Here's the magnitude plot of the board TF. As mentioned above, this was done with Marconi+Scope, so we were not able to get the phase of this transfer function. 

Oddly enough, the bump that I saw is not included in Minicircuit's data on the SCLF-5.

 We've been having trouble tuning the ALS DIFF matrix. Trying to see if the MC2 EXC can be cancelled in ALS DARM by adjusting the relative gains in ALSX and ALSY Phase Tracker outputs.

There's a bunch of intermittent behavior. Between different ALS locks, we get more or less cancellation. We were checking this by driving MC2 at ~100-400 Hz and checking the ALS response (with the ALS loops closed). We noticed that the X and Y readbacks were different by ~5-10 degrees and that we could not cancel this MC2 signal in DARM by more than a factor of 4-5 or so. In the middle of this, we had one lock loss and it came back up with 100x cancellation?

Attached is a PDF showing a swept sine measurement of the ALSX, ALSY, and DARM signals. You can see that there is some phase shift between the two repsonses leading to imperfect cancellation. Any ideas? Whitening filters? HOM resonance? Alignment?

 We used to do violin mode and test mass body mode notches in the SUS-LSC filter modules. Now we want them balanced in the LSC and triggered by the LSC, so they're in the filter modules which go from the the LSC output matrix to the SUS.

Today, we were getting ETM violin mode ringups while doing ALS hunt and so we moved the bandstops into the LSC. I also changed the bandstop from a wide one which missed the ETMX mode to a double bandstop which gets both the ETMX and the ETMY mode. See attached image of the Bode mag.

Riju did the measurement of the MCREFL PD.
I found data files in her directory on the control machine.

I was not sure how much was the transimpedance of the DC out.
I assumed the default number from the circuit diagram which was 66.7Ohm.
This may cause the error in absolute caribration of the transimpedance but the shape does not change.

The RF preamp is gain-peeking at 250MHz.

Here is further characterization of the PD response.
As you can see in the second attachment, the 3dB cut off of the resonance is about 2.3MHz.

The game plan file in dropbox was also modified.

 To help development of the data visualization project, we've assigned the .101 and .102 IP to DataVis. This is being used by the iMac in the control room via port 8 of the CDS switch near the Blue Plataeu Tournant.

We tried using one of the free ports, but Jamie realized that we had to use one of the already assigned ones due to some 'Smart' switch management software. So for the moment, please leave the iMac alone so that Bill can use it.

1. Before doing anything, we centered the IOO QPDs.
2. With the WFS enabled, we offloaded the control signals onto the bias sliders. Then we saved the slider values. The MC LSC diode had a DC value of ~0.5
3. Turned down power with half wave plate before PMC.  Power injected to vacuum ~ 100mW.
4. We did a beam scan of MC REFL, it looks smaller than what Andres predicted based on the MC eigenmode by 10-20%.
5. We made many changes on the table, pictures to be added by Andres.
6. We didn't have the 80% reflector we wanted to increase the WFS power, so it's still a 98%.
6. Beams were aligned on MC REFL PL, camera, beam dumps, WFSs.
7. Clean up
8. PSL power increased to 1.2W, MC locked right away.
9 We didn't change the IOO WFS output matrix, but we changed some signs and gains to make everything stable. MC autolocker brings it back from cold just fine.
10. All time bombs that we've left will be E.Q.'s to clean up. Sorry.\
11. Yay

FYI and FMI

Phase tracker UGF is  Q_AMP * G * 2 PI / 360 where Q_AMP is the amplitude of the Q_ERR output and G is the gain of the phase tracker.

For example: Q_AMP = 270, G = 4000\ => UGF = 1.9kHz

 Jenne asked me to simulate the signals on POP QPD when moving different mirrors, as a function of the Gouy phase where the QPD is placed.

I used the opportunity to create a MIST simulation file of the entire 40m interferometer, essentially based on my aLIGO configuration file. I used the recycling cavity lengths obtained from our survey, and other parameters from the wiki page. The configuration file is attached (fortymeters.mist).

Coming back to the main simulation, here is the result, both for the "regular" POP QPD and for a 22MHz demodulated one. The Gouy phase is measured starting from PR2. Cavity mirrors are easily decoupled from PRM in the "regular" QPD. As already demonstrated in a previous simulation, ETMs signals are very small in the 22 MHz QPD. Moreover, it is possible to zero the contribution from ITMs by choosing the right Gouy phase, at the price of a reduction of the PRM signal by a factor of 3-4. Simulation files are attached.

I re-centered the ITMX & ITMY Optical lever beams today since they were off. First I aligned the beam into the vacuum so that it went through the center of the on table optics and then tweaked the receiver optics alignment.

There are several bad practices on these which probably makes them drift:

• plastic bases on some lens mounts
• some lens mounts are fastened with a single dog instead of two
• there is no need to use dogs on mounts that have screw holes. Just put the mount so that 2 screws with washers can be used. The placement for these is not so critical.
• Use less steering mirrors! The ITMY OL path has 5 optics the beam enters the vacuum!!!

According to the datasheets, the laser has a beam diameter of 0.6 mm and a divergence angle of 1.3/2 mrad. So we can just calculate the right lens positions next time and not have to experiment with the whole visible laser lens kit.

For next Wednesday's cleanup, someone should volunteer to make the mounts more stable for the ITMs.

[Koji Manasa]

We made quantitative inspection of the X/Y green beat setup on the PSL table.

DC output of the BBPD for each arm was measured by blockiing the beams at either or both side of the recombination BS.

The power over lap for the X arm beat note setup was 7.8% and is now 53%.
There is 3dB of headroom for the improvement of the mode overlap.

The power over lap for the Y arm beat note setup was 1.2% and is now 35%.
There is 4dB of headroom for the improvement of the mode overlap.

The RF analyzer monitor for the beat power is about 10dB lower than expected. Can we explain this only by the cable loss?
If not it there something causing the big attenuation?

             XARM   YARM
o BBPD DC output (mV)
 V_DARK:   -  3.3  + 1.9
 V_PSL:    +  4.3  +22.5
 V_ARM:    +187.0  + 8.4

o BBPD DC photocurrent (uA)
I_DC = V_DC / R_DC ... R_DC: DC transimpedance (2kOhm)

 I_PSL:       3.8   10.3
 I_ARM:      95.0    3.3

o Expected beat note amplitude
I_beat_full = I1 + I2 + 2 sqrt(e I1 I2) cos(w t) ... e: mode overwrap (in power)

I_beat_RF = 2 sqrt(e I1 I2)

V_RF = 2 R sqrt(e I1 I2) ... R: RF transimpedance (2kOhm)

P_RF = V_RF^2/2/50 [Watt]
     = 10 log10(V_RF^2/2/50*1000) [dBm]
     = 10 log10(e I1 I2) + 82.0412 [dBm]
     = 10 log10(e) +10 log10(I1 I2) + 82.0412 [dBm]

for e=1, the expected RF power at the PDs [dBm]
 P_RF:      -12.4  -22.6

o Measured beat note power (before the alignment)     
 P_RF:      -23.5  -41.7  [dBm] (38.3MHz and 34.4MHz) 
    e:        7.8    1.2  [%]                         
o Measured beat note power (after the alignment)      
 P_RF:      -15.2  -27.1  [dBm] (26.6MHz and 26.8MHz) 
    e:       53     35    [%]                         
Measured beat note power at the RF analyzer in the control room
 P_CR:      -25    -20    [dBm]
Expected    -17    - 9    [dBm]

Expected Power:
Pin + External Amp Gain (0dB for X, 20dB for Y)
    - Isolation trans (1dB)
    + GAV81 amp (10dB)
    - Coupler (10.5dB)

      Sept. 5, 2014              new 1103P, sn P893516  installed at SP table for aLIGO oplev use qualification

1.  tweaked gains for POS, PIT, YAW, SIDE by ~10-20% to get nice ringdowns with Q~5.
2. Measured bounce rool freqs = 16.43 / 23.99 Hz. Updated the Mech Res Wiki page. Tightened up the bandstops to get back a few deg of phase. Propagated these new bandstops into the SRM SUS damping filter banks.
3. Made and turned on a LP filters for the loops.
4. Added a ~0.3 Hz gain boost / bubble.
5. Set UGF to be ~2.5x below where it rings up. Estimate this to be ~3.5 Hz.
6. First PDF shows bounce/roll peaks in OSEMs. Notice how f_roll is > sqrt(2)*f_bounce. ??
7. Second PDF shows the OL spectra with the loops on/off. Previously there was no Boost and no LP (!!) turned on.
8. 3rd PDF shows the modeled Bode plot of the OLG. yellow/blue is boost off/on

[Koji, Rana, Jenne]

One coil of the TT produce 36nrad/rtHz at DC.

- C1:IOO-TT2_UL_EXC was excited with 5 count_pk at 0.04Hz.

- LSC_TRY exhibited the symmetric reduction of the transmission from 0.95 to 0.90.

1 - (theta/theta0)^2 /2 = 0.90 / 0.95

=> theta / theta0 = 0.32

- 40m beam waist radius is 3.1mm. This means the divergence angle is 1.1e-4 rad.

=> 1.1e-4*0.32 = 3.6e-5 rad

=> 3.6e-5/5 = 7.2 urad/count (per coil)

- DAC noise 1/sqrt(12 fs), where fs is the sampling rate (fs = 16384)

=> 0.002 cnt/rtHz

- One coil causes 7.2u*0.002 = 14 nrad/rtHz (at DC)

- One suspension cause 29 nrad/rtHz (at DC)

I modified the /cvs/cds/caltech/target/c1psl/psl.db file to adjust the records for the FSS-FAST signal (to make it go yellow / red at the correct voltages). This was needed to match 5V offset which Koji added to the output of the FSS board back in August.

I also manually adjusted the alarm levels with caput so that we don't have to reboot c1psl. Beware of potential tiimebomb / boot issues if I made a typo! psl.db update in the SVN (also, there were ~12 uncomitted changes in that directory....please be responsible and commit ALL changes you make in the scripts directory, even if its just a little thing and you are too cool for SVN)

Attached is the timeline for Frequency Offset Locking related activities. All activities will be done mostly in morning and early afternoon hours.

[Diego, Manasa]

We looked into the configuration and settings that the frequency counters (FC) and Domenica (the R pi to which the FCs talk to) were left at . After poking around for a few hours, we were able to readout the FC output and see it on StripTool as well.

We have made a list of modifications that should be done on Domenica and to the readout scripts to make the FC module automated and user-friendly.

I will prepare a user manual that will go on the wiki once these changes are made.

 OUTDATED: see elog 10779

I started working on the scripts/FOL directory (I did a backup before tampering around!):

• I still need to make some serious polishing in the folder, and into the Raspberry Pi itself, in order to have a clean and understandable environment;
• as of now, I created an single armFC.c program, which takes as arguments the device (/dev/hidraw0 for the X arm, and /dev/hidraw1 for the Y arm) and the value to write into the frequency counter (0x3 for initialization and 0x2 for actual use); hence, no more need for recompilation!
• I improved the codetorun.py script (and gave the fellow a proper name, epics_channels.py) which handles the initialization AND the availability of the channels;
• On the Raspberry Pi, I created two init scripts, /etc/init.d/epics_server.sh and /etc/init.d/epics_channels.sh, which start at the end of the boot process with default runlevels; the former starts the softIOc process (epics itself), while the latter executes the constantly running epics_channels.py script; as they are services, they can be started/stopped with the usual sudo /etc/init.d/NAME start|stop|restart

As a result, as soon as the Raspberry Pi completes its boot process, the two beatnote channels are immediately available.

Elaborate to do list:

1. The FC module should be mounted on the IOO rack. Domenica has to be powered up appropriately to the rack power supply.

2. The fiber chassis needs to be built. This will hold all the fiber components and will sit inside the PSL enclosure.
Fiber connectors and fiber couplers need to be installed in the chassis. Attached is the cartoon sketch of layout in the chassis.

3. User guide for FC module (work in progress)

 OUTDATED: see elog 10779

 Update and corrections:

• I forgot to log that I added a udev rule in /etc/udev/rules.d/98-hidraw-permissions.rules in order to let the controls user access the devices without having to sudo all the time;
• I updated the ~/.bashrc and /opt/epics/epics-euser-env.sh files to fix syntax errors and add some aliases we usually use;
• since /etc/init.d/ doesn't support automatic respawn of processes, I purged the two scripts I did yesterday and added two lines to /etc/inittab. This works just as fine (I tried a couple of reboots to verify that) and the two processes now respawn automatically even if killed (and, I assume, if they die for any other reason)
• Another thing I forgot: for the time being, during the cleanup, the Raspberry Pi works on the network share script directory. Once cleaning is done and everything is fixed, everything will run locally on the RPi, and the scripts/FOL directory on chiara will be used as backup/repository.

1. FC module has been mounted on the IOO rack. The module gets it AC supply from the powerstrip already installed on the back side of the rack.

2. The fiber chassis has not been put together completely. We have still not received the front and back panels for the chassis; which is keeping me on hold. Diego is almost done with his housekeeping on Domenica. He will post an elog with all the details.

3. User guide for FC module (work in progress)

I was working around the PSL table today.

I wanted to modify the telescope that couples PSL light into the fiber; now that I have the translation stages for the lenses. I could not finish it as the locking work started earlier than usual this afternoon. I measured the out of loop noise for ALS error signals before I opened the PSL enclosure. X and Y beat notes were at -18dBm at 49.3MHz and -29.56dBm at 62.2MHz for this measurement. DTT data can be found in /users/manasa/data/141210/ALSoutLoop.xml; so there is reference to go back to in case of any damage done due to the work on the PSL table.

Also, I received the front and back panels for the Fiber chassis and put it together. Find photos (front panel and inside) of chassis in attachment. This will go inside the PSL enclosure tomorrow.

 I assembled the telescope to couple PSL light into the fiber. The maximum coupling that I could obtain was 10mW out of 65mW (~15%).

I was expecting to achieve 80-90% coupling from my design estimates. It makes me wonder if the beam waist measurements made by Harry during summer were correct in the first place. I would like to go back and check the beam waist at the PSL table.

Also, we need a pair of 8m (~25 feet) long SMA cables to carry the RF signal from the beat PD on the PSL table to frequency counter module on the IOO rack.

Steve says that we had a spool of SMA cable and it was borrowed by someone a few months ago. Any updates on either who is holding it or if it has been used up already would help.

The X end slow computer was down this morning. So I used only the Y arm ALS to record the noise level for reference. DTT data for ALSY out of loop noise before opening PSL enclosure is saved in /users/manasa/data/141211/ALSYoutLoop.xml

 I missed to elog this earlier. I have temporarily removed the DC photodiode for GTRY to install the fiber holder on the PSL table. So GTRY will not be seeing anything right now.

 After some confusion, I discovered this a few hours ago.

Unfortunately the order placed for beam samplers last week did not go through. These will be used at the X and Y end tables to dump the unwanted light appropriately. Since they will not be here until Tuesday, I revised the timeline for FOL related activities accordingly.

I was working on the PSL table today. 

Since the rejected 1064nm light after the SHG crystal is not easily reachable to measure beam widths close to the waist, I put a lens f=300mm and measured the beam size around its focus. I used this data and redesigned the telescope using 'a la mode'.

I used a beam splitter to attenuate the beam directed towards the fiber. The reflected beam from BS has been dumped (I need to find a better beam dump than what is being used right now. 

I have only ~200uW at the input of the fiber coupler after the BS and 86uW at the output of the fiber (43% coupling). 

I moved the GTRY DC photodiode and the lens in front of it to make space for the fiber coupler mount.

The layout on the PSL table right now is as shown below.

I have also put the fiber chassis inside the PSL enclosure on the rack. I moved the coherent spectrum analyser controller that is not being used to make space on the rack.

 Found that the PMC gain has been set to 5.3 dB instead of 10 dB since 9 AM this morning, with no elog entry.

I also re-aligned the beam into the PMC to minimize the reflection. It was almost all in pitch.

I was working around the PSL table and Y endtable today.

I modified the Y arm optical layout that couples the 1064nm light leaking from the SHG crystal into the fiber for frequency offset locking.

The ND filter that was used to attenuate the power coupled into the fiber has been replaced with a beam sampler (Thor labs BSF-10C). The reflected power after this optic is ~1.3mW and the trasmitted power has been dumped to a razor blade beam dump (~210mW).

Since we have a spare fiber running from the Y end  to the PSL table, I installed an FC/APC fiber connector on the PSL table to connect them and monitored the output power at the Y end itself. After setting up, I have ~620uW of Y arm light on the PSL table (~48% coupling).

During the course of the alignment, I lowered the power of the Y end NPRO and disengaged the ETMY oplev. These were reset after I closed the end table.

Attached is the out of loop noise measurement of the Y arm ALS error signal before (ref plots) and after.

IMC OL TF has been measured from 10K to 10M

1. Calibrated the Phase Adjust slider for the PMC RF Modulation; did this by putting the LO and RF Mod out on the TDS 3034 oscope and triggering on the LO. This scope has a differential phase measurement feature for periodic signals.
2. Calibrated the RF Amp Adj slider for the PMC RF Modulation (on the phase shifter screen)
3. The PMC 35.5 MHz Frequency reference card is now in our 40m DCC Tree.
4.  The LO and RF signals both look fairly sinusoidal !
5. Took photos of our Osc board - they are on the DCC page. Our board is D980353-B-C, but there are no such modern version in any DCC.
6. The PMC board's Mixer Out shows a few mV of RF at multiples of the 35.5 MHz mod freq. This comes in via the LO, and can't be gotten rid of by using a BALUN or BP filters.
7. In installed the LARK 35.5 MHz BP filter that Valera sent us awhile ago (Steve has the datasheet to scan and upload to this entry). It is narrow and has a 2 dB insertion loss.

For tuning the phase and amplitude of the mod. drive:

- since we don't have access to both RF phases, I just maximized the gain using the RF phase slider. First, I flipped the sign using the 'phase flip' button so that we would be near the linear range of the slider. Then I put the servo close to oscillation and adjusted the phase to maximize the height of the ~13 kHz body mode. For the amplitude, I just cranked the modulation depth until it started to show up as a reduction in the transmission by ~0.2%, then reduced it by a factor of ~3. That makes it ~5x larger than before.

Here's a summary of the changes made to the D990511 serial 115 (formerly known as REFL 33), as well as a short procedure. It needed tuning to 29.5MHz and also had some other issues that we found along the way. 

So here's a picture of it as built:

The changes made are:

1. U11 and U12 changed from 5MHz LP to 10 MHz LP filters.

2. Resistors R8 and R9 moved from their PCB locations to between pins 1 (signal) and 3 (ground) of U11 and U12, respectively. These were put in the wrong place for proper termination so it made sense to shift them while I was already replacing the filters.

Also, please note- whoever labeled the voltages on this board needed an extra cup of coffee that day. There are two separate 15V power supplies, one converted from 24V, one directly supplied. The directly supplied one is labeled 15A. This does NOT mean 15 AMPS.

Transfer functions:

Equipment: 4395A, Signal generator (29.5 MHz), two splitters, one mixer

You can't take the TF from PD in to I/Q out directly. Since this is a demod board, there's a demodulating (downconverting) mixer in the I and Q PD in paths. Negligible signal will get through without some signal applied to the L input of the mixer. In theory, this signal could be at DC, but there are blocking capacitors in the LO in paths. Therefore, you have to upconvert the signal you're using to probe the board's behavior before it hits the board.  Using the 4395A as a network analyzer, split the RF out. RFout1 goes to input R, RFout2 goes to the IF port of the mixer. Split the signal generator (SG). SG1 goes to LO in, SG2 goes to the L port of the mixer. The RF port of the mixer (your upconverted RFout2) goes to PD in, and the I/Q out goes back to the A/B port of the 4395A - at the same frequency as the input, thanks to the board's internal downconversion. 

Phase measurement:

Equipment: Signal generator (29.5 MHz), signal generator (29.501 MHz), oscilloscope

Much simpler: 29.5 MHz to the LO input (0 dBm), 29.501 MHz to the PD input (0 dBm), compare the phases of the I/Q outputs on the oscilloscope. There are four variable capacitors in the circuit that are not on the DCC revision of the board - C28-31. On the LO path, C28 tunes the I phase, C30 tunes the Q phase. On the PD path, C29 and 31 appear to be purely decorative - both are in parallel with each other on the PD in Q path, I'm guessing C29 was supposed to be on the PD in I path. Fortunately, C28 and C30 had enough dynamic range to tune the I/Q phase difference to 90 degrees.

Before tuning:

After tuning:

I show here the matrix formalism to calculate analytically the loop TF relationships for the IMC w/ both FSS actuators so that it would be easier to interperet the results.

The attached PDF shows the Mathematica notebook and the associated block diagram.

In the notebook, I have written the single hop connection gains into the K matrix. P is the optical plant, C is the Common electronic gain, F is the 'fast' NPRO PZT path, and M is the phase Modulator.

G is the closed loop gain matrix. The notation is similar to matlab SS systems; the first index is the row and the second index is the column. If you want to find the TF from node 2 to node 3, you would ask for G[[3,2]].

As examples, I've shown how to get the FAST gain TF that I recently made with the Koji filter box as well as the usual OLG measurement that we make from the MC servo board front panel.

X-Arm ASS was fixed.
ASS_DITHER_ON.snap was updated so that the new setting can be loaded from the ASS screen.

The input and output matrices and the servo gains were adjusted as found in the attached image.
The output matrix was adjusted by looking at the static response of the error signals when a DC offset
was applied to each actuator.

The servo was tested with misalignment of the ITM, ETM, and BS. In fact, the servo restored transmission
from 0.15 to 1.

The resulting contrast after ASSing was ~99% level. (I forgot to record the measurement but the dark fringe level of ASDC was 4~5count.)

Please remember that Xarm ASS needs FM6 (Bounce filters) to be ON in order to work properly.

I wanted to check the status of the ISS. The AOM driver response was measured on Friday night.
The beam path has not been disturbed yet.

- I found the AOM crystal was removed from the beam path. It was left so.

- The AOM crystal has +24V power supply in stead of specified +28V.
  I wanted to check the functionality of the AOM driver.

- I've inserted a 20dB directional coupler between the driver and the crystal.
  To do so, I first turned off the power supply by removing the corresponding fuse block at the side panel of the 1X1 Rack.
  Then ZFDC-20-5-S+ was inserted, the coupled output was connected to a 100MHz oscilloscope with 50Ohm termination.
  Then plugged in the fuse block again to energize the driver box.

  Note that the oscilloscope bandwidth caused reduction the amplitude by a factor of 0.78. In the result, this has already been compensated.

- First, I checked the applied offset from a signal generator (SG) and the actual voltage at the AOM input. The SG OUT
  and the AOM control input are supposed to have an impedance of 50Ohm. However, apparently the voltage seen at the
  AOM in was low. It behaved as if the input impedance of the AOM driver is 25Ohm.
  In any case, we want to use low output impedance source to drive the AOM driver, but we should keep this in mind.

- The first attachment shows the output RF amplitude as a function of the DC offset. The horizontal axis is the DC voltage AT THE AOM INPUT (not at the SG out).
  Above 0.5V offset some non linearity is seen. I wasn't sure if this is related to the lower supply voltage or not. I'd use the nominal DC of 0.5V@AOM.

  The output with the input of 1V does not reach the specified output of 2W (33dBm). I didn't touch the RF output adjustment yet. And again the suppy is not +28V but +24V.

- I decided to measure the frequency response at the offset of 0.53V@AOM, this corresponds to the DC offset of 0.8V. 0.3Vpp oscillation was given.
  i.e. The SG out seen by a high-Z scope is V_SG(t) = 1.59 + 0.3 Sin(2 pi f t) [V]. The AOM drive voltage V_AOM(t) = 0.53 + 0.099 Sin(2 pi f t).
  From the max and min amplitudes observed in the osciiloscope, the response was checked. (Attachment 2)
  The plot shows how much is the modulation depth (0~1) when the amplitude of 1Vpk is applied at the AOM input.
  The value is ~2 [1/V] at DC. This makes sense as the control amplitude is 0.5, the applied voltage swings from 0V-1V and yields 100% modulation.

  At 10MHz the first sign of reduction is seen, then the response starts dropping above 10MHz. The specification says the rise time of the driver is 12nsec.
  If the system has a single pole, there is a relationship between the rise time (t_rise) and the cut-off freq (fc) as fc*t_rise = 0.35 (cf Wikipedia "Rise Time").
  If we beieve this, the specification of fc is 30MHz. That sounds too high compared to the measurement (fc ~15MHz).
  In any case the response is pretty flat up to 3MHz.

This is good news. It means that the driver probably won't limit the response of the loop - I expect we'll get 20-30 deg of phase lag @ 100 kHz just because of the acoustic response of the AOM PZT + crystal.

33MHz sidebands can be elliminated by careful choice of the modulation depths and the relative phase between the modulation signals.
If this condition is realized, the REFL33 signals will have even more immunity to the arm cavity signals because the carrier signal will lose
its counterpart to produce the signal at 33MHz.

Formulation of double phase modulation

m1: modulation depth of the f1 modulation
m2: modulation depth of the f2 (=5xf1) modulation

The electric field of the beam after the EOM

Therefore what we want to realize is the following "extinction" condition

We are in the small modulation regime. i.e. J₀(m) = 1, J₁(m) = m/2, J₂(m) = m²/8, J₃(m) = m³/48
Therefore we can simplify the above exitinction condition as

m2 < 0 means the start phase of the m2 modulation needs to be 180deg off from the phase of the m1 modulation.

Optical Setup

[Attachment 1]

Right before the PSL beam goes into the vacuum chamber, it goes through an AR-wedged plate.
This AR plate produces two beams. One of them is for the IO beam angle/position monitor.
And the other was usually dumped. I decided to use this beam.

A G&H mirror reflects the beam towards the edge of the table.
A 45deg HR mirror brings this beam to the beat set up at the south side of the table.
This beam is S-polarlized as it directly comes from the EOM.

[Attachment 2]

The beam from the PSL goes through a HWP and some matching lenses before the combining beam splitter (50% 45deg P).
The AUX laser beam is attenuated by a HWP and a PBS. The transmitted beam from the PBS is supposed
to have P-polarization. The beam alignment is usually done at the PSL beam side.

The combined beam is steered by a HR mirror and introduced to Thorlabs PDA10CF. As the PD has small diameter
of 0.5mm, the beam needed to be focused by a strong lens.

After careful adjustment of the beam mode matching, polarization, and alignment, the beatnote was ~1Vpp for 2.5Vdc.
In the end, I reduced the AUX laser power such that the beat amplitude went down to ~0.18Vpp (-11dBm at the PD,
-18dBm at the mixer, -27dBm at the spectrum analyzer) in order to minimize nonlinearity of the RF system and
in order that the spectrum analyzer didn't need input attenuation.

Electrical Setup

[Attachment 3]

The PD signal is mixed with a local oscillator signal at 95MHz, and then used to lock the PLL loop.
The PLL loop allows us to observe the peaks with more integration time, and thus with a better signal-to-noise ratio.

The signal from the PD output goes through a DC block, then 6dB attenuator. This attenuator is added to damp reflection
and distortion between the PD and the mixer. When the PLL is locked, the dominant signal is the one at 95MHz. Without this attenuator,
this strong 95MHz signal cause harmonic distortions like 190MHz. As a result, it causes series of spurious peaks at 190MHz +/- n* 11MHz.

10dB coupler is used to peep the PD signal without much disturbing the main line. Considering we have 6dB attanuator,
we can use this coupler output for the PLL and can use the main line for the RF monitor, next time.

The mixer takes the PD signal and the LO signal from Marconi. Marconi is set to have +7dBm output at 95MHz.
FOr the image rejection, SLP1.9 was used. The minicirsuit filters have high-Z at the stop band, we need a 50Ohm temrinator
between the mixer and the LPF.

The error signal from the LPF is fed to SR560 (G=+500, 1Hz 1st-order LPF). I still don't understand why I had to use a LPF
for the locking. As the NPRO PZT is a frequency actuator, and the PLL is sensitive to the phase, we are supposed to use
a flat response for PLL locking. But it didn't work. Once we check the open loop TF of the system, it will become obvious (but I didn't).

The actuation signal is fed to the fast PZT input of the AUX NPRO laser.
 

Experimental results

- PD response [Attachment 1]

The AUX laser temperature was swept along with the note by Annalisa [http://nodus.ligo.caltech.edu:8080/40m/8369]
It is easier to observe the beat note by closing the PSL shutter as the MC locking yields more fluctuation of the PSL
laser freuqency at low frequency. Once I got the beat note and maximized it, I immediately noticed that the PD response
is not flat. For the next trial, we should use Newfocus 1611. For the measurement today, I decided to characterize the
response by sweeping the beat frequency and use the MAXHOLD function of the spectrum analyzer.

The measured and modelled response of the PD are shown in the attachment 1. It has non-intuitive shape.
Therefore the response is first modelled by two complex pole pair at 127.5MHz with Q of 1, and then the residual was
empirically fitted with 29th polynomial of f.

- Modulation profile of the nominal setting [Attachment 2]

Now the spectrum of the PD output was measured. This is a stiched data of the spectrum between 1~101MHz and 99~199MHz
that was almost simultaneously measured (i.e. Display 1 and Display 2). The IF bandwidth was 1kHz. The PD response correction
described above was applied.

It obviously had the peaks associated with our main modulations. In addition, there are more peaks seen.
The attachment 2 breaks down what is causing the peaks.

• Carrier: The PLL LO frequency is 95MHz. Therefore the carrier is locked at 95MHz.
• Modulation sidebands (11/55MHz series):
  Series of sidebands are seen at the both side of the carrier. Their frequency is 95MHz +/- n * fmod  (fmod = 11.066128MHz).
  Note that the sidebands for n>10 were above 200MHz, and n<-9 (indicated in gray) were folded at 0Hz.
  With this measurement BW, the following sidebands were buried in the noise floor.
  n = -8, -12, -13, and -14, n<= -16, and n>=+7
• Modulation sidebands for IMC and PMC (29.5MHz and 35.5MHz):
  First order sidebands for the IMC and PMC modulations of sidebands are seen at the both side of the carrier.
  Their frequency is 95MHz +/- 29.5MHz or 33.5MHz. The PMC modulation sidebands are supposed to be blocked
  by the PMC. However, due to finite finesse of the PMC, small fraction of the PMC sidebands are transmitted.
  In deed, it is comparable to the modulation depth of the IMC one.
• RF AM or RF EMI for the main modulation and the IMC modulationand:
  If there is residual RF AM in the PSL beam associated with the IMC and main modulations, it appears as the
  peaks at the modulation frequency and its harmonics. Also EM radiation couples into this measument RF system
  also appears at these frequencies. They are seen at n * fmod  (n=1,2,4,5) and 29.5MHz.
• Reflection/distortion or leakage from mixer IF to RF:
  The IF port of the mixer naturally has 190MHz signal when the PLL is locked. If the isolation from the IF port to the RF port
  is not enough, this signal can appear in the RF monitor signal via an imperfection of the coupler or a reflection from the PD.
  Also, if the reflecrtion/distortion exist between the PD and the mixer RF input, it also cause the signal around 190MHz.
  It is seen at 190MHz +/- n* fmod. In the plot, the peak at n=0, -1 are visible. In fact these peak were secondarily dominant
  in the spectrum when there was no 6dB attenuation in the PD line. WIth the attenuator, they are well damped and don't disturb
  the main measurment.

From the measured peak height, we are able to estimate the modulation depths for 11MHz, 55MHz, IMC modulations, as well as
the relative phase of the 11MHz and 55MHz modulation. (It is not yet done).

- 3f modulation reduction [Attachment 3]

Now, the redcution of the 3f modulation was tried. The measured modulation levels for the 11MHz and 55MHz were almost the same.
The calculation predicts that the modulation for the 55MHz needs to be 1/3 of the 11MHz one. Therefore the attenuation of 9dB and 10dB
of the modulation attenuation knob at the frequency generation box were tried.

To give the variable delay time in the 55MHz line, EG&G ORTEC delay line unit was used. This allows us to change the delay time from
0ns to 63.5ns with the resolution of 0.5ns. The frequency of 55MHz yields a phase sensitivity of ~20deg/ns (360deg/18ns).
Therefore we can adjust the phase with the precision of 10deg over 1275deg.

The 3rd-order peak at 61.8MHz was observed with measurement span of 1kHz with very narrow BW like 30Hz(? not so sure). The delay
time was swept while measuring the peak height each time. For both the atteuation, the peak height clearly showed the repeatitive dependence
with the period of 18ns, and the 10dB case gave the better result. The difference between the best (1.24e-7 Vpk) and the worst (2.63e-6 Vpk)
was more than a factor of 20. The 3rd-order peak in the above broadband spectrum measurement was 6.38e-6 Vpk. Considering the attenuation
of the 55MHz modulation by 10dB, we were at the exact unluck phase difference. The improvement expected from the 3f reduction (in the 33MHz signal)
will be about 50, assuming there is no other coupling mechanism from CARM to REFL33.

I decided to declare the best setting is "10dB attenuation & 28ns delay".

- Resulting modulation profile [Attachment 4]

As a confirmation, the modulation profie was measured as done before the adjustment.
It is clear that the 3rd-order modulation was buried in the floor noise. 10dB attenuation of the 55MHz modulation yields corresponding reduction of the sidebands.
This will impact the signal quality for the 55MHz series error signals, particularly 165MHz ones. We should consider to install the Teledyne Cougar amplifier
next to the EOM so that we can increase the over all modulation depth.

When I finished my measurements, the modulation setup was reverted to the conventional one.
If someone wants to use the 3f cancellation setting, it can be done along with this HOW-TO.

The 3f cancellation can be realized by adding a carefully adjusted delay line and attenuation for the 55MHz modulation
on the frequency generation box at the 1X2 rack.  Here is the procedure:

1) Turn off the frequency generation box

There is a toggle switch at the rear of the unit. It's better to turn it off before any cable action.
The outputs of the frequency generation box are high in general. We don't want to operate
the amplifiers without proper impedance matching in any occasion.

2) Remove the small SMA cable between 55MHz out and 55MHz in (Left arrow in the attachment 1).

According to the photo by Alberto (svn: /docs/upgrade08/RFsystem/frequencyGenerationBox/photos/DSC_2410.JPG),
this 55MHz out is the output of the frequency multiplier. The 55MHz in is the input for the amplifier stages.
Therefore, the cable length between these two connectors changes the relative phase between the modulations at 11MHz and 55MHz.

3) Add a delay line box with cables (Attachment 2).

Connect the cables from the delay line box to the 55MHz in/out connectors. I used 1.5m BNC cables.
The delay line box was set to have 28ns delay.

4) Set the attenuation of the 55MHz EOM drive (Right arrow in the attachment 1) to be 10dB.

Rotate the attenuation for 55MHz EOM from 0dB nominal to 10dB.

5) Turn on the frequency modulation box

For reference, the 3rd attachment shows the characteristics of the delay line cable/box combo when the 3f modualtion reduction
was realized. It had 1.37dB attenuation and +124deg phase shift. This phase change corresponds to the time delay of 48ns.
Note that the response of a short cable used for the measurement has been calibrated out using the CAL function of the network analyzer.

Summary of the ELOGS

3f modulation cancellation theory http://nodus.ligo.caltech.edu:8080/40m/11005

3f modulation cancellation adjustment setup http://nodus.ligo.caltech.edu:8080/40m/11029

Experiment http://nodus.ligo.caltech.edu:8080/40m/11031

Receipe for the 3f modulation cancellation http://nodus.ligo.caltech.edu:8080/40m/11032

Modulation depth analysis http://nodus.ligo.caltech.edu:8080/40m/11036

I wonder if DRMI can be locked on 3f using this lower 55 MHz modulation depth. It seems that PRMI should be unaffected, but that the 3*f2 signals for SRCL will be too puny. Is it really possible to scale up the overall modulation depths by 3x to compensate for this?

This KTP crystal has the maximum allowed RF power of 10W (=32Vpk) and V_pi = 230V. This corresponds to the maximum allowed
modulation depth of 32*Pi/230 = 0.44. So we probably can achieve gamma_1 of ~0.4 and gamma_2 of ~0.13. That's not x3 but x2,
so sounds not too bad.

Then Kiwamu's triple resonant circuit LIGO-G1000297-v1 actually shows the modulation up to ~0.7. Therefore it is purely an issue
how to deliver sufficient modulation power. (In fact his measurement shows some nonlinearity above the modulation depth of ~0.4
so we should keep the maximum power consumption of 10W at the crystal)

This means that we need to review our RF system (again!)

- Review infamous crazy attn/amp combinations in the frequency generation box.
- Use Teledyne Cougar ampilfier (A2CP2596) right before the triple resonant box. This should be installed closely to the triple resonant box in order to
minimize the effects of the reflection due to imperferct impedance matching.
- Review and refine the triple resonant circuit - it's not built on a PCB but on a universal board. I think that we don't need triple
resonance, but double is OK as the 29.5MHz signal is small.

We want +28V supply at 1X1 for the Teledyne amp and the AOM driver. Do we have any unused Sorensen?

Based on the measured modulation profiles, the depth of each modulation was estimated.
Least square sum minimization of the relative error was used for the cost function.
-8th, -12th~-14th, n=>7th are not included in the estimation for the nominal case.
-7th~-9th, -11th~-15th, n=>7th are not included in the estimation for the 3f reduced case.

Nominal modulation

m_f1 = 0.194
m_f2 = 0.234
theta_f1f2 = 41.35deg
m_IMC = 0.00153

3f reduced modulation

m_f1 = 0.191
m_f2 = 0.0579
theta_f1f2 = 180deg
m_IMC = 0.00149

(Sorry! There is no error bars. The data have too few statistics...)

In the attached plot you can see that the MC REFL fluctuations started getting larger on Feb 24 just after midnight. Its been bad ever since. What happened that night or the afternoon of Feb 23?
The WFS DC spot positions were far off (~0.9), so I unlocked the IMC and aligned the spots on there using the nearby steering mirrors - lets see if this helps.

Also, these mounts should be improved. Steve, can you please prepare 5 mounts with the Thorlabs BA2 or BA3 base, the 3/4" diameter steel posts, and the Polanski steel mirror mounts? We should replace the mirror mounts for the 1" diameter mirrors during the daytime next week to reduce drift.

I was asked by Koji to point out where a schematic of the triple resonant circuit is.
It seems that I had posted a schematic of what currently is installed (see elog 4562 from almost 4 yrs ago!).

(Some transfomer story)
Then I immediately noticed that it did not show two components which were wideband RF transformers. In order to get an effective turns ratio of 1:9.8 (as indicated in the schematic) from a CoilCrfat's transformer kit in the electronics table, I had put two more transformers in series to a PWB1040L which is shown in the schematic. If I am not mistaken, this PWB1040L must be followed by a PWB1015L and PWB-16-AL in the order from the input side to the EOM side. This gives an impedance ratio of 96 or an effective turns ratio of sqrt(96) = 9.8.

(An upgrade plan document)

Also, if one wants to review and/or upgrade the circuit, this document may be helpful:
https://wiki-40m.ligo.caltech.edu/Electronics/Multi_Resonant_EOM?action=AttachFile&do=get&target=design_EOM.pdf
This is a document that I wrote some time ago describing how I wanted to make the circuit better. Apparently I did not get a chance to do it.

MC Refl alignment follow up: the alignment from last night seems still good today. We should keep an  on the MC WFS DC spots and not let them get beyond 0.5.

I made very rough calibration of the DARM spectra before and after the transition for the second lock on Mar 8.

The cavity pole (expected to be 4.3kHz) was not compensated. Also the servo bump was not compensated.

[Error calibration]

While the DARM/CARM were controlled with ALS, the calibration of them are provided by the ALS phase tracker calibration.
i.e 1 degree = 19.23kHz

This means that the calibration factor is

DARM [deg] * 19.23e3 [Hz/deg] / c [m Hz] * lambda [m] * L_arm [m]
= DARM* 19.23e3/299792458*1064e-9*38.5 = 2.6e-9 *DARM [m]

[Feedback calibration]

Then, the feedback signal was calibrated by the suspension response (f=1Hz, Q=5)
so that the error and feedback signals can match at 100Hz.

This gave me the DC factor of 5e-8.

The spectra at 1109832200 (ALS only, even not on the resonance) and 1109832500 (after DARM/CARM transitions) were taken.
Jenne said that the whitening filters for AS55Q was not on.

Polaris mounts ordered.