I re-adjusted coil gains and f2a filters for PRM and BS.
I'm not sure what happened to PRM since I balanced on Feb 16(elog #8093).
Let's see if it helps PRMI locking or not.

========== PRM ==========

- Original DC coil gains

C1:SUS-PRM_ULCOIL_GAIN 1.049901772380000e+00
C1:SUS-PRM_URCOIL_GAIN -9.833961907160000e-01
C1:SUS-PRM_LRCOIL_GAIN 9.543042546630000e-01
C1:SUS-PRM_LLCOIL_GAIN -9.713568522590000e-01
- New DC coil gains

multiplier factors are :
UL = 0.928167
UR = 1.061448
LR = 0.941659
LL = 1.068726
Set C1:SUS-PRM_ULCOIL_GAIN to 0.974482231437
Set C1:SUS-PRM_URCOIL_GAIN to -1.04382410014
Set C1:SUS-PRM_LRCOIL_GAIN to 0.898628670041
Set C1:SUS-PRM_LLCOIL_GAIN to -1.03811466772

C1:SUS-BS_ULCOIL_GAIN 1.037692431800000e+00
C1:SUS-BS_URCOIL_GAIN -1.016268296990000e+00
C1:SUS-BS_LRCOIL_GAIN 9.660800075010000e-01
C1:SUS-BS_LLCOIL_GAIN -9.791833500410000e-01
- New DC coil gains

multiplier factors are :
UL = 1.017855
UR = 1.023207
LR = 0.956184
LL = 1.002755
Set C1:SUS-BS_ULCOIL_GAIN to 1.0562177496
Set C1:SUS-BS_URCOIL_GAIN to -1.03985422464
Set C1:SUS-BS_LRCOIL_GAIN to 0.923750146975
Set C1:SUS-BS_LLCOIL_GAIN to -0.981880297098

Since we have setup POP22 PD now(elog #8192), we could confirm that sideband power builds up when PRMI is sideband locked.

Plot:
Here's some plot of PRC intra-cavity powers and MICH,PRCL error signals. As you can see from POP22, we locked at the peak of 11MHz sideband. There was oscillation at ~500 Hz, but we couldn't optimize the gain yet.

Movie:
Here's 30 sec movie of AS, POP, REFL when acquiring (and losing) PRMI sideband lock. It was pretty hard to take a movie because it locks pretty seldom (~1 lock / 10 min).

Locking details: For MICH lock, we used ITMs instead of BS for reducing coupling between PRCL.
Also, AS55 phase rotation angle was coarsely optimized by minimizing MICH signal in I.
For PRCL lock, we used REFL55_I_ERR instead of REFL33_I_ERR. It had better PDH signal and we coarsely optimized phase rotation angle by minimizing PRCL PDH signal in Q.

Issues: - We tried to use REFL55_Q_ERR to lock MICH, but couldn't. It looks like REFL error signals are bad.
- We tried to use POP22_I_ERR to trigger PRCL lock, but it didn't work.

We locked PRMI in carrier. Measured power recycling gain was ~25. Plot:
Here's some plot of PRC intra-cavity powers and MICH,PRCL error signals. As you can see from POPDC, cavity buildup was about 400, which means power recycling gain was ~25. Power recyling gain is fluctuating up to ~45 during lock. We need some gain normalization or something.

Movie:
Here's 30 sec movie of AS, POP, REFL when acquiring PRMI carrier lock. Although there's oscillation when acquiring lock, beam spot motion is less and stable compared with the past(before flipping PR2).

I swept the frequency of RF input to the beatbox to calibrate and check linearity range of phase tracker. Calibration factors are; C1:ALS-BEATX_FINE_PHASE_OUT 52.1643 +/- 0.0003 deg/MHz
C1:ALS-BEATY_FINE_PHASE_OUT 51.4788 +/- 0.0003 deg/MHz

There was systematic error to the linearity check, but at least, calibration factor changes less than 50 % in the frequency range of 10 MHz to more than 500 MHz.

What I did:
Used network analyzer(Aligent 4395A) to sweep the frequency RF input to the beatbox and getdata of phase tracker signal. I swept from 10 Hz to 500 MHz with 501 points in 50 sec. This sweep is slow enough considering we could lock the 40m arms (typical speed of a mirror is 1 um/s, so bandwidth of the phase tracker should be more than 1 um/sec / 40 m * 3e14 Hz = 75 MHz/s).
RF amplitude was set to be -3 dBm and splitted into BEATX and BEATY.

Result:
Plots for BEATX and BEATY are below;

Discussion:
- Considering delay line length is ~30m, expected calibration factor is;

- Since frequency sweep of network analyzer is not continuous, phase tracker output is like steps with some ringdown. This makes some systematic error for checking linearity. I'm planning to do slower sweep or continuous sweep. Also, the phase tracker seems like he can exceed 500 MHz.

I measured noise level of the phase tracker by inputting constant frequency RF signal from marconi. Measured frequency noise was ~2 Hz/rtHz @ 100 Hz. It's not so good.

What I did:
1. Unplugged 11MHz marconi and put RF signal to the beatbox from this. Frequency and amplitude I put are 100 MHz and -3 dBm.
2. Measured spectra of phase tracker outputs, C1:ALS-BEATX_FINE_PHASE_OUT, C1:ALS-BEATY_FINE_PHASE_OUT.
3. Calibrated using the factor I measured (elog #8199).
4. Put marconi back to orignal settings.

Result:

Discussion:
- According to Schilt et al., this noise level is not so good.
- By changing the delay-line cable length or optimizing whitening filter etc., we can improve this.

POX11 oscillation at 630 Hz was stopped by installing 630 Hz resonant gain to LSC_XARM.
After few hours, oscillation stopped. So I removed the resonant gain.
Our guess is that 630 Hz peak is some violin mode or something, and it was excited somehow, and didn't stopped for very long time because of its high Q. It coupled into POY11 somehow (scattering, electronics, etc).

I tuned alignment, gains and filters to achieve stable lock of PRMI.
It now locks quite stably with UGF of ~100 Hz. Measured power recycling gain at maximum is ~ 25.

MICH servo is always on. PRCL loop turns on by trigger using POP DC. Boost filters and resonant gains turn on by triggers using POP DC.
Gain normalization was not used.

Openloop transferfunctions:
MICH: UGF ~90 Hz, phase margin ~40 deg
PRCL: UGF ~100 Hz, phase margin ~50 deg (cf. Fitted gain was same as half-PRC: elog #8053)

Power recycling gain:
POP DC when unlocked is 6, when locked is 2200-2500, and when dark is 0. So, power recycling gain is ~ 22 to 25. Value without any loss in PRMI is 45 (elog #6947). Alignment was pretty critical to achieve this recycling gain and stable lock. There was oscillation at 630 Hz when locked, which is similar to the one we saw in POX11 (elog #8203).

Youtube:

AS(top left), POP(top right), REFL(bottom left), and ETMYT(bottom right). ETMY was mis-aligned, but you can see the beam at ETMYT after PRMI was carrier locked.

MICH/PRCL coupling:
I measured "sensing matrix" of PRMI by tickling PRM/ITMs/BS at 8.5 Hz and measuring 8.5 Hz peak height of AS55_Q, REFL55_I spectra during PRMI lock (attached is an example measurement of PRM). Below table is the result. AS55_Q has ~5% of sensitivity to PRCL compared with MICH. Also, BS introduces REFL55_I signal considerably. And also, there seems to be an imbalance in actuation efficiency between ITMX and ITMY.

AS clipping:
AS was clipped inside the vaccuum the other day(elog #8198). So, I tried to avoid AS clipping by aligning BS this morning. But it turned out that avoiding AS clipping by BS makes ITMX beam centering worse. Maybe we should center the beam on Yarm first next week.

Next:
- calculate expected PRMI recycling gain with loss, PR2 filpped
- beam centering on the arms
- IPANG, IPPOS, Y green, X green
- PRMI g-factor measurement

We found that our phase tracker noise is currently limited by the noise introduced in DAQ.
We confirmed that the frequency noise was improved from 2 Hz/rtHz to 0.4 Hz/rtHz by increasing the gain of the whitening filter.
The whitening filters should definitely be refined.

What we did:
1. Put constant frequency RF input to the beatbox from Marconi and measured noise spectrum of the beatbox output(BEATX I) after the whitening filter with a spectrum analyzer. Noise floor level was ~0.2 Hz/rtHz at carrier frequency range of 15-100 MHz. Calibration factor of the beatbox output was ~380 mV/MHz.

2. Measured noise spectrum of C1:ALS-BEATX_FINE_I_OUTPUT(figure below). The noise floor didn't change when there was RF input of 100 MHz from Marconi(blue) and DAQ input was terminated (green). Also, C1:ALS-BEATX_FINE_I_IN1(which is before unwhitening filter) showed a flat spectrum. These show our spectrum is limited by DAQ noise, which is introduced after the whitening filter.

3. We increased the gain of whitening filter by x20 to show frequency noise performance can be improved by better whitening filter(red). But we can not use this setup as the other quadrature will be saturated by a too much gain at DC. Thus we need to carefully consider the signal level and the gain distribution of the whitening filters.

Next:
- Better whitening filters. The current one consists of zero 1 Hz and pole 10 Hz with DC gain of 5 using SR560.
- Better beatbox. We can increase the RF input power to the mixer and unify the preamplifier and the whitening filter in the box.

We calibrated oplev for PRM. Calibration factor for C1:SUS-PRM_OL(PIT|YAW)_IN1 are; OLPIT: 15.6 +/- 0.3 counts/mrad
OLYAW: 17.8 +/- 0.3 counts/mrad

We needed these values for g-factor measurement of PRC using angle dithering method.

What we did:
1. Adjusted QPD offsets (C1:SUS-PRM_OL[1-4]_OFFSET) by zeroing the output when turned oplev laser was turned off.
2. Centered PRM oplev beam on QPD using steering mirror.
3. Mounted PRM oplev QPD on a xy-stage and centered the beam on QPD.
4. Moved QPD in x and y using micrometers and measured dependance of C1:SUS-PRM_OL(PIT|YAW)_IN1 on QPD displacement.
5. Measured the path length of PRM oplev returning beam. We get the in-vac path length using optical layout CAD. We measured out of vac path using scale and tape measure.
6. Dismounted PRM QPD from the stage and put it back to the original position.

Result:
1. Figures below are OLPIT/OLYAW dependance on micrometer displacement moved in x and y. Error bars are measured fluctuation in the signal.

moved in x: moved in y:

2. We fitted the result by error function to get slope at zero crossing point. We also linear-fitted the other degree of freedom to get cross coupling between x and y. Slopes we get were;
micrometer OLPIT OLYAW
moved in x 4.68 +/- 0.08 0.01 +/- 0.03
moved in y -5.32 +/- 0.10 0.11 +/- 0.03 (counts/mm)

3. Measured the path length of PRM oplev returning beam was 3340 +/- 20 mm. This gives you the calibration factors above.

Discussion: [Precision] According to Jamie's calculation, expected g-factor for PRC in PR2-flipped PRMI is 0.966/0.939 (elog #8068). We care about the g-factor change in ~0.01. Also, intra-cavity power dependance on mirror angle is proportional to 1/(1-g). So, we need to calibrate mirror angle in ~few 10 % of precision in order to get useful g-factor from angle dithering measurement. Measurement precision here meets this requirement.

[x/y coupling] Measured x/y coupling was less than 2 %. We assumed gains in 4 QPD quadrants are same, and assumed QPD is mounted well in x/y axes. These assumptions are OK considering precision we need.

[x/y difference] Calibration factors for OLPIT/OLYAW are different by ~10 %. This is not so crazy considering the incident angle on the QPD (~20 deg) and elliptic beam shape.

I measured intra-cavity power dependance on mirror misalignment. Intra-cavity power of PRC in PRMI degrates roughly 20 % when there's 0.5 mrad 5 urad misalignment. (edited by YM) Currently, PRMI lock is not so stable, so it is hard to do this measurement and error bars are huge.

Measurement method:
0. Align the cavity and lock.
1. Misalign one optic and measure oplev output value and intra-cavity power.
2. Also, dither the optic in pitch or yaw in 8.5 Hz and get demodulated amplitudes at 8.5 Hz of oplev output and intra-cavity power using tdsdmd.
3. Misalign the optic again and do the same things.

1. gives intra-cavity power dependence on mirror misalignment directly, but 2. should give better S/N because of dithering.

Scripts: /opt/rtcds/caltech/c1/scripts/dither/dithergfactor.py does these things, and ./plotgfactor.py plots the result.
They work quite well, but it should be made better so that

- it checks if the cavity is locked
- automatically change the oplev calibration factor for each optic
- automatically adjusts the region and modulation amplitude
- read data with better error evaluation

etc...

PRMI alignment:
Y green looks like it drifted quite a lot somehow. If we start aligning Yarm to Y green, we get AS and POP beam at different spot on camera compared with last week. Also, TRY and TRX only goes as high as ~0.7. Since we have A2L now (elog #8229), let's start using Yarm spot positions as input pointing reference.

PRMI locking details:
Same as in elog #8212, but I changed gains in the lock acquisition mode.

I made gainx5 in LSC_MICH filter bank so that it increases the overall gain when locked by trigger.
I also made gainx0.3 in LSC_PRCL filter bank so that it reduces the overall gain when locked by trigger.

Result for PRC in PRMI:
For PRMI, I couldn't done dithering method because dithering takes time to measure and I could not hold PRMI locking during the measurement.
Below is the result when reading just the DC values. Mirror angle is calibrated by oplev (elog #8221). Error bars are huge because of beam motion mainly in yaw.

PRM in pitch: PRM in yaw:

Results for the arms:
For the arms, I could do both in DC and dithering. Below are the results, but ITMs misalignments are not calibrated because we don't have calibrated oplev yet.
Results for the arms can be used to verify this method because we know g-factors of the arms from mode scan.

ITMX in yaw: ITMY in yaw:

By the way: I found C1:SUS-ITMY_LSC_GAIN is somehow set to be 2.895 recently. I think this should be 1.0. Maybe this is why we had actuation imbalance in ITMs(elog #8212).

Next:
- more stable lock
- calibrate ITM oplevs to apply this method to the arms
- derive g-factor from these measurements
- measure PRM angular motion spectra using calibrated oplev

We calibrated oplev for ITMY. Calibration factor for C1:SUS-ITMY_OL(PIT|YAW)_IN1 are; OLPIT: 6.29 +/- 0.11 counts/mrad OLYAW: 5.74 +/- 0.09 counts/mrad Note that there was ~10% of coupling between pitch and yaw. This is large considering statistical error, but I think this is from QPD mounted rotated (by ~5 deg).

I fitted intra-cavity power dependance on mirror misalignment plot with parabola to get the g-factor.

Y arm (tangential) g = 0.44 +0.01 -0.01 (measured value before was 0.3765 +/- 0.003elog #6938) PRC (sagittal) g = 0.97 +0.01 -0.04 (expected value is 0.939elog #8068) PRC (tangential) g = 0.96 +0.02 -0.05 (expected value is 0.966elog #8068)

Error bars are just statistical errors from the fitting. Estimated systematic error is ~0.04 (or more). Here, I assumed PR2/PR3 to be flat to make the calculation simple. I assumed PRC to be curved PRM - flat ITM cavity, and Y arm to be curved ETMY - flat ITMY cavity.

g-factor calculation:
Intra-cavity power decrease can be written as

dP/P = (dx/w0)**2 + (dt/a0)**2

where dx and dt are translation and tilt of the beam axis introduced by mirror misalignment. w0 is waist size and a0 is divergence angle (= lamb/(pi*w0)).

When considering a flat-curved cavity with cavity length L, dx and dt can be expressed as;

using misalignments of mirrors(a1,a2). Here, mirror1 is curved, and mirror2 is flat. See Kakeru document /users/OLD/kakeru/oplev_calibration/oplev.pdf for derivation.

So, power decrease by flat mirror misalignment can be expressed as

dP/P = pi*L/lamb * g/(1-g)/sqrt(g*(1-g)) * a2**2

For curved mirror is

dP/P = pi*L/lamb * 1/(1-g)/sqrt(g*(1-g)) * a1**2

We can derive g-factor by measuring dP dependance on a1/a2.

Script:
My script lives in /opt/rtcds/caltech/c1/scripts/dither/gfactormeasurement/plotgfactor.py.
It least fitts data with parabola (scipy.optimize.leastsq) and gets g-factor value from bisection (scipy.optimize.bisect).

Result:
Below are the plots of fitted curves.

Systematic effect: [oplev calibration] We noticed QPD rotation when calibration oplevs (elog #8232). ~5 deg of rotation makes 10% of systematic error to the oplev calibration and this introduces ~0.04 of error to g-factor values. This

[oplev linear range] Oplev linear range is ~100 urad, so this is OK.

[assumption of flat PR2/PR3]Result here doesn't tell you g-factor of PRM itself, but some "effective g-factor" of PRM/PR2/PR3 combination. We can compare with FINESSE result.

[intra-cavity power drift] If there's significant intra-cavity power drift during the measurement, if effects parabola fitting. We can make this affect small by sweeping the mirror alignment in both direction and take average.

By the way:
I kept getting PRC g-factor of something like 0.999999 because I had power normalization mistake in my calculation. My script worked for Yarm because TRY is already normalized.
Also, I was multiplying the oplev calibration factor wrong last night (see elog #8230).

Next:
- Compare with FINESSE result.
- Is this g-factor enough? Is this presicion enough? Calculate from mirror angluar motion.
- More stable lock of PRMI.
- Try dithering method to measure g-factor to check consistency and also to study systematic effect.

I measured PRM angular motion spectra (in daytime today).
PRM angular motion is ~ 10 urad in RMS when undamped and ~1 urad in RMS when damped.
If PR2/PR3 angular motions are something like this, and their motion are not enhanced when PRC is locked, measured g-factor of PRC looks OK. But considering the error we have, maybe we are not OK yet. We need calculation.

Free swing MI differential length is 86 nm RMS and residual length when locked is 0.045 nm RMS(in-loop).
Looks very quiet. Comparison with PRMI is the next step.

Openloop transfer function:
OLTF of simple MI lock using AS55_Q_ERR as error signal and ITMs as actuators is below.
UGF ~ 90 Hz, phase margin ~ 40deg
I added 16 Hz resonant gain to suppress bounce mode.

MI differential length spectra:
Below. Calibration was done using calibrated AS55_Q_ERR and actuator response(elog #8242)

Expected free swing is calculated using

x_free = (1+G)/G * A * fb

where G is openloop transfer function, A is actuator response, fb is feedback signal(C1:LSC_ITMX/Y_IN1) spectrum. I used A as simple pendulum with resonant frequency at 1 Hz, Q = 5. Since free swing RMS is dominated by this resonance, RMS depends on this Q assumption.

We temporarily centered the beam on IPANG to see input pointing drift. From eyeball, drift was ~ 0.1 mrad/h in pitch.
What we did:
1. Aligned TT1/TT2 and aligned input pointing to Yarm.

2. Tweaked TT2 in pitch to center the beam on the first steering mirror of IPANG path. We still saw Yarm flash in higher order modes at this point. Before tweaking, the beam was hitting at the top edge.

3. Centered the beam on IPANG QPD.

4. Moved IPPOS first steering mirror because IPPOS beam was not on the mirror (off in yaw, on mirror edge). Also, IPPOS beam was coming out clipped in yaw.

5. Centered the beam on IPPOS QPD. We put lens in the path to focus the beam on the QPD.

6. Left input pointing untouched for 4 hours.

7. Restored TT2 again. We tried to align Y arm with IPANG available, but it was not possible without touching TRY path and AS was also clipped.

Result:
Below is the trend of IPANG sum, X, and Y. IPANG Y (IBQPD_Y) drifted by ~0.8 counts in 4 hours. IPANG is not calibrated yet, but Jenne used her eyeball to measure beam position shift on IPANG steering mirror. It shifted by ~2 mm. This means, input pointing drifts ~0.1 mrad/h in pitch.

Discussion:
Compared with yaw, pitch drift is quite large considering beam size at ETMY(~5 mm). We can monitor input pointing drift in weekends get longer trend.

Note:
- IPANG and IPPOS are both changed from the state before pumping.

We measured AC response of PRM actuator using PRM-ITMY cavity.
Result is

PRM: (19.6 +/- 0.3) x 10^{-9} (Hz/f)^2 m/counts

It is almost the same as in 2011 (elog #5583). We took the same procedure as what Kiwamu did.

What we did:
1. Aligned PRMI in usual procedure, mis-aligned ITMX and locked PRM-ITMY cavity using REFL55_Q_ERR. POP DC was about 18 when locked.

2. Made UGF of PRM-ITMY cavity lock at 10 Hz and introduced elliptic LPF at 50 Hz(OLTF below).

3. Measured transfer function from C1:LSC_ITMY_EXC to C1:LSC_REFL55_Q_ERR. Dividing this by ITMY actuator response(measured in elog #8242) gives calibration of REFL55_Q.

4. Measured transfer function from C1:LSC_PRM_EXC to C1:LSC_REFL55_Q_ERR to calibrate PRM actuator.

Result:
Calibration factor for REFL55_Q for PRM-ITMY cavity was (1.37 +/- 0.02) x 10^9 counts/m (plot below). Error is mainly from statistical error of the average.

Measured AC response (50-200 Hz) of PRM is below.

Next:
- Measure free-run length spectrum of PRM-ITMY cavity and compare with MICH free-run.

Measured free swing PRM-ITMY length was 230 nm RMS.
MI differential length was 85 nm RMS(elog #8248). This tells you that PR2, PR3 are not so noisy compared with usual suspensions.

Openloop transfer function:
OLTF of PRM-ITMY cavity lock using REFL55_Q_ERR as error signal and PRM as actuator is below.
UGF ~ 120 Hz, phase margin ~ 50 deg.
Somehow, phase delay was 460 usec, which is smaller than the empirical value 550 usec.

PRM-ITMY length spectra:
Below. Calibration was done using calibrated REFL55_Q_ERR and actuator response(elog #8255).

Mechanical shutter for PSL green is installed right in front of PSL doubling crystal.
This is for blocking PSL green when we want to measure the power of green beam from the arms.

The shutter was previously sitting on AS table un-used. Channel name to control this shutter was C1:AUX-SPS_Shutter. This should be renamed as C1:AUX-GREEN_PSL_Shutter.

Next: We are going to restore both arm green in parallel to PRMI work.

- Coarsely align IR input pointing and arms using A2L
- Align X green
- Install green DC PDs and cameras on PSL table

We should focus our work both on PRMI and ALS-FPMI(elog #8250).

CDS:
- Check out ASS and A2L working -JENNE (ALS done, ASS on going elog #8229) - Are all whitening filters for PDs toggling correctly? -JENNE, JAMIE (POX11 was OK, elog #8246)

PRMI locking:
- Adjust I/Q rotation angles for error signals -JENNE, YUTA (coarsely done elog #8212) - Adjust filters -JENNE, YUTA (coarsely done elog #8212) - Coil balancing for BS (and ITMs/ETMs) -YUTA (done elog #8182)
- Calculate sensing matrix for PRMI and convert them into physical units -JENNE, JAMIE - Measure sensing matrix for PRMI -JENNE, MANASA
- Measure 55 MHz modulation depth -KOJI

PRC characterization in PRMI:
- Measure PR2 loss from flipping -MANASA(on going elog #8063)
- Measure mode matching ratio -JENNE, YUTA - Measure finesse, PR gain -JENNE, YUTA (done elog #8212) - Calibrate PRM and/or ITM oplevs -MANASA, YUTA (done elog #8221)
- Measure g-factor by tilting PRM or ITMs -JAMIE, YUTA (coarsely done elog #8235, use other methods to check)
- Simulate intra-cavity power dependance on PRM tilt -JAMIE (see elog #8235)
- Calculate expected finesse, PR gain -JENNE
- Mode match and align aux laser from POY -ANNALISA (on going elog #8257)

ALS:
- Prepare for installation of new end tables on next vent -MANASA
- Install green DC PDs and cameras on PSL table -JENNE, MANASA
- Make ALS handing off to DARM/CARM LSC script -JENNE, YUTA
- Demonstrate FPMI using ALS -JENNE, YUTA - Phase tracker characterization -YUTA, KOJI (bad whitening elog #8214)
- better beatbox with whitening filters -JAMIE, KOJI

- I took the shutter from AS table to use it for the PSL green. It was sitting near MC REFL path unused (elog #8259).

- If X green lock is not tight, maybe temporarily increasing loop gain helps. This can be done by increasing the amplitude of the frequency modulation or increasing green refl PD gain. Also, if X green beam spot is too wiggly compared with Y green, it is maybe because of air flow from the air conditioner (elog #6849). I temporarily turned it off when I did X green steering last summer.

- X green transmission on PSL table reached ~270 uW last summer (elog #6849, elog #6914). Y green transmission is now ~240 uW and ~2700 counts at maximum. So, X green transmission should reach ~3000 in counts.

- Did you have to re-align TRX path? We moved the harmonic separator on X end table horizontally to avoid IR TRX clipping before beam centering on X arm (elog #8162). I wonder what is the current situation after the beam centering.

Summary:
We split the old SDSEN filters to SDSEN, SDSIDE, SDCOIL last week.
Along with this change, the TP channel number changed unfortunately.
So, we fixed them.
Also, we made FM9 do the output filter analog/digital switching.

What we did:
1. Changed the Simulink logic so that FM9 do the output filter switching, and checked the logic by probing
MAX333A for SDCOILs.

2. After making a new Simulink model and rebuilding, run the following incantation to burt restore filter
settings in /opt/rtcds/caltech/c1/target/c1SYS/c1SYSepics/ (See elog #3706)
sed -i 's/RO \(.*SW[12]R.*\)/\1/' autoBurt.req

3. DAQ channel numbers are listed in C1SYS.ini files in /cvs/cds/rtcds/caltech/c1/chans/daq/.
Channels with # signs are not activated. So, we changed, for example,

Plan:
- measure TFs and see if input and output filter switchings are working correctly
- make a switch that does all filter switching for all 5 OSEMS or 5 COILS
- put optical lever stuff
- fix offset sliders and offset switch
- put F2A filters in TO_COIL matrix (see elog #3769)
- make a nice graphical screen for MCs (like /cvs/cds/caltech/medm/c1/ioo/C1IOO_ModeCleaner.adl)
- write a script that activates DAQ we need
- make a plan

I report the results of the measurement to know how offset voltage of common mode servo changes when the gain is changed.

- Motivation: If discontinuous change of the offset happens when we change the gain, it could cause saturation somewhere and so make the length control down. So, we want to estimate effect of such discontinuous change.

- Method: In 1 (or In 2) was terminated with 50 ohm, and the output voltage at Out 2 was measured with a multimeter (D040180-B).

- Results are shown below. Acquired data are attached in .zip.

The upper shows input equiv. offset. The lower shows offset measured at Out 2.

As for both In1 and In2, strange behaviors can be seen between -17 dB and -16 dB.

This is because 5 amplifiers (or attenuators) are simultaneously enabled/disabled here. Similar situation occurs every change of 8 dB gain.

I fitted the data obtained with the FSR and linewidth measurements and I've got FSR and finesse of y-arm by fitting.

The fitted data and the fitting results are attached.

Summary:

FSR = 3.9704 MHz (ave. of two FSRs, 3.9727 MHz and 3.9681 MHz)

finesse = 401 +/- 11

estimated loss = 1812 (+456 / - 431) ppm

Detail:

I found peaks from the data and fitted each peak by Lorentzian, automatically with Python (the sourse code I used is attached).

3 parameters of Lorentzian for each peak and their fitting errors are attached.

Then, using 3 peaks of carrier resonance, I calculated FSR, finesse, and loss.

The error of finesse came from that of linewidth.

When calculating the loss, I used the value of 1.384 % for transmission of ITMY.

Note:

Since the finesse is mostly determined by the transmission of ITM, the relative error of loss estimation is larger (about 25 % ) though the relative error of finesse is about 3 %. Therefor we have to find the reason why each estimated linewidth varies that largely, and measure finesse more accurately.

I'd like to add a few calculation results, mode matching ratio for Y arm and modulation depth.

Here I assumed peaks marked in the bottom figure shown in elog 11738 as resonances of carrier and modulated sidebands and others as resonances of HOM.

- mode matching ratio = 94.92 +/- 0.19 %WRONG

How I calculated: for each peak of carrier, you can find 6 peaks of HOM resonaces. Then I calculated the sum of the hight of 6 peaks divided by the hight of carrier resonance peak, and took average of this values for 3 resonance peaks of carrier.

- modulation depth = 0.390 +/- 0.062WRONG

How I calculated: I took average of the hight of 6 peaks of modulated sideband resonance, and normalized it with the hight of peaks of carrier resonance. Using the relation 'normalized hight' = (J_1(m)/J_0(m))^2, I got modulation depth, m.

There are two modulation frequencies that make it to the arm cavities, at ~11MHz and ~55MHz. Each of these will have their own modulation depth indepedent of each other. Bundling them together into one number doesn't tell us what's really going on.

I'm sorry. I misunderstood two things when writing elog 11741: the number of modulation frequencies, and how to distinguish modulation peaks and HOM peaks.

Now, I report about interpretation of the peaks marked in grey in Attachment #1 in elog 11745.

Summary:

The peaks marked in grey are interpreted as 3rd and 4th HOM resonance, if we assume that the radius of curvature of ETMY is slightly different from measured value. (measured: 57.6 m --> assumed: 59.3 m)

What I have done:

I plotted the differences in frequency between HOM peaks and 00 mode peaks (see Attachment #1) vs. expected orders of modes. The plot is shown in Attachement #2.

By fitting these data points, I calculated most likely value of gradient of this plot. This value corresponds: g_ITMYg_ETMY=0.3781. However, measured data of the radii of curvature suggests that g_ITMYg_ETMY=0.358. Assuming that this disagreement comes from the difference between measured and real values of ROC of ETMY (ITM is almost flat so that change of ROC of ITM doesn't have significant effect on g_ITMg_ETM), ROC of ETMY should be 59.3 m, different from measured value 57.6 m.

What I'd like to know:

-- Is such disagreement of ROC usual? Could it happen?

-- Are there any other possible explanations for this disagreement (or interpretations of the peaks marked in grey)?

The uncertainty came from the residual of linear fitting and based on my estimation,

ROC_ETMY = 59.3 +/- 0.1 m.

And I attach the updated figure of the fitting (with residual zoomed up).

Data points in the lower are (intentionally) slightly shifted horizontally to make it easy for us to see them.

It is hard, I think, to estimate the error of each data point, but I used 17 kHz for the errors of all data points; 17 kHz is the error of FSR estimation of this measurement, and since FSR is the distance between two carrier peaks we can consider that HOM distances, which are the distance between carrier peaks and HOM peaks, have similar order errors comared with that of FSR.

In preparation for the measurement of loss maps of arm cavities, I measured the relationship between:

the offset just after the demodulation of dithering loop (C1:ASS-YARM_ETM_PIT_L_DEMOD_I_OFFSET and C1:ASS-YARM_ETM_YAW_L_DEMOD_I_OFFSET)

and

the angle of ETMY measured with oplev (C1:SUS-ETMY_OL_PIT_INMONC1:SUS-ETMY_OL_PIT_INMON and C1:SUS-ETMY_OL_PIT_INMONC1:SUS-ETMY_OL_PIT_INMON)

while the dithering script is running. With the angle of ETMY, we can calculate the beam spot on the ETMY assuming that the beam spot on the ITMY is not changed thanks to the dithering. What we have to do is to check the calbration of oplev with another way to measure the angle, to see if the results are reliable or not.

I got linear relation between these. The results and method are below.

Quote:

In preparation for the measurement of loss maps of arm cavities, I measured the relationship between:

the offset just after the demodulation of dithering loop (C1:ASS-YARM_ETM_PIT_L_DEMOD_I_OFFSET and C1:ASS-YARM_ETM_YAW_L_DEMOD_I_OFFSET)

and

the angle of ETMY measured with oplev (C1:SUS-ETMY_OL_PIT_INMONC1:SUS-ETMY_OL_PIT_INMON and C1:SUS-ETMY_OL_PIT_INMONC1:SUS-ETMY_OL_PIT_INMON)

while the dithering script is running. With the angle of ETMY, we can calculate the beam spot on the ETMY assuming that the beam spot on the ITMY is not changed thanks to the dithering. What we have to do is to check the calbration of oplev with another way to measure the angle, to see if the results are reliable or not.

I will report the results later.

RESULTS

METHOD

I added offset (C1:ASS-YARM_ETM_PIT_L_DEMOD_I_OFFSET and C1:ASS-YARM_ETM_YAW_L_DEMOD_I_OFFSET) to shift the beam spot on ETMY. For each data point, I measured the difference in angle of ETMY with oplev before and after adding offset. The precedure for each measurement I employed is following:

-- run dither

-- wait until error signals of dithering settle down

-- freeze dither

-- measure angle (10s avg)

-- add offset

-- wait until error signals of dithering settle down

-- freeze dither

-- measure angle (10s avg)

The reason why I measured the angle without offset for each measurement is that the angle which oplev shows changed with time (~several tens of minutes or something).

DISCUSSION

At the maximum values of offsets, the arm transmission power started to degrade, so the range where I can do this measurement is limited by these values as for now. However, we have to shift the beam spot more in order to make loss maps of sufficiently broad area on the mirror (the beam width (w) on ETM; w ~ 5 mm). Then, we have to find out how to shift the beam spot more.

Based on elog 1403, I calibrated the oplevs for ITMY/ETMY.

Summary of this method is following:

We lock an arm, and slightly misalign one mirror of the arm. Then, the transmission of the arm starts to decrease quadratically as the misalign angle of the mirror changes. Here, how much the transmission decreases in terms of the misalign angle is determined by geometry of optics, so we can see how much the angle really changes from this quadratic curve.

RESULTS

These are the relationship between misalign angles measured by oplev (the units are based on the calibration for now) and transmission power.

(I updated following figures on Nov 19 2015. You can find the figures I attached once here in the zipped folder attached.)

According to this measurement, ratio of the calibration factor derived with this measurement (NEW) and the calibration factor for now (OLD), i.e. NEW/OLD was:

ETMY_PIT: 5.0265 --->> 5.3922 (without an outlier; the outlier I removed is shown in the figure in zipped folder attached.)

ETMY_YAW: 4.6205

ITMY_PIT: 1.5010

ITMY_YAW: 1.2970

This results show that calibration of oplevs for ITMY is kind of OK, but that for ETMY is so BAD and the calibration factors should be updated.

NOTE

The calibration factors of the oplevs for ETMY/ITMY are NOT UPDATED YET.I updated on Dec 11, 2015

If these results are reliable, I will update them tomorrow.

I'm sorry. I will be careful about that. And I updated the plots in elog 11785.

Quote:

OMG. Please try to use larger fonts and PDF so that we can read the plots.

Quote:

Quote:

Based on elog 1403, I calibrated the oplevs for ITMY/ETMY.

I'm not sure that these calibration measurements are reliable. I would feel better if Steve can confirm them using our low accuracy method of moving the QPD by 1 mm and doing trigonometry.

In this morning, Steve and I looked at the ETMY table and we found that the measurement you suggested might interfere with other optics or detectors because of space constraint. So, before doing this measurement, I roughly estimated the calibration factors for ETMY oplev by using the rough value of the arm length of the optical lever and the beam width of the light just before the QPD.

How I got the arm length and the beam width:

I measured the length of the optical path between ETMY and the QPD. Then I measured the beam width with an iris to screen the beam. To get the beam width from the decrease of the power of the beam detected by QPD, I used this formula: .

Then I got: (arm length) = 1.8 +/-0.2 m, w= 0.56 +/- 0.5 mm.

How I estimated the calibration factors from these:

The calibration factors (such as C1:SUS-ETMY_OL_PIT_CALIB; (real angle) / (normalized output of QPDXorY)) can be calculated with: . Then, I got

,

though the calibration factors, C1:SUS-ETMY_OL_PIT_CALIB C1:SUS-ETMY_OL_YAW_CALIB, right now are 26.0 and 31.0, respectively. (If I express this in the same way as elog 11785, 5.0 and 4.2 for ETMY_PIT and ETMY_YAW, respectively. they are consistent with yesterday's results.)

I believe that the calibration factors I estimated today are not different from the true values by a factor of 2 or something, so this estimation indicates that the oplev calibration measurements I did yesterday are reliable, at least for the oplev for ETMY.

I measured round trip loss of Y arm. The alignment of relevant mirrors was set ideal with dithering (no offset).

Summary:

round trip loss of Y arm: 166.2 +/- 9.3 ppm

(In the error, only statistic error is included.)

How I measured it:

I compared the power of light reflected by Y arm (measured at AS) when the arm was locked (P_L) and when ETMY was misaligned (P_M). P_L and P_M can be described as

.

The reason why P_L takes this form is: (1-alpha)*4T_ITM/(T_tot)^2 is intracavity power and then product of intracavity power and loss describes the power of light that is not reflected back. Here, alpha is power ratio of light that does not resonate in the arm (power of mismatched mode and modulated sideband), and T_tot is T_ITM+T_loss. Transmissivity of ETM is included in T_loss. I assumed alpha = 7%(mode mismatch) + 2 % (modulation) (elog 11745)

After some calculation we get

.

Here, higher order terms of T_ITM and (T_loss/T_ITM) are ignored. Then we get

.

Using this formula, I calculated T_loss. P_L and P_M were measured 100 times (each measurement consisted of 1.5 sec ave.) each and I took average of them. T_ETM =13.7 ppm is used.

Discussion:

-- This value is not so different from the value ericq reported in July (elog 10248).

-- This method of measuring arm loss is NOT sensitive to T_ITM. In contrast, the method in which loss is obtained from finesse (for example, elog 11740) is sensitive to T_ITM.

In the method I'm now reporting,

,

but in the method with finesse,

.

In the latter case, if relative error of T_ITM is 10%, error of T_loss would be 1000 ppm.

So it would be better to use power of reflected light when you want to measure arm loss.

We disconnected the cable that was connected to CH5 of the whitening filter in 1Y2, then connected POYDC cable to there (CH5). This channel is where POYDC used to connect.

Then we turned on the whitening filter for POYDC (C1:LSC-POYDC FM1) and changed the gain of analog whitening filter for POYDC from 0 dB to 39 dB (C1:LSC-POYDC_WhiteGain).

I slightly changed the orientation of a few mirrors on AS table that are used to make the AS light get into PDs, in order to confirm that the strange behavior of ASDC (I will report later) is not caused by clipping related to these mirrors or miscentering on PDs.

Then output level of ASDC, AS55, and AS165 could have changed.

So take care of this possible change when you do something related to them. But the relative change of them would be at most several %, I think.

I noticed that ASDC level changes depending on the angle of ITMY when trying to take some data for loss map of YARM. We finally found that ASDC level behaves strangely when the angle of ITMY in yaw direction is varied, as you can see in Attachment 1. Now, AS port recieved only the reflection of ITMY.

NOTE: This behavior indicates that angular motion could couple to length signal in AS port.

Koji suggested that this behavior might be caused by interference at SR2 or SR3 between main path light and the light reflected by the AR surface. By rough estimation, we confirmed that this scenario would be possible. So it would be better to measure AR reflection of the same mirror to ones used for SR2 and SR3 in term of incident angle.

Ed by KA: This senario could be true if the AR reflection of teh G&H mirrors have several % due to large angle of incidence. But then we still need think about the overlap between the ghost beam and the main beam. It's not so trivial.

Due to the strange behavior (elog 11815) of ASDC level, we checked if it is possible to use POYDC instead of ASDC to measure the power of reflected light of YARM. Attached below is the spectrum of them when the arm is locked. This spectrum shows that it is not bad to use POYDC, in terms of noise. The spectrum of them when ETMY is misaligned looked similar.

So I am going to use POYDC instead of ASDC to measure arm loss of YARM.

Ed by KA:
The spectra of POYDC and ASDC were measured. We foudn that they have coherence at around 1Hz (good).
It told us that POYDC is about 1/50 smaller than ASDC. Therefore in the attached plot, POYDC x50 is shown.
That's the meaning of the vertical axis unit "ASDC".

Tonight I measured "loss map" of ETMY. The method to calculate round trip loss is same as written in elog 11810, except that I used POYDC instead of ASDC this time.

The correspondence between the loss shown above and the beam spot on ETMY is shown in the following figure. In the figure, "downward" and "left" indicate direction of shift of the beam spot when you watch it via the camera (ex. 494.9 ppm corresponds to the lowest and rightest point).

Edited below on 28th Nov.

To shift the beam spot on ETMY, I added offset in YARM dither loop. The offset was [-30,-15,0,15,30]x[-10,-5,0,5,10] for pitch and yaw, respectively. How I calibrated the beam spot is basically based on elog 11779, but I multiplied 5.3922 for vertical direction and 4.6205 for horizontal direction which I had obtained by caliblation of oplev (elog 11785).

Here, I upload data I took last night, including the power of reflected power (locked/misaligned) and transmitted power for each point (attachement 1).

And I would like to write about possible reason why the loss I measured with POYDC and the loss I measured with ASDC are different by about 60 - 70 ppm (elog 11810 and 11818). The conclusion I have reached is:

It could be due to the strange bahavior of ASDC level.

This difference corresponds to the error of ~2% in the value of P_L/P_M. As reported in elog 11815, ASDC level changes when angle of the light reflected by ITMY changes, and 2% change of ASDC level corresponds to 10 urad change of the angle of the light according to my rough estimation with the figure shown in elog 11815 and attachment 2. This means that 2% error in P_L/P_M could occur if the angle of the light incident to YARM and that of resonant light in YARM differ by 10 urad. Since the waist width of the beam is ~3 mm, with the 10 urad difference, the ratio of the power of TEM10 mode is , where . This value is reasonable; in elog 11743 Gautam reported that the ratio of the power of TEM10 was ~ 0.03, from the result of cavity scan. Therefore it is possible that the angle of the light incident to YARM and that of resonant light in YARM differ by 10 urad and this difference causes the error of ~2% in P_L/P_M, which could exlain the 60 - 70 ppm difference.

I found that TRY level degraded and the beam shape seen with CCD camera at AS port was splitted when the beam spot on ETMY was not close to the center. This was because dither started not working well. I suspect so because in such a case TRY level went up when I did iteration with TT1 and TT2 after freezing dither. Splitted beam shape indicates that incident light did not match well with the cavity mode.

In the worst case, TRY level was 70 % of the maximum level. Assuming that this degrade was totally due to the mode mismatch, this corresponds to ~50 urad difference between the angle of incident light and resonant lighe in the arm (see elog 11819).

It might have, so I think I need to estimate shift of beam spot more preciely.

According to Steve's drawing, radius of the hole of the baffle is 19.8 mm.

Intensity distribution of fundamental mode in x axis direction is this (y is integrated out):

.

With the radius of curvature of ETMY of 60 m and the arm length of 37.78 m, the beam width on ETMY is estimated to be 5.14 mm. From this expression of the intensity, , for example. If round trip loss is considered, these values are doubled.

Although maximum shift of beam spot from the ideal spot on ETMY is estimated to be sqrt(6.0^2+(1.7+1.7)^2)=6.9 mm, this value could have error of several tens of % because I am not sure to what exten the calibration is precise, which means that the maximum shift could be ~10 mm and seperation between the baffle and the beam could be ~10 mm.

Therefore, I need to check how much the beam spot shifts with another way, maybe with captured image of the CCD camera.

With captured images of ETMYF, I measured the shift of the beam spot on ETMY.

The conclusions are:

the baffle would have almost no effect on loss map measurement and

the calibration of beam spot shift is confirmed to be not so bad.

What I did:

I captured ETMYF images in the cases that (i)beam spot is centered on ETMY, beam spot is at the rightest and lowest point of my loss map measurement (corresponding to [0,0] component of the matrix shown in elog 11818), and beam spot is at the leftest and highest point of my loss map measurement ([4,4] component). Each captured image is attached.

Then using ImageJ, I measured the shift of the beam spot. I calibrated lengh in horizontal direction and vertical direction with the diameter of the mirror.

Results:

The amount of the beam shift was 7.2 mm and 8.0 mm for each case.

These values indicate that clapping loss due to the baffle is less than 10 ppm in a round trip.

Today's results support the previous calibration with oplev, which says the amount of the beam shift is 7.0 mm. Two values derived by different calibrations coincide within ~10 % though they are totally different methods. This also support the calibration of the oplev for ETMY (elog 11785) indirectly.

With the same method as reported in elog 11785, I calibrated oplevs for ITMX/ETMX.

RESULTS

According to this measurement, ratio of the calibration factor derived with this measurement (NEW) and the calibration factor for now (OLD), i.e. NEW/OLD was:

ETMX_PIT: 4.470

ETMX_YAW: 2.5970

ITMX_PIT: (-)1.1102

ITMX_YAW: 1.8173

NOTE

The calibration factors of the oplevs for ETMY/ITMY are NOT UPDATED YET. I updated on Dec 11, 2015