No more illegal power supply at the LSC rack 

The amplifiers are now being powered by the rack power supply through fuse blocks.

To make new connections, I shutdown the +/-15 V low noise power supplies. They were turned back ON after the work.

I shutdown the +/-15V and the +/-24V sorensons on the IOO rack to connect the FOL RF PDs to the rack power supply.

They were turned back ON after the work. PMC and MC were relocked.

I pulled out the RF amplifier box from the IOO rack and swapped the amplifiers for FOL beat frequency amplification. The earlier gain of 62dB (ZFL500LN + ZFL500LN) was reduced to 40dB gain (ZFL500LN+ZFL2AD).

I also swapped one of the broken sma cables that was connecting the two amplifiers with a good one. Front ports of the module were relabeled and the box was put back on the rack.

During the course of this work, I had to turn OFF the green BBPDs on the PSL table to protect them and they have been powered up after putting the module back.

Working around the PSL table

I have put the FOL fiber box on the PSL table. The fibers carrying AUX and PSL light are connected and the RFPDs have been powered up. I can see the beat frequency on the frequency counters; but for some reason Domenica (that brings the frequency counter values on the medm screens) is not visible on the network even after hard reboot of the raspberry pi. I am neither able to ping nor ssh into the machine. I have to pull the module out and add a monitor cable to troubleshoot (my bad I should have left the monitor cable with the raspberry pi in the first place). Anyways, I have handed over the IFO to Q and will play with things again sometime later.

The fiber box on the PSL table is only left there temporariliy till I have things working. It will be stowed on the rack properly later.

In case someone wants the fiber box out of the PSL table, please make sure to power down the RFPDs using the black rocker switches on the side of the box and then disconnect the cables and fibers.

[EricQ, Manasa]

Domenica:
Since Domenica was not picking up an IP address and hence not responding to pings or ssh even after power cycling, I pulled it out from the IOO rack and connected it to a monitor. After a bunch of hit and trials, we figured out that the problem was related to the power adapter of the Rpi discussed here : http://www.raspberrypi.org/forums/viewtopic.php?f=28&t=39055

The power adapter has been swapped and this issue has been resolved. Domenica has been remounted on the IOO rack but left with the top lid off for the timebeing.

RF amplifier box:
The frequency counter was setup to read the beat frequency after amplification of the RFPD signals. The output as seen on the frequency counter screen as well as the epics values was intermittent. Also, locking the arms and changing the end laser frequencies did not change the frequency counter outputs. It looks like the RF amplifier is oscillating (Oscillating frequencies were ~107 MHz and 218 MHz) and the input circuit needs to be modified and the connections need better insulation.

As of now, I have connected the RFPD outputs to the frequency counter sans any amplification and we are able to get a readout of the beat frequency at > 40MHz (Frequency counter requires much higher amplitude signals for frequencies lower than that).

Figuring out the problem with frequency counter readouts:

The frequency counter has 4 ranges of operation: 
Range 1 : 1 - 40MHz
Range 2: 40 - 190MHz
Range 3: 190 - 1400MHz  
Range 4: 1400 - 6000MHz

I set up the beat frequency readout in various configurations to troubleshoot and have recorded my observation (attachments). The amplifiers in all cases is just a single ZFL-500LN.

There seems to be a problem with the RF amplifier and the frequency counter when they are set together. I am not able to figure it out and stuck right here

Attachment 1: schematic for readout and corresponding observations

Attachment 2: Oscilloscope screen snapshot for schematic 3

Attachment 3: Spectrum analyzer screen snapshot for schematic 3

More info: RFPD used is Thorlabs FPD310 and frequency counter is Mini Circuits UFC-6000. The RF amplifier has decoupling capacitors soldered across the power supply.

PMC was locked in a bad state. FSS slow actuator adjust was at ~ -0.7 and PZT voltage at ~45.

So I set these right by moving the appropriate sliders and relocked it. FSS slow actuator adjust brought back to zero and PZT voltage ~115. PMC trans after relock is 0.789.
 

[Koji, Manasa]

This problem was solved by changing the Frequency Counter range settings.

Frequency counter automatic range setting has been modified and now the range can be manually set depending on the input frequency. New codes have been written to do this. The scripts will be polished and wrapped up shortly.

I was around the 1Y1 rack today. Trials were done to get the PDFR of AS55.

The autolocker was struggling to lock the IMC. I disabled the autolocker and locked the IMC manually. It seems happy right now. 

With PMC trans at 0.717 counts, the IMC trans sum is ~15230.

I found that the scripts in FOL and PDFR directories were not in the svn. These were added to the svn.

[Koji, Manasa]

I have created new slow channels for FOL. To do so, I have edited the fcreadout.db file in Domenica and the C0EDCU.ini file in /chans/daq

Domenica and frame builder were restarted after the edits.

Koji has moved the following files from /opt/rtcds/caltech/c1/chans/daq/ to /opt/rtcds/caltech/c1/chans/daq/trash  as they are not being used anymore.

C0EDCU1.ini
C1EDCU_X00.ini
C1EDCU_X10.ini
C1EDCU_X14.ini
C1X00.ini
C1X10.ini
C1X99.ini

Since none of us here are experts in pearl, I have put together a python script for a simple PID controller. This can be imported into any main scripts that will run the actual PID loop. The script, PID.py, exists in /scripts/general/

The BS oplev has been misbehaving and kicking the optic from time to time since noon. The kicks are not strong enough to trip the watchdogs (current watchdog max counts for the sensors is 135).

I took a look at the spectrum of the BS oplev error in pit and yaw with both loops enabled while the optic was stable. There is nothing alarmingly big except for some additional noise above 4Hz.

I have turned the BS oplev servo OFF for now.

I was poking around with the PDFR hardware today.

I moved the Agilent which had its screen projected on the monitor. I have put it back...but please verify the settings before using it for tonight.

Since the Frequency counters have not been a reliable error signal for FOL PID loop, we will put together an analog delay line frequency dicriminator as an alternative method to obtain the beat frequency.

The configuration will be similar to what was done in elog 4254 in the first place.

For a delay line frequency dicriminator, the output at the mixer is proportional to  where 

L - cable length asymmetry, f_b - beat frequency and v - velocity of light in the cable.

The linear output signal canbe obtained for  

For our purpose in FOL, if we would like to measure beat frequency over a bandwidth of 200MHz, this would correspond to a cable length difference of 0.5 m (assuming the speed of light in the coaxial cable is ~ 2x10⁸m/s.

[Koji, Manasa]

Since the bandwidth of the fiber PD is ~ 1GHz, we could design the frequency discriminator to have a wider bandwidth (~ 500MHz). The output from the frequency discriminator could then be used to define the range setting of the frequency counter for readout or may be even error signal to the PID loop.

A test run for the analog DFD with cable length difference of 27cm gave a linear output signal with zero-crossing at ~206MHz.

Detailed schematic of the setup and plot (voltage vs frequency) will be updated shortly.

Attached is the schematic of the analog DFD and the plot showing the zero-crossing for a delay line length of 27cm. The bandwidth for the linear output signal obtained roughly matches what is expected from the length difference (370MHz) .

We could use a smaller cable to further increase our bandwidth. I propose we use this analog DFD to determine the range at which the frequency counter needs to be set and then use the frequency counter readout as the error signal for FOL.

Koji suggested that I make a cosine fit for the curve instead of a linear fit.

I fit the data to  
where L - cable length asymmetry (27 cm) , f_b - beat frequency and v - velocity of light in the cable (2*10⁸ m/s)

The plot with the cosine fit is attached. 

Fit coefficients (with 95% confidence bounds):
       A =      0.4177  (0.3763, 0.4591)
       B =       2.941  (2.89, 2.992)

I found the c1lsp and c1sup models not running anymore on c1lsc (white blocks for status lights on medm).

To fix this, I ssh'd into c1lsc. c1lsc status did not show c1lsp and c1sup models running on it.

I tried the usual rtcds restart <model name> for both and that returned error "Cannot start/stop model 'c1XXX' on host c1lsc".

I also tried rtcds restart all on c1lsc, but that has NOT brought back the models alive.

Does anyone know how I can fix this??

c1sup runs some the suspension controls. So I am afraid that the drift and frequent unlocking of the arms we see might be related to this.

P.S. We might also want to add the FE status channels to the summary pages.

The last MC_F calibration was done by Ayaka : Elog 7823

I just found out that c1lsp and c1sup models no more exist on the FE status medm screens. I am assuming some changes were done to the models as well.

Earlier today, I was looking at some of the old medm screens running on Donatella that did not reflect this modification. 

Did I miss any elogs about this or was this change not elogged??

Arm powers had drifted to ~ 0.5 in transmission.

X and Y arms were locked and ASS'd to bring the arm transmission powers to ~1.

* Relocked IMC. I guess it was stuck somewhere in the autlocker loop. I disabled autolocker and locked it manually. Autolocker has been reenabled and seems to be running just fine.

* The X arm has been having trouble staying locked. There seemed to be some amount of gain peaking. I reduced the gain from 0.007 to 0.006.

*  I disabled the triggered BounceRG filter : FM8 in the Xarm filter module.  We already have a triggered Bounce filter: FM6 that takes care of the noise at bounce/roll frequencies. FM8 was just adding too much gain at 16.5Hz. Once this filter was disabled the X arm lock has been much more stable. 
Also, the Y arm doesn't use FM8 for locking either.

Measuring the voltage noise and frequency response of the Analog Delay-line Frequency Discriminator (DFD)

The schematic and an actual photo of the setup is shown below. The setup was checked to be physically sturdy with no loose connections or moving parts.

The voltage noise at the output of the DFD was measured using an SR785 signal analyzer while simultaneously monitoring the signal on an oscilloscope.

The noise at the output of the DFD was measured for no RF input and at several RF input frequencies including the zero crossing frequency and the optimum operating frequency of the DFD (20MHz).

The plot below show the voltage noise for different RF inputs to the DFD. It can be seen that the noise level is slightly lower at the zero crossing frequency where the amplitude noise is eliminated by the DFD.

I also did measurements to obtain the frequency response of the setup as the cable length difference has changed from the prior setup. The cable length difference is 21cm and the obtained linear signal at the output of the DFD extends over ~ 380MHz which is good enough for our purposes in FOL. A cosine fit to the data was done as before. //edit- Manasa: The gain of SR560 was set to 20 to obtain the data shown below//

Fit Coefficients (with 95% confidence bounds):
       a =     -0.8763  (-1.076, -0.6763)
       b =       3.771  (3.441, 4.102)

Data and matlab scripts are zipped and attached.

There was an earthquake: M4.0 - 40km SSW of South Dos Palos, California 

No noticeable effects on the IFO. MC did not lose lock; however the arms did unlock.

 Video captures when power recycling cavity is locked (videos 1 & 2) and flashing (video 3). Arms stayed misaligned.

1. CH1 and CH2 are loooking at PRM front and back faces. CH3 and CH4 are looking at POP and REFL

 2. CH1 and CH2 are loooking at PRM front and back faces. CH3 and CH4 are looking at the ITMs

3. CH1 and CH2 are loooking at PRM front and back faces. CH3 and CH4 are looking at POP and REFL

I centered optical levers of ITMX,BS,ETMY. I also change the position of optical levers of ITMX, ETMY, ITMY, BS on Friday night(9/21), of ITMX, ETMY, BS on Monday night. Both are around 6:00 ~ 7:00.But centering on Monday was totally wrong, because I centered with not good IFO alignment.

The attachment is the 5 days trend of the opt lev of ITMX. First gap is alignment on Friday and Second gap is the alignment on Monday. Now I centered after  locking the FPMI.

The attachment 2 is the last 6 hours data.  The gap on 9/25 00:00 and 1:30(UTC)  is because the alignment of the cavity and the last gap is because of  centering of the optical lever.

 [Manasa, Masayuki]

[revised at 10/1 pm 5:00]

As we mentioned in previous entry (elog#9171), the phase margin of ALS control was at most 20 degree. We modified the filter of C1ALS_XARM and C1ALS_YARM. The OLTF is in attachment1. Now the phase margins of both arms are more than 35 degree. I modified the FM5 filters of both servo.

FM5 filter is the filter for the phase compensation. It had the one pole at 1000 Hz and one zero at 1Hz. As you can see in attachment2, it start to lose the phase at 50 Hz. But the UGF of our ALS control loop is higher than 100 Hz, so I changed the pole from 1 kHz to 3 kHz in order to get more phase margin at UGF. The new servo have 10dB larger gain than previous filter at higer than 1kHz, but the control loop do nothing in that region, so it's no problem.

We have phase lag between 2 arms. I used same filters for both arms, so I'm wondering where these phase lag came from.

 [Manasa, Masayuki]

We made a new flowchart of ALS autolocker. We added the additional step to find the beat note frequency. We have to find a way to read the PSL temperature. By reading the PSL temperature we can decide the sweep range for the end green laser temperature with the curve which measured in previous measurement (in this entry)

We have three thresholds of error signal. One is the threshold for checking the arms are stabilized or not. It should be some hundreds count. Another threshold is to check that the suspensions are not kicked. This should be some thousands counts (in flow chart, it is 2K counts). The other is to check the optimal servo gain. If the servo gain is too high, the UGF is also too high and we will not have enough gain margin. The error signal start to oscillate at the UGF. We will check this oscillation and find the optimal gain. In flow chart this threshold is 1K counts.

I wrote the scripts for cdsutils.

1. fft

usage: fft.py [-h] [-c N_CYCL] [-a N_AVG] freq channel [channel ...]

Measures the frequency content of one or more NDS channels at the specified frequecy.
    The measurement results are  magnitude, phase, real part imaginary part, and the standard deviation of the real and imaginary parts.

positional arguments:
  freq        measurement frequency
  channel     list of measurement channel

optional arguments:
  -h, --help  show this help message and exit
  -c N_CYCL   define number of cycles. Default is 10
  -a N_AVG    define number of average. Default is 100

2. tf

usage: tf.py [-h] [-c N_CYCL] [-a N_AVG] [--dB] freq input output

Measures the transfer funtion of one NDS channels pair  at the specified frequecy.
    The measurement results are the coherence, magnitude, phase, real part, imaginary part, and the standard deviation of the real and imaginary parts.

positional arguments:
  freq        measurement frequency
  input       list of measurement input channel
  output      list of measurement output channel

optional arguments:
  -h, --help  show this help message and exit
  -c N_CYCL   define number of cycles. Default is 10
  -a N_AVG    define number of average. Default is 100
  --dB        print the amplitude in dB
 

3.offsets

usage: offset.py [-h] [-t SECONDS] filterbank [filterbank ...]

Zero the offset of one or more filterbank. Take average of OUT16 channel, and put (-1 * average / gain) into offset.  After change offsets, it will turn on the offset.
    example usage) offset -d 25 C1:LSC-AS55_Q C1:LSC-AS55_I

positional arguments:
  filterbank  list of filterbank to zero offset

optional arguments:
  -h, --help  show this help message and exit
  -t SECONDS  define the averaging time. default value is 10

I put these scripts in /opt/rtcds/cdsutils/trunk/lib/cdsutils.
I couldn't put them into cds library, but I will left tomorrow to Japan...

So please help me Jamie or Joe !!

By the way,

I modified the LSCoffset script  (script)/LSC/LSCoffsets.py.

usage: LSCoffsets.py [-h] [-d SECONDS] [--PDlist]

 Zero the offsets of LSC PDs. During taking average, we will close the PSL and green shutter. After zeroing, it will turn on the offsets switch.
    example usgae) LSCoffset2.py -d 20    

optional arguments:
  -h, --help  show this help message and exit
  -d SECONDS  define the averaging time. default value is 10
  --PDlist    print PD list for LSC and exit

i made new directory 'offset_backup' for old offset script. I move all old offset script into there.

But unfortunately that cannot use right now, because cds offsets script is not available yet...

Last Friday, Matt made a frequency discriminator circuit on a bread board in order to test the idea and study the noise level. I think it will work for phase lock acquisition of Green locking.

As a result a response of 100kHz/V and a noise level of 2uV/rtHz @ 10Hz are yielded. This corresponds to 0.2Hz/rtHz @ 10Hz.

The motivation of using frequency discriminators is that  it makes a frequency range wider and easier for lock acquisition of PLLs in green locking experiment.

For the other possibility to help phase lock acquisition, Rana suggested to use a commercial discriminator from Miteq.

(principle idea)

The diagram below shows a schematic of the circuit which Matt has built.

Basically an input signal is split into two signals right after the input, then one signal goes through directly to a NAND comparator.

On the other hand another split signal goes through a delay line which composed by some RC filters, then arrive at the NAND comparator with a certain amount of delay.

After going through the NAND comparator, the signal looks like a periodic pulses (see below).

If we put a signal of higher frequency we get more number of pulses after passing through the NAND.

Finally the pulse-signal will be integrated at the low pass filter and converted to a DC signal.

Thus the amplitude of DC signal depends on the number of the pulses per unit time, so that the output DC signal is proportional to the frequency of an input signal.

(result)

By putting a TTL high-low signal, an output of the circuit shows 100kHz/V linear response.

It means we can get DC voltage of 1 V if a signal of 100kHz is injected into the input.

And the noise measurement has been done while injecting a input signal. The noise level of 0.2Hz/rtHz @ 10 Hz was yielded.

Therefore we can lock the green PLL by using an ordinary VCO loop after we roughly guide a beat note by using this kind of discriminator.

I have set up new summary pages for the 40m: http://www.ligo.caltech.edu/~misi/summary/
This website shows plots (time series, spectra, spectrograms, Rayleigh statistics) of relevant channels and is updated with new data every 30 min.

The content and structure of the pages is determined by configuration files stored in nodus:/users/public_html/gwsumm-ini/ . The code looks at all files in that directory matching c1*.ini. You can look at the c1hoft.ini file to see how this works. Besides, a quick guide to the format can be found here http://www.ligo.caltech.edu/~misi/iniguide.pdf

Please look at the pages and edit the config files to make them useful to you. The files are under version control, so don’t worry about breaking anything.

Do let me know if you have any questions (or leave a comment in the pages).

I have created a wiki page with introductory info about the summary page configuration: https://wiki-40m.ligo.caltech.edu/Daily summary help

We can also use that to collect tips for editing the configuration files, etc.

Thanks for the great entry!

In order to make this work for higher frequencies, I would add Hartmut's suggestion of a frequency dividing input stage.  If we divide the input down by 100, the overall range will be about 200MHz, and the noise will be about 20Hz/rtHz.  That might be good enough... but we can hope that the commercial device is lower noise!

Today we tried the Schmitt trigger DFD, and while it works it does not improve the noise performance.  At least part of our problem is coming from the discrete nature of our DFD algorithm, so I would propose that an industrious day job person codes up a new DFD which avoids switching.  We can probably do this by mixing the input signal (after high-passing) with a time-delayed copy of itself... as we do now, but without the comparator.  This has the disadvantage of giving an amplitude dependent output, but since we are working in the digital land we can DIVIDE.  If we mix the signal with itself (without delay) to get a rectified version, and low-pass it a little, we can use this for normalization.  The net result should be something like:

output = LP2[ s(t) * s(t - dt) / LP1[ s(t) * s(t) ]],

where s(t) is the high-passed input and LP is a low-pass filter.  Remember not to divide by zero.

Power Spectral Density plot using PyNDS, comparing 5 fast data channels for ETMX.

**EDIT** Script here:

import nds
import numpy as np
import matplotlib.pyplot as plt
import time
daq=nds.daq('fb', 8088)
channels=daq.recv_channel_list()
e=0
start=int(time.time()-315964819)
rqst=['C1:SUS-ETMX_SENSOR_UR','C1:SUS-ETMX_SENSOR_UL','C1:SUS-ETMX_SENSOR_LL','C1:SUS-ETMX_SENSOR_LR','C1:SUS-ETMX_SENSOR_SIDE']    #Requested Channels
for c in channels:
    if c.name in rqst:
        daq=nds.daq('fb', 8088)
        data=daq.fetch(start-100, start, c.name)
        vars()['psddata'+str(e)], vars()['psdfreq'+str(e)]=plt.psd(data[0],NFFT=16384,Fs=c.rate)
        vars()['label'+str(e)]=c.name
        e+=1
plt.figure(1)
plt.clf()
plt.title('PSD Comparison')
plt.grid(True, which='majorminor')
plt.xlabel(r'Frequency $Hz$')
plt.ylabel(r'Decibels $\frac{dB}{Hz}$')       
for x in np.arange(0,e):
    plt.loglog(psdfreq0, 10*vars()['psddata'+str(x)], label=vars()['label'+str(x)])
plt.legend()
plt.show()

 I tried to calculate the frequency of resonance using Rayleigh's method.  approximated the geometry of lead to be that of a perfect cylinder, and  the deformation in the lead by the deflection in a cantilever under  a shear strain.

this rough calculation gives an answer of 170Hz and depends on the dimensions of each lead, number of leads, and mass of the granite. But the flaw pointed out is that this calculation doesnot depend on the dimension of the granite slab, nor on the exact placing of the lead spheres with respect toteh COM of the slab.

I will put up the calculations details later, and also try to do a FEM analysis of the problem.

BTW, latex launched this new thing for writing pdfs. doesnot require any installations.  check  http://docs.latexlab.org

i added my laptop's mac address to teh martian at port 13 today.

This week I attended a whole lot of orientations, lectures, and meetings related to SURF. Done with general and laser safety training.

read Nergis' thesis for, and other material on WFS.

got confused with how the sidebands and shifted carrier frequencies are chosen for the Interferometer, read initial chapters of Regehr's thesis for teh same.

Made a plan for proceeding with the WFS work through discussions with Koji.

Understood the MC cavity and drew a diagram for it and the sensors.

Did Calculations for Electric field amplitudes inside and outside the MC cavity.

Saw the hardware of the WFS and QPD inside, and their routes to computers. Figured out which computer shows up the conditioned data from teh sensors.

Tried calculating the cavity axis for MC using geometry and ray tracing. Too complicated to be done manually.

Read some material (mainly Seigman) for physics of calculating the eigen-axis of the MC cavity with mirrors mis-aligned. Will calculate that using simulations, using the ABCD matrices approach.

Made a simple feedback simulink model yesterday to learn simulink. Made it run/compile. Saw the behaviour thru time signals at different points.

in the night, Made a simulink model of the sensor-mirror thing, with transfer functions for everything as dummy TFs. Compiles, shows signals in time. Remaining part is to put in real/near-real TFs in the model.

Wednesday Morning E-log :

Most of the time through this week, i was working towards making the simulink model work.

It involved learning simulink functions better, and also improving on the knowledge of control theory in general, and control theory of our system.

1. Thusrday : found tfs for the feedback loop. and tried many different filters and gains to stabilize the system (using the transient response of the system). - not through

2. Friday : decided to use error response and nullify the steady state error instead of looking at convergence of output. tried many other filter functions for that.

Rana then showed me his files for WFS.

3. Sunday - played with rana's files, learnt how to club simluink with matlab, and also about how to plot tfs using bode plots in matlab.

4. Monday : Read about state-space models, and also how to linearize in matlab. done with the latter, but the former still needs deeper understanding.

read ray-optics theory to calculate the geometric sensing matrix.

It first requires to calculate the eigen mode of the cavity with tilted mirrors. this eigen mode is needed to be found out using ray-optics transfer matrices for the optics involved  . figured out  matrices for the tilted plane mirrors, and am working on computing the same for MC2.

5. Tuesday : went to Universal Studios , Hollywood :P

6. Wednesday (today) : Writing the report to be submitted to SFP.

Wednesday after the meeting - Started report, learnt mode cleaner locking from Kiwamu and Rana, saw how to move optics on the tables with Rana and kiwamu.

Thursday - Made the report

Tuesday - report.

Today - am trying locking the MC with kiwamu's help to see the WFS signals and also to start characterizing the QPD.

Nancy and Koji:

This is what I and Koji measured after aligning the MC in the afternoon.

MC_Trans 4.595 (avg)

MC_Refl 0.203 (avg)

MC2_trans :

power = 1.34mW

13.5% width : x=6747.8 +- 20.7 um  , y = 6699.4+- 20.7 um

The WFS error signals were recorded in the order

WFS1_PIT

WFS1_YAW

WFS2_PIT

WFS2_YAW

these measurements are made in the linear region, that is the MC is nearly perfectly aligned.

This is  the average and std. dev.of 5 measurements taken of the same signals over 10 secs each. The std. dev are under 10%. And hence, I will be using 10 secs for measurements for the WFS signals after perturbations to the mirrors.

avg =

829.4408
-517.1884
297.4168
-944.7892


std_dev =

9.0506
22.9317
15.4580
8.9827

I perturbed the Pitch and Yaw of the Three mirrors (in order MC1,2,3), using ezcastep and calculated the coefficients that relate these perturbations to the WFS error signals.

The perturbation made is of -0.01 in each dof , and after measuring the WFS error for it, the system is reverted back to the previous point before making the other perturbation.

I was able to calculate the coefficients since I have assumed a linear relationship..

Following are the coefficients calculated using 10 secs measurements

coef_mat =

   1.0e+05 *

                            MC1_P   MC1_Y  MC2_P   MC2_Y    MC3_P   MC3_Y  constant
WFS1_PIT        -0.1262    0.3677   -0.4539   -0.6297   -0.1889   -0.1356   0.013664
WFS1_YAW     -0.0112   -0.7415   -0.1844    2.4509   -0.0023   -0.3531  -0.016199
WFS2_PIT         0.1251    0.4824   -0.2028   -0.6188    0.0099   -0.1490   0.006890
WFS2_YAW      0.0120   -0.7957   -0.1793    0.9962   -0.0493    0.2672 -0.013695

Also, I measured the same thing for 100s, and to my surprize, even the signs of coeficients are different.

coef_mat =

   1.0e+05 *

                           MC1_P   MC1_Y  MC2_P   MC2_Y    MC3_P   MC3_Y   constant
WFS1_PIT       -0.1981    0.3065   -0.6084   -0.9349   -0.4002   -0.3538   0.009796
WFS1_YAW     0.0607   -0.6977    0.0592    2.8753    0.3507    0.0373   -0.008194
WFS2_PIT        0.0690    0.4769   -0.2859   -0.7821   -0.1115   -0.2953  0.004150
WFS2_YAW     0.0580   -0.8153   -0.0937    1.1424    0.0650    0.4203  -0.010629

The reason I can understand is that the measurements were not made at the same time, and hence conditions might have changed.

A thing to note in all these coefficients is that they relate the error signals to the 'perturbation' around a certain point (given below). That point is assumed to lie in the linear region.

MC1_PIT      2.6129
MC1_YAW   -5.1781
MC2_PIT       3.6383
MC2_YAW    -1.2872
MC3_PIT      -1.9393
MC3_YAW    -7.518

I and Koji were trying to lock the mode cleaner for measuring the beam power at MC2 end. That is when we obtained the trans and refl values.

The beam characteristics at the MC2 were measured so that we could now use a dummy beam of similar power to test and characterize the QPD we are about to install at the MC2 end. This QPD wil provide two more signals in pitch and yaw, and hence complete 6 signals for 6 rotatioanl dof of the cavity. (4 are coming from WFS).

Once the QPD is characterised, it can be used to see the spot position at MC2. This is related to the mirror angles.

The width measurements were done using a beam scan. the beam scan was properly adjusted so that the maxima of the intensity of the sopt was at its center.

We also fitted gaussian curve to the beam profile, and it was a substantially good fit.

The whole idea is that I am trying  to look how the Wavefront sensors respond to the perturbations in the mirror angles. Once this is known, we should be able to control the mirror-movements.

the starting point would be to do just the DC measurements (which I did today). For proper analysis, AC measurements are obviously required.(will be done later).

The matrices so calculated can be inverted, and if found enough singular, the method can be used to control.

The first shot is to see teh dependency of teh error signals only on MC1 and MC3, and see if that is kind of enough to control these two mirrors.

If this works, the QPD signals could be used to control MC2 movements.

I just found the singular values and the condition number of the 4*4 matrix relating the WFS error signals and the MC1 and MC2 movements.

the condition number is ~12.5. I think its small enough to continue with the scheme. (if the measurements and all are reliable).

I and koji setup the measurement of the QPD response to the pitch and yaw displacements of the beam spot.

We did this using a 100mW 1064nm laser. Its power was attenuated to ~ 1.9mW, and the spot size at the QPD position was 6000-7000 um .

The QPD was put on a translation stage, using which, the center of teh QPD wrt the beam spot could be moved in pitch and yaw.

Following are the measurements :

For yaw

:

The slope of teh linear region is -8356 /inch

 For pitch

The slope of the linear region in this is 9085/inch