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ID Date Author Type Category Subject
7187   Wed Aug 15 04:03:55 2012 ranaSummaryLSCY-Arm Locking

0) Did a bunch of alignment to get beams roughly centered on ETMY and ITMY and maximize power. Adjusted the aperture and focus on ETMY camera to get nice image. Camera needs to be screwed in tightly and cables given some real strain relief, Steve.

1) snapshots not working on many MEDM screens. Who's on top of this?

2) save/restore not working for PZT2 sliders

3) changed power and filter triggers on yarm to match xarm

4) yarm filters copied from xarm (need to handtune RGs)

5) DTT wasn't working on rossa. Used the Date/Time GUI to reset the system time to match fb and then it stopped giving 'Test Timed Out'. Jamie check rossa ntpd.

6) Removed the high 3.2 Hz RG filter. We don't have any sharp features like that in the spectrum.
---then added it back. The 3.2 Hz comes and goes depending on what Yoichi is doing over in the MC area. Leaving it in by default, but lowering the Q from 2 to 1.5.

7) Attached is the noise spectra, coherence, and loop gain model for this yarm condition. For the plant model, I assume a pendulum (f=1 Hz, Q = 9) and a cavity pole of 1600 Hz. Gain is scaled to set the UGF at 165 Hz (as guessed by looking at the servo gain peaking frequency). This cheezy model doesn't include any of the delays from DAC, AA, or AI. Eric and Sasha should have something more useful for us by Friday.

8) Change the DQ channels: need XARM and YARM IN1 at 16k. e.g. XARM_ERR, etc.

9) To get the DTT plots to make thumbnails in the elog, I print a .ps file and then use 'epstopdf' to make the PDF.

7190   Wed Aug 15 11:40:15 2012 YaakovSummarySTACISWeekly Summary

This week I've been focusing mainly on two things: 1) Designing a port for the STACIS that will allow external actuation and/or local feedback and 2) Investigating the seismic differential motion along the interferometer arms.

The circuit for the port is just a signal summing junction (in case we want to do feedforward and feedback at the same time) with BNC inputs for the external signal and switches that allow you to turn the external signal or feedback signal on/off. I'll test this on a breadboard and post the schematic if it works. I looked at the noise of the geophone pre-amp and DAC, which would be the feedback and external signal sources, respectively. According to Rolf Bork, the DAC noise is 700 nV/rtHz, and I measured the pre-amp board's minimum noise level at 20*10^-6 V/rtHz (which seems quite high). Both these noises are higher than the op-amp noise for my circuit (I'm considering the op-amp LT1012), which according to the specs is 30 nV/rtHz. This confirms that my circuit will not be the limiting noise source

Along with Den, I calibrated the seismometers in the lab and measured the displacement differential arm motion (see eLog 7186: http://nodus.ligo.caltech.edu:8080/40m/7186). I'm trying to find a transfer function for the seismic stacks (and pendulum, but that's simpler) so I can calculate the differential motion in the chamber. After doing this offline, I'll make new channels in the PEM to look at the ground and chamber differential motion along the arms online.

I also am looking at the noise of the geophones with their shunt resistor (4k resistor across the coil) removed, to see if it improves the noise at low frequencies. My motivation for this was that the geophone specs show a better V/m/s sensitivity at low frequencies when the shunt resistor is removed, so the actual signal may become larger than the internal noise at these frequencies.

7191   Wed Aug 15 11:44:35 2012 jamieSummaryLSCntp installed on all workstations

 Quote: 5) DTT wasn't working on rossa. Used the Date/Time GUI to reset the system time to match fb and then it stopped giving 'Test Timed Out'. Jamie check rossa ntpd.

ntp is now installed on all the workstations.  I also added it to the /users/controls/workstation-setup.sh script

7192   Wed Aug 15 13:23:34 2012 LizSummaryComputer Scripts / ProgramsLast Weekly Update

Over the past week I have been continuing to finalize the daily summary pages, attempting to keep the total run time under half an hour so that they can be run frequently.  I have had many hang ups with the spectrograms and am currently using second trends (with this method, the entire script takes 15 minutes to run).  I also have a backup method that takes 3 minutes of data for every 12 minutes, but could not implement any interpolation correctly.  This might be a future focus, or the summary pages could be configured to run in parallel and full data for the spectrograms can be used.  I configured Steve's tab to include one page of images and one page of plots and fixed the scripts so that it corrects for daylight savings time (at the beginning of the running, the program prints 'DST' or 'Not DST').

Right now, I am focusing on making coherence plots in a spectrogram style (similar to the matlab 'coh_carpet' function) and a spectrogram depicting Gaussianity (similar to the plots made by the RayleighMonitor).  I have also been working on my  final paper and presentation.

7195   Wed Aug 15 16:29:59 2012 Eric SummaryGeneralSURF Update

This week I took more data for the calibration of YARM. The summary of measurements taken is:

1. Peak-to-peak on Michelson
2. Michelson open loop
3. Excite ITMY and measure on AS55_Q_ERR
4. Excite ITMY and measure on POY11_I_ERR
5. Excite ETMY and measure on POY11_I_ERR
6. YARM open loop

Then I worked on comparing these measurements to the Simulink model of the interferometer control loop. The measured open loop transfer function of the YARM matched well with the model above about 20 Hz, after the gain was scaled properly to fit the data. Next is to fit the length response function of the model and the measurements, and then use DTT to calibrate the arm cavity's power spectrum.

7203   Thu Aug 16 13:04:36 2012 LizSummaryComputer Scripts / ProgramsDaily Summary Details

I just wrote a short description of how to run the daily summary pages and the configuration process for making changes to the site.  It can be found in /users/public_html/40m-summary and is named README.txt.  If I need to clarify anything, please let me know!  The configuration process should be relatively straightforward, so it will be easy to add plots or change them when there are changes at the 40 meter.

7211   Fri Aug 17 00:16:30 2012 EricSummaryLSCYARM Calibration

I modified my Simulink model of the YARM to match the new filter modules Rana installed on YARM. I also scaled the open loop transfer function of the model to fit the measured open loop transfer function at the unity gain frequency, as shown in the figure below. From this I produced the length response function correctly scaled, also shown below.  Then I applied the calibration factor to the YARM data measured in /users/Templates/Y-Arm_120815.xml. Both the uncalibrated and calibrated spectra are included below.

7213   Fri Aug 17 04:54:01 2012 Yoichi, KojiSummaryLSCPRMI Locking

To taste the strangeness of the current 40m PRC, I locked the PRMI with the guide of Koji.

We first aligned MICH by mostly tweaking ITMX, assuming that ITMY is in a good place as the Y-arm locks. MICH lock was stable.

Then we restored the IFO to the PRM_SBres mode. With a bit of alignment work on PRM and gain tweaking, the PRMI locked.

## Yes, the beam spots look UGLY !

Also the PRMI was not so stable. Especially, when the alignment fluctuates, the optical gain changes and the loop becomes temporarily unstable. We took POP_DC as the guide for the gain change and normalized the PRCL error signal with it. To do this smoothly, we first changed the input matrix to route the PRCL error signal, which is REFL33_I, so that the signal also goes to the MC filter bank. Then with dtt, we monitored the spectra of the PRCL_IN1 and MC_IN1. We tweaked the value of the element in the normalization matrix for the MC path until the two spectra look the same (at this moment, the normalizing factor for the PRCL path was still zero). During this process, we noticed that the MC path signal (normalized by POP_DC) is noisier at above 500Hz. This was because the POP_DC has a large noise at high frequencies. So we put a low pass filter (100Hz 2nd order Butterworth) to the POP_DC filter bank to reduce the noise. Then the two spectra looked almost the same. The correct normalization factor found in this way was 0.03. So we put this number in the normalization matrix for PRCL. It did not break the PRMI lock.

After the normalization is turned on, the PRMI lock became somewhat more stable. However, the POP_DC was still fluctuating a lot, especially when the alignment is good. So I made a boost filter: 5Hz pole Q=2, 15Hz zero Q=1.5. I also made this filter automatically triggered when the PRMI is locked. This made the PRMI lock acquisition quicker. However, still the POP_DC fluctuation is large. It seems that the alignment of PRC is really fluctuating a lot.

The current UGF of PRMI is about 150Hz with the phase margin over 50deg.

7224   Sat Aug 18 03:55:12 2012 YoichiSummaryLSCX-arm locking again

Tonight, I worked on the X-arm locking again. I did not have any significant progress, but observed several issues and will give some suggestions for future work here.

What I did tonight was basically re-alignment of the X-arm (because Rana touched the PZT mirrors for the Y-arm alignment, the X-arm alignment was screwed up). Then I measured the open loop gain. Of course it was almost identical to the one posted in this entry. It reminded myself of how small the phase bubble is. This means we have to finely adjust the gain to set the UGF at the right frequency, i.e. 100Hz. So I decided to do the signal normalization using the TRX power. Using the MC path method described here,  the appropriate normalization coefficient was determined to be 1.6, when the XARM gain is set to 0.05. Using burtgooey, I updated the burt snapshot used by the X-arm restore script.

Now I observed the following things:

When the normalization is used, the lock itself is stable, but the lock acquisition takes loner (i.e. fails more often).

I don't know the exact reason, but here is my guess: Usually, the error signal is divided by the square root of the transmitted power to widen the linear range of the PDH error signal. However, what I'm doing here is dividing the error signal with the power itself, not the sqrt. This might distort the error signal in a not-friendly-for-lock way ? I don't know.

I checked the c1lsc FE code. There seems to be the sqrt(TRX) and sqrt(TRY) signals computed in the code. However, these are not used for the normalization.

Now, there are two requirements. When dragging the mirrors into the resonance, we want to normalize the error signal with sqrt(TRX). When the mirrors reach the resonance, the gain of the loop must be normalized by TRX. How do we smoothly connect those two states ? Someone should spend some time on this. Maybe I will work on this in Japan.

We really need a time delay in the filter trigger

The automatic filter trigger is awesome. However, the [0^2:5^2] filter, which is an integrator, takes time to switch on and off. Every time the cavity passes by a resonance, this filter gets turned on and off slowly, giving some large transients. This transient combined with the bad coil balance of ETMX sometimes made the optical lever of ETMX crazy. This can be avoided by turning on this filter a few seconds after the power reaches the threshold. As Rana suggested, we should be able to put an arbitrary time delay to the filter trigger.

Someone should balance the coils

The coil balance of ETMX is bad and causing the above mentioned problem. I tweaked the coil balance by injecting a sinusoidal signal (10Hz) into ETMX pos and trying to minimizing the spectral peak in the optical lever signals. Of course, this is a cheesy work. Someone should put more serious effort on this.

A civilized interferometer should have an auto-alignment capability

After my alignment work, the X-arm power got to about 0.7. (This is probably because the MC transmission power has been low for the past 5 hours or so (attachment 1)).

In anyway, after the cavity locked to the TEM00 mode, the alignment has to be automatically improved by dithering. It is anachronism to sit down and click on the MEDM screen until the power gets big enough.

7238   Tue Aug 21 00:02:05 2012 ranaSummaryComputer Scripts / ProgramsGDS/DTT bug: 10 digit GPS times not accepted

I've noticed that we're experiencing this bug which was previously seen at LHO. We cannot enter 10 digit GPS times into the time fields for DTT due to a limit in TLGEntry.cc, which Jim Batch fixed in September of last year. Seems like we're running an old version of the GDS tools.

I checked the Lidax tool (which you can get from the GDS Mainmenu). It does, in fact, allow 10 digit entries.

7239   Tue Aug 21 00:35:25 2012 ranaSummaryIOOVisibilities and Chrome

MC and PMC vis:

MC REFL Unlocked    = 4.4

MC REFL Locked      = 0.67

1 - Locked/Unlocked = 85%

PMC REFL Unlocked   = 0.270

PMC REFL Locked     = 0.013

1 - Locked/Unlocked = 95%

I checked (by looking through recent trends) that the zero level is zero on both channels. I tried to do a proper mode scan, but we have lost the PSL fast channels during the upgrade sadly. Also, the DC signal for the PMC REFL needs some gain. Unlocked level should be more like 3-5 V.

Also used the instructions from this page to add Google's sources to rosalba's apt-get list and then installed Chrome.

7249   Wed Aug 22 15:47:34 2012 jamieSummaryGeneralvent prepartion for fast-track vent

We are discussing venting first thing next week, with the goal of
diagnosing what's going on in the PRC.

Reminder of the overall vent plan:

https://wiki-40m.ligo.caltech.edu/vent

Since we won't be prepared for tip-tilt installation (item 2), we should
focus most of the effort on diagnosing what's going on in the PRC.  Of
the other planned activities:

(1) dichroic mirror replacement for PR3 and SR3

Given that we'll be working on the PRC, we might consider going ahead
with this replacement, especially if the folding mirror becomes
suspect for whatever reason.  In any case we should have the new
mirrors ready to install, which means we should get the phase map
measurements asap.

(3) black glass beam dumps:

Install as time and manpower permits.  We need to make sure all needed
components are baked and ready to install.

(4) OSEM mount screws:

Delay until next vent.

(5) new periscope plate:

Delay until next vent.

(6) cavity scattering measurement setup

Delay until next vent.

7259   Thu Aug 23 17:17:49 2012 MashaSummaryComputersCode Folder Status

I cleaned up my directory (/users/masha) today. A lot of the files are just code that I experimented with, but the important files for training the classification neural network are in "neural_network_classification". The "EarthquakeData" subdirectory contains my entire dataset. Files of the form "GenerateRNNInput" are used to create input vector sets to the network, while files of the "*NeuralNetworkClassification* actually run the code that generates the neural network vectors for the classification code block in the c1pem model.

Also, the folder "feed_c", which can also be found in Den's directory, contains the neural network controller code we played around with.

7271   Fri Aug 24 14:46:08 2012 JenneSummaryGeneralDetailed alignment plan

Friday / pre-vent:

[done] Align the MC mirrors for the incident beam so that the mirrors can be the alignment reference [Koji]

[in progress] Center spots on MC mirrors [Jenne]

Put beam attenuator optics (PBS + waveplate) on PSL table, realign input beam to MC mirror centers

[In progress] See if we can design a set of nuts and bolts to use at bottom of tiptilt optic ring, to do small adjustments of pitch alignment [Steve]

After doors open:

Use CCD (Watek, with AGC on) to take images of everything we can think of, to see current status of clipping

Check that we get through the Faraday without clipping

Move PZT1 and MMT mirrors to get good spot positions on PR3, PR2.  Make sure we're clearing the Faraday's housing

Install dichroic optics, perhaps completely readjust pitch alignment of those tiptilts (we will measure the spares later, and call that good enough for our phase mapping).

Use some kind of oplev setup to check pitch alignment of PR2, PR3.

Tweak (if necessary) PR2 & PR3 pitch to go through center of PRM, BS, hit center of ITMY

Check that we're not clipping on the BS cage anywhere

Use CCD to take images with Sensoray of everything we can think of, to confirm we don't have clipping anywhere.  Want to see the edges of the beam on the targets, which would mean that the beam is hitting the center of the optic.  If necessary, we'll stay open an extra day to get good camera images everywhere, so we have a good record of what's going on inside.

Note:  While having good arm alignment would be good, we're willing to sacrifice some arm alignment to have good DRMI alignment, since we're re-venting and installing the new active tiptilts in another month or so.

Things I'm leaving for Jamie-the-Vent-Czar to plan:

Order of door opening

Beam dump assembly and placement

7435   Mon Sep 24 20:28:13 2012 ranaSummaryelogrestarted elog: was unresponsive
7558   Tue Oct 16 16:46:20 2012 Vent Czar and CzarinaSummaryGeneralvent stuff

We're discussing the plan for the next vent.  Now that we have all the tip-tilt stuff in hand, we should get ready for the big TT installation vent ASAP.  The question is what remains to be done, and when can we be ready

Stuff that needs doing:

* characterize TTs, check electrical connection of quadrupus cables, bake cables and base plates - a week or so (not including baking)

* phase map of LaserOptik mirrors (decide on needed resolution) - a week or so?

* get ready to swap G&H mirrors with LaserOptik mirrors (PR2, PR3, SR2, SR3)

* assembly of black glass beam dumps - one afternoon

* green periscope moving - day or so to make sure greens are resonant in arms, so we have something to align to

* redraw of REFL path?? (rotate 2nd refl mirror to reflect beam to the east, then add mirror to get beam out of IOO chamber viewport), cut hole in BS oplev table's box, install black beam tube

* FI camera mount - make sure it's here, baked

* active TT pitch damping plan

* passive TT weight addition and pitch alignment plan

* camera plan for taking in-chamber photos without touching the tables

* look at layout of ITMY table.  POY pick-off too close to main beam.  Can we move POY pick-off to BS table?

* remount black glass baffles on SOS cages.

Stuff to bake:

* TT base plates

* FI mirror mount for FI camera

* stuff to add to active TTs

* stuff to add to passive TTs

7560   Tue Oct 16 17:13:23 2012 CzarinaSummaryGeneralvent stuff - 4 paths

I see 4+ possible paths for us to take, in terms of a possible vent in the next few weeks:

No Vent - Just do FPPRMI, using AS55

Mini Vent - Fix REFL path, nothing else.  ~1 day at atmosphere

Medium Vent - Fix REFL path, swap G&H mirrors for LaserOptik mirrors (so also resuspend passive TTs, maybe add pitch adjustment option). ~1 week or so at atmosphere - do this rather than Mini if Jan's Finesse calc says the G&H mirrors are too rough

Mega Vent - Fix all the things, do all the things.  Long time at atmosphere

The "+" is to take into account all the possible variations on "medium vent".  The No, Mini and Medium options assume we'll do the Mega option later, just not immediately.

7703   Tue Nov 13 08:34:11 2012 SteveSummaryVACpumpdown after 24days at atmosphere

7742   Mon Nov 26 10:06:51 2012 ranaSummaryIOOMC slides from 2002
7844   Mon Dec 17 21:41:30 2012 ranaSummarySUSBeCu wire

Just in case we want to retrofit the Tip/Tils with Beryllium Copper wire, here are links to a few sources which have a supply of the right composition and temper:

http://www.lfa-wire.com/Tempered-Alloy-25_C17200.htm

http://www.alloywire.com/beryllium_copper_CB_101.html

http://www.ngk.co.jp/english/products/electronics/berylliumcopper/wire/index.html

http://www.goodfellow.com/E/Copper-Beryllium-Wire.html

I don't think its worth it to do something to modify them unless we get a real reduction in the hysteresis - need a benchtop test setup ASAP.

7845   Mon Dec 17 22:42:27 2012 KojiSummaryGeneralThe projector lamp ended its life?

i just heard a rather large exploding sound in the control room.
I tried to locate the source and found the projector is not illuminating the wall anymore.
There is a slight smell of burning, but nothing is smoking.

Probably the lamp ended its life.

Rana and I just talked about the projector life time an hour ago! It must have been hearing!

7846   Mon Dec 17 22:49:33 2012 ManasaSummaryGeneralThe projector lamp ended its life?

 Quote: i just heard a rather large exploding sound in the control room. I tried to locate the source and found the projector is not illuminating the wall anymore. There is a slight smell of burning, but nothing is smoking. Probably the lamp ended its life. Rana and I just talked about the projector life time an hour ago! It must have been hearing!

LOL

We should try purchase a projector with LED this time...longer lifetime! I guess the price of replacing the lamp in the one we have will be more or less same as a new one!

7847   Tue Dec 18 00:45:19 2012 KojiSummaryGeneralThe projector lamp ended its life?

...Nah. The projector is pretty new (t<1yr) and this is the first time to have the lamp busted after the installation last year in Jan.

We just should purchase two bulbs.

7860   Wed Dec 19 21:35:33 2012 KojiSummaryGeneralFirst Contact Training with Margot

[Koji, Steve]

First Contact Training with Margot

7885   Wed Jan 9 13:34:34 2013 KojiSummaryGeneralThe projector lamp ended its life?

[Koji, Manasa]

- A new projector lamp installed.

- The old lamp lasted 8751 "equivalent lamp hours".

- The old lamp was found being shattered inside. It contains mercury.
So next time you hear the explosion sound of the lamp, establish the ventilation of the room and escape for an hour.

7904   Wed Jan 16 10:57:37 2013 taraSummaryIOONoise budget for MC

I calculated thermal noise in mode cleaner (MC) mirrors and compared it with the measured MC noise. Thermal noise won't be a significant noise source for MC.

== Motivation==

There is an idea of using MC and a refcav to measure coating thermal noise. One laser is frequency locked to MC, another laser is locked to an 8" refcav. Then the two transmitted beams are recombined so that we can readout the frequency noise. In this case, the transmitted beam from MC is a better reference (less frequency noise) than the beam from refcav. However, we need to make sure that we understand the noise sources, for example brownian noise, thermoelastic noise in both substrates and coatings, in MC more thoroughly.

==Calculation==

I used Rana's code for MC's technical noise sources from, svn. The same plot can be found in appendix C of his thesis. Then I added my calculation to the plot.  Jenne pointed me to 40m:2984 for the spot size and the cavity length. The spot radius on MC1 and MC3 is ~ 1.5mm, and ~3.4 mm@MC2, The round trip length is ~27m, thus the frequency fluctuation due to thermal noise is lower than that of refcav by 2-3 orders of magnitude. I calculated Brownian noise in coatings, Brownian noise in substrate, Thermoelastic noise in substrate. I assumed that the coatings are SiO2/Ta2O5, quarter stacks, coatings thickness for MC1/3 = 5um, for MC2 = 8um. The code can be found in the attachment.

==result==

Total thermal noise on MC (Brownian + Thermoelastic on substrate and coatings of MC1-MC3) is plotted in dashed red. It is already below 10^-5 Hz/rtHz at ~20 Hz. This is sufficiently low compared to other noise sources. Beat signal from CTN measurement with 8" cavities is plotted in pink, the estimated coating brownian noise is plotted in a yellow strip. They are well above the measured MC noise between 100 Hz to a few kHz. Measuring coating thermal noise on 8" refcav seems plausible with this method. We can beat the two transmitted beams from IMC and refcav and readout the beat signal to extract the displacement noise of refcav. I'll discuss this with Koji if this is a good surf project.

[the internal thermal noise in the original plotted is removed and replaced with the total thermal noise plot instead]

note:I'm not sure about the current 40m MC configuration. The parameters used in this calculation are summarized in mcnoiseS2L1.m (in the svn page).

7908   Wed Jan 16 19:08:51 2013 KojiSummaryIOONoise budget for MC

I missed the point.
Do you mean that we can measure the coating thermal noise of the ref cav at the 40m as the IMC is quiet enough?

7911   Thu Jan 17 01:27:54 2013 Tara(?)SummaryIOONoise budget for MC

 Quote: I missed the point. Do you mean that we can measure the coating thermal noise of the ref cav at the 40m as the IMC is quiet enough?

Yes, it should be. However, what I did was calculating thermal noise of MC. I'm not sure about the 40m IMC's actual noise level. The plot in the entry was taken from LLO's MC in 2003.

7979   Thu Jan 31 22:14:11 2013 ranaSummaryASCOptics lit

Gouy not Guoy:

http://www.rp-photonics.com/gouy_phase_shift.html

pronounced Goo-eee, with the emphasis on the second syllable.

7982   Fri Feb 1 12:22:27 2013 ZachSummaryASCOptics lit

It's OK; even Siegman got it wrong---48 times.

RA: NO, stil not OK.

 Quote: Gouy not Guoy: http://www.rp-photonics.com/gouy_phase_shift.html pronounced Goo-eee, with the emphasis on the second syllable.

7989   Sun Feb 3 13:20:02 2013 KojiSummaryGeneralHypothesis

Rana mentioned the possibility that the PR2 curvature makes the impact on the mode stability. Entry 7988
Here is the extended discussion.

Hypothesis:

The small but non-negligible curvatures of the TT mirrors made the recycling cavity unstable or nearly unstable.

Conclusion:

If the RoC of the TT mirrors are -600 m (convex), the cavity would be barely stable.
If the RoC of the TT mirrors are less than -550m, the horizontal modes start to be unstable.
Assumption that all of the TT mirrors are concave should be confirmed.

Fact (I): Cavity stability

- The folded PRMI showed the mode stability issue. (L=6.78m from Jenne's entry 7973)
- The folded PRM-PR2-PR3-flat mirror cavity also showed the similar mode issue. (L=4.34m)
- The unfolded PRM-PR2 cavity demonstrated stable cavity modes. (L=1.91m)

Fact (II): Incident angle

- PRM 0deg
- PR2 1.5deg
- PR3 41deg

Fact (III): Mirror curvature

- RoC of PRM (PRMU02): +122.1m (measured, concave), or +115.6m (measured by the vendor)
- RoC of G&H mirrors: -600m ~ -700m (measured, I suppose the negative number means convex) (Jenne's entry 7851)
[Note that there is no measurement of the phase map for the PR2 mirror itself.]
- RoC of LaserOptik mirrors: -625m ~ -750m (measured, I suppose that the measurement shows the mirrors are convex.) (Jan's entry 7627 and 7638)

Let's assume that the TT mirrors are always convex and have a single number for the curvature radius, say RTT

Cavity mode calculation with Zach's arbcav

1) The unfolded PRM-PR2 cavity:

The cavity becomes unstable when 0 > RTT > -122m  (This is obvious from the g-factor calculation)
==> The measured RoC of the TT mirrors predicts the cavity is stable. (g=0.98, Transverse Mode Spacing 3.54MHz)

2) The folded PRM-PR2-PR3-flat mirror cavity:

The cavity becomes unstable when RTT < -550 m
==> The measured RoC of the TT mirrors (RTT ~ -600m) predicts the cavity is barely stable (g=0.997, TMS ~600kHz).

- The instability occurs much faster than the unfolded case.
- The horizontal mode hits unstable condition faster than the vertical mode.
- The astigmatism mainly comes from PR3.

3) The folded PRMI:

The cavity becomes unstable when RTT < -550 m
==> The measured RoC of the TT mirrors (RTT ~ -600m) predicts the cavity is barely stable. (g=0.995, TMS ~500kHz)

- The instability occurs with almost same condition as the case 2)

The calculation result for the PRMI with RTT of -600 m. The code was also attached.

Q&A:

Q. What is the difference between unfolded and folded?
A. For the unfolded case, the PR2 reflect the beam only once in a round-trip.
For the folded case, each TT mirror reflects the beam twice. Therefore the lens power by the mirror is doubled.

Q. Why the astigmatism mainly comes from PR3?
A. As the angle of incidence is much bigger than the others (41deg).

Q. Why the horizontal mode is more unstable than the vertical mode?
A. Off-axis reflection of a spherical mirror induces astigmatism. The effective curvature of the mirror in
the horizontal direction
is R / Cos(theta) (i.e. longer), while it is R Cos(theta) (i.e. shorter). Indeed, the vertical and horizontal ROCs are factor of 2 different
for the 45deg incidence.

Q. Why the stability criteria for the case 2) and 3) similar?
A. Probably, once the effective curvature of the PRM-PR2-PR3 becomes
negative when RTT < -550 m.

Q. You said the case 2 and 3 are barely stable. If the TMS is enough distant form the carrier, do we expect no problem?
A. Not really. As the cavity get close to the instability, the mode starts to be inflated and get highly astigmatic.
For the case 2), the waist radii are 5.0mm and 3.7mm for the horzontal and vertical, respectively.
For the case 3), they are 5.6mm and 4.1mm for the horzontal and vertical, respectively.
(Note: Nominally the waist radius is 3.1mm)

Q. What do you predict for the stability of the PRM-PR2-Flat_Mirror cavity?
A. It will be stable. The cavity is stable until
RTT becomes smaller than -240 m.

Q. If the TT mirrors are concave, will the cavity stable?
A. Yes. Particularly if PR3 is concave.

Q. Rana mentioned the possibility that the mirrors are deformed by too tight mounting of the mirror in a ring.
Does it impact the stability of the cavity?

A. Possible. If the curvature is marginal and the mounting emphasizes the curvature, it may meet the unstable condition.

Q. How can we avoid this instability issue?
A.
1. Use flatter mirrors or at least concave mirrors.

2. Smaller incident angle to avoid emphasis of the RoC in the horizontal direction
3. Use weaker squishing force for mounting of the mirrors
4. Flip the PR3 mirror in the mounting ring by accepting the compromise that the AR surface is in the cavity.

7990   Mon Feb 4 10:45:51 2013 JamieSummaryGeneralrough analysis of aligned PRM-PR2 mode scan

Here's a sort of rough analysis of the aligned PRM-PR2 cavity mode scan.

On Friday we took some mode scan measurements of the PRM-PR2 cavity by pushing PRM (C1:SUS-PRM_LSC_EXT) with a 0.01 Hz, 300 count sine wave.  We looked at the transmitted power on the POP DC PD and the error signal on REFL11_I.

Below is a detail of the scan, chosen because the actuation was in its linear region and there were three relatively ok looking transmission peaks with nice PDH response curves:

The vertical green lines on the bottom plot indicate the rough averaged separation of the 11 MHz side-band resonances from the carrier, at +- 0.0275 s.  If we take this for our calibration, we get roughly 400 MHz / second.

The three peaks in top plot have an average FWHM of 0.00381 s.  Given the calibration above, the average FWHM = ~1.52 MHz.

If we assume a cavity length of 1.91 m, FSR = 78.5 MHz.

Putting this together we get a finesse = ~51.6.

Analysis of misaligned mode scans to follow.

7991   Mon Feb 4 11:10:59 2013 KojiSummaryGeneralrough analysis of aligned PRM-PR2 mode scan

The expected finesse is 100ish. How much can we beleive the measured number of 50?
From the number we need to assume PR2 has ~93% reflectivity.
This does not agree with my feeling that the cavity is overcoupled.
Another way is to reduce the reflectivity of the PRM but that is also unlikely from the data sheet.

The scan passed the peak in 4ms according to the fitting.
How do the analog and digital antialiasing filters affect this number?

7992   Mon Feb 4 15:06:56 2013 KojiSummaryGeneralHypothesis

 Quote: Q. How can we avoid this instability issue? A. 1. Use flatter mirrors or at least concave mirrors. 2. Smaller incident angle to avoid emphasis of the RoC in the horizontal direction 3. Use weaker squishing force for mounting of the mirrors 4. Flip the PR3 mirror in the mounting ring by accepting the compromise that the AR surface is in the cavity.

Another possibility is to use a ring heater to correct the curvature. I talked a bit with Aidan about this.

7994   Mon Feb 4 19:33:19 2013 yutaSummaryGeneralrough analysis of aligned PRM-PR2 mode scan

[Jenne, Yuta]

We redid PRM-PR2 cavity scan because last one (elog #7990) was taken with the sampling frequency of 2 KHz. We have also done TMS measurement.

Method:
1. Align input TTs and PRM to align PRM-PR2 cavity.
2. Sweep cavity length using C1:SUS-PRM_LSC_EXC.
3. Get data using Jamie's getdata and fitted peaks using /users/jrollins/modescan/prc-pr2_aligned/run.py
4. Calculated cavity parameters

Results:
Below is the figure containing peaks used to do the calculation.

From 11 MHz sidebands, calibration factor is 462 +/- 22 MHz/sec (supposing linear scan around peaks)
FWHM is 1.45 +/- 0.03 MHz.
TMS is 2.64 +/- 0.05 MHz.
Error bars are statistical errors of the average over 3 TEM00 peaks.

If we believe cavity length L to be 1.91 m, FSR is 78.5 MHz.
So, Finesse will be 54 +/- 1 and cavity g-factor will be 0.9944 +/- 0.0002. 0.9889 +/- 0.0004   (Edited by YM; see elog #8056)
If we believe RoC of PRM is exactly +122.1 m, measured g-factor insists RoC of PR2 to be -187 +/- 4.
If we believe RoC of PR2 is exactly -600 m, measured g-factor insists RoC of PRM to be 218 +/- 6.

Discussion:
1. Finesse is too small (expected to be ~100). This time, data was taken 16 KHz. Cut-off frequency of the digital antialiasing filter is ~ 5 kHz (see /opt/rtcds/rtscore/release/src/fe/controller.c). FWHM is about 0.003 sec, so it should not effect much according to my simulation.

2. I don't know why FWHM measurement from the last one is similar to this one. The last one was taken 2 KHz, this means anti-aliasing filter of 600 Hz. This should double FWHM.

3. Oscilloscope measurement may clear anti-aliasing suspicion.

7995   Mon Feb 4 19:48:32 2013 JamieSummaryGeneralarbcav recalc of PRC with correct ITM transmission

I noticed that Koji used a high reflector for the ITMs for his full PRC arbcav calculation. I just redo it here with the correct ITM transmission and RoC for completeness.

In this case the finesse is 95, instead of 121.

7996   Mon Feb 4 22:46:03 2013 JamieSummaryGeneralarbcav for SRC with curved TTs

I ran Zach's arbcav on our SRC with curved TTs and the situation looks much worse than the PRC.

I used the following parameters

SRM: RoC = 142 m, T = 10%
ITM: RoC = 83.1e3 m, T = 1.4%
SRC length: 5.37 m

In this case, with TT RoC of -600, the combined cavity g-factor = 0.9986, and astigmatism from SR3 makes the cavity patently not stable.  You have to go up to an RoC of -710 before the cavity is just over the edge.

7997   Tue Feb 5 02:04:44 2013 yutaSummaryGeneralrough analysis of aligned PRM-PR2 mode scan

I redid PRM-PR2 cavity scan using oscilloscope to avoid anti-aliasing effect.
Measured Finesse was 104 +/- 1.

Method:
1. Splitted POP DC output into three and plugged two into oscilloscope TDS 3034B. Ch1 and Ch2 was set to 1 V/div and 20 mV/div respectively to take the whole signal and higer resolution one at the same time (Koji's suggestion). Sampling frequency was 50 kHz. Sweeping time through FWHM was about 0.001 sec, which is slow enough.
2. Took mode scan data from the oscilloscope via network.

Preliminary results:
Below is the plot of the data for one TEM00 peak.

The data was taken twice.
Measured FWHM was 0.764 MHz and 0.751 MHz. By taking the average, FWHM = 0.757 +/- 0.005 MHz.
This gives you Finesse = 104 +/- 1, which is OK compared with the expectation.

What I need:
I need better oscilloscope so that we can take longer data (~1 sec) with higher resolution (~0.004 V/count, ~50kHz).
TDS 3034B can take data only for 10 ksamples, one channel by one!  I prefer Yokogawa DL750 or later.

7998   Tue Feb 5 03:16:51 2013 KojiSummaryGeneralrough analysis of aligned PRM-PR2 mode scan

0.764 and 0.751 do not give us the stdev of 0.005.

I have never seen any Yokogawa in vicinity.

 Quote: Measured FWHM was 0.764 MHz and 0.751 MHz. By taking the average, FWHM = 0.757 +/- 0.005 MHz.  This gives you Finesse = 104 +/- 1, which is OK compared with the expectation. What I need  I need better oscilloscope so that we can take longer data (~1 sec) with higher resolution (~0.004 V/count, ~50kHz).  TDS 3034B can take data only for 10 ksamples, one channel by one!  I prefer Yokogawa DL750 or later.

8000   Tue Feb 5 10:09:08 2013 yutaSummaryGeneralrough analysis of aligned PRM-PR2 mode scan

stdev of [0.764, 0.751] is 0.007, but what we need is the error of the averaged number. Statistical error of the averaged number is stdev/sqrt(n).

 Quote: 0.764 and 0.751 do not give us the stdev of 0.005.

8002   Tue Feb 5 11:30:19 2013 KojiSummaryGeneralrough analysis of aligned PRM-PR2 mode scan

Makes sense. I mixed up n and n-1

Probability function: X = (x1 + x2 + ... + xn)/n, where xi = xavg +/- dx

Xavg = xavg*n/n = xavg

dXavg^2 = n*dx^2/n^2
=> dXavg = dx/sqrt(n)

Xavg +/- dXavg = xavg +/- dx/sqrt(n)

8005   Tue Feb 5 19:16:22 2013 JamieSummaryGeneralarbcav of PRC with +600 RoC PR2/3

This is just a simple rerun of arbcav from #7995 but with the PR2/3 RoCs set to 600, instead of -600.  Overall g-factor = 0.922, and the modes are well separated:

This doesn't take into account the effect of traveling through the substrates (still working on it).  It assumes the PR2/3 have been moved such that the cavity fold lengths remain the same.

This is something that we need to keep in mind: we will need to adjust the position of the PR2/3 to keep the fold lengths the same.

8006   Tue Feb 5 19:32:47 2013 yutaSummaryGeneralPR2/PR3 flipping and PRC stability

We are considering of flipping PR2 and/or PR3 to make PRMI stable because PR2/PR3 seems to be convex.
I calculated dependency of the PRC stability on the PR2/PR3 curvature when PR2/PR3 flipped and not flipped.
Flipping looks OK, from the stability point of view.

Assumption:
 PRM-PR2 distance = 1.91 m  PR2-PR3 distance = 2.33 m  PR3-ITM distance = 2.54 m  PRM RoC = +122.1 m  ITM RoC = Inf
 theta_inc PRM = 0 deg  theta_inc PR2 = 1.5 deg  theta_inc PR3 = 41 deg           (all numbers from elog #7989)

Here, RoC means RoC measured from HR side. RoC measured from AR side will be -n_sub*RoC, assuming flat AR surface.
I also assumed mirror thickness to be negligible.

Method:
1. I used Zach's arbcav and modified it so that it only tells you your cavity is stable or not.
(It lives in /users/yuta/scripts/mode_density_PRC/stableornot.m)

2. Swept PR2/PR3 RoC (1/RoC from -0.005 to 0.005 1/m) to see the stability condition.

Results:
1. Stability condition of the PRMI when PR2 and PR3 is not flipped is depicted in the graph below. Black region is the unstable region. We all know that current PRMI is unstable, so we are in the black region.

2. Stability conditions of PRMI with one of the PR2/PR3 flipped are depicted in the graphs below. If we flip one of them, PRMI will likely to be stable, but if the flipped one is close to flat and the RoC of the other one is  >~ -250 m (more convex than -250 m), PRMI will remain unstable.

3. Stability condition of PRMI with both PR2 and PR3 flipped is depicted in the graph below. If we flip both, PRMI will be stable.

Discussion:
1. Flipping one of PR2/PR3 seems OK, but I cannot guarantee. TMS measurement insists RoC of PR2 to be ~ -190 m, if we believe PRM RoC = +122.1 m (elog #7997). We need more precise measurement if we need to be sure before flipping. I prefer PR2 flipping because PR3 flipping gives us longer path in the substrate and larger astigmatism. Also, PR3 RoC is phase-map-measured to be ~ -600 m and PR2 RoC seems to be more convex than -600 m from the TMS measurement.

2. Flipping both is good from stability point of view. We need calculation of the loss in the PRC (and mode-mismatch to the arms). Are there any requirements?

3. If we are going to flip PR3, are there any possibilities of clipping the beam at PR3? We need to check.

4. I need to calculate whether mirror thickness and AR surface curvature are negligible or not.

Conclusion:
I want to flip only PR2 and lock PRMI.

By the way:
I don't like matlab plots.

8012   Wed Feb 6 15:20:55 2013 yutaSummaryGeneralFWHM was wrong

I have to blame Jamie for putting extra 2 randomly.
Measured PRM-PR2 cavity finesse was actually 108 +/- 3 (even if you use digital system to get data).

Lorentzian fit:
Lorentzian function is;

f(x;x0,gamma,A) = A * gamma**2/((x-x0)**2+gamma**2)

where x0 is the location of the peak, gamma is HWHM, and A is the peak height.
Lorentzian fitting function in my original code (/users/yuta/scripts/modescanresults/analyzemodescan.py) was

fitFunc = lambda p,x,m: (m-p[2])*p[0]**4/(4*(x-p[1])**2+p[0]**4)+p[2]

In this function, p[0] is sqrt(FWHM), not sqrt(HWHM). I doubled gamma to make it FWHM and squared it because they should be positive.
During Jamie's modification of my code, he doubled p[0]**2 to get FWHM, which is wrong (/users/jrollins/modescan/modescan.py).

I should have commented that p[0] is sqrt(FWHM).

Redoing the analysis:
1. I pulled 2 out, and modified Jamie's modescan.py so that you can name each peak with peakdistinguish=True option. I also modified fitpeak function so that it throws away "peaks" which don't look like a peak.

2. If you run /users/yuta/PRCmodescan/run.py and name each peak, you will get peaks.csv which includes peak position, FWHM, and the type of the peak;

0.065017,0.001458,l
0.070446,0.001463,3
0.075940,0.001509,2
0.081552,0.001526,1
0.087273,0.001565,0
0.112027,0.001911,u
0.278660,0.002211,u
0.306486,0.001658,0
0.312480,0.001576,1
0.313626,2.507910,
0.318486,0.001626,2
0.319730,2.633097,
0.324801,0.001739,3
0.331848,0.001922,l
0.527509,0.001603,l
0.533231,0.001445,3
0.538648,0.001488,2
0.544081,0.001455,1
0.549517,0.001498,0
0.551725,2.422759,
0.570972,0.001346,u

3. /users/yuta/PRCmodescan/calcmodescanresults.py reads peaks.csv and tells you the results;

Time between TEM00 and sideband  0.0239435  pm  0.00115999887452  sec
Calibration factor is  462.167602898  pm  22.3907907867  MHz/sec
FSR is  78.4797010471  MHz
FWHM is  0.729828720682  pm  0.0174145743828  MHz
TMS is  2.64718671684  pm  0.0538858477824  MHz
Finesse is  107.53166986  pm  2.5658325169
Cavity g-factor is  0.994390582331  pm  0.000228155661075
Cavity g-factor is  0.988812630228  pm  0.000453751681357   (Edited by YM; see elog #8056)
RoC of PR2 is  -187.384503001  pm  4.26100999578  m (assuming PRM RoC= 122.1  m)
RoC of PRM is  217.915890722  pm  5.65451518991  m (assuming PR2 RoC= -600  m)

8022   Thu Feb 7 12:56:18 2013 JamieSummaryGeneralPRC/arm mode matching calculations

NOTE: There was a small bug in my initial calculation.  The plots and numbers have been updated with the fixed values.  The conclusion remains the same.

Using Nic's a la mode mode matching program, I've calculated the PRC mode and g-parameter for various PR2/3 scenarios.  I then looked at the overlap of the resultant PRC eigenmodes with the ARM eigenmode.  Here are the results:

NOTE: each optical element below (PR2, ITM, etc.) is represented by a compound M matrix.  The z axis in these plots is actually just the free space propagation between the elements, not the overall optical path length.

## ARM

This is the ARM mode I used for all comparisons:

 tangential sagittal gouy shift, one-way 55.63 55.63 g (from gouy) 0.303 0.303 g (product of individual mirror g) 0.303 0.303

## PRC, nominal design (flat PR2/3)

This is the nominal "as designed" PRC, with flat PR2/3 folding mirrors.

 tangential sagittal gouy shift, one-way 14.05 14.05 g (from gouy) 0.941 0.941 g (product of individual mirror g) 0.942 0.942

## PRC, both PR2/3 flipped

This assumes both PR2 and PR3 have a RoC of -600 when not flipped, and includes the affect of propagation through the substrates.

 tangential sagittal gouy shift, one-way 19.76 18.45 g (from gouy) 0.886 0.900 g (product of individual mirror g) 0.888 0.902

## PRC, only PR2 flipped

In this case we only flip PR2 and leave PR3 with it's bad -600 RoC:

 tangential sagittal gouy shift, one-way 18.37 18.31 g (from gouy) 0.901 0.901 g (product of individual mirror g) 0.903 0.903

# Discussion

I left out the current situation (PR2/3 with -600 RoC) and the case where only PR3 is flipped, since those are both unstable according to a la mode.

### I guess the main take away is that we get slightly better PRC stability and mode matching to the arms by only flipping PR2.

8025   Thu Feb 7 17:10:11 2013 KojiSummaryGeneralPRC/arm mode matching calculations

 Quote: I left out the current situation (PR2/3 with -600 RoC) and the case where only PR3 is flipped, since those are both unstable according to a la mode.

This surprises me. I am curious to know the reason why we can't make the cavity stable by flipping the PR3 as PR3 was supposed to have more lensing effect than PR2 according to my statement.

8029   Fri Feb 8 00:23:33 2013 ranaSummaryGeneralPRC/arm mode matching calculations

I would guess that either flipping PR2 or PR3 would give nearly the same effect (g = 0.9) and that flipping both makes it even more stable (smaller g). But what we really need is to see the cavity scan / HOM resonance plot to compare the cases.

The difference of 0.5% in mode-matching is not a strong motivation to make a choice, but sensitivity to accidental HOM resonance of either the carrier or f1 or f2 sidebands would be. Should also check for 2*f2 and 2*f1 resonances since our modulation depth may be as high as 0.3. Accidental 2f resonance may disturb the 3f error signals.

8033   Fri Feb 8 11:07:07 2013 JamieSummaryGeneralPRC/arm mode matching calculations

 Quote: I would guess that either flipping PR2 or PR3 would give nearly the same effect (g = 0.9) and that flipping both makes it even more stable (smaller g). But what we really need is to see the cavity scan / HOM resonance plot to compare the cases. The difference of 0.5% in mode-matching is not a strong motivation to make a choice, but sensitivity to accidental HOM resonance of either the carrier or f1 or f2 sidebands would be. Should also check for 2*f2 and 2*f1 resonances since our modulation depth may be as high as 0.3. Accidental 2f resonance may disturb the 3f error signals.

You would guess, and I would have guessed too, but the calculations tell the story.   Flipping both does not increase the stability.  The main issue is that flipping PR3 induces considerable astigmatism.  This is why flipping PR3 alone does not make the cavity stable.  I will do some simple calculations today that will demonstrate this effect.

But again, we should only change one thing at a time and understand that before moving on.  Given that the calculations show that flipping only PR2 should alone have a positive affect, we should do just that first, and verify that we understand what's going on, before we move on to making more changes.

I will try to make some more arbcav runs as well, for just the flipped PR2.

8035   Fri Feb 8 12:42:45 2013 nicolasSummaryGeneralPRC/arm mode matching calculations

 Quote: The main issue is that flipping PR3 induces considerable astigmatism.

Yes, at 45degrees PR3 will only have a curvature of about 850m for the vertical mode of the beam, apparently not enough to stabilize the cavity.

8040   Fri Feb 8 18:23:32 2013 JamieSummaryGeneralarbcav of half PRC with flipped PR2

Arbcav with half PRC (flat temporary mirror in front of BS), PR2 RoC = 600m, PR3 RoC = -600m:

NOTE: this does NOT include the affect of the PR2 substrate in the cavity.  Arbcav does not handle that.  It would have to be modified to accept arbitrary ABCD matrices.

NOTE: I added to the mode plot the frequency separation of the first HOMs from the carrier (\omega_{10/01}), in units of carrier FSR.

ELOG V3.1.3-