ELOG 40m

Transfer Function for IMC mirrors using appropriately filtered noise

does Anyone understand why the broadband noise injection is so bad around 1 Hz? we do not see this issue with swept sine. noise seems good at other frequencies.

Does it have anything to do with the time constant of the resonances?

17500

Thu Mar 9 10:29:15 2023

Step response test on MC1, MC2, and MC3 YAW

Tomohiro, Anchal and I completed the following processs for acquiring a new Output Yaw matrix for the "C1IOO_WFS_OUTMATRIX".

To did this by following the same process in 17493 but instead of adding our offsets in the WFS1, WFS2 and MC Trans filter banks, offsets were added at the end of the feedback loop at the optics, MC1, MC2 and MC3 YAW.

Optimal offset values were found such that the offset change did not disrupt the output WFS transmission signal by more than about a one thousand counts. Each limit was set to come close to this limit.

Our final offset values were:

Optic	Offset Value
MC1	55
MC2	15
MC3	35

The step response was than observed in Diaggui, but the entire 800 s run was unable to be viewed at once. We then utilized our python script from the previous step response data that we took to develop the following:

The measured response from stepping the optics was:

$\begin{pmatrix} 1.31\pm0.24 & 54.2\pm1.3 & -0.28\pm0.03\\ -2.13\pm0.23 & -20.7\pm1.6 & 1.11\pm0.03\\ 1.82\pm0.27 & -25.8\pm1.5 & 0.16\pm0.03\\ \end{pmatrix} \begin{pmatrix} MC_{1Y}\\ MC_{2Y}\\ MC_{3Y}\\ \end{pmatrix} = \begin{pmatrix} WFS_{1Y}\\ WFS_{2Y}\\ MC_{2Y-TRANS}\\ \end{pmatrix}$

*The values in this matrix represent the number of counts/offset count. Thus all ovalues found from the step response were divided by the number of counts on each offset.

To find the new yaw matrix, we then take the inverse of the step response output matrix to get:

$\begin{pmatrix} MC_{1Y}\\ MC_{2Y}\\ MC_{3Y}\\ \end{pmatrix} = \begin{pmatrix} 0.188 & -0.009 & 0.403 \\ 0.017 & 0.005 & -0.006 \\ 0.689 & 0.987 & 0.656 \end{pmatrix} \begin{pmatrix} WFS_{1Y}\\ WFS_{2Y}\\ MC_{2Y-TRANS}\\ \end{pmatrix}$

The results from the step response may also be seen graphically in attachment 1. The first plot shows all 3 response signals. Then each following plot shows the individual signals and the step responses overlayed for each one.

The plots also include horizontal lines that represent the average for the stepped signals and the average of the signal at rest along with shading for their associated uncertainties.

This was then tested in C1IOO_WFS_BASIS Yaw matrix, and at first did not work well. The WFS1 Yaw output would rail toward the limits. To fix this, the sign of the gain was flipped (from 0.5 to -0.5) which seemed to solve this issue.

This was then transmitted to the matrix to give:

$\begin{pmatrix} MC_{1Y}\\ MC_{2Y}\\ MC_{3Y}\\ \end{pmatrix} = \begin{pmatrix} -0.188 & -0.009 & 0.403 \\ - 0.017 & 0.005 & -0.006 \\ -0.689 & 0.987 & 0.656 \end{pmatrix} \begin{pmatrix} WFS_{1Y}\\ WFS_{2Y}\\ MC_{2Y-TRANS}\\ \end{pmatrix}$

This did not solve all issues, the overall ouput signals from the WFS filters still seemed to have large fluctuations. I then began adjusting the gains of the WFS1, WFS2 and MC Trans yaw output filters and achieved much steadier signals.

The following table describes the current best gain valuse for our Yaw matrix:

Sensor	Gain Value
WFS1 YAW	5.94
WFS2 YAW	6.44
MC TRANS YAW	1.9

The results from our found matrix and gain changes can be seen on the left of attachement 2 that displays the ouputs on the Error Signal Monitor. The original output yaw matrix signals can be seen on the right hand side. There is work to still be done on adressing these issues, but overall this may be improved by some additional changes in the gains on each channel.

Attachment 1: step_response_080323.pdf

Attachment 2: Screenshot_2023-03-08_18-17-35.png

17501

Thu Mar 9 14:22:24 2023

Computer Scripts / Programs

Update to toggleWFSoffsets.py for step response testing

I have pushed changes made to the toggleWFSoffsets.py script to the git.

This file may be found in: "/opt/rtcds/caltech/c1/Git/40m/scripts/MC/WFS/"

The changes made are:

Updated the script to allow for toggling step responses on either optics or sensors (default = optics), chosen by user

The script orignally asked user to make any last changes to the offsets before hitting enter to run without displaying the new changes.

Now the script checks for changes made by the user to the offsets and displays them if detected. If no changes are made, the code starts running the steps.

17503

Fri Mar 10 16:42:16 2023

Tomohiro

Step response test on MC1, MC2, and MC3 YAW

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 $A$ . Thus, we derived the new output matrix $O_1$ from taking the inverse of $A$ , $O_1 = A^{-1}$ . If the new output matrix is well derived, the matrix can diagonalize the product of $A$ and $O_1$ , $A O_1 = \bf{I}$ , where $\bf{I}$ is the identity matrix. $AO_1$ can be measured by the step response test from ``SensIn'' to ``SensOut.'' Therefore we checked the output matrix by measuring $AO_1$ . We call the measured matrix $S_1 (\equiv A O_1)$ as a sensing matrix.

To evaluate that $S_1$ is diagonalized, we computed the sum of the absolute values of the off-diagonal components in $S_1$

$D_1 \equiv \sum_{j \neq k} \left| S_1 (j, k) \right| .$

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 $O_2$ from $O_2 \equiv O_1 {S_1}^{-1}$ , and did the same step response test with $O_2$ . Then we got the new sensing matrix $S_2$ . We computed the sum of the absolute values of the off-diagonal components in $S_2$ , $D_2$ . We can get the relation $D_1 > D_2$ if $O_2$ is better than $O_1$ . Therefore we compared $D_2$ with $D_1$ .

Note: If $D_n$ and $D_{n+1}$ have the relation $D_n > D_{n+1} (\geq 0)$ , the output matrix $O_n \equiv O_{n-1} {S_{n-1}}^{-1}$ will get better and better.

We also did the step response test with $O_0$ , which is defined as the output matrix now used. Then we compare $D_0$ with $D_{1, 2}$ .

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. $O_i~(i = 0, 1, 2)$ are specifically the following matrix:

$O_0 = \begin{pmatrix} -4.0940 & -3.0383 & 34.0917 \\ -0.1259 & 0.27008 & -16.081 \\ -7.1811 & 0.74271 & 28.9458 \end{pmatrix}$ $O_1 = \begin{pmatrix} 0.342 & 0.117 & 1.967 \\ -0.016 & 0.036 & 2.82 \\ 0.732 & -0.042 & 1.873 \end{pmatrix}$ $O_2 = \begin{pmatrix} 0.812 & -0.819 & -2.289 \\ -0.036 & 0.761 & 2.998 \\ 0.085 & 0.386 & 2.835 \end{pmatrix}$

Note: $O_1$ 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 $O_{1, 2}$ and $D_{0, 1, 2}$ 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 $S_{1, 2, 0}$ 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:

$S_1$

The matrix of $S_1$ is written from Attachment 1:

$S_1 = \begin{pmatrix} -140 \pm 10 & 90 \pm 10 & 290 \pm 10 \\ 2 \pm 1 & -32 \pm 1 & 28 \pm 1 \\ -9 \pm 7 & -40 \pm 7 & -234 \pm 7 \end{pmatrix} .$

Focusing on each column in $S_1$ and the plot, only the step response for WFS1 is well diagonalized. The result of $D_1$ is $D_1 = 5.6 \pm 0.8$ . Note that all the sign of the step offset in Attachment 1 is negative because we set each gain of the filter as -1.

$S_2$

The matrix of $S_2$ is written from Attachment 2:

$S_2 = \begin{pmatrix} 140 \pm 10 & 206 \pm 9 & -102 \pm 7 \\ 50 \pm 20 & 360 \pm 10 & -340 \pm 10 \\ -11 \pm 3 & -55 \pm 2 & 84 \pm 2 \end{pmatrix} .$

The output matrix $O_2$ has worse normalization to WFS1 than $O_1$ from comparing $S_2$ with $S_1$ . $D_2$ also gets worse value than $D_1$ : $D_2 = 6.4 \pm 0.4$ .

$S_0$

The matrix of $S_0$ is written from Attachment 3:

$S_0 = \begin{pmatrix} -1700 \pm 100 & -130 \pm 120 & 2100 \pm 100 \\ -240 \pm 80 & -1100 \pm 70 & 1440 \pm 60 \\ 110 \pm 160 & 200 \pm 100 & -1400 \pm 100 \end{pmatrix} .$

Although $S_0$ has relatively better normalization to WFS1 and 2 than $S_{1, 2}$ , it is characterized by a large overall error. $D_0$ has minimum value with relatively large uncertainty: $D_0 = 3.1 \pm 0.7$ .

Discussion

We compare each value $D_{1, 2, 0}$ , which is plotted in the left of Attachment 5. From the figure, we can find $D_1$ and $D_2$ agree within the margin of error, and $D_0$ is significantly smaller than $D_1$ and $D_2$ . Also we compare $D_{1, 2, 0}$ focusing on WFS1 column shown in the right of Attachment 5. $D_{1, 0}$ have almost the same value, and $D_2$ has slightly larger value than other. This result shows $O_0$ is relatively good to WFS1/2 and MC2_TRANS whereas $O_1$ is useful only to WFS1.

Attachment 1: step_response_YAW_S1_100323.pdf

Attachment 2: step_response_YAW_S2_100323.pdf

Attachment 3: step_response_YAW_S0_100323.pdf

Attachment 4: Mar10_FlowDiagram.pdf

Attachment 5: Mar10_Dfactor.pdf

17504

Mon Mar 13 14:48:37 2023

Diagonalizing YAW output matrix using a different method

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.

Attachment 1: WFS_YAW_OLTF_Measurements.pdf

17505

Mon Mar 13 15:37:13 2023

Step Response of newly diagonalizing YAW output matrix

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.

Attachment 1: step_response_YAW_130323.pdf

Attachment 2: WFS1_YAW_OLTF_NI.pdf

Attachment 3: WFS2_YAW_OLTF_NI.pdf

Attachment 4: MC2_YAW_OLTF_NI.pdf

Attachment 5: Mar13_Dfactor.pdf

17506

Mon Mar 13 19:53:36 2023

yuta

FPMI BHD sensing matrix measurement with individual lines

BHD

FPMI BHD sensing matrix was measured by an updated method with updated RF demodulation phases for REFL55 and AS55.
Now audio demodulation phase for CARM components is 90 deg to make the sign correct.
Also, oscillators are turned on one by one to reduce contamination between DoFs (especially between MICH and CARM).
These helped a lot in reducing errors.

Sensing matrix with FPMI locked in RF, LO_PHASE locked with BH55_Q using LO1

Sensing matrix with the following demodulation phases (counts/m) {'AS55': -177.9, 'REFL55': 77.06, 'BH55': -110.0, 'BH44': -8.9} Sensors DARM @307.88 Hz CARM @309.21 Hz MICH @311.1 Hz LO1 @315.17 Hz AS55_I (+3.25+/-0.67)e+11 [90] (-8.63+/-0.41)e+11 [90] (-1.02+/-1.49)e+09 [0] (+0.44+/-1.39)e+07 [0] AS55_Q (-6.04+/-0.05)e+11 [90] (+0.92+/-3.10)e+10 [90] (+9.10+/-6.78)e+08 [0] (+0.12+/-2.08)e+07 [0] REFL55_I (+1.18+/-0.03)e+11 [90] (+2.78+/-0.12)e+12 [90] (-0.35+/-2.34)e+09 [0] (-0.94+/-2.38)e+07 [0] REFL55_Q (+5.85+/-0.43)e+09 [90] (-2.34+/-0.13)e+10 [90] (+2.39+/-0.38)e+08 [0] (+3.56+/-7.44)e+06 [0] BH55_I (-3.51+/-3.45)e+10 [90] (-6.65+/-0.82)e+10 [90] (-4.91+/-3.03)e+08 [0] (-1.82+/-0.09)e+09 [0] BH55_Q (+7.86+/-0.29)e+11 [90] (+2.99+/-0.42)e+11 [90] (-2.87+/-7.76)e+08 [0] (+2.81+/-0.15)e+09 [0] BH44_I (-0.34+/-1.99)e+12 [90] (+0.02+/-1.49)e+12 [90] (-0.42+/-8.53)e+10 [0] (-0.01+/-3.08)e+10 [0] BH44_Q (-0.60+/-3.95)e+13 [90] (-0.01+/-3.00)e+13 [90] (+0.00+/-1.68)e+12 [0] (-0.15+/-5.77)e+11 [0] BHDC_DIFF (-9.18+/-0.29)e+11 [90] (-4.11+/-4.66)e+10 [90] (+1.46+/-0.10)e+09 [0] (-1.70+/-0.41)e+08 [0] BHDC_SUM (+2.97+/-0.21)e+11 [90] (+0.44+/-1.57)e+10 [90] (-1.01+/-0.06)e+09 [0] (+2.68+/-0.84)e+07 [0]

- AS55_Q now has 70% more gain to DARM for some reason (see 40m/17478). Whitening gain haven't changed from 24 dB.
- There's still some room to tune AS55 RF demodulation phase to maximize DARM response.
- CARM to REFL55_Q is 100 times smaller than that to REFL55_I; this is good.
- There's still some room to tune BH55 RF demodulation phase to maximize LO1 response.
- BH44 doesn't have much response to LO1, probably because LO_PHASE is locked with orthogonal BH55.

Sensing matrix with FPMI locked in RF, LO_PHASE locked with BH44_Q using LO1

Sensing matrix with the following demodulation phases (counts/m) {'AS55': -177.9, 'REFL55': 77.06, 'BH55': -110.0, 'BH44': -8.9} Sensors DARM @307.88 Hz CARM @309.21 Hz MICH @311.1 Hz LO1 @315.17 Hz AS55_I (+3.94+/-0.52)e+11 [90] (-1.00+/-0.05)e+12 [90] (-1.61+/-1.17)e+09 [0] (+0.45+/-1.52)e+07 [0] AS55_Q (-5.52+/-0.24)e+11 [90] (+1.19+/-2.99)e+10 [90] (+1.10+/-0.43)e+09 [0] (-1.06+/-2.30)e+07 [0] REFL55_I (+8.97+/-0.49)e+10 [90] (+2.71+/-0.11)e+12 [90] (-0.38+/-2.28)e+09 [0] (-0.97+/-2.10)e+07 [0] REFL55_Q (+6.30+/-0.65)e+09 [90] (-2.01+/-0.12)e+10 [90] (+2.26+/-0.69)e+08 [0] (-2.61+/-6.97)e+06 [0] BH55_I (+4.46+/-0.52)e+11 [90] (-1.52+/-0.27)e+11 [90] (-1.82+/-0.56)e+09 [0] (+0.68+/-1.24)e+08 [0] BH55_Q (+9.59+/-0.44)e+11 [90] (+2.79+/-0.52)e+11 [90] (+2.75+/-2.49)e+08 [0] (+2.45+/-1.06)e+08 [0] BH44_I (-0.40+/-2.42)e+12 [90] (-0.03+/-1.88)e+12 [90] (-0.03+/-1.13)e+11 [0] (+0.12+/-4.18)e+10 [0] BH44_Q (-0.19+/-1.09)e+13 [90] (+0.70+/-7.91)e+12 [90] (-0.09+/-4.65)e+11 [0] (+0.11+/-1.34)e+11 [0] BHDC_DIFF (+3.90+/-0.46)e+11 [90] (+1.06+/-0.18)e+11 [90] (-4.62+/-1.89)e+08 [0] (+3.60+/-0.40)e+08 [0] BHDC_SUM (+1.96+/-0.18)e+11 [90] (-1.08+/-1.29)e+10 [90] (-8.93+/-1.41)e+08 [0] (-8.67+/-0.81)e+07 [0]

- BHDC_DIFF sensitivity to DARM is less than that with LO_PHASE locked with BH55.
- BH44 sensing matrix has too much error. Requires more averaging time and oscillator amplitude.

Jupyter notebook: /opt/rtcds/caltech/c1/Git/40m/scripts/CAL/SensingMatrix/ReadSensMat.ipynb

Next:
- Tune AS55, BH55, BH44 RF demodulation phases
- Try measuring sensing matrix for BH44 with more averaging time, oscillator amplitude, and PD whitening gain
- Repeat measurement in 40m/17351 with BH44 under MICH configuration.
- Compare LO phase noise in MICH configuration when LO_PHASE is locked with BH44 and BH55.
- Make a noise budget in MICH BHD.
- Investigate 28 Hz noise in FPMI
- Tune BS local damping loops

17508

Tue Mar 14 11:38:44 2023

Turned on 6:3lead FM7 on WFS1 and WFS2 YAW loops

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.

Attachment 1: Screenshot_2023-03-14_11-57-34.png

17509

Tue Mar 14 13:59:11 2023

IMC WFS aligned and offsets reset

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.

17510

Tue Mar 14 15:46:06 2023

Tomohiro

Diagonalizing YAW output matrix using a different method

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:

	MC2_TRANS
MC1	-5.5196
MC2	-2.8778
MC3	-5.2232

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.

Attachment 1: step_response_YAW_140323.pdf

Attachment 2: Mar14_Dfactor.pdf

17511

Tue Mar 14 18:44:39 2023

yuta

LO phase noise measurements in ITMX single bounce, MICH and FPMI

BHD

[Anchal, Yuta]

We have measured LO phase noise in ITMX single bounce, simple MICH and FPMI configurations with LO phase locked with BH55 or BH44.
We found that BH55 and BH44 have almost exactly same noise in ITMX single bounce, but BH44 is noisier than BH55 in MICH and FPMI configurations.
In any case, LO phase can be locked within 0.1 rad RMS, so optical gain fluctuations in BHD_DIFF should be fine for BHD locking.

Method:
- We have locked ITMX single bounce vs LO, AS beam under MICH locked with AS55_Q vs LO, and AS beam under FPMI locked with REFL55 & AS55 vs LO, using BH55_Q or BH44_Q
- In each IFO configuration, we have minimized I phase to set RF demodulation phases for BH55 and BH44.
- In each IFO configuration, optical gain of BH55_Q and BH44_Q was measured by elliptic fit of X-Y plot for BH55_Q vs BHDC_A or BH44_Q vs BH55_Q.
- For each LO_PHASE lock, feedback gain was adjusted to set the UGF to around 50 Hz, and actuator used was LO1.
- LO_PHASE_IN1 was calibrated using the measured optical gain, and LO_PHASE_OUT was calibrated using LO1 actuator gain of 26.34e-9 /f^2 m/counts measured in 40m/17285.
- To convert meters in radians, 2*pi/lambda is used (which means dark fringe to dark fringe is pi).
- Below summarizes the result of RF demodulation phases and optical gains (whitening gains were 45 dB for BH55 and 39 dB for BH44). RF demod phases aligns well with previous measurement, but optical gain for BH44 seems higher by an order of magnitude compared with 40m/17478 (whitening gain changed??). Optical gain for BH55_Q is consistent with previous measurement in 40m/17506 (note the demodulation phase change).

LO_PHASE lock in ITMX single bounce Demod phase Optical gain filter gain BH55_Q -99.8 deg 7.6e9 counts/m -0.3 BH44_Q -6.5 deg 1.3e10 counts/m -0.15

LO_PHASE lock in MICH Demod phase Optical gain filter gain BH55_Q -67.7 deg 6.1e8 counts/m -3.9 BH44_Q -31.9 deg 8.5e8 counts/m -3.1

LO_PHASE lock in FPMI Demod phase Optical gain filter gain BH55_Q 35.7 deg 3.4e9 counts/m -0.65 BH44_Q -9.3 deg 4.3e10 counts/m -0.84

Result:
- Attached are calibrated LO phase noise spectrum in different IFO configurations.
- In ITMX single bounce, LO phase noise estimated using BH55 and BH44 are almost equivalent, and LO phase noise in-loop is ~0.04 rad RMS.
- In MICH, LO phase noise estimated using BH44 is noisier than BH44 at around 20-60 Hz for some reason. LO phase noise in-loop is ~0.04 rad RMS for both cases.
- In FPMI, LO phase noise estimated using BH44 is noisier than BH44 above ~20 Hz for some reason. LO phase noise in-loop is ~0.03 rad RMS for both cases. Dark noise is not limiting the measurement at least below 1 kHz.

Jupyter notebook: /opt/rtcds/caltech/c1/Git/40m/measurements/BHD/BH55_BH44_Comparison.ipynb

Next:
- Lock MICH BHD with BH55 and BH44, and compare LO phase noise contributions to MICH sensitivity
- Investigate why BH44 is noisier than BH55 in MICH and FPMI (offsets? contrast defect? mode-matching?)
- Reduce 60 Hz + harmonics in BH55 and BH44

Attachment 1: BH555_BH44_LO_PHase_Control_Comparison.pdf

17512

Thu Mar 16 13:31:25 2023

Tomohiro

Diagonalizing YAW output matrix using a different method

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

	From	To
MC1	-1.3029	-1.8548
MC2	0.15206	-0.1357
MC3	0.92391	0.40158

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.

Attachment 1: step_response_YAW_160323.pdf

Attachment 2: Mar16_Dfactor.pdf

17513

Fri Mar 17 17:27:58 2023

Alex, Tomohiro

Arm Cavity Noise injection with WFS1/2 PIT and YAW

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:

Control Signal with Noise	Corelated signals (order)
WFS1 PIT	WFS1 YAW, WFS2PIT, WFS2 YAW (all equally corelated)
WFS1 YAW	WFS1 PIT, WFS2 YAW, WFS2 PIT (most to least)
WFS2 PIT	WFS1 PIT, WFS2 YAW, WFS1 YAW (most to least)
WFS2 YAW	WFS2 PIT, WFS1 YAW (all equally corelated)

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?

Attachment 1: ArmCavityNoise_230317_2.pdf

Attachment 2: ArmCavityNoise_230317_2_WFS1_PIT.pdf

Attachment 3: ArmCavityNoise_230317_2_WFS2_PIT.pdf

Attachment 4: ArmCavityNoise_230317_2_WFS1_YAW.pdf

Attachment 5: ArmCavityNoise_230317_2_WFS2_YAW.pdf

Attachment 6: Screenshot_2023-03-17_17-23-34.png

Attachment 7: Screenshot_2023-03-17_17-24-47.png

Attachment 8: Screenshot_2023-03-17_17-24-00.png

17514

Mon Mar 20 20:27:30 2023

yuta

LO phase noise contribution in MICH BHD

BHD

[Paco, Yuta]

MICH was locked with balanced homodyne readout with LO phase locked using BH55_Q and BH44_Q.
It turned out that BH44_Q gives better LO phase in MICH configuration (in FPMI, BH55_Q is better; see 40m/17506).
LO phase noise seems to contribute to MICH sensitivity in 30-200 Hz region in BH55 case, and 30-100 Hz in BH44 case (this was not the case in FPMI BHD, see 40m/17392).
The mechanism for this coupling needs investigation.

MICH BHD sensing matrix:
- MICH BHD sensing matrix was measured when MICH is locked with AS55_Q and LO_PHASE is locked with BH55_Q or BH44_Q.
- MICH UGF was at around 50 Hz, and LO_PHASE UGF was at around 10 Hz.
- BHDC_DIFF had better sensitivity to MICH when LO_PHASE was locked with BH44_Q.
- BH44 component was not measured well.

MICH sensing matrix with MICH locked with AS55_Q and LO_PHASE locked with BH55_Q

Sensing matrix with the following demodulation phases (counts/m) {'AS55': 2.1, 'REFL55': 76.01784975834194, 'BH55': -63.16236453101908, 'BH44': -39.01036239539396} Sensors MICH @311.1 Hz LO1 @315.17 Hz AS55_I (+0.40+/-6.23)e+07 [0] (-0.83+/-3.01)e+07 [0] AS55_Q (+1.38+/-0.26)e+09 [0] (+0.76+/-6.58)e+07 [0] BH55_I (-3.22+/-0.37)e+09 [0] (-0.81+/-8.42)e+07 [0] BH55_Q (+4.03+/-0.52)e+09 [0] (-4.01+/-1.05)e+08 [0] BH44_I (-0.06+/-4.22)e+10 [0] (+0.29+/-4.63)e+10 [0] BH44_Q (-0.03+/-3.21)e+11 [0] (+0.21+/-3.12)e+11 [0] BHDC_DIFF (-1.07+/-0.39)e+09 [0] (-3.35+/-7.47)e+07 [0] BHDC_SUM (+2.07+/-0.57)e+08 [0] (+0.32+/-1.65)e+07 [0]

MICH sensing matrix with MICH locked with AS55_Q and LO_PHASE locked with BH44_Q

Sensing matrix with the following demodulation phases (counts/m) {'AS55': 2.1, 'REFL55': 76.01784975834194, 'BH55': -63.16236453101908, 'BH44': -39.01036239539396} Sensors MICH @311.1 Hz LO1 @315.17 Hz AS55_I (+0.22+/-5.36)e+07 [0] (+0.91+/-3.10)e+07 [0] AS55_Q (+1.43+/-0.08)e+09 [0] (-0.78+/-7.45)e+07 [0] BH55_I (+4.92+/-5.18)e+08 [0] (-5.20+/-7.93)e+07 [0] BH55_Q (-1.45+/-0.75)e+09 [0] (+1.76+/-0.59)e+08 [0] BH44_I (+0.01+/-1.14)e+11 [0] (+0.02+/-1.08)e+11 [0] BH44_Q (+0.03+/-1.95)e+11 [0] (+0.07+/-1.98)e+11 [0] BHDC_DIFF (+3.05+/-0.17)e+09 [0] (+1.70+/-2.51)e+07 [0] BHDC_SUM (-2.33+/-0.23)e+08 [0] (+0.19+/-1.53)e+07 [0]

- Jupyter notebook: /opt/rtcds/caltech/c1/Git/40m/scripts/CAL/SensingMatrix/ReadSensMat.ipynb

MICH BHD locking:
- MICH lock with AS55_Q was handed over to BHD_DIFF using following ratio:
C1:LSC-PD_DOF_MTRX_3_4 = 1 (AS55_Q to MICH_A)
C1:LSC-PD_DOF_MTRX_4_34 = -1.34 (BHDC_DIFF to MICH_B, when BH55_Q is used)
C1:LSC-PD_DOF_MTRX_4_34 = 0.47 (BHDC_DIFF to MICH_B, when BH44_Q is used)

MICH BHD noise budget:
- FM2 of C1:CAL-MICH_CINV was updated to 1/1.4e9 = 7.14e-10 to use measured optical gain.
- Dark noise was measured at C1:CAL-MICH_W_OUT with PSL shutter closed, PD DOF matrix at various settings for various readout scheme.
- Attachment #1 shows MICH sensitivity with MICH locked using AS55_Q (green), BHD_DIFF under BH55_Q (blue), BHD_DIFF under BH44_Q (red). BH44 case gives the least noise due to larger optical gain. However, there are excess noise at around 100 Hz, when MICH is locked with BHD_DIFF. The excess noise (bump at around 50 Hz) was similar to what we saw in LO phase noise estimate (40m/17511).
- At low frequencies below ~30 Hz, the MICH sensitivity is probably limited by seismic noise, as it alignes with FPMI DARM sensitivity (orange curve; measured in 40m/17468).
- Attachemnt #2 and #3 show estimate of LO phase noise contribution to MICH sensitivity in BH55 case and BH44 case. The coupling was estimated by measuring a transfer fuction from BH55_Q/BH44_Q to MICH_W_OUT. As there was significant coherence in 30-200 Hz region in BH55 case, and 30-100 Hz in BH44 case, transfer function value in that regions was used to estimate the coupling.
- The coupling was estimated to be the following

2e-10 m/count for BH55_Q to MICH_W_OUT (0.035 m/m using BH55_Q calibration factor to LO1 motion of 1.76e8 counts/m)
2e-11 m/count for BH44_Q to MICH_W_OUT

- Diaggui file: /opt/rtcds/caltech/c1/Git/40m/measurements/LSC/MICH/MICH_Sensitivity_Live.xml

Next:
- Calibrate BH44_Q to LO1 motion
- Measure transfer function from LO1 motion to BHD_DIFF under BH44 and BH55
- Find out the cause of 50 Hz bump in LO phase noise
- Compare LO phase noise coupling with simulations

Attachment 1: MICH_Sensitivity_20230320.pdf

Attachment 2: MICH_Sensitivity_20230320_BH55Contribution.pdf

Attachment 3: MICH_Sensitivity_20230320_BH44Contribution.pdf

17515

Tue Mar 21 18:41:12 2023

Dither Lines set on MC1, MC2, MC3 for the night

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:

Mirror	Frequency	Amplitude
MC1	21.12 Hz	2000
MC2	25.52 Hz	1000
MC3	27.27 Hz	2500

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.

Attachment 1: 21032023_Dither_lines_plot

17516

Wed Mar 22 15:51:44 2023

Beam offset calculation for MC1,2,3 from dither results

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	$f_l$	Avg Re (+/- 1000)	Avg Im (+/- 1000)	Peak Power ( $\delta f$ )	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 $\Delta Y$ :

$\Delta L = \Delta Y \cdot \theta_{AC}$

Where $\Delta L$ is the change in length in result of the dithering and $\Delta Y$ is the overall change in beam spot position

Delta L can be calculated by:

$\Delta L = \frac{\delta f}{v_{laser}} \cdot L_{IMC}$

where $\delta f$ 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, $v_{laser}$ is frequency the laser light is traveling at (281 THz) and $L_{IMC}$ is the lenght of the IMC (13.5 meters).

$\theta_{AC}$ can then be calculated by:

$\theta_{AC} = \theta_{DC}/f_l^2$

where $\theta_{AC}$ is the angle at which the mirror was shaken at a given frequency. We can find $\theta_{DC}$ 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.

$\theta_{AC}$ is then shown to be found by this angle diveded by the line frequency.

The final values are calculated and displayed bellow:

Mirror	$\theta_{DC}$	$\theta_{AC}$	$\Delta L$	$\Delta Y$
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

Attachment 1: 22032023_Dither_lines_demod_MC1_21-12.pdf

17519

Thu Mar 23 16:21:10 2023

rana

Beam offset calculation for MC1,2,3 from dither results

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:

copy the DoF vector from DoF column into the LOCKIN1 column.
Turn on the OSC/LOCKIN for the optics / DoF in question (in this example its MC2 PITCH)
Monitor the peak in the MC_F spectrum
Also monitor the mag and phase of the TF of MC_F/LOCKIN_LO
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.

Attachment 1: TuninMC2OutMat-A2L-beaucoup.png

Attachment 2: IMC-A2Lnomore_cawcaw.png

17520

Thu Mar 23 17:47:53 2023

Paco

LO phase noise budget (BH55_Q)

NoiseBudget

I drafted a calibrated LO Phase noise budget using diaggui whose template is saved under /opt/rtcds/caltech/c1/Git/40m/measurements/BHD/LO_PHASE_cal_nb.xml which includes new estimates for laser frequency and intensity noises at the LO phase when MICH is locked (whether they couple through MICH or the LO path is to be determined with noise coupling measurements in the near future, but we expect them to couple through the LO phat mostly).

Attachment #1 shows the result.

Laser Frequency Noise

To calibrate the laser frequency noise contribution, I used the LO PHASE error point away from the control bandwidth (~ 20 Hz) and the calibrated C1:IOO-MC_F control point (in Hz) which should represent the laser frequency noise above 100 Hz. and dithered MC2 at frequencies around to 130, 215, and 325 Hz to match the LO phase error point with the MC_F signal. I was expecting to use a single 0 Hz pole + gain (to get the phase equivalent of the laser frequency noise) but in the end I managed to calibrate with a single gain of 3.6e-7 rad/Hz and no pole. Since the way the laser frequency noise couples into our BHD readout may be complicated (especially when using BH55 RF sensor) I didn't think much of this for now.

Laser Intensity Noise

For the intensity noise, I followed more or less a similar prescription as for laser frequency noise. This time, I used the AOM in the PSL table to actuate on the 0th order intensity going into the interferometer. Attachments #2-3 show the connection made to the RF driver where I added a 50 mVpp sine (at an offset of 0.1 V) excitation in the AM port to inject intensity noise calibration lines at 215 and 325 Hz and matched the LO_PHASE error point with the BHDC_SUM noise spectrum.

Attachment 1: lophase_cal_nb_20230322.png

Attachment 2: PXL_20230323_202125206.jpg

Attachment 3: PXL_20230323_194150923.jpg

17527

Wed Mar 29 15:59:01 2023

c1ioo model updated to add sensing to optic angle matrices

IOO

I've updated c1ioo model with adding WFS sensor to optic angle matrix and output filter module option. The output filter modules are named like EST_MC1_PIT to signify that that these are "estimated" angles of the optic. We can change this naming convention if we don't like it. I've also started DQ on the outputs of these filter moduels at 512 Hz sampling rate.

No medm screens have been made for these changes yet. One can still access them through:

For SENS_TO_OPT_P Matrix

medm -x /cvs/cds/rtcds/caltech/c1/medm/c1ioo/C1IOO_SENS_TO_OPT_P.adl

For SENS_TO_OPT_Y Matrix

medm -x /cvs/cds/rtcds/caltech/c1/medm/c1ioo/C1IOO_SENS_TO_OPT_Y.adl

For filter modules:

medm -x /cvs/cds/rtcds/caltech/c1/medm/c1ioo/C1IOO_EST_MC1_PIT.adl

Attachment 1: WFSSensToOptAngMatrices.png

17529

Wed Mar 29 17:00:23 2023

MC Length feedback is present but not visible in MEDM

IOO

I confirmed that MC Length feedback path to MC2 position is present and has been turned off in recent history. Feedback filter module can be seen in sitemap>IOO>Lock MC>MC2_LSC where the bottom fitler module is for feeding back MC Length to MC2. See attached screenshot.

This feedback signal goes and gets added to MC2 suspension longitudnal signal through ALTPOS path which is nominally not shown in any of the suspension screens (including the old ones). Note that this path is different than the LSC path that comes into each suspension screen.

Today, I tried a quick turning ON of this apth without playing around with any of the filters to see if the feedback helps. On first glance, it does not seem to help. Probably the gain values and filter modules need ot be adjusted. See attachment 2.

I'm turning this off again and in future someone should take a look at this loop.

Attachment 1: MC2_LSC.png

Attachment 2: 20230329_MC_L_Feedback_test.pdf

17530

Wed Mar 29 19:19:41 2023

Koji

X end green now indefinitely locking

ALS

Stable lock of the X End green laser was recovered.

- The biggest issue was that the laser PZT input had been terminated with a 50ohm at the laser head. (See Attachment 1: The terminator has already been removed in the photo.) Since the PZT output of the servo box (output impedance 10Ohm) goes through 680Ohm at the summing node for the modulation, the PZT output was attenuated by a factor of 15. This made the required servo gain for locking more than the box could deliver. More importantly, the PZT range (in terms of the laser frequency) was also limited. Momentary locks were still possible with the reduced range and gain. However, the actuation signal hit the rail within a few seconds because of the pendulum motion.

Once the terminator was removed from the head, the Xarm was locked with the green laser like a charm.

- On the way to the resolution, I had to go through the full scrutinization of the loop components one by one. Here is the record of the findings:

Inspected the green Refl PD (Thorlabs PFA36A). The gain setting of the PD was 40 dB, and the unlocked output voltage was 10.8 V. This is not only very close to saturation, but also the bandwidth drops below the modulation frequency (150 kHz according to Thorlabs' manual). The gain was changed to 20dB. This made the unlocked PD output to be 1.08V and the BW was expected to be 1MHz.
Checked the LO setting. The box has a label saying "LO 7dBm". The function generator setting of "0.66 Vrms" resulted in 7.0dBm at the mixer LO input. So this number is used. Exactly the same amount goes to the PZT summing node.
Checked the mod freq. The PDH error signal amplitude was maximized at 278.5kHz (mixer output observed with 50Ohm: 46.0mV), however, the signal looked distorted from the text-book shape of the PDF error. This means that the demod phase was not optimized.
The mod freq of 287.5kHz made the PDH error signal look better while the response was weaker (mixer out: 31.2mV). It turned out that the cavity locking didn't like these mod freq between 280kHz~290kHz. The momentary lock stretches showed a lot of quasi-sinusoidal fluctuation ~600Hz in the error and transmission signals. Instead, the modulation of 210.5kHz was used. This made the error signal during lock stretches clean and tight.
Box inspection: Checked the signal ratio between the error in and the error mon. The monitor gain seemed x20~x21. The PZT output and the PZT mon had identical gains. The transfer function of the box was measured with the gain knob changed from 0.00 to 7.00 where the transfer function started to get distorted with the given input. The gain was increased by 5dB/turn (i.e., 1 turn increases the gain by 5dB). ? It does not match with the info on the schematic and the datasheet? Anyways, the gain knob is working fine.
To resurrect the SLOW THERMAL servo, the monitor channels were connected to the DAQ interface. The existing slow channel servo/setting worked fine, wh
Usual caution: a slight touch to the satellite amp caused the UR OSEM PD completely black out. It means that just your presence at the X end can make some changes to the suspension.

Attachment 1: PXL_20230330_021330919.jpg

Attachment 2: PXL_20230330_021305080.jpg

Attachment 3: PXL_20230330_021024076.jpg

Attachment 4: PXL_20230330_021029670.MP.jpg

Attachment 5: PXL_20230330_021048654.jpg

Attachment 6: Screen_Shot_2023-03-29_at_23.19.16.png

17531

Thu Mar 30 09:51:41 2023

Paco