I redid the PZT Phase Modulation measurement out to 5 MHz for both the Innolight and the Lightwave.  The previous measurement stopped at 2MHz, and we wanted to see if there were any sweet spots above 2MHz.  I also reduced the sweep bandwidth and increased the source amplitude at high frequency to reduce the noise (the Lighwave measurement, especially, was noise dominated above 1MHz).  I also plotted the ratio of PM/AM in rad/RIN, since this is the ultimate criterion on which we want to make a determination.

It looks like there is nothing extremely useful above 2MHz for either laser.  There are several candidates for the lightwave at about 140 kHz and again at about 1.4 MHz.  The most compelling peak, however, is in the innolight at 216 kHz, where the peak is about 2.3e5 rad/RIN.

Below about 30kHz, the loop suppresses the measurement, so one should focus on the region above there.

Bob, Steve, and Koji

We opened North heavy door of the BS chamber in the afternoon.

In the evening, Koji worked on the PRM/SRM removal.

- Cleaned up the OPLEV mirrors to create some spaces near the door.

- Clamped PRM/SRM.

- Removed OSEMs. Made a record of the OSEMs. The record is on the wiki (http://lhocds.ligo-wa.caltech.edu:8000/40m/Upgrade_09/Suspensions)

- Found the SOSs are quite easy to remove from the table as they are shorter than the MOSs.

- Put a new Al sheet on a wagon. Put the SOSs on it. Wrapped them by the Al foils.

- Carried it to the clean room. They are on the right flow bench. Confirmed the wires are still fine.

- Closed up the chamber putting a light door.

The 1979 vintage RF spectrum analyzer HP4195A  sn2904J01587 shipped out  for repair today to http://www.avalontest.com

It has a 25 MHZ oscillation when you go  below 150 MHZ in your sweep....atm1 with the larger amplitude shows this 25 MHZ

Atm2 is displaying  full sweep-sign scans from 1 to 500 MHZ.....here one can clearly see the three segment of the scan:

1, large amplitude 25 MHZ oscillation dominating the spectrum up to 150 MHZ

2, the mid section from 150 MHZ  to 300 MHZ with medium size amplitude is normal

3, from 300 MHZ to 500 MHZ the amplitude is decreasing.......showing the disadvantage of using a 300 MHZ oscilloscope

I pulled the Guralp breakout box from the rack, and it's sitting on the EE bench here.  The game plan is to check out the Gur2X channel.  

Rana and Steve have been investigating, and found that the X channel has been funky (which has been known for ~a month or two) when the seismometer has been plugged in, and also when the seismometers have been unplugged, but the box is left on.  The funkyness goes away when the box is turned off.  Since it's not there when the box is off, it seems that it's not a problem with the cable from the box to the ADC, or in the ADC channel.  Since it is there when the box is on, but the seismometer is unplugged, it's clear that it's probably in the box itself.  

Preliminarily, I've connected a set of BNC clipdoodles to the input testpoints, and another set to the output.  They're both connected to a 'scope (which is on it's battery so it's not connected to any Ground), and when I tap on the circuit board the input trace is totally unchanged, but the output trace goes kind of crazy, and gets more fuzzy, and picks up a DC offset.  Koji is concerned that some of the big capacitors may have an iffy connection to the board. 

Investigations will continue Monday morning. 

Steve and Koji

We aligned the peeping mirrors to look at the surface of the ITMs.
They had been misligned as we move the positions of the ITMs, but now they are fine.

NOTE: This measurement is wrong and only remains for documentation purposes.

Koji asked me to take a profile of the output of the 1W NPRO that will be used for green locking. I used the razor-scan method, plotting the voltage output of a PD vs the position of the razor across the beam, both vertically and horizontally. This was done at 6 points along the beam path out of the laser box.

I determined the beam spot size at each point by doing a least-squares fit on the plots above in Matlab (using w as one of the fitting parameters) to the cumulative distribution functions (error functions) they should approximate.

I then did another least-squares fit, fitting the above "measured" beam profiles to the gaussian form for w vs z. Below is a summary.

It seems reasonable, though I know that M² < 1 is fishy, as it implies less divergence than ideal for that waist size. Also, like Koji feared, the waist is inside the box and thus the scan is almost entirely in the linear regime.

There is a clearly a difference in the divergence angle of the x and y beams - maybe 10-20%. Since the measurements are outside the Rayleigh range and approximately in the linear regime, the slope of the divergence in this plot should be inversely proportional to the waists - meaning the x- and y- waist sizes should differ by about 10-20%. You should check your fitting program for the waist.

Jenne, Koji and I opened up the package from Raicol and examined the crystals under the microscope. The results were mixed and are summarized below. There are quite a few scratches and there is residue on some of the polished sides. There is a large chip in one and there appear to be gaps or bands in the AR coatings on the sides.

There are two albums on Picassa

1. The package is opened ...

2. The crystals under the microscope.

Koji and Kevin

We unpacked the Innolight 2W laser, took an inventory, and scanned the operations manual.

[Edit by KA]

The scanned PDFs are placed on the following wiki page

http://lhocds.ligo-wa.caltech.edu:8000/40m/Upgrade_09/PSL

We will measure the P-I curve, the mode profile, frequency actuator responses, and so on.

 The Guralp Box appears to be back in working order.  It's reinstalled with the 2 seismometers plugged in.

In order:

* Koji suggested retouching the through-board solder joints on the broken channel (EW2 = Gur2X) with a bit of solder to ensure the connections were good.  Check.

* "C7", one of the giant 1uF capacitors on each channel is totally bypassed, and since that was one of the original suspects, Rana removed the (possibly) offending capacitor from EW2.

* Rana and I isolated the craziness to the final differential output stage.  We tried each of the testpoints after the individual gain / filter stages, and found that the signals were all fine, until after the output stage.

* I started to remove the resistors in the output stage (with the plan to go through the resistors, capacitors, and even the amplifier chip if neccessary), and noticed that 2 of the 1k resistors came off too easily, as if they were just barely connected in the first place.  After replacing only the 4 1k resistors, the craziness seemed to be gone.  I poked and gently bent the board, but the output wouldn't go crazy.  I declared victory.

* I reinstalled the box in its normal spot, and put Gur2 (which had been out by the bench for use as a test signal) back next to the other seismometers.  We are in nominal condition, and should be able to do a huddle test this week.

I looked at the time traces of all the seismometer channels, and they all looked good.  I'll put a spectra in in the morning....I'm too impatient to wait around for the low frequency FFTs.

Attached are the before and after pictures of the output stage of EW2 / Gur2X.  The "before" is the one with the OUT+ and OUT- words upsidedown.  The "after" picture has them right side up.

We found ref-cavity HV was off yesterday afternoon. It was turned back on.

ETMY sus damping was restored

 Here is Crystal 724 polished side 2 with all photos along the length stitched together

 I restarted the elog with the restart script as it was down.

EDIT: I used an IFIT (inverse fast idiot transform) to change the x-axis of the plot from Hz to m. I think xlabel('Frequency [Hz]') is in my muscle memory now..

I have redone the beam fit, this time omitting the M², which I believe was superfluous. I have made the requested changes to the plot, save for the error analysis, which I am still trying to work out (the function I used for the least squares fit does not work out standard error in fit parameters). I will figure out a way to do this and amend the plot to have error bars.

Quote:

I have redone the beam fit, this time omitting the M2, which I believe was superfluous. I have made the requested changes to the plot, save for the error analysis, which I am still trying to work out (the function I used for the least squares fit does not work out standard error in fit parameters). I will figure out a way to do this and amend the plot to have error bars.

 Are you sure about your x-axis label? 

[Jenne, Steve]

We removed the old SRM and PRM from their cages, and are temporarily storing them in the rings which we use to hold the optics while baking.  Steve will work on a way to store them more permanently.

We then hung the new SRM (SRMU03) and new PRM (SRMU04) in the cages.  We were careful not to break the wires, so the heights will not have changed from the old heights.

The optics have not been balanced yet.  That will hopefully happen later this week.

Beautiful fitting.

Quote:

EDIT: I used an IFIT (inverse fast idiot transform) to change the x-axis of the plot from Hz to m. I think xlabel('Frequency [Hz]') is in my muscle memory now.. I have redone the beam fit, this time omitting the M2, which I believe was superfluous. I have made the requested changes to the plot, save for the error analysis, which I am still trying to work out (the function I used for the least squares fit does not work out standard error in fit parameters). I will figure out a way to do this and amend the plot to have error bars.

Koji and Kevin measured the output power vs injection current for the Innolight 2W laser.

The threshold current is 0.75 A.

The following data was taken with the laser crystal temperature at 25.04ºC (dial setting: 0.12).

Theoretically the waist position of a Gaussian beam (1064) in our PPKTP crystal differs by ~6.7 mm from that of the incident Gaussian beam.

So far I have neglected such position change of the beam waist in optical layouts because it is tiny compared with the entire optical path.

But from the point of view of practical experiments, it is better to think about it.

In fact the result suggests the rough positioning of our PPKTP crystals;

we should put our PPKTP crystal so that the center of the crystal is 6.7 mm far from the waist of a Gaussian beam in free space.

(How to)

The calculation is very very simple.

The waist position of a Gaussian beam propagating in a dielectric material should change by a factor of n, where n is the refractive index of the material.

In our case, PPKTP has  n=1.8, so that the waist position from the surface of the crystal becomes longer by n.

Now remember the fact that the maximum conversion efficiency can be achieved if the waist locates at exact center of a crystal.

Therefore the waist position in the crystal should be satisfied this relation; z*n=15 mm, where z is the waist position of the incident beam from the surface and 15 mm is half length of our crystal.

Then we can find z must be ~8.3 mm, which is 6.7 mm shorter than the position in crystal.

The attached figure shows the relation clearly. Note that the waist radius doesn't change.

This is mostly a reminder to myself about what I discussed with Jay and Alex this morning.

The big black IO chassis are "almost" done.  Except for the missing parts.  We have 2 Dolphin, 1 Large and 1 Small I/O Chassis due to us.  One Dolphin is effectively done and is sitting in the test stand.  However, 2 are missing timing boards, and 3 are missing the boards necessary for the connection to the computer.  The parts were ordered a long time ago, but its possible they were "sucked to one of the sites" by Rolf (remember this is according to Jay).  They need to either track them down in Downs (possibly they're floating around and were just confused by the recent move), get them sent back from the sites, or order new ones (I was told by one person that the place they order from them notoriously takes a long time, sometimes up to 6 weeks.  I don't know if this is exaggeration or not...).  Other than the missing parts, they still need to wire up the fans and install new momentary power switches (apparently the Dolphin boards want momentary on/off buttons).  Otherwise, they're done.

We are due another CPU, just need to figure out which one it was in the test stand.

6 more BIO boards are done.  When I went over the plans with Jay, we realized we needed 7 more, not 6, so they're putting another one together.  Some ADC/DAC interface boards are done.  I promised to do another count here, to determine how many we have, how many we need, and then report that back to Jay before I steal the ones which are complete.  Unfortunately, he did not have a new drawing for the ASC/vertex wiring, so we don't have a solid count of stuff needed for them.  I'll be taking a look at the old drawings and also looking at what we physically have.

I did get Jay to place the new LSC wiring diagram into the DCC (which apparently the old one never was put in or we simply couldn't find it).  Its located at: https://dcc.ligo.org/cgi-bin/private/DocDB/ShowDocument?docid=10985

I talked briefly with Alex, reminded him of feature requests and added a new one:

1) Single part representing a matrix of filter banks

2) Automatic generation of Simulated shared memory locations and an overall on/off switch for ADC/DACs

3) Individual excitation and test point pieces (as opposed to having to use a full filter bank).  He says these already exist, so when I do the CVS checkout, I'll see if they work.

I also asked where the adl default files lived, and he pointed me at ~/cds/advLigo/src/epics/util/

In that directory are FILTER.adl, GDS_TP.adl, MONITOR.adl.  Those are the templates.  We also discovered the timing signal at some point was changed from something like SYS-DCU_ID to FEC-DCU_ID, so I basically just need to modify the .adl files to fix the time stamp channel as well.  I basically need to do a CVS checkout, put the fixes in, then commit back to the CVS.  Hopefully I can do that sometime today.

I also brought over 9 Contec DO-32L-PE boards, which are PCIe isolated digital output boards which do into the IO chassis.  These have been placed above the 2 new computers, behind the 1Y6 rack.

The 3 seismometers are now on the granite slab.  The Ranger is now aligned with the Xarm (perpendicular to the Mode Cleaner) since that's the only way all 3 would fit on the slab.

Alberto and myself went to downs and acquired the 3rd 4x processor (Dual core, so 8x cores total) computer.  We also retrieved 6 BIO interface boards (blue front thin boxes), 4 DAC interface boards, and 1 ADC interface boards.  The tops have not been put on yet, but we have the tops and a set of screws for them.  For the moment, these things have been placed behind the 1Y6 rack and under the table behind the 1Y5 rack

.

The 6 BIO boards have LIGO travelers associated with them: SN LIGO-S1000217 through SN LIGO-S1000222.

Zach and Koji

We measured uncalibrated angle-to-length coupling using tdssine and tdsdmd.
We made a simple shell script to measure the a2l coupling.

Details:

- Opened the IMC/OMC light door.

- Saw the large misalignment mostly in pitch. Aligned using MC2 and MC3.

- Locked the MC in the low power mode. (script/MC/mcloopson AND MC length gain 0.3->1.0)

- Further aligned MC2/3. We got the transmission of 0.16, reflection of 0.2

- Tried to detect angle-to-length coupling so that we get the diagnosis of the spot positions.

- Tried to use ezcademod. Failed. They seems excite the mirror  but returned NaN.

- We used tdssine and tdsdmd instead. Succeeded.

- We made simple shell script to measure the a2l coupling. It is so far located users/koji/100421/MCspot

- We blocked the beam on the PSL table. We closed the chamber and left.

Koji and Kevin measured the vertical beam profile of the Innolight 2W laser at one point.

This data was taken with the laser crystal temperature at 25.04°C and the injection current at 2.092A.

The distance from the razor blade to the flat black face on the front of the laser was 13.2cm.

The data was fit to the function y(x)=a*erf(sqrt(x)*(x-x0)/w)+b with the following results.

Reduced chi squared = 14.07

x0 = (1.964 +- 0.002) mm

w  = (0.216 +- 0.004) mm

a  = (3.39  +- 0.03) V

b  = (3.46  +- 0.03) V

Back in Gainesville in 1997, I learned how to do this using the chopper wheel. We had to make the assumption that the wheel's blade was moving horizontally during the time of the chop.

One advantage is that the repetitive slices reduces the random errors by a lot - you can trigger the scope and average. Another advantage is that you can download the average scope trace using USB, floppy, or ethernet instead of pencil and paper.

But, I never analyzed it in enough detail to see if there was some kind of nasty systematic error.

Good fit. I assumed sqrt(x) is a typo of sqrt(2).

I updated the default FILTER.adl file located in /home/controls/cds/advLigo/src/epics/util/ on megatron.  I moved the yellow ! button up slightly, and fixed the time string in the upper right.

 So, as it turns out (surprise), I'm a spaz and forgot a 2*pi when calibrating the Guralp noise spectra from the spec sheet.  I noticed this when redoing the Huddle Test, and comparing my Spec Sheet Guralp noise with Rana's, which he shows in elog 2689.  When going from m/s^2, the units in the spec sheet, I just tilted the line by a factor of frequency.  Koji pointed out that I needed a factor of 2*pi*f.  That moves the Guralp spec line in the plot in elog 2237 (to which this entry is a reply) down by ~6, so that my measured noise is not, in fact, below the spec.  This makes things much more right with the world.

In other news, I redid the Huddle analysis of the 2 Guralp seismometers, ala Rana's elog 2689. The difference is now we are on the granite slab, with soft rubber feet between the floor and the granite.  We have not yet cut holes in the linoleum (which we'll do so that we're sitting directly on the 40m's slab).

Rana> this seems horrible. Its like there's a monster in there at 6-7 Hz! Either the seismos are not centered or the rubber balls are bad or Steve is dancing on the granite slab again.

 What kind of fit did you use? How are the uncertainties in the parameters obtained?

Joe and I started working on the new LSC FE control today. We made a diagram of the system in Simulink, but were unable to compile it.

Joe checked out the latest CDS software out of their new SVN and put it somewhere (perhaps his home directory).

We then copied the directory with the .mdl files and the CDS parts library into our real Simulink Model Directory:

/cvs/cds/caltech/cds/advLigo/src/epics/simLink

Use this and not someplace in Alex or Rob's home directory !

Joe will put in more details on Monday once he figures out how to build the new stuff. Basically, we decided not to support multiple versions of the CDS real time code here. We'll just stay synced to the latest stable ~versions.

I exported the current version of the LSC FE into our public_html/FE/ area on nodus where we will put all of the self-documenting FE diagrams:

https://nodus.ligo.caltech.edu:30889/FE/lsc_slwebview_files/index.html

To make a web setup like this, you just use the "Export to Web" feature from the top-level Simulink diagram (e.g. lsc.mdl). Choose the following options:

Note: in order to get the web page to work, I had to change the apache httpd.conf file to allow AddType file overriding. Here's the term cap of the diff:

nodus:etc>diff httpd.conf httpd.conf~
155c155
< ServerAdmin jenne@caltech.edu
---
> ServerAdmin aso@caltech.edu
225d224
<     AllowOverride FileInfo

The vertical beam profile of the Innolight 2W laser was measured at eight points along the axis of the laser.

These measurements were made with the laser crystal temperature at 25.04°C and the injection current at 2.091A. z is the distance from the razor blade to the flat black face of the front of the laser.

The voltage from a photodiode was measured for the razor at a number of heights. Except for the first two points, one scan was made with the razor moving down and a second scan was made with the razor moving up. This data was fit to

y = a*erf(sqrt(2)*(x-x₀)/w) + b with the following results:

The values for w and its uncertainty were estimated with a weighted average between the two scans for the last six points and all eight points were fit to

w = w₀*sqrt(1+(z-z₀)²/z_R²) with the following results:

chi^2/ndf = 17.88

w₀ = (0.07 ± 0.13) mm

z₀ = (-27 ± 121) mm

z_R = (65 ± 93) mm

It looks like all of the data points were made in the linear region so it is hard to estimate these parameters with reasonable uncertainty.

1. The vertical axis should start from zero. The horizontal axis should be extended so that it includes the waist. See Zach's plot http://nodus.ligo.caltech.edu:8080/40m/2818

2. Even if you are measuring only the linear region, you can guess w0 and z0, in principle. w0 is determined by the divergence angle (pi w0/lambda) and z0 is determined by the linear profile and w0. Indeed your data have some fluctuation from the linear line. That could cause the fitting prescision to be worse.

3. Probably the biggest reason of the bad fitting would be that you are fitting with three parameters (w0, z0, zR) instead of two (w0, z0). Use the relation ship zR= pi w0^2/lambda.

LSC Plant Model. That is all.

Once you made a CDS model, please update the following wiki page. This will eventually help you.

http://lhocds.ligo-wa.caltech.edu:8000/40m/Electronics/Existing_RCG_DCUID_and_gds_ids

The SVN checkout was done on megatron.  It is located under /home/controls/cds/advLigoRTS

So, to compile (or at least try to) you need to copy the .mdl file from /cvs/cds/caltech/cds/advLigo/src/epics/simLink to /home/controls/cds/advLigoRTS/src/epics/simLink on megatron, then run make SYS in the advLigoRTS directory on megatron.

The old checkout from CVS exists on megatron under /home/controls/cds/advLigo.

I scanned the temperature of the crystal oven on Friday night in order that we can find the optimal temperature of the crystal for SHG.

The optimal temperature for this crystal was found to be 36.2 deg.

The crystal is on the PSL table. The incident beam on the crystal is 27.0mW with the Newport power-meter configured for 1064nm.
The outgoing beam had 26.5mW.

The outgoing beam was filtered by Y1-45S to eliminate 1064nm. According to Mott's measurements, Y1-45S has 0.5% transmission for 1064nm, while 90% transmission for 532nm. This means I still had ~100uW after the Y1-45S. This is somewhat consistent with the offset seen in the power-meter reading.

First, I scanned the temperature from 28deg to 40deg with 1deg interval.The temperature was scaned by changing the set point on the temperature controller TC-200.The measurements were done with the temperature were running. So, the crystal may have been thermally non-equilibrium.

Later, I cut the heater output so that the temperature could be falling down slowly for the finer scan. The measurement was done from 38deg to 34deg with interval of 0.1deg with the temperature running.

I clearly see the brightness of the green increase at around 36 deg. The data also shows the peak centered at 36.2deg. We also find two lobes at 30deg and 42deg. I am not sure how significant they are.

To fix a problem one of the models was having, I checked the CVS version of the Bitwise.pm file into the SVN (located in /home/controls/cds/advLigoRTS/src/epics/util/lib), which adds left and right bit shifting funtionality.  The yec model now builds with the SVN checkout.

Also while trying to get things to work, I discovered the cdsRfmIO piece (used to read and write to the RFM card) now only accepts 8 bit offsets.  This means we're going to have to change virtually all of the RFM memory locations for the various channels, rather than using the values from its previous incarnation, since most were 4 bit numbers.  It also means it going to eat up roughly twice as much space, as far as I can tell.

Turns out the problem we were having getting to compile was nicely answered by Koji's elog post.  The shmem_daq value was not set to be equal to 1.  This caused it to look for myrimnet header files which did not exist, and caused compile time errors.  The model now compiles on megatron.

[Edit by KA: 4 bit and 8 bit would mean "bytes". I don't recall which e-log of mine Joe is referring.]

Talked with Jay briefly this morning.

We are due another 1-U 4 core (8 CPU) machine, which is one of the ones currently in the test stand.  I'm hoping sometime this week I can convince Alex to help me remove it from said test stand.

The megatron machine we have is definitely going to be used in the 40m upgrade (to answer a question of Rana's from last Wednesday's meeting).  Thats apparently the only machine of that class we get, so moving it to the vertex for use as the LSC or SUS vertex machine may make sense.  Overall we'll have the ASS, OMC, Megatron (SUS?), along with the new 4 1-U machines, for LSC, IO, End Y and End X.  We are getting 4 more IO chassis, for a total 5.  ASS and OMC machine will be going without full new chassis.

Speaking of IO chassis, they are still being worked on.  Still need a few cards put in and some wiring work done.  I also didn't see any other adapter boards finished either.

I tried Koji's suggestions for improving the fit to the vertical beam profile; however, I could not improve the uncertainties in the fit parameters.

I started retaking the data today with the same laser settings used last time and noticed that the photodiode was saturating. We were using an ND 4.0 neutral density filter on the photodiode. Koji and I noticed that the coating on the filter was reduced in the center and added an additional ND 0.6 filter to the photodiode. This seemed to fix the photodiode saturation.

I think that the photodiode was also saturating to a lesser extent when I took the last set of data. I will take another vertical beam profile tomorrow.

[Edit by KA: Metallic coating started being evaporated and the ND filters reduced their attenuation. We decided to use absorptive one as the first incident filter, and put a thinner one behind. This looked fine.]

Give me the plot of the fit, otherwise I am not convinced.

Kiwamu and Koji

The PRM/SRM were balanced with the standoffs. We glued them to the mirror.

This was the last gluing so far until we get new PRM/ETMs.

The mode profile of Gaussian beams in our PPKTP crystals was calculated.

I confirmed that the Rayleigh range of the incoming beam (1064 nm) and that of the outgoing beam (532 nm) is the same.

And it turned out that the waist postion for the incoming beam and the outgoing beam should be different by 13.4 mm toward the direction of propagation.

These facts will help us making optical layouts precisely for our green locking.

(detail)

The result is shown in the attached figure, which is essentially the same as the previous one (see the entry).

The horizontal axis is the length of the propagation direction, the vertical axis is the waist size of Gaussian beams.

Here I put x=0 as the entering surface of the crystal, and x=30 mm as the other surface.

The red and green solid curve represent the incoming beam and the outgoing beam respectively. They are supposed to  propagate in free space.

And the dashed curve represents the beams inside the crystal.

A trick in this calculation is that: we can assume that  the waist size of 532 nm is equal to that of 1064 nm divided by sqrt(2) . 

If you want to know about this treatment in detail,  you can find some descriptions in this paper;

"Third-harmonic generation by use of focused Gaussian beams in an optical super lattice" J.Opt.Soc.Am.B 20,360 (2003)"

I thought that the micrometer I was using to move the razor through the laser beam was metric; however, it is actually english.

After discovering this mistake, I converted my previous measurements to centimeters and fit the data to

w = sqrt(w0^2+lambda^2*(z-z0)^2/(pi*w0)^2) with the following results:

reduced chi squared = 14.94

z0 = (-4.2 ± 1.9) cm

w0 = (0.013 ± 0.001) cm

Beginning last week, I have been helping Koji with some of the IO work that must be done for the 40m upgrade. The first thing he asked me to do is to help with the alignment of the MC.

As I understand, it became apparent that the IFO beam was not centered on all (or any) of the MC mirrors, which is disadvantageous for obvious reasons. We are trying to correct this, using the following strategy:

1. Adjust the MC mirrors into rough alignment, isolate a strong TEM₀₀, and lock the cavity
2. Fine-tune the alignment by minimizing the REFL power when locked (in these first two steps, we adjusted only MC2 & MC3, assuming that the REFL beam was centered on the PD, and wanting to keep it that way). At this point, the cavity is resonating some asymmetric mode, looking something like (not to scale---for illustration only):
3. Shake all three mirrors (in succession) in pitch and yaw, each time demodulating the error signal at the frequency used for the excitation and recording the magnitude and phase of the response.
4. Move one mirror's DC orientation, repeat step 3, and then restore the mirror to its original position
5. Repeat step 4 for both angular degrees of freedom of each mirror

Using the results of these measurements, it is possible to evaluate the components of a block-diagonal matrix M which relates the tilt-to-displacement coupling of each DOF to each mirror's misalignment in that degree, i.e.,

a = M x

with a a 6-dimensional vector containing the coupling of each degree of freedom to the length of the cavity and x a 6-dimensional vector containing the angular misalignments of each. Due to orthogonality of pitch and yaw, M will take the form of a 6x6 matrix with two non-zero 3x3 blocks along the diagonal and zero matrices on the off-diagonal blocks.

The idea is to isolate components of M by moving one mirror at a time, solve for them, then find the inverse M^-1 that should give us the required angular adjustments to obtain the beam-centered ideal cavity mode.

In theory, this need only be done once; in practice, our measurement error will compound and M will not be accurate enough to get the beams exactly centered, so we will have to iterate.

NOTE: The fact that we are adjusting the three cavity mirrors to obtain the ideal mode means that we will necessarily tarnish our coupling into the cavity. Once we have adjusted the mirrors once, we will need to re-steer the input beam and center it on the REFL diode. 

Status: This process has been completed once through step 5. I am in the process of trying to construct the matrix for the first adjustment.

 Restarted the elog with the script as it was down.

And again.

I have worked out the first set of adjustments to make on the MC mirrors (all angle figures are in units of the increments on the control screen)

Using the method described in the previous post, I obtained the following matrix relating the angle-to-length coupling and the angular deviations. In the following matrix, M_ij corresponds to the contribution of the j^th degree of freedom to the i^th A-to-L coupling, with the state vector defined as xⁱ = (MC1_P, MC2_P, MC3_P, MC1_Y, MC2_Y, MC3_Y), where each element is understood as the angular deviation of the specific mirror in the specific direction from the ideal position, such that x = 0 when the cavity eigenmode is the correct one and the beams are centered on the mirrors (thus giving no A-to-L coupling regardless of the components of M).

M =

   1.0e+03 *

   -0.2843   -0.4279   -0.1254         0         0         0

   -0.8903   -0.4820   -0.6623         0         0         0

    0.5024    0.0484   -0.0099         0         0         0

         0         0         0         0.1145   -0.1941   -0.3407

         0         0         0         0.0265    1.5601    0.2115

         0         0         0         0.1015    0.1805   -0.0103,

giving an inverse

M^-1 =  

    0.0003   -0.0001    0.0020         0         0         0

   -0.0031    0.0006   -0.0007         0         0         0

    0.0018   -0.0018   -0.0022         0         0         0

         0         0         0        -0.0013   -0.0015    0.0117

         0         0         0         0.0005    0.0008   -0.0008

         0         0         0        -0.0037   -0.0010    0.0044

The initial coupling vector is then acted on with this inverse matrix to give an approximate state vector x containing the angular misalignments of each mirror in pitch and yaw. The results are below:

x = 

   1P:  0.0223

   2P: -0.0733

   3P:  0.3010

  1Y:  -0.1372

  2Y:   0.0194

  3Y:  -0.0681

 That's interesting.

Would it be possible to write about the technique on a wiki page as you get measurements and results?

I used the Mathematica CurveFit package that we use in Ph6/7 to make the fits for the beam profile data. I wrote two functions that use CurveFit shown in the attachment to make the fits to the error function and square root.