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

Com'on. This is just a 60ppm change of the mod frequency from the nominal. How can it change the recycling cav length by more than a cm?

https://wiki-40m.ligo.caltech.edu/IFO_Modeling/RC_lengths

This describes how the desirable recycling cavity lengths are affected by the phase of the sidebands at non-resonant reflection of the arms.

If we believe these numbers, L_PRC = 6.7538 [m] and L_SRC = 5.39915 [m].

Compare them with the measured numbers

• Lprc = 6.752 m
• Lsrc  = 5.474 m

You should definitely run MIST to see what is the optimal length of the RCs, and what is the effect of the given length deviations.

Today the network connection of OTTAVIA was sporadic.

Then in the evening OTTAVIA lost completely it. I tried jiggle the cables to recover it, but in vain.

We wonder if the network card (on-board one) has an issue.

[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)

This is great.

And I got confused. Is REFL11 going through the CM board?
If so how the demod phase for REFL11 take an effect for the sensing?

Maybe I understood. CM SERVO SLOW has been connected to REFL11I? whitening.
Therefore using REFL11 in the CM SERVO gives us REFL11I at the usual channels.
And then how can we ensure the gain matching between I & Q?

Then is the next step 3f DRMI? How is REFL165 healthy?
I also wonder how the relative phase and modulation depths improves the sensing matrix.

 Didn't you take this opportunity to replace the cooling fan of the innolight controller?

• Suppose you have a dtt template name test.xml
• The file test.dtt
  
  open
restore test.xml
run -w
save test2.xml
quit
 
• Run diag < test.dtt
• The result is saved in test2.xml

[Eric Koji]

We made sensing matrix measurements for the IMC WFS and the MC2 QPD.

The data is under further analysis but here is some record of the current state to show
IMC Trans RIN and the ASC error signals with/without IMC ASC loops

The measureents were done automatically running DTT. This can be done by

/users/Templates/MC/wfsTFs/run_measurements

The analysis is in preparation so that it provides us a diagnostic report in a PDF file.

There are several non scientific reasons.

CPU load seems extremely high. You need to reboot it, I think

controls@fb /proc 0$ cat loadavg
36.85 30.52 22.66 1/163 19295

Last night the sensing matrix for IMC WFS&QPD were measured.

C1:IOO-MC(1, 2, 3)_(ASCPIT, ASCYAW)_EXC were excited at 5.01Hz with 100 count
The output of the WFS1/WFS2/QPD were measured. They all looked well responding
i.e. Pitch motion shows pitch error signals, Yaw motion shows yaw error signals.

The below is the transfer function from each suspension to the error signals

MC1P      MC2P     MC3P
-3.16e-4  1.14e-2  4.62e-3 -> WFS1P
 5.43e-3  8.22e-3 -2.79e-3 -> WFS2P
-4.03e-5 -3.98e-5 -3.94e-5 -> QPDP

MC1Y      MC2Y     MC3Y
-6.17e-4  6.03e-4  1.45e-4 -> WFS1Y
-2.43e-4  4.57e-3 -2.16e-3 -> WFS2Y
 7.08e-7  2.40e-6  1.32e-6 -> QPDY

Taking the inverse of these matrices, the scale was adjusted so that the dc response.



Preparations

- According to Diego's report, the MC WFS gains were too high. We'll fix this later by tweaking the servo shapes.
But for now, all of the WFS gains were reduced by 40%.
i.e. WFS(1|2)(PIT|YAW) gains from 5 to 3, MC2TRANS(PIT|YAW) gains from 50 to 30.

- Aligned IMC carefully and ran the offset nulling script. MC REFL became 0.435~0.445 and MC TRANS was ~16600.

- Locked the arms and ran ASS.

PRMI

- Started locking PRMI. I just used REFL33I&Q as suggested by the configure script. The PRMI locking was not so robust.
Particularly, the third violin mode of PRM and BS seemed to get excited and dominated the signals.
I modified Vio3 filter in the violin filter for BS and PRM to include zero at 1921Hz where the growing peak was seen.

- We probably want to start from the 1f signals for DRMI lock acquisition. So I wanted to check how REFL11s are.
Measured the demod phase and relative gain between 33I and 11I. (By the way, REFL11I whitening gain was lowered to 0dB).
REFL11I had about x10 gain and the same phase compared to REFL33I. The demod phase for REFL11 was +21deg.
Also checked REFL55 phase and gain. 55Q has almost the same gain as 33Q. And the adjusted phase was 25deg.
These were just rough adjustment of the demod phases.

- Then the servo configuration was transtioned to Configuration 1 (below), and then Configuration 2.

- This configuration was very stable and the PRMI stayed locked about ~1 hour. During this long lock, I could measure 
PSDs, sensing matrix, and etc. Also I could play with the PRM ASC. I wasn't sure if the POP is actually stabilized or not.
(I have no data)

- I noticed that something was ringinging up at 1883Hz. Another 3rd order viloin mode???

- The lock was lost due to too strong injection. But also it reacquired without touching.

- Precise demod phase adjustment has been done by elliminating PRCL from the Q signals.

REFL11 16.75
REFL33 133.0
REFL55 31.0
REFL165 -142 
AS55 -53

- Configiration1 (REFL11I&REFL55Q)

REFL11: WTN 0dB PHASE 21deg, REFL11I x0.1 -> PRCL
REFL33: WTN 30dB PHASE 145deg
REFL55: WTN 21dB PHASE 25deg, REFL55Q x1 -> MICH

PRCL: GAIN -0.04 FM4/5 ON, Triggered FM 2/3/6/9, Servo trigger: POP22I 50up 10down, No Normaization.
MICH: GAIN 10 FM4/5 ON, Triggered FM 2/3/6/9, Servo trigger: POP22I 50up 10down, No Normaization.

PRCL -> PRM +1
MICH -> PRM -0.2625, BS +0.50 BS

- Configuration 2 (REFL11I&Q)

Same as above except:
REFL11Q x-0.1 -> MICH

Calibration

Let's use these entries 

PRM: http://nodus.ligo.caltech.edu:8080/40m/8255
PRM:  (19.6 +/- 0.3) x 10^{-9} (Hz/f)^2 m/counts

BS/ITMs http://nodus.ligo.caltech.edu:8080/40m/8242
BS     = (20.7 +/- 0.1)    x 10 ^-9 / f²
ITMX = (4.70 +/- 0.02)  x 10 ^-9/ f²
ITMY = (4.66 +/- 0.02) x 10 ^-9/ f²

- PRCL Calibration

Lockin oscillator module 675.13Hz 100 -> +1 PRM

Measurement bandwidth 0.1Hz -> Signal power BW 0.471232 (FLATTOP window)

C1:SUS-PRM_LSC_IN1: 118.99 cnt/rtHz => 5.12pm/rtHz
REFL11I: 17.84  cnt/rtHz => 3.49e12 cnt/m
REFL33I:  2.28  cnt/rtHz => 4.46e11 cnt/m
REFL55I:  0.158 cnt/rtHz => 3.09e10 cnt/m
REFL165I: 1.63  cnt/rtHz => 3.19e11 cnt/m

- MICH Calibration

Lockin oscillator module 675.13Hz 100 -> -1 ITMX +1 ITMY

Measurement bandwidth 0.1Hz -> Signal power BW 0.471232 (FLATTOP window)

C1:SUS-ITMX_LSC_IN1: 121.79 cnt/rtHz => 1.26pm/rtHz
C1:SUS-ITMY_LSC_IN1: 121.79 cnt/rtHz => 1.25pm/rtHz
REFL11Q:  0.0329   cnt/rtHz => 1.32e10 cnt/m (PRCL/MICH ratio 265)
REFL33Q:  0.00773  cnt/rtHz => 3.09e9  cnt/m (144)
REFL55Q:  0.001645 cnt/rtHz => 6.58e8  cnt/m (47)
REFL165Q: 0.00374  cnt/rtHz => 1.50e9  cnt/m (213) !?
AS55Q:    0.0696   cnt/rtHz => 2.78e10 cnt/m

Openloop TF measurements
Servo filter TF measuremnts

The UGFs were ~250Hz for PRCL and ~120Hz for MICH, respectively.
The OLTF was modelled by the servo and violin filters TF from foton, estimated TF of the AA/AI filters, and the constant time delay.

Displacement spectra measurement

SELF NOTE: DON'T FORGET TO TURN ON the whitening of the unused signals! (USE MC DOF or manual switch)

- PRCL

The PRCL displacement was measured with REFL I signals. In the attachment 3, the in-loop and free-run equivalent displacements are shown (red and blue).
Other out-of-loop sensors (33/55/165) were also plotted together.

FIrst of all, the uncompensated displacement noise level of PRCL is around 1e-7 m/rtHz. This is a good indication that the calibration was not crazy.

The sensing noise of REFL11 seems to be 1e-15~1e-16 m/rtHz at high frequency which is enough for now.
As expected, REFL11I has the best noise level among the REFLs. At low frequency, it seemed that the noise level is limited by something at 1e-12 m/rtHz.
Of course, we can't say this is just the sensing noise of the other REFLs or the noise of the REFL11I. But this noise level is enough small for the locking of
the low finesse (F<100) PRCL cavity.

Remembering we had no trouble locking PRCL with REFL33/55/165, this plot indicates that the PRCL was suppressed too much below 2Hz.
And we want more supression between 5Hz to 30Hz. We have resonant gains in ther PRCL servo but not sure how effective they were.
If we consider the contamination of PRCL in MICH, we should try to optimize the PRCL servo.

- MICH

The MICH displacement was similary calibrated to PRCL. The signal sources were the REFL Qs and AS55Q.
In the attachment 4, the in-loop and free-run equivalent displacements are shown (red and blue).
Other out-of-loop sensors were also plotted together.

The problem here is that the out-of-loop levels (REFL33/55/165 and AS55) show almost the same levels
and thus it is likely that the actual (out-of-loop) stability of MICH is this kind of level. If we believe it, we only have
~1/100 supression between 1-10Hz and ~1/10Hz below 0.5Hz. The strong servo control does nothing to stablize
MICH. From the out-of-loop noise level of MICH, this comes for the contamination from leakage PRCL.
We really need to improve the signal quality of MICH.

The MICH servo filter has quite complicated shape, but is not necessary according to the estimated free-runing MICH.

The MICH free-running motion is quieter than the PRCL one between 1Hz to 30Hz. The reasonable explanation is
that it comes from poor vibration isolation of the tip-tilts. It means that SRCL also has the similar noise level to PRCL.

I'm leaving the iFO now. It is left with the IR arm mode.

I pretty much messed up LSC configurations for my DRMI locking. If one needs to recover the previous setting, use burtrestore.
I have all records of my LSC settings, so you don't need to preserve it. (Of course we can always use the hourly snapshots
to come back this DRMI setting)

Continued from ELOG 10659

DRMI locking

Following Jenne's elog entry in Aug 2013 (9049), DRMI was configured and locked. The lock was stable, indefinite, and repeatitive.

- DRMI Configuration

Demod phases has not been changed from PRMI

REFL11: WTN 0dB PHASE 21deg, REFL11I x0.1 -> PRCL
REFL55: WTN 21dB PHASE 25deg, REFL55Q x1 -> MICH, REFL55I x1 -> SRCL

AS110 phase was adjusted to maximize Q during the lock: +1deg (AS110Q_ERR was +4400 ~ +5500)

PRCL: GAIN -0.05 FM4/5 ON, Triggered FM 2/3/6/9, Servo trigger: POP22I 20up 10down, No Normaization.
MICH: GAIN +1 FM4/5 ON, Triggered FM 2/3/6/9, Servo trigger: POP22I 20up 10down, No Normaization.

SRCL: GAIN +2 FM4/5 ON, Triggered FM2/3/6/8/9, Servo trigger: AS110Q up 500 down 5, No Normaization.
(FM8 was set to be x2.5 flat gain such that the gain is increased after the lock)

MICH actuation is still BS+PRM and does not include SRCL decoupling yet.
This should be fixed ASAP.

DRMI Calibration

Let's use these entries 

SRM: http://nodus.ligo.caltech.edu:8080/40m/10664
SRM = (19.0 +/- 0.7) x 10 ^-9/ f²

PRM: http://nodus.ligo.caltech.edu:8080/40m/8255
PRM:  (19.6 +/- 0.3) x 10 ^-9 / f² m/counts

BS/ITMs http://nodus.ligo.caltech.edu:8080/40m/8242
BS     = (20.7 +/- 0.1)    x 10 ^-9 / f² m/counts
ITMX = (4.70 +/- 0.02)  x 10 ^-9/ f² m/counts
ITMY = (4.66 +/- 0.02) x 10 ^-9/ f² m/counts

- PRCL Calibration

Lock-in oscillator module 675.13Hz 100 -> +1 PRM

Measurement bandwidth 0.1Hz -> Signal power BW 0.471232 (FLATTOP window)

C1:SUS-PRM_LSC_IN1: 97.45 cnt/rtHz => 4.19 pm/rtHz

REFL11I: 12.55   cnt/rtHz => 3.00e12 cnt/m
REFL11Q:  0.197  cnt/rtHz => 4.70e10 cnt/m => 0.90 deg rotated! (GOOD)

REFL33I:  1.63   cnt/rtHz => 3.89e11 cnt/m
REFL33Q:  0.196  cnt/rtHz => 4.68e10 cnt/m => 8.32 deg rotated!

REFL55I:  0.0495 cnt/rtHz => 1.18e10 cnt/m
REFL55Q:  0.548  cnt/rtHz => 1.31e11 cnt/m => 84.8 deg rotated! (WHAT!)

REFL165I: 1.20   cnt/rtHz => 2.86e11 cnt/m
REFL165Q: 0.458  cnt/rtHz => 1.09e11 cnt/m => 20.9 deg rotated!

- MICH Calibration

Lock-in oscillator module 675.13Hz 100 -> -1 ITMX +1 ITMY

Measurement bandwidth 0.1Hz -> Signal power BW 0.471232 (FLATTOP window)

C1:SUS-ITMX_LSC_IN1: 121.79 cnt/rtHz => 1.26pm/rtHz
C1:SUS-ITMY_LSC_IN1: 121.79 cnt/rtHz => 1.25pm/rtHz

AS55Q:   12.45   cnt/rtHz => 4.96e12 cnt/m (STRONG)

REFL11I:  0.0703 cnt/rtHz => 2.80e10 cnt/m
REFL11Q:  0.0142 cnt/rtHz => 5.66e09 cnt/m => 78.5 deg rotated! (WHAT!)

REFL33I:  0.0473 cnt/rtHz => 1.88e10 cnt/m
REFL33Q:  0.0291 cnt/rtHz => 1.16e10 cnt/m => 58.4 deg rotated!


REFL55I:  0.00668cnt/rtHz => 2.66e09 cnt/m
REFL55Q:  0.0261 cnt/rtHz => 1.04e10 cnt/m => 14.4 deg rotated! (OK)

REFL165I: 0.0233 cnt/rtHz => 9.28e09 cnt/m
REFL165Q: 0.0512 cnt/rtHz => 2.04e10 cnt/m => 24.5 deg rotated! (GOOD)

- SRCL Calibration

Lock-in oscillator module 675.13Hz 100 -> SRM

Measurement bandwidth 0.1Hz -> Signal power BW 0.471232 (FLATTOP window)

C1:SUS-SRM_LSC_IN1: 121.77 cnt/rtHz => 5.08pm/rtHz

AS55I:    0.256   cnt/rtHz => 5.05e10 cnt/m
AS55Q:    0.3498  cnt/rtHz => 6.90e10 cnt/m

REFL11I:  0.00624 cnt/rtHz => 1.23e09 cnt/m
REFL11Q:  0.00204 cnt/rtHz => 4.02e08 cnt/m

REFL33I:  0.00835 cnt/rtHz => 1.65e09 cnt/m
REFL33Q:  0.0659  cnt/rtHz => 1.30e10 cnt/m


REFL55I:  0.0201  cnt/rtHz => 3.97e09 cnt/m
REFL55Q:  0.01505 cnt/rtHz => 2.97e09 cnt/m

REFL165I: 0.0238  cnt/rtHz => 4.69e09 cnt/m
REFL165Q: 0.0247  cnt/rtHz => 4.87e09 cnt/m

DRMI Openloop measurements
Servo filter TF measurements

The UGFs were ~250Hz for PRCL and ~100Hz for MICH, and ~250Hz for SRCL, respectively.
MICH showed (presumably) crosscoupling related peak ~350Hz. SRCL had small deviation from the model.
This may also be related to the cross couplig.

The OLTF was modelled by the servo and violin filters TF from foton, estimated TF of the AA/AI filters, and the constant time delay.

Displacement spectra measurement

- PRCL

The OLTF compensation was not actually succesfull at 300Hz, but otherwise the situation is very similar to the one with PRMI.

- MICH

Again the servo compensation at 300Hz was not successful. If we believe that AS55Q is the best MICH sensor, the out-of-loop
noise level of MICH was quite similar to the one in PRMI. We should try to use AS55Q for DRMI MICH for investigation purpose
to see which REFL signal has the best MICH quality. REFL165 seems to be iproved in the signal amplitude. Can we use this
for locking now?

- SRCL

It is in fact difficult to tell what is the correct out-of-loop noise level. AS55I has too much contamination from MICH and is not indicating
useful info. This measurement should be tried once the sensor diagonalization is done.

REFL55I is not seeing anything real abobe 30Hz. We should be able to reduce the UGF and the servo gain.

The absolute motion level of SRCL is something similar to PRCL, rather than MICH.

I wonder if this is the coherence caused by the beam itself, or caused by the same ground motion.
Jenne should be able to tell us...

SRM Calibration

After the DRMI measurements on Friday, SRY cavity was locked in order to compare ITMY and SRM actuators.

SRY cavity was locked with AS55Q ->  SRM servo with gain of +10?
(My memory is fading. I tried +50 and noticed it was saturated at the limiter. So I thought it was 10)

Then the transfer functions between SRM->AS55Q TF and ITMY->AS55Q TF were measured.

The ratio between two transfer functions was obtained as seen in the second attachment.
The average at f<100Hz was 4.07 +/- 0.15. Therefore the calibration is ... as you can find below

SRM: http://nodus.ligo.caltech.edu:8080/40m/10664
SRM = (19.0 +/- 0.7) x 10 ^-9/ f²

PRM: http://nodus.ligo.caltech.edu:8080/40m/8255
PRM:  (19.6 +/- 0.3) x 10 ^-9 / f² m/counts

BS/ITMs http://nodus.ligo.caltech.edu:8080/40m/8242
BS     = (20.7 +/- 0.1)    x 10 ^-9 / f² m/counts
ITMX = (4.70 +/- 0.02)  x 10 ^-9/ f² m/counts
ITMY = (4.66 +/- 0.02) x 10 ^-9/ f² m/counts

If you look at the intermodulation at 14 (4+10) and 16 (6+10), 15 (5+10) would make any problem, thanks to the notch at 1f and 5f.

BUT, this absolute level of 165MHz is too tiny for the demodulator. From the level of the demodulated signal, I can say REFL165 has
too little SNR. We want to amplify it before the demodulator.

Can you measure this again with a directional coupler instead of the direct measurement with an attenuator?
The downstream has bunch of non-50Ohm components and may cause unknown effect on the tiny 165MHz signal.
We want to measure the spectrum as close situation as possible to the nominal configuration.

90MHz crap is the amplifier noise due to bad power bypassing or bad circuit shielding.

I have no comment on REFL33 as it has completely different amplification stages.

Where is the PD out spectrum measured with the coupler???

IMC WFS operating point seemed to get degraded.

- IMC WFS feedback was relieved.

- WFS servo was turned off.

- IMC alignment was tuned carefully

- /opt/rtcds/caltech/c1/scripts/MC/WFS/WFS_FilterBank_offsets was run

- WFS servo was turned on again 

To further reduce the RF power at 110MHz in the REFL165 chain, I made a twin-t notch in a pomona box.

It is tuned at 110.66MHz.

The inductor is Coil Craft 5mm tunable (164-09A06SL 100-134nH).
Without the 10Ohm resister (like a usual notch), the dip was ~20dB. With this configuration, the notch of -42dB was realized.

Q >> Please measure the RF spectrum again with the notch.

Sensing matrix calculation using DTT + Matlab

Note: If the signal phase is, for example,  '47 deg', the phase rotation angle is -47deg in order to bring this signal to 'I' phase.

Note2: As I didn't have the DQ channels for the actuation, only the relative signs between the PDs are used to produce the radar chart.
This means that it may contain 180deg uncertainty for a particular actuator. But this does not change the independence (or degeneracy) of the signals.


=== Sensing Matrix Report ===
Test time: 2014-11-11 08:14:00
Starting GPS Time: 1099728855.0
 

== PRCL ==
Actuation frequency: 621.13 Hz
Suspension (PRM) response at the act. freq.: 5.0803e-14/f^2 m/cnt
Actuation amplitude: 20.3948 cnt/rtHz
Actuation displacement: 1.0361e-12 m/rtHz
 
C1:LSC-AS55_I_ERR_DQ 4.20e+10
C1:LSC-AS55_Q_ERR_DQ -1.91e+11
==> AS55: 1.95e+11 [m/cnt] -24.58 [deg]
C1:LSC-REFL11_I_ERR_DQ 3.17e+12
C1:LSC-REFL11_Q_ERR_DQ -8.04e+10
==> REFL11: 3.17e+12 [m/cnt] -18.20 [deg]
C1:LSC-REFL33_I_ERR_DQ 4.15e+11
C1:LSC-REFL33_Q_ERR_DQ 4.28e+10
==> REFL33: 4.17e+11 [m/cnt] -137.11 [deg]
C1:LSC-REFL55_I_ERR_DQ 1.90e+10
C1:LSC-REFL55_Q_ERR_DQ -9.91e+09
==> REFL55: 2.14e+10 [m/cnt] -58.58 [deg]
C1:LSC-REFL165_I_ERR_DQ -1.16e+11
C1:LSC-REFL165_Q_ERR_DQ -3.14e+10
==> REFL165: 1.20e+11 [m/cnt] 45.20 [deg]
 
 
== MICH ==
Actuation frequency: 675.13 Hz
Suspension (ITMX) response at the act. freq.: 1.0312e-14/f^2 m/cnt
Suspension (ITMY) response at the act. freq.: 1.0224e-14/f^2 m/cnt
Actuation amplitude: 974.2957 cnt/rtHz
Actuation displacement (ITMX+ITMY): 2.0007e-11 m/rtHz
 
C1:LSC-AS55_I_ERR_DQ 2.55e+12
C1:LSC-AS55_Q_ERR_DQ 4.51e+12
==> AS55: 5.18e+12 [m/cnt] 113.51 [deg]
C1:LSC-REFL11_I_ERR_DQ -4.84e+10
C1:LSC-REFL11_Q_ERR_DQ -4.07e+09
==> REFL11: 4.85e+10 [m/cnt] 168.06 [deg]
C1:LSC-REFL33_I_ERR_DQ 2.06e+10
C1:LSC-REFL33_Q_ERR_DQ -9.39e+09
==> REFL33: 2.26e+10 [m/cnt] -167.51 [deg]
C1:LSC-REFL55_I_ERR_DQ 2.52e+09
C1:LSC-REFL55_Q_ERR_DQ -1.02e+10
==> REFL55: 1.05e+10 [m/cnt] -107.09 [deg]
C1:LSC-REFL165_I_ERR_DQ -1.79e+10
C1:LSC-REFL165_Q_ERR_DQ -5.50e+10
==> REFL165: 5.79e+10 [m/cnt] 102.02 [deg]


== SRCL ==
Actuation frequency: 585.13 Hz
Suspension (SRM) response at the act. freq.: 5.5494e-14/f^2 m/cnt
Actuation amplitude: 1176.3066 cnt/rtHz
Actuation displacement: 6.5278e-11 m/rtHz
 
C1:LSC-AS55_I_ERR_DQ -9.90e+10
C1:LSC-AS55_Q_ERR_DQ -1.18e+11
==> AS55: 1.54e+11 [m/cnt] -76.89 [deg]
C1:LSC-REFL11_I_ERR_DQ 2.96e+08
C1:LSC-REFL11_Q_ERR_DQ 4.78e+08
==> REFL11: 5.62e+08 [m/cnt] 41.42 [deg]
C1:LSC-REFL33_I_ERR_DQ -2.93e+09
C1:LSC-REFL33_Q_ERR_DQ 1.23e+10
==> REFL33: 1.27e+10 [m/cnt] -39.63 [deg]
C1:LSC-REFL55_I_ERR_DQ 3.71e+09
C1:LSC-REFL55_Q_ERR_DQ 2.78e+09
==> REFL55: 4.63e+09 [m/cnt] 5.86 [deg]
C1:LSC-REFL165_I_ERR_DQ -1.80e+10
C1:LSC-REFL165_Q_ERR_DQ 2.68e+10
==> REFL165: 3.23e+10 [m/cnt] -26.02 [deg]
 

Demodulation phases of the day

    'C1:LSC-AS55_PHASE_R = -53'
    'C1:LSC-REFL11_PHASE_R = 16.75'
    'C1:LSC-REFL33_PHASE_R = 143'
    'C1:LSC-REFL55_PHASE_R = 31'
    'C1:LSC-REFL165_PHASE_R = 150'


MC WFS was oscillative at 1Hz. I've reduced the servo gain further (x1, x1, x10, x1, x1, and x10).

The MC mirrors were realigned, and the WFS offsets were reset.

[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)

From the measured OLTF, the dynamics of the damped suspension was inferred by calculating H_damped = H_pend / (1+OLTF).
Here H_pend is a pendulum transfer function. For simplicity, the DC gain of the unity is used. The resonant frequency of the mode
is estimated from the OLTF measurement. Because of inprecise resonant frequency for each mode, calculated damped pendulum
has glitches at the resonant frequency. In fact measurement of the OLTF at the resonant freq was not precise (of course). We can
just ignore this glitchiness (numerically I don't know how to do it particularly when the residual Q is high).

Here is my recommended values to have the residual Q of 3~5 for each mode.

MC1 SUS POS current  75   -> x3   = 225
MC1 SUS PIT current   7.5 -> x2   =  22.5
MC1 SUS YAW current  11   -> x2   =  22
MC1 SUS SD  current 300   -> x2   = 600

MC2 SUS POS current  75   -> x3   = 225
MC2 SUS PIT current  20   -> x0.5 =  10
MC2 SUS YAW current   8   -> x1.5 =  12
MC2 SUS SD  current 300   -> x2   = 600

MC3 SUS POS current  95   -> x3   = 300
MC3 SUS PIT current   9   -> x1.5 =  13.5
MC3 SUS YAW current   6   -> x1.5 =   9
MC3 SUS SD  current 250   -> x3   = 750

This is the current setting in the end.

MC1 SUS POS 150
MC1 SUS PIT  15
MC1 SUS YAW  15
MC1 SUS SD  450

MC2 SUS POS 150
MC2 SUS PIT  10
MC2 SUS YAW  10
MC2 SUS SD  450


MC3 SUS POS 200
MC3 SUS PIT  12
MC3 SUS YAW   8
MC3 SUS SD  500

Where did these 200Hz, 6kHz come from?

I wonder what are the correct filters to be incorporated in the filter banks for the cav pole compensarion.

Facts:

1. ALS Common and Diff have the cavity pole for the green (fcav_GR)

2. IR DARM has the cavity pole of the arms for IR (fcav_IR_DARM)

3. IR CARM (REFL, POP, POX, or POY) has the double cavity pole (fcav_IR_CARM)

Calculations:

1. T(ITM_GR) = 1.094%, T(ETM_GR) = 4.579% => F=108.6 (cf. https://wiki-40m.ligo.caltech.edu/Core_Optics)
L = 37.8 m (cf. http://nodus.ligo.caltech.edu:8080/40m/9804)
=> fcav_GR = c /( 4 L F) = 18.3 kHz ... ignore

2. T(ITM_IR) = 1.384%, T(ETM_IR) = 13.7ppm => F=450.4
=> fcav_IR_DARM = 4.40 kHz

3. The common cavity pole is lower than fcav_IR by factor of power recycling gain.
=> fcav_IR_CARM = fcav_IR / (P_TR * T_PRM)
P_TR is normalized for the locked arm cavity with the PRM misaligned.
T_PRM is 5.637%

e.g. for the TR of 100, fcav_IR_CARM = 4.40/(100*0.05637) = 780Hz

                         (IR CARM) o--|
                                      +--[CARM 780Hz zero / ??? pole]
(ALSX) o--|   |-[ALS C 780Hz pole]----|
          | M |
(ALSY) o--|   |-[ALS D 4.40kHz pole]--|
                                      +--[DARM 4.40kHz zero / ??? pole]
                         (IR DARM) o--|
???Hz pole is to ensure the servo filters does not have infinite gain at f=infinite, but in practice we probably can ignore it as long as it is provided by a roll-off filter

The other night (before the holidays), I tried ALS offset tuning  with IR POX/POY signals and it worked pretty good.
I didn't need to tune the offset after the scanning script stopped.

Once we are at the foot hill of the main resonance, I ran something like

ezcaservo -r C1:LSC-POX11_I_MON C1:LSC-ALSX_OFFSET -g -0.003 &
ezcaservo -r C1:LSC-POY11_I_MON C1:LSC-ALSY_OFFSET -g -0.003 &

(... I am writing this with my memory. I could be wrong but conceptually the commands looked like these)

I wonder what to do with the X arm.

The primary purpose of the ASS is to align the arm (=transmission), and the secondary purpose is to adjust the input pointing.

As the BS is the only steering actuator, we can't adjust two dof out of 8 dof.
In the old (my) topology, the spot position on ITMX was left unadjusted.

If my understanding of the latest configuration, the alignment of the cavity (=matching of the input axis with the cavity axis)
is deteriorated in order to move the cavity axis at the center of the two test masses. This is not what we want as this causes
deterioration of the power recycling gain.

I tried to find my own entry and faced with a strange behavior of the elog.

The search button invoked the following link and no real search has been done:

http://nodus.ligo.caltech.edu:8080/40m/?mode=summvry&reverse=0&reverse=1&npp=50&m&y&Authorthor=Koji

Summvry? Authorthor?

If I ran the following link, it returned correct search. So something must be wrong.

http://nodus.ligo.caltech.edu:8080/40m/?mode=summary&npp=50&Author=Koji

Was the screen modified directly on LSC_OVERVIEW.adl?
Even if so, that's OK. I'll incorporate the change to the screen making script once I'm back.

I checked the situation of ASS. I wanted to know how much we are away from the maximum transmittion.

Conclusion:
ASS makes the X arm shifted from the maximum transmission. This causes the contrast degraded by ~3%.
We need to fix the Xarm ASS so that it can maximize the transmission and ignor the spot centering at ITMX.

Conditioning before the measurement:

- ASDC offset was removed
- X&Y arm was aligned by ASS

With ASS:

Average transmission: 0.86
Pmax = 1045 +/- 9 cnts
Pmin = 22 +/- 4 cnts

==> Contrast = (Pmax - Pmin)/(Pmax+Pmin) = 0.960+/-0.007

After manual alignment of the X arm (ignoring spot centering):

Average transmission: 0.88
Pmax = 1103 +/- 11 cnts
Pmin = 5 +/- 1 cnts

==> Contrast = (Pmax - Pmin)/(Pmax+Pmin) = 0.991+/-0.002

PMC aligned.

PMC Trans increased from 0.740 to 0.782

IMC Trans increased from 16200 to 17100

The X-end IR Trans path was cleaned up.

I have been investigating the Xarm ASS issue. The Xarm ASS sensors behaved not so straight forward.
I went to the X-end table and found some suspect of clipping and large misalignmnet in the IR trans path.
Facing with the usual chaos of the end table, I decided to clean-up the IR trans path.

The optical layout is now slightly better. But the table is, in general, still dirty with bunch of stray optics,
loose cables and fibers. We need more effort to make the table maintained in a professional manner.

- Removed unnecessary snaking optical path. Now the beam from the 1064/532 separator is divided by a 50-50 BS before the QPD without
any other steering mirrors. This means the spot size on the QPD was changed as well as the alignment. The spot on the QPD was aligned
with the arm aligned with the current (=not modified) ASS. This should be the right procedure as the spot must be centered on the end mirror
with the current ASS.

- After the 50-50 BS there is an HR steering mirror for the Thorlab PD.

- A VIS rejection filter was placed before the 50-50 BS. The reflection from the filter is blocked with a razor blade dump.

Important note to everyone including Steve:
The transmission of the VIS rejection filter at 1064nm is SUPER angular sensitive.
A slight tilt causes significant reduction of 1064nm light. Be careful.

- As we don't need double VIS filter, I removed the filter on the QPD.

- X-End QPD was inspected. There seemed large (+/-10%) gain difference between the segments.
They were corrected so that the values are matched when the beam is only on one segment.
The corrections were applied at C1:SUS-ETMX_QPDx_GAIN (x=1, 2, 3, or 4).

I decided to put "-20dB" filters on C1:SUS-ETMi_QPD_SUM and C1:SUS-ETMi_TRY (i = X or Y)
in order to make their gain to be reasonable (like 0.123 instead 0.000123 which is unreadable).
Jenne's normalization script reads relative values and the current gains instead of the absolute values.
Therefore the script is not affected.

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.)

c1lsc had 60 full-rate (16kS/s) channels to record. This yielded the LSC to FB connection to handle 4MB/s (mega-byte) data rate.
This was almost at the data rate limit of the CDS and we had frequent halt of the diagnostic systems (i.e. DTT and/or dataviewer)

Jenne and I reviewed DAQ channel list and decided to remove some channels.  We also reviewed the recording rate of them
and reduced the rate of some channels. c1lsc model was rebuilt, re-installed, and restarted. FB was also restarted. These are running as they were.
The data rate is now reduyced to ~3MB nominal.

The following is the list of the channels removed from the DQ channels:

AS11_I_ERR
AS11_Q_ERR
AS165_I_ERR
AS165_Q_ERR
POP55_I_ERR
POP55_Q_ERR

The following is the list of the channels with the new recording rate:

TRX_SQRTINV_OUT 2048
TRY_SQRTINV_OUT 2048
DARM_A_ERR 2048
DARM_B_ERR 2048
MICH_A_ERR 2048
MICH_B_ERR 2048
PRCL_A_ERR 2048
PRCL_B_ERR 2048
CARM_A_ERR 2048
CARM_B_ERR 2048

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

We had persistent frustration by occasional unlock during ASSing.
Today, I added triggers to the servo gains in order to elliminate this annoyance.

Each ASS servo gain slider is multiplied with the corresponding LSC Trigger EPICS channel (i.e. C1:LSC-iARM_TRIG_MON, where i=X or Y).
This has been done by ezcaread modules in RCG.

The model and screen have been commited to svn.

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.

As the measurements have been done under feedback control, the lower RF peak height does not necessary mean
the lower optical gain although it may be the case this time.

These non-33MHz signals are embarassingly high!
We also need to check how these non-primary RF signals may cause spourious contributions in the error signals,
including the other PDs.

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.

The goals are:

- When the REFL path is dead (e.g. S_REFL = 0), the system goes back to the ordinary ALS loop. => True (Good)

- When the REFL path is working, the system becomes insensityve to the ALS loop
(i.e. The ALS loop is inactivated without turning off the loop.) => True when (...) = 0

Are they correct?

Then I just repeat the same question as yesterday:

S is a constant, and Ps are cavity poles. So,  approximately to say, (...) = 0 is realized by making D = 1/G_REFL.
In fact, if we tap the D-path before the G_REFL, we remove this G_REFL from (...). (=simpler)
But then, this means that the method is rather cancellation between the error signals than
cancellation between the actuation. Is this intuitively reasonable? Or my goal above is wrong?

- I built another beat setup on the PSL table at the South East side of the table.
- The main beam is not touched, no RF signal is touched, but recognize that I was present at the PSL table.
- The beat note is found. The 3rd order sideband was not seen so far.
- A PLL will be built tomorrow. The amplifier box Manasa made will be inspected tomorrow.

- One of the two beams from the picked-off beam from the main beam line was introduced to the beat setup.
(The other beam is used of for the beam pointing monitors)
There is another laser at that corner and the output from this beam is introduced into the beat setup.
The combined beam is introduced to PDA10CF (~150MHz BW).

- The matching of the beam there is poor. But without much effort I found the beat note.
  The PSL laser had 31.33 deg Xtal temp. When the beat was found, the aux laser had the Xtal temp of 40.88.

- I could observe the sidebands easily, with a narrower BW of the RF analizer I could see the sidebands up to the 2nd order.
  The 3rd order was not seen at all.

- The beat note had the amplitude of about -30dBm. One possibility is to amplify the signal. I wanted to use a spare channel
of the ALS/FOLL amplifier box. But it gave me rather attenuation than any amplification. I'll look at the box tomorrow.

- Also the matching of two beams are not great. The PD also has clipping I guess. These will also be improved tomorrow

- Then the beat note will be locked at a certain frequency using PLL so that we can reduce the measurement BW more.

The RF analyzer was returned to the control room. There are two beat notes from X/Y confirmed.

I locked the arms and aligned them with ASS.

When the end greens are locked at TEM00, X/Y beat amplitudes were ~33dBm and ~17dBm. respectively.
I don't judge if they are OK or not, as I don't recall the nominal values.

[SUCCESS] The 3f sideband cancellation seemed worked nicely.

- Beat effeciency improved: ~30% contrast (no need for amplification)

- PLL locked

- 3f modulation sideband was seen

- The attenuation of the 55MHz modulation and the delay time between the modulation source was adjusted to
have maximum reduction of the 3f sidebands as much as allowed in the setup. This adjustment has been done
at the frequency generation box at 1X2 rack.

- The measurement and receipe for the sideband cancellation come later.

- This means that I jiggled the modulation setup at 1X2 rack. Now the modulation setup was reverted to the original,
but just be careful to any change of the sensing behavior.

- The RF analyzer was returned to the control room.

- The HEPA speed was reduced from 100% (during the action on the table) to 40%.

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

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...)

Wonkey shape: Looks like a loop supression. Your http://nodus.ligo.caltech.edu:8080/40m/11016 also suggests it too, doesn't it?