Koji has modified the script for the hysteresis measurement.
A new test started from 16:05 PT, Dec 18th and takes a couple of hours to finish the measurement.
Do not touch the suspensions until further notice.
The hysteresis test has been aborted.
The measurement finished at ~ 21:50 PT.
Ant season has set in. I spotted and killed a few ants around the optics and the enclosure of the PSL table yesterday. TIme for our pest control crew to get busy!
Summary: The aim is to design an analog anti-aliasing (AA) filter placed before the ADC, whose function is to filter out components of the input spectrum that have frequencies higher than the Nyquist frequency. This needs to be done so that there is no contamination of aliased downconverted high-frequency signals into the ADC output. I have put down and simulated a circuit to do this, based on the spectra of a few interferometer signals that eric Provided. Attachment 1 shows such an input PSD, treated with whitening filter, before the AA. The sampling rate is 65536 Hz and hence the Nyquist freq. is 32768 Hz.
Motivation: Attachments 2 and 3 show the plot of required attenuation for various frequencies above the Nyquist. We can see a peak at 36 kHz, which will alias to about 29kHz. It will require about 70 dB attenuation here. This indicates that use of a notch filter combined with a low pass filter can be used.
Details of Schematic: Attachment 4 shows the schematic of a Boctor low pass notch filter, cascaded by a 2nd order LPF. The stopband frequency of the boctor filter can be tuned to around 36 kHz. Its main advantage for the boctor is better insensitivity to component value tolerances, use of a single op amp, and relatively independent tuning of parameters. The various component values are calculated from here. The transfer functions for the circuit shown in attachment 4 were simulated using TINA - a spice based simulation software. The transfer function is shown in attachment 5.
A few more calculations: Attachment 6 shows the output psd after the signal has been treated with AA. Attachments 7 and 8 show the ratio of aliased downconverted signal and the unaliased signal of the output. Here, we can see that above about 13 kHz, the ratios go above -40dB, which is apparently undesirable. However, we also see from the transfer function of the filter that the gain falls to less than -20dB after about this frequency, and the aliased signals are atleast 20 dB lower than this, atleast upto about 29 kHz in attachment 7 and about 25 kHz in attachment 8. This means that the aliased signals are negligible as compared to the low frequencies even if they are not negligible as compared to the higher frequencies (above 13 kHz) into which they would get downconverted due to sampling. But these higher frequencies (above 13 kHz) themselves are small.
The filter overall, is 4th order. Considering this and the above discussion, I need to decide what changes to make in the existing schematic. For now, I could discuss with eric to finalize the opamp and start building the pcb board design.
I found an anti-aliasing circuit on the 40m wiki. It consists of A differential LPF made using THS4131 low noise differential op-amp (one of the main applications of which is preprocessing before the ADC), and a notch. I modified it to arrange for the desired bandwidth (about 8 kHz) and notch after the Nyquist frequency at 36 kHz. I simulated it to get the attached results:
Attachment 1: It shows the input PSD (same as the one posted in the previous elog), the filter transfer function, and The resulting output.
Attachment 2: The circuit schematic. The initial part using THS4131 is a differential LPF and the subsequent RC network is the notch.
Attachment 3: This shows the ratio of the aliased downconverted signal to the the in-band signal, representative of the contamination in each bin. Here too, the aliased signals are negligible as compared to the low frequencies but they are not negligible as compared to the higher frequencies (above 10 kHz) into which they would get downconverted due to sampling. However, here, the attenuation at 8kHz is less than 6 dB while in the previous circuit, it was about 12 dB. One problem with this circuit is at about 6kHz, there is aliased signal from the 65k to 98kHz band, but this can be taken care of by adding an LPF later.
Eric gave me a psd plot of a signal which would be the input of a channel of the AA filter. the Nyquist freq. is about 32.8kHz.
Following are plots depicting the ratio of the aliased downconverted signal and the signal below 32.8 kHz. The first plot is for (to-be) aliased signal frequencies from 32.8 to 65.5k, and the second plot is for (to-be) aliased signals from 65.5k to 98.3k. In case of the first plot, the 36kHz peak will alias to 29kHz, and is about 30 times (29.5dB) greater than the signal there. Hence, the filter should give about 70dB attenuation there. Since this attenuation is not required by most other frequencies up to 65.5k, an option could be to use a notch filter to remove the frequency peak at 36k, and put a requirement of 45-50 dB attenuation on other frequencies.
In case of the second plot, the frequencies between 90 to 100k again need to be attenuated by more than 70 dB. However, if there is a -20dB/decade slope in stop band, we already have about 10 dB attenuation here as compared to around 32k.
The X axis of both plots is in Hz.
EDIT: some images look bad on the elog, and the notebook is parsed, which is is bad. Almost everything posted here is in the compressed file attachment.
As we've been discussing, we want to reduce the laser's jitter effect on the QPDs of the OpLevs, without losing sensitivity to angular motion of the mirror; the current setup is roughly described in this picture:
The idea is to place an additional lens (or lenses) between the mirror and the QPD, as shown in the proposed setup in this picture:
I did some ray tracing calculations to find out how the system would change with the addition of the lens. The step-by-step calculations are done at the several points shown in the pictures, but here I will just summarize. I chose to put the telescope at a variable relative distance x from the QPD, such that x=0 at the QPD, and x=1 at the mirror.
Here are the components that I used in the calculations:
I used a 3x3 matrix formalism in order to have easier calculations and reduce everything to matrix multiplications; that because the tilted mirror has an annoying addictive term, which I could get rid of:
Therefore, n the results the third line is a dummy line and has no meaning.
For the first case (first schematic), we have, for the final r and Theta seen at the QPD:
In the second case, we have a quite heavy output, which depend also on x and f:
Now, some plots to help understand the situation.
What we want if to reduce the angular effect on the laser displacement, without sacrificing the sensitivity on the mirror signal. I defined two quantities:
Beta is the laser jitter we want to reduce, while Gamma is the mirror signal we don't want to lose. I plotted both of them as a function of the position x of the new lens, for a range of focal lengths f. I used d1 = d2 = 2m, which should be a realistic value for the 40m's OpLevs.
Plot of Beta
Plot of Gamma
Even if it is a bit cluttered, it is useful to see both of the same plot:
Plot of Beta & Gamma
Apart from any kind of horrific mistakes that I may have done in my calculations, it seems that for converging lenses our signal Gamma is always reduced more than the jitter we want to suppress. For diverging lenses, the opposite happens, but we would have to put the lens very near to the mirror, which is somehow not what I would expect. Negative values of Beta and Gamma should mean that the final values at the QPD level are on the opposite side of the axis/center of symmetry of the QPD with respect to their initial position.
I will stare at the plots and calculations a bit more, and try to figure out if I missed something obvious. The Mathematica notebook is attached.
I stared a bit longer at the plots and thanks to Eric's feedback I noticed I payed too much attention to the comparison between Beta and Gamma and not enough attention to the fact that Beta has some zero-crossings...
I made new plots, focusing on this fact and using some real values for the focal lengths; some of them are still a bit extreme, but I wanted to plot also the zero-crossings for high values of x, to see if they make sense.
If we are not interested in the sign of our signals/noises (apart from knowing what it is), it is maybe more clear to see regions of interest by plotting Beta and Gamma in absolute value:
I don't know if putting the telescope far from the QPD and near the mirror has some disadvantage, but that is the region with the most benefit, according to these plots.
The plots shown so far only consider the coefficients of the various terms; this makes sense if we want to exploit the zero-crossing of Beta's coefficient and see how things work, but the real noise and signal values also depend on the Alpha and Theta themselves. Therefore I made another kind of plot, where I put the ratio r'(Alpha)/r'(Theta) and called it Tau. This may be, in a very rough way, an estimate of our "S/N" ratio, as Alpha is the tilt of the mirror and Theta is the laser jitter; in order to plot this quantity, I had to introduce the laser parameters r and Theta (taken from the Edmund Optics 1103P datasheet), and also estimate a mean value for Alpha; I used Alpha = 200 urad. In these plots, the contribute of r'(r) is not considered because it doesn't change adding the telescope, and it is overall small.
In these plots the dashed line is the No Telescope case (as there is no variable quantity), and after the general plot I made two zoomed subplots for positive and negative focal lengths.
If these plot can be trusted as meaningful, they show that for negative focal lengths our tentative "S/N" ratio is always decreasing which, given the plots shown before, it does little sense: although for these negative f Gamma never crosses zero, Beta surely does, so I would expect one singular value each.
I am trying to design an antialiasing filter, which also has two switchable whitening stages. I have designed a first version of a PCB for this.
The board takes differential input through PCB mountable BNCs. It consists of an instrumentaiton amplifier made using quad opamp ADA4004, followed by two whitening blocks, also made using ADA4004, which can be bypassed if needed, depending upon a control input. The mux used for this purpose is Maxim MAX4158EUA. These two whitening blocks are followed by 2 the LPF stages. A third LPF stage could be added if needed. These use AD829 opamps. After the LPFs are two amplifiers for giving a differential output through two output BNCs. The schematic is shown in attachment 1: "AA.pdf". The top layers of the layout are shown in attachment 2 (AAtop.pdf), the bottom layers in attachment 3 (AAbottom.pdf), and the entire layout in attachment 4 (AAbrd.pdf).
The board has 6 layers (in the order from top to bottom):
1) Top signal layer;
2) Internal plane 1 (GND),
3) Internal plane 2 (+15V),
4) Internal plane 3 (-15V),
5) Internal plane 4 (GND),
6) Bottom signal layer.
Power: +15, -15 and GND is given through a 4 pin header connector.
The dimensions of the board are 1550 mil 6115 mil (38.1mm155.3mm) and the overall dimensions including the protruding BNC edges are 1550 mil 7675 mil (38.1mm194.9mm)
I would like to have inputs on the layout telling me if any component/trace needs to be changed/better placed, any other things about the board need to be changed, etc.
P.S.: I have also added a zipped folder "AA.zip" containing the schematic and board files, as well as the above pdfs.
Comments on the schematic:
Inspecting the AS table to make an inventory of the photodiodes in use around the interferometer, I found a mysterious photodetector hiding behind PD1 (AS166).
It turned out the detector was an old type of QPD from the Squeezing Experiment a few years ago.
We removed the box and the cable to which it was connected from the table. We stored it in the optics cabinet along the X arm.
I made a short stop at the 40m on Sunday night and found that hundreds ants are in the coffee maker.
I removed ants around the sink and washed the coffee maker.
It looked the ants were everywhere in the lab tonight. They seemed to prefer warm places like in the coffee maker and below the coffee mill.
So, I recommend that Steve should confirm there is no ants in the coffee maker again before the first coffee of the week is made.
Othewise they will add some more acidity to your cup.
We still had some ants visiting the sink area this morning. These ants seem to be addicted to our our Peet's coffe
Spectracide: Bug Stop insect killer was sprayed. Please wash your eating dishes well ! and keep area clean.
I updated my bandpass filter and have included the bode plot below in Figure 1. It is a fourth order elliptic bandpass filter with a passband ripple of 1dB and a stopband attenuation of 30 dB. It emphasizes the area between 3 and 40 Hz.
Below, I applied this filter to the huddle test data. The results from this were only slightly better in the targeted region than when no pre-filter was applied.
When I pre-filtered the mode cleaner data and then used an IIR wiener filter, I found that the results did not differ much from the data that was not pre-filtered. I'm not sure yet if I'm targeting the right region of this data with my bandpass filter, and will be looking more into choosing a better region. Also, I am only using certain regions of ff when calculating the transfer function, and need to optimize that region also. I uploaded the code I used to make these plots to github.
After asking Alex specifically what he did yesterday after I left, he indicated he copied a bunch of stuff from Hanford, including the latest gds, fftw, libframe, root. We also now have the new dtt code as well. But those apparently were for the Gentoo build After asking Alex about the ezca tools this morning, he discovered they weren't complied in the gds code he brought over. We are in the process of getting the source over here and compiling the ezca tools.
Alex is indicating to me that the currently compiled new gds code may not run on the Centos 5.5 since it was compiled Gentoo (which is what our new fb is running and apparently what they're using for the front ends at Hanford). We may need to recompile the source on our local Centos 5.5 control machines to get some working gds code. We're in the process of transferring the source code from Hanford. Apparently this latest code is not in SVN yet, because at some point he needs to merge it with some other work other people have been doing in parallel and he hasn't had the time yet to do the work necessary for the merge.
For the moment, Alex is undoing the soft link changes he did pointing gds at the latest gds code he copied, and pointing back at the original install we had.
I have modified Arbcav to be way cooler than it used to be.
Since the information is already there, I will have the output structure include things like the input beam q parameter, which could then be fed directly to mode matching tools like ModeMatchr.
The function takes as input the same arguments as before. Example for a square cavity:
out = arbcav([200e-6 50e-6 200e-6 50e-6],[0.75 0.75 0.75 0.75],[1e10 9 1e10 9],[45 45 45 45],29.189e6,10e-6,1064e-9,1000);
out = arbcav(transmissivity_list, length_list, RoC_list, angle_list, modulation_freq, loss_list_or_loss_per_mirror, wavelength, num_pts_for_plot);
If you don't give it a modulation frequency, it will just plot carrier HOMs. If you don't give it RoCs and angles, it will just plot the transmission spectrum.
I'm still fine-tuning some functionality, but I should have it up on the SVN relatively soon. Comments or suggestions are welcome!
Cavity geometry plots (linear, triangular, square, bowtie):
Transmission and HOM spectra (these correspond to the square cavity at lower left, above):
I haven't finished debugging the scripts so that the measurement is fully automatic, like the MC, but I did measure the arm spot positions just now.
These numbers aren't especially precise....I just picked numbers off of a StripTool plot, but they give us a good idea of how very far off we are. Also, I don't know yet which way the signs go...I have to think about that in terms of the direction I mis-balanced the coils. It's the same convention as the MC though. You can see in the attached quad camera image (quadrants match the corners of the table) that these numbers aren't unreasonable.
EDIT: It occurs to me now, a little later, that it had been at least half an hour since I last realigned the cavities, so some of this apparent miscentering is due to the input pointing drift. That doesn't account for all of it though. Even when the cavities have very high transmitted power, the spots are visibly miscentered.
In either .../scripts/XARM or ...../scripts/YARM run either A2L_XARM or A2L_YARM.
The wrapper script will, like the MC script, open a striptool so you can monitor the lockin outputs, setup the measurement, run the measurement, including misbalancing coils on the optics for calibration, and then calculates the spot positions. It records the measurement in a log file in /data_spotMeasurements under each arm's directory. The wrapper script then runs the plotting script which reads the logfile, and plots all past measurements.
Here is that plot for the Yarm:
The first two points were measured within a few minutes of eachother, the third set of points was after input pointing adjustment during IFO alignment. Clearly the pointing that optimized the cavity transmission (trying to leave the test mass mirrors alone, and only moving TT1 and TT2) does not also give the best spot centering. I claim that this is a result of the arm being aligned to the green beam, which was never locked to the 00 mode when we were at air. This is a lesson learned....take the time to deal with the green beams.
After Den's work with the ASS model this week, all of the channel names were changed (this wasn't pointed out in his elog....grrr), so none of the A2L scripts worked.
They are now back, however there is still some problem with the plotting that I'm not sure I understand yet. So, the measurement works, but I don't think we're saving the results and we certainly aren't plotting them yet.
I wanted to check where the spots are on the mirrors, to make sure Den's stuff is doing what we think it's doing. All of the numbers were within ~1.5mm of center, although Rossa keeps crashing (twice this afternoon?!?), so I can't copy and paste the numbers into the elog.
A near-term goal is to copy over Den's work on the Yarm to the Xarm, so that both arms will auto-align. Also, I need to put the set of alignment scripts in a wrapper, and have that wrapper call-able from the IFO Configure screen.
Also, while thinking about the IFO Configure screen, the "save" scripts weren't working (on Rossa) today, even though I just made them work a week or so ago. Rossa, at least, was unhappy running csh, so I changed the "save" script over to bash.
We had persistent frustration by occasional unlock during ASSing.
Today, I added triggers to the servo gains in order to elliminate this annoyance.
Each ASS servo gain slider is multiplied with the corresponding LSC Trigger EPICS channel (i.e. C1:LSC-iARM_TRIG_MON, where i=X or Y).
This has been done by ezcaread modules in RCG.
The model and screen have been commited to svn.
I'm going to work on the X arm to measure the arm cavity finesse.
The idea is to measure the cavity transfer function to estimate the frequency of its cavity pole. That should be a more accurate measurement than that based on the cavity decay time.
I'm starting now and I'm going to inject a swept sine excitation on the OMC_ISS_EXC input cable laying on the floor nearby the AP table (see pic).
In orderf to do that I disconnected the cable from the OMC breakout box laying on the floor. I'm going to plug the cable back in as soon as I'm done.
Since I need to measure the transfer function between TRX and MC_TRANS_DC I picked off the beam going to RFAM PD to send it to a PDA255 photodiode (cannibalized from the AbsL's PLL) which I installed on the PSL table.
I centerd the beam on the PD and I was able to see the injected signal.
I think I'm ready to measure the transfer function.
Except for the RFAM PD everything is as before.
I'm gonna go grab dinner and I should be back to keep working on that in about one hour.
Since I need to measure the transfer function between TRX and MC_TRANS_DC I picked off the beam going to RFAM PD to send it to a PDA255 photodiode (cannibalized from the AbsL's PLL) which I installed on the PSL table.
Back from dinner. Taking measurements.
dfmn = ----- * (m+n) * acos(sqrt(g1*g2))
Last week we vented and we cleaned the main optics of the arm cavities.
I measured the frequency of the cavity poles for both the arm cavities to see how they changed (see previous elog entry 2226). These the results:
fp_X = 1616 +/- 14 Hz
fp_Y = 1590 +/- 4 Hz
The Y arm cavity pole moved down by 130 Hz, whereas the X arm moved by only 34 Hz. I wonder if that is because Kiwamu spent much more time on cleaning ITMY than on any other optic.
ALS noise suppressed to 1KHz/rtHz. 1kHz RMS.
Plot 1: Scan of X arm by changing offset into Phase Tracker -> Xarm loop. Filter bank ramp time set to 120 s + using a 30 mHz low pass filter. IR beam is aligned to x arm, but not well.
Plot 2: ALS error signal with loop open (BLUE), closed with old filters (PURPLE), and with new, better boost (RED).
Plot 3: Bode plot of new boost (FM10), v. old, sad boost (1:50 pole:zero). RMS is now less than 1 kHz or ~50 pm. (in your face, Kiwamu!)
Changes made to the ALS servo:
ALS-TRX has been calibrated to read from 0-1 instead of counts in 1000 s. Calibration factor = 1/4500 = 0.00022
Old antiwhitening filter has been removed. Added LPF at 1000Hz to remove glitches at high frequencies.
No changes made.
FIlter FM5 modified. 1000:1 changed to 3000:1
5. Offset for ALS scan were given through C1ALS_OFFSETTER1 with LPF50m enabled.
The filter modules of the servo were:
Check PZT out range for ALS. Figure out what the deal is with ALS SLOW servos.
Add DQ channels for ALS.
Automatic ALS up script (enable and disable phase tracker included).
RMS is now less than 1 kHz or ~50 pm. (in your face, Kiwamu!)
Isn't this still a factor of 2 away from the limit in the paper?
My understanding is that that number is an in-loop evaluation of the loop so far (as the first step of the loop evaluation).
This is not what we can directly compare with the number in the paper.
Basically the entry 8741 is telling us that the new filter suppresses the error signal better than before.
That's clearly shown in the attachment 2.
The interferometer is warming up!
I had some issues locking the IMC at first. It turned out that the MC3 side OSEM signal wasn't getting to the ADC. A satellite box sqush fixed it.
I touched up the PMC alignment; the best I could do is 0.75V, probably due to the AOM being in place.
I haven't touched the WFS offsets, but the current ones seem to be doing ok. I'll touch them up tonight when the seismic activity has calmed.
I made some changes to the state of the PZT/PC crossover gain in the mcdown script, resulting in the IMC catching lock quicker.
Thankfully, the tip tilt pointing stayed good during the upgrade. I barely had to touch the ETM alignment to lock the arms. ETMX is showing some errant motion, though...
1) Turn off feedback to ETMY (the ETMY button on the LSC screen).
2) Put a 1 into the YARM->MC2 output matrix element on the LSC screen.
3) Turn off FM6 (comb), FM7 (0.1:10) on the MC2_MCL filter bank. This is to make the IOO-MCL loop more stable and to reduce the IOO-MCL low frequency gain.
4) Set the MC2-LSC gain to 0.5, turn the output ON, turn ON FM4 & FM5 & FM6 of the MC2-LSC filter bank.
5) Turn on the input of MC2-LSC and the arm should now lock.
6) After locking, set the MC2-MCL gain to zero. Hopefully with a few second ramp time.
(A comment by KA - c.f. this entry )
Summary: After today's meeting, Gabriele and I looked into the arm loss situation, to see if we should really believe the losses that had been suggested by my previous measurements. We made some observations that we're not sure how to explain, and we're thinking about other ways to try and estimate the losses to corroborate previous findings.
We first looked to see if the ASS had some effective offset, leaving the alignment not quite right. Once ASS'd, we twiddled each arm cavity mirror in pitch and yaw to see if we could achieve higher transmission. We could not, so this suggested that ASS works properly.
We then looked at potential offsets in the Xarm loop. We found that an input offset of 25 counts increased the transmission, but only very slightly. With this offset adjusted, we confirmed the qualitative observation that locking/unlocking the xarm causes a much bigger change in ASDC than doing the same with the harm.
However, we noted that the ASDC data (which is the DC value of the AS55 RFPD) was quite noisy, hovering around 50 counts. Looking at the c1lsc model, we found that we were looking at direct ADC counts, so the signal conditioning was not so great. We went to the LSC rack and stole the SR560 that had been hooked up as a REFLDC offsetter, and used it to give ASDC a gain of 100, and a LP at 100Hz, since we only care about DC values. We then undid the gain in the input FM; and this calmed the trace down a fair bit. The effects due to each arm locking/unlocking was still consistent with previous observations.
At this point, we looked at the arm transmission and ASDC signals simultaneously. Normally, when misaligning a cavity, one would expect the reflected power to rise and the transmission to fall.
However, we saw that when misalignment the Yarm in yaw in either direction, or the Xarm in one direction, both the IR transmission and ASDC would fall. This initially made us think of clipping effects.
So, we checked out the AS beam situation on the AP table. On a card, the beam looks round as we could tell, and the beam spot on AS55 was nice and small. (We tweaked its steering a little bit in pitch to put it at the center of the "falling-off" points) The reflection and transmission falling effect remained.
At this point, we're not really sure what could be causing this effect. After the reflected beams recombine at the BS, the output path is common, so it's strange that this odd effect would be the same for both arms.
Lastly, we discussed other ways that we may be able to see if the Xarm really has ~500ppm loss. Since its transmission is ~1.4%, Gabriele estimated that we may be able to see a ~300Hz difference in the arm cavity pole frequency between the two arms, based on the modification of the cavity finesse due to loss. Since we don't currently have the AOM set up to inject intensity noise, we talked about using frequency noise injection to measure the arm cavity poles, though this would be coupled with the IMC pole, but this could hopefully be accounted for.
We took the data for the new absolute length measurement of both arms, after the latest vent and move. We will analyze soonly. We had done a round of analysis, but then Koji pointed out that our data wasn't so clean because the whitening filters were on (and saturated the ADC). We now have the data (but not the analysis) for the better data with the WF off.
So our dirty-data preliminary number for the X arm is 37.73meters, which is 14cm different from our old length. We were supposed to move by ~20cm, so....either this measurement is bad because the data sucked (which it did), or we are 6cm off. Or both.
I'll do another analysis with the clean data for both arms later today/tomorrow.
After analyzing the cleaner data, I get the following:
Y_Length_long = 37.757 meters
X_Length_long = 37.772 meters
As stated in the wiki, the goal arm length was L = 37.7974 m for each arm.
So we're within 2cm for X, and within 4cm for Y.
According to Kiwamu's awesome tolerance calculation, we need to be within 2cm for each arm. Given that we started out 20cm wrong for X and 25cm wrong for Y, we're a lot closer now, even though we aren't meeting our Yarm requirement yet.
Probably some Optickle action is in order, to see what these new lengths give us in terms of sideband phase and other stuff.
If you want more digits on my calculated numbers (which are probably meaningless, but I haven't done a careful error analysis), in my directory ...../users/jenne/Xarm and ..../users/jenne/Yarm run Xarm_find_peaks_and_length.m and Yarm_find_peaks_and_length.m respectively. These will output the lengths.
The second sideband is resonant in the arms for a cavity length of 37.9299m.
The nearest antiresonant arm lengths for f2 (55MHz) are 36.5753m and 39.2845m.
If we don't touch the ITMs, and we use the room we still have now on the end tables, we can get to 37.5m.
This is how the power spectrum at REFL would look like for perfect antiresonance:
And this is how it looks like for 37.5m:
Or, god forbid, we change the modulation frequencies...
Last night (Oct 07), I ran armLoss script in order to obtain the latest numbers for the arm cavity loss.
Here is the summary
Measured arm reflectivity R_cav: 0.875 +/- 0.005
Estimated round trip loss L_RT: 157ppm +/- 8ppm
Estimated finesse F: 1213+/-2
Data Points: 34
Measured arm reflectivity R_cav: 0.869 +/- 0.006
Estimated round trip loss L_RT: 166ppm +/- 8ppm
Estimated finesse F: 1211+/-2
Data Points: 26
TE=10ppm, LE=L_RT/2, RE=1-TE-LE
TF=0.005, LF=L_RT/2, RF=1-TF-LF
rcav = -rF +(tF^2 rE)/(1-rF rE)
R_cav = rcav^2
F = pi Sqrt(rF rE)/(1-rF rE)
I like to ask someone to review the calculation on the wiki.
Yesterday evening Nic and me were in the lab. The Mode Cleaner was unlocked, but after many attempt we could fix it and we did many scans of the Y arm cavity.
Today I was not able to keep the MC locked. Koji helped me remotely, and eventually the MC locked back, but after half an hour of measurements I had to stop.
I made some more scan of the Y arm though. I also tried to do the same for the X arm, but the MC unlocked before the measurement was finished. I'll try to come back in the night.