spectrum of YARM.

Performing this measurement was done using diaggui and awggui. The diaggui files for each test are saved at: "users/Templates/singleArmCal/ArmCavityNoise_230317_2_WFS1_PIT"

To properly fix each of the control signals to the same magnitude plotted for YARM output, we callibrated each plot using the settings seen in Attachment 7. First the units were changed on the plots to represent the true scale of each measurement:

We found that the ETMY actuation strength is 10.843e-9 / f^2 (from 17376) and used this to clibrate the plots to the nanometer scale. Next the gain was adjusted such that each plot would align over the YARM output when noise was injected onto it, setting a basis for all four measurements.

Finally, some filtering poles were added to the callibration for each plot such that it resembled that of the filters seen by the YARM ouput signal. (RXA: this is the 28 Hz ELP filter to simulate the dewhitening filters)

The measurements were taken with the settings seen in Attachment 8, and noise injected using the parameters seen in attachment 9.

RXA: Some edits/comments:

The noise was injected as band-limited random noise with a Normal distribution. We used noise rather than lines so as to capture the linear and bilinear noise contributions. In the case where the coupling is mostly bilinear, we would not expect to see much coherence.

The first attachment is a ASC noise budget for the single arm - in the high gain mode, the noise does not limit the noise as seen by the arm. Next is to see if its due to the MC dewhitening filters being on/off?

With Anchal's help, I have setup dither lines for Rana on MC1,2,3 that will be running overnight. The oscilations were set on MC1,2,3, oscillator screens.
The following table describes the current setup:

These frequencies and amplitudes were set on LOCKIN1 for each MC1,2,3. The output filters matrix for MC1,2,3 was also updated to reflect the degree of freedom being tested: PITCH.

The frequencies were picked to avoid the dewhitening frequency: 28Hz, and the Bounce/Roll frequencies: 16 Hz & 24 Hz. Furthermore, decimal value frequencies were utilized to avoid the multiples of 1 Hz.

The oscilators were originally started at 1363480200 and will be turned off at 1363535157.

See attachment 1 for the plot of the power spectrum. This test is done to find the beam offset for pitch.

I have organized the resulting data from running dither lines on MC1,2,3. The data has been collected from diaggui as shown in attachment 1.

Mirror		Avg Re (+/- 1000)	Avg Im (+/- 1000)	Peak Power ()	Cts/urad
MC1	21.12	7000	4000	8062	12.66
MC2	25.52	13000	10000	16401	6.83
MC3	27.27	4000	-600	4044	11.03

Next using the following equations we can find :

Where is the change in length in result of the dithering and is the overall change in beam spot position

Delta L can be calculated by:

where is the peak power of the line frequency and is found by taking the square root of the magnitude of the Real and imaginary terms, is frequency the laser light is traveling at (281 THz) and is the lenght of the IMC (13.5 meters).

can then be calculated by:

where  is the angle at which the mirror was shaken at a given frequency. We can find  by converting the amplitude of the frequency that the mirror was shaken at and converting it into radians using the conversion constants found here: 17481.

is then shown to be found by this angle diveded by the line frequency.

The final values are calculated and displayed bellow:

Mirror
MC1	157.9 urad	0.35 urad	0.38 nm	1.08 mm
MC2	146.4 urad	0.23 urad	0.78 nm	3.39 mm
MC3	226.7 urad	0.31 urad	0.19 nm	0.61 mm

I have changed the MC SUS output matrices by a few % for some A2L decoupling - if it causes trouble, please feel free to revert.

Anchal came to me and said, "I think those beam offsets are a bunch of stinkin malarkey!", so I decided to investigate.

Instead of Alex's "method" of trusting the actuator calibration, I resolved to have less systematics by adjusting the SUS output matrices ot minimize the A2L and then see what's what vis a vis geometry.

The attached screenshot shows you the measurement setup:

1. copy the DoF vector from DoF column into the LOCKIN1 column.
2. Turn on the OSC/LOCKIN for the optics / DoF in question (in this example its MC2 PITCH)
3. Monitor the peak in the MC_F spectrum
4. Also monitor the mag and phase of the TF of MC_F/LOCKIN_LO
5. use the script stepOutMat.py to step the matrix

Next I'm going to modify the script so that it can handle input arguments for optic/ DOF, etc.

FYI, the LOCKIN screens do have a TRAMP field, but its not on the screens for some reason . Also the screens don't have the optic name on them. :

SUS>caput C1:SUS-MC2_LOCKIN1_OSC_TRAMP 3
Old : C1:SUS-MC2_LOCKIN1_OSC_TRAMP   0
New : C1:SUS-MC2_LOCKIN1_OSC_TRAMP   3

After finishing the tuning of all 3 IMC optics, I have discovered that 27.5 Hz is a bad frequency to tune at: the Mc1/MC3 dewhtiening filters have a 28 Hz cutoff, so they all have slightly different phase shifts at 27-28 Hz due to the different poles due to tolerances in the capacitors (probably).

*Also, I am not able to get a real zero coupling through this method. There always is an orthogonal phase component that can't be cancelled by adjusting gains. On MC3, this is really bad and I don't know why.
 

Today, we ran dither lines on the MC1,2,3 mirrors in YAW from 136598007 to 1365981967 and similarly on PIT from 1365982917 to 1365984618.

The following frequencies and amplitudes were recorded for each dither line:

The urad conversions used to calculate theta DC and AC can be found at 17481

The dither lines were then demodulated in python and the steps shown in 17516 were followed to calculate the beam offset that each dither line represented in pitch and yaw. 

The following results were found:

Attatched bellow is the power spectrums for both yaw and pitch.

Mayank and I worked on finalizing the plots for the beam offset from the dithering test done in 17552. Plotted in attachment 1 are the beamspot demodulated signals from MC_F_DQ which are averaged over 1 second each (blue) for YAW and PIT in MC1,2,3. The yellow line over each plot shows the 3 Hz lowpassed signal of the beamspot movement.

Additionally, we have seen no direct correlation to the WFS1 or 2 sensors due to the MC movements. This may be because the WFS display a complete signal that includes all changes in the cavity length due to the shaking of the mirrors. Thus, the signal (shown in red) of the WFS sensors will show a combined average of movement from all 3 dither lines.

It has happened multiple times today that IMC has tripped on its own. Yehonathan and I have had to come back to manually lock IMC multiple times.

Wed Apr 26 10:24:07 2023 [EDIT]

[Paco] I aligned the MC by hand, let it run locked for 30 minutes without angular controls, and then switched on the WFS loops yesterday at ~ 6 PM. IMC has been locked ever since.

I had to realign the IMC today. When I came in, it was very bad, not much flashing at all, I had to do it from scratch. CH01 Camera on MON7 in the control room is completely white. Did the camera go out over the weekend? I will come back to poke around later, I have headed over to WB for a moment and will be back soon. sitemapsi

It took a while, but I was finally able to align IMC. It seems like WFS has been getting really whacky lately when we arent in the lab watching it . The picture attached has an arrow of where the beam spot was at this morning

MC1     28.21625 kHz
MC2     28.036   kHz
MC3     28.21637 kHz

- Turn off the MC autolocker. Relock the MC with only the acquisition settings; no boosts
  and no RGs. This makes it re-acquire fast. Turn the MC-WFS gain down to 0.001 so that
  it keeps it slowly aligned but does not drift off when you lose lock.

- Use low-ish gain on the FSS. 10 dB lower than nominal is fine.

- Setup the o'scope (100 MHz BW or greater) to do single shot trigger on the MC2 trans.

- Flip FSS sign.

- Quickly flip sign back and waggle common gain to get FSS to stop oscillating. MC
  should relock in seconds.

3  fsr =  33 195 439 Hz
12 fsr = 132 781 756 Hz
15 fsr = 165 977 195 Hz
18 fsr = 199 172 634 Hz

• Made sure MC trans was high with the WFS off.
  
• Moved the Sliders on the MC Align screen until spot was centered (by eye)
  
• Moved some more until power was maximized.
  
• Unlock MC
  
• Center spots on McWFS
  
• Re-enable autolocker and McWFS loops.
  

- AD797 is used after the mixer. This is an unreliable, noisy part. We need to change this out
  with some OP27s so that this becomes reliable and has a more reasonable noise figure.

- Hard wire the whitening filters ON. We never want these to be off. Then we can turn on the
  anti-whitening. This will give us a factor of 100 better noise without filtering.

- The AD602 on the front of the whitening board has a 100 Ohm internal impedance and the 
  resistor between the demod board and the AD602 is 909 Ohms. This results in dividing the
  signal by 10.

- The signal at the ADC is ~100 cts peak-peak. The full ADC range is, of course, 65000 cts. So
  we could use a lot more gain. The mean quadrant signals are also ~100 cts so we could easily
  up the analog DC gain by a factor of 30 on top of the whitening filter increase.

- The AD602 at the input and the AD620 on the output are both variable gain stages but because
  of our lack of control are set to ambiguous gain levels. We should set the AD602 on the input
  to its max gain of 30 dB. With the -20 dB from the x10 voltage division, this will give us
  an overall gain of 3 for the puny demod signals.