v: Edit on Dec 15 10PM
v: Edit on Dec 16 10PM
JD: We should check OSEMs for all optics *after* table leveling. Some of them (esp. BS and ITMX) are currently close to their limits right now.
KA: Check green alignment.
Take photos of the tables.
Fix the leveling weights
Location Optics Action
@ITMX - v POX alignment
v POP1/POP2 alignment
v Table Leveling
@ITMY - POY mirror replacement (45deg->0deg) / alignment
v SR2-TT alignment
v SRM Tower alignment / EQ-stop release
v SRM alignment
v SRM OSEM
vvSRM OPLEV (X2) install (VIS)/ alignment
v ITMY OPLEV (X2) install (VIS)/ alignment
v OM1/OM2 install (DLC 45deg)/ alignment
v Table Leveling
@BSC - v OM3 install (DLC 45deg/ alignment)
v OM4(PZT) neutralize, adjustment
IPPOS steering alignment
v BS OPLEV alignment
v PRM OPLEV(x2) alignment
@BSC - v OM3 install (DLC 45deg/ alignment)
OM4(PZT) neutralize, adjustment
IPPOS steering alignment
v BS OPLEV alignment
PRM OPLEV(x2) alignment
@IMC - v REFL mirror replacement (45deg->0deg)
@ETMX - Al foil removal
@ETMY - ETMY damping
Al foil removal
@OMC - v OM5(PZT) neutralize, adjustment
@ITM/ETM - Mirror Wiping
The (masked) tech accessed all areas in the lab (office area, control room, VEA) between ~230pm-3pm. The laser safety goggles he used have been kept aside for appropriate sanitaiton.
A technician came to the lab today at ~4pm. He entered the VEA (with booties and googles), and also the clean and bake lab. The whole procedure lasted ~10 minutes. I did not follow him around, but was available in the control room throughout the process. I think the whole episode went without incident.
BTW, this guy didn't ring the doorbell, I just happened to be here when he came by. I don't know if this is usual practise - are we happy with the technicians entering the VEA and/or clean and bake labs without supervision? AFAIK, this wasn't scheduled.
Had to restart the elog many times. For some reason firefox 8 on Win 7 kills the elog pretty consistently when trying to make a new entry. IE9 works fine ....
[Jon, Keerthana, Sandrine]
Thu.-Fri. we continued with PRC scans using the AUX laser, but now the "scanned" parameter is the frequency of AM sidebands, rather than the frequency of the AUX carrier itself. The switch to AM (or PM) allows us to coherently measure the cavity transfer as a function of modulation frequency.
In order to make a sentinel measurement, I installed a broadband PDA255 at an unused pickoff behind the first AUX steering mirror on the AS table. The sentinel PD measures the AM actually imprinted on the light going into the IFO, making our measurement independent of the AOM response. This technique removes not only the (non-flat) AOM transfer function, but also any non-linearities from, e.g., overdriving the AOM. The below photo shows the new PD (center) on the AS table.
With the sentinel PD installed, we proceeded as follows.
The below photo shows the measured transfer function [AUX Reflection / AUX Injection]. The measurement coherence is high to ~55 MHz (the AOM bandwidth is 60 MHz). We clearly resolve two FSRs, visible as Lorentzian dips at which more AUX power couples into the cavity. The SURFs have these data and will be separately posting figures for the measurements.
With the basic system working, we attempted to produce HOMs, first by partially occluding the injected AUX beam with a razor blade, then by placing a thin two-prong fork in the beam path. We also experimented with using a razor blade on the output to partially occlude the reflection beam just before the sensor. We were able to observe an apparent secondary dip indicative of an HOM a few times, as shown below, but could not repeat this deterministically. Besides not having fine control over the occlusion of the beams, there is also large few-Hz angular noise shaking the AS beam position. I suspect from moment to moment the HOM content is varying considerably due to the movement of the AS beam relative to the occluding object. I'm now thinking about more systematic ways to approach this.
How much was the osc freq of the marconi? And then how much was the resulting freq offset between PSL and AUX?
Are we supposed to see two dips with the separation of an FSR? Or four dips (you have two sidebands)?
And the distance between the dips (28MHz-ish?) seems too large to be the FSR (22MHz-ish).
(Jon, Keerthana, Sandrine)
I am attaching the plots of the Reflected and transmitted AUX beam. In the transmission graph, we are getting peak corresponding to the resonance frequencies, as at that frequency maximum power goes to the cavity. But in the Reflection graph, we are obtaining dips corresponding to the resonance frequency because maximum power goes to the cavity and the reflected beam intensity becomes very less at those points.
First Contact Training with Margot
Made a dry run of the in-situ cleaning for a 3inch optic.
Attachment 1: The Al dummy mass is clamped in the suspension cage.
Attachment 2: The front surface was painted. The nominal brush with the FC bottle was used.
Attachment 3: Zoom in of the front surface.
Attachment 4: The back surface was painted.
Attachment 5: The back surface was peeled.
Attachment 6: The front surface was peeled too.
Attachment 7: The peeled layers.
1. To paint a thick layer (particlarly on the rim) is the key to peel it nicely.
2. It was helpful for easier peeling to have mutiple peek tabs. Two tabs were sufficient for ~1" circle.
3. The nominal brush with the bottle was OK although one has to apply the liquid many times to cover such a large area. A larger brush may cause dripping.
4. The nominal brush was sufficiently long once the OSEMs are removed. In any case it is better to remove the OSEMs.
After much fussing, we got a picture of MMT1 with the beam.
Using the iris doesn't seem feasible. Since it has to be significantly separated from the optic, it is hard to judge whether it is centered, especially in yaw.
It took ~30 min to get this picture. Comments on whether this kind of picture is good enough are welcomed, since there are many more to be taken.
Looks good. Any way that you can tell in an unambiguous way, where the beam is, is very good. Ideally we want to have1-2 mm accuracy.
[Jenne, Kiwamu, Steve]
Round 1 of measuring the MC mode is pretty much done. Yay.
Earlier today, Steve and I launched the MC beam off the flat mirror just after the Faraday, and sent it down toward ETMY(new convention). We ended up not being able to see it all the way at the ETM because we were hitting the beam tube, but at the ITM chamber we could see that the beam looked nice and circle-y, so wasn't being clipped in the Faraday or anywhere else. To do this we removed 2 1inch oplev optics. One was removed from the BS table, and wrapped in foil and put in a plastic box. The other was just layed on its' side on the BS table.
I then took the beam out of the BS chamber, in order to begin measuring the mode. I left the flat fixed mirror in the place of what will be PZT SM1, and instead used the PZT mirror to turn the beam and get it out the BS chamber door. (Thoughts of getting the beam to the BS oplev table were abandoned since this was way easier, since Kiwamu and Steve had made the nifty table leg things.) Kiwamu and I borrowed an 2inch 45P Y1 optic from the collection on Koji's desk (since we have ZERO 2inch optics on the random-optic-shelf....no good), to shoot the beam down the hallway of the Yarm (new convention). We used the beam scan on a rolling cart to measure the beam at various distances. I made some sweet impromptu plum bobs to help make our distance measurements a bit more accurate.
We stopped at ~25 feet from the BS chamber, since the spot was getting too big for the beam scanner. If it turns out that I can't get a good fit with the points I have, I'll keep everything in-chamber the same, and do the farther distances using the good ol' razor blade technique.
I have measurements for the distances between the beam scan head and the opening of the BS chamber. Tomorrow, or very soon after, I need to measure the distances in-chamber between the MC and the BS chamber opening. Plots etc will come after I have those distances.
Next on the to-do list:
1. Measure distances in-chamber for first mode scan.
2. Plot spot size vs. distance, see if we need more points. Take more points if needed.
3. Put in MMT1, repeat measurements.
4. Put in MMT2, rinse and repeat.
5. Move the PZT mirror to its new place as SM1, and figure out how to connect it. Right now the little wires are hooked up on the BS table, but we're going to need to make / find a connector to the outside world from the IOO table. This is potentially a pretty big pain, if we don't by happenstance have open connectors on the IOO table.
[Jenne, Jamie, Mirko]
We got the first version of the oaf code based on Matt"s code running!! :-)
Produces already data for e.g. MICH DOF. But don"t trust that. It's only 10 taps long and delay is not adjusted.
Today, we finally crossed the last hurdle and got a successful converging coil balancing run.
This week I wrote Matlab code, most of which can be found in /users/masha
First, I wrote a simulation seismicFilter.m which filters noisy seismic noise with a desired signal of non-seismic noise. The signals are purely simulated, so I played around with zero-pole-gain generation of transfer functions to obtain them. The function takes the number of taps, the filter type (Wiener or adaptive nlms) as well as an iteration step size and number of iterations, and generates PSD plots of the witness signal, the desired signal, the estimated (filtered) signal, and the error. I'm not sure that I am properly implementing the Wiener part of the code, and I assume the line "[W, R, P] = miso_firlev(TAPS, noisySeismicSignal1, seismicSignal2); " generates W, a filter with TAPS number of weights, but then "[y, error] = filter(W, 1, noisySeismicSignal1);" generates an error signal of size TAPS rather than N, the size of the original signal. Perhaps I should calculate error using e(t) = d(t + a) - w(t)*x(t), where "a" is the delay.
I have various screenshots in my directory of what seismicFilter.m generates, and I will take a larger screenshot, as well as generate a learning curve (for error vs. number of taps) when I can use Sasha's computer for a bit, since it both has more computing power and a larger screen.
The funciton filterConvergence.m, meanwhile, is similar, except it takes two file names as real data, and uses realDataFilter.m to run the filtering. Currently, I am working with data from C1:IOO-MC_F_DQ-Online and C1:PEM-SEIS_GUR1_X_IN1_DQ-Online, and I will include screenshots of these once I get on Sasha's computer.
In order to generate the data, meanwhile, I had to modify the python script, and thus wrote mashaImportingData.py for myself. Likewise, plotSignalFromFile.m visualizes this data, both in the time domain and in the frequency domain.
On the side, I wrote an NLMS filter in adaptiveFilterSimulationNLMS.m, and compared is to Matlab's NLMS filter in NLMStest.m (using generated data) and adaptiveFilterSimulation.m using twn input signals. Right now, it's faster on smaller inputs and smaller tap sizes, but then begins to choke and run slower than the Matlab one when these get to big. In order to improve it, I have to develop a better method of generating the initial weights.
As far as machine learning goes, once I find the number of taps for the convergence of both the Wiener filter and the NLMS filter, I will email Denis for further instructions. At some point, however, I should generate learning sets from the seismometers and the MCL (or the DARM), and thus have to find adequate times at which I can take data (probably not from the DARM, however, because it was rarely on).
Thanks for reading!
This week, the other SURF students and I got acquainted with the caltech campus, LIGO 40m lab and the expectations of the SURF program. We went to a lot of safety meetings and lectures that established a framework for the jobs we will be doing over the course of the summer. I went on several tours of the 40m interferometer (one each with Jenne, Jamie and Steve) to get an overview of the layout and specifics of the setup. I read parts of R. Ward and A. Parameswaran's theses and Saulson's book in order to prepare myself and gain a broader understanding of the purpose of LIGO.
I also began working in Python this week, primarily graphing PSDs of data from the C1:SUS-ETMY_SENSOR_LR, C1:SUS-ETMY_SENSOR_LL, C1:SUS-ETMY_SENSOR_UR, and C1:SUS-ETMY_SENSOR_UL channels. I will eventually be using Python to generate the plots for the summary pages, so this is good practice. The code that I have been working on can be found in /users/elizabeth.davison/script5.py. Additionally, I have been going through the G1 summary pages and attempting to understand the plots available on them and the code that is available.
My plans for the upcoming week begin with modifying my code and potentially calibrating the channel data so that it is in units of length instead of counts. I will also access the code from the G1 pages and go over it in depth, hopefully gaining insight into the structure of the website.
[Jenne, Steve, Nancy, Gopal]
We made an attempt at hanging some of the Tip Tilt eddy current dampers today.
Photo 1 shows the 2 ECDs suspended.
(1) Loosen the #4-40 screws on the side of the ECDs, so the wire can be threaded through the clamps.
(2) Place the ECDs in the locator jigs (not shown), and the locator jigs in the backplane (removed from main TT structure), all laying flat on the table.
(3) Get a length of Tungsten wire (0.007 inch OD = 180um OD), wipe it with acetone, and cut it into 4 ~8cm long segments (long enough to go from the top of the backplane to the bottom).
(4) Thread a length of wire through the clamps on the ECDs, one length going through both ECDs' clamps.
(5) One person hold the wire taught, and straight, and as horizontal as possible, the other person tightened the clamping screws on the ECDs.
(6) Again holding the wire in place, one person put the clamps onto the backplane (the horizontal 'sticks' with 3 screws in them).
(7) The end. In the future, we'll also clip off extra pieces of wire.
When we held up the backplane to check out our handy work, it was clear that the bottom ECD was a much softer pendulum than the top one, since the top one has the wire held above and below, while the bottom one only has the wire held on the top. I assume we'll trim the wire so that the upper ECD is only held on the top as well?
* This may be a 3 person job, or a 2 people who are good at multitasking job. The wire needs to be held, the ECDs need to be held in place so they don't move during the screwing/clamping process, and the screws need to be tightened.
* Make sure to actually hold the wire taught. This didn't end up happening successfully for the leftmost wire in the photo, and the wire is a bit loose between the 2 ECDs. This will need to be redone.
* We aren't sure that we have the correct screws for the clamps holding the wire to the backplane. We only have 3/16" screws, and we aren't getting very many threads into the aluminum of the backplane. Rana is ordering some 316 Stainless Steel (low magnetism) 1/4" #4-40 screws. We're going for Stainless because Brass (the screws in the photo), while they passed their RGA scan, aren't really good for the vacuum. And titanium is very expensive.
The 2nd photo is of the magnet sticking out of the optic holder. The hole that the magnet is sitting in has an aluminum piece ~2/3 of the way through. A steel disk has been placed on one side, and the magnet on the other. By doing this, we don't need to do any press-fitting (which was a concern whether or not the magnets could withstand that procedure), and we don't need to do any epoxying. We'll have to wait until the ECDs are hung, and the optic holder suspended, to see whether or not the magnet is sticking out far enough to get to the ECDs.
The efficiency of the mode matching (MM) to PRC (Power-Recycling Cavity) has been estimated by using the interferometer.
The estimated MM efficiency is about 74 % when losses in the cavity are assumed to be zero.
Here are the measured values in REFLDC
Anyways the estimated MM efficiency with the sidebands effect included and without loss effect is
MM efficiency = 73.7 +/- 1.7 % (1 sigma error) or +/- 8.7 % (5 sigma error)
"^2"s are missing in the second equation, but the calculation results seem correct.
PRX and PRY have different mode matching because of the Michelson asymmetry.
Are individually estimated mode matching indicates any sign of reasonable mode mismatch?
(The difference can be very small because the asymmetry is not so big.)
On the topic of high AS55_Q RFPD offset, it seems it stems from a small residual offset on top of the 42 dB whitening filter gain (previously 3 dB). We verified this by looking in the past using dtt and seeing an offset of ~ 100 counts, which are consistent with the hotfix. We reverted the whitening filter gain to +24 dB, in order to accomodate the 10% power difference from AS2. We decided to move forward, and try locking MICH using AS55_Q_ERR. The IQ mixing angle was changed to -167 deg from -122 deg to minimize the signal in AS55_I_ERR. We have also added comb60 filters for AS55. The LSC_MICH filter gain was adjusted to -6 (used to be -13 in the configuration script) to get a MICH_OLTF UGF of 90 Hz (which is the previously measured value as of 2021 July), see Attachment #1 for the MICH OLTF estimate.
We then calibrate MICH using the fringe amplitude, so that , where is the amplitude of the error point (C1:LSC-AS55_Q_ERR_DQ) in our case ~ 110 +- 2 counts. The calibrated error point spectral density is shown in Attachment #2. Calibration is done into meters in terms of difference between BS to ITMX length and BS to ITMY length.
In brief, I trained a deep neural network (DNN) to recosntuct the cavity length, using as input only the transmitted power and the reflection PDH signals. The training was performed with simulated data, computed along 0.25s long trajectories sampled at 8kHz, with random ending point in the [-lambda/4, lambda/4] unique region and with random velocity.
The goal of thsi work is to validate the whole approach of length reconstruction witn DNN in the Fabry-Perot case, by comparing the DNN reconstruction with the ALS caivity lenght measurement. The final target is to deploy a system to lock PRMI and DRMI. Actually, the Fabry-Perot cavity problem is harder for a DNN: the cavity linewidth is quite narrow, forcing me to use very high sampling frequency (8kHz) to be able to capture a few samples at each resonance crossing. I'm using a recurrent neural network (RNN), in the input layers of the DNN, and this is traine using truncated backpropagation in time (TBPT): during training each layer of RNN is unrolled into as many copies as there are input time samples (8192 * 0.25 = 2048). So in practice I'm training a DNN with >2000 layers! The limit here is computational, mostly the GPU memory. That's why I'm not able to use longer data stretches.
But in brief, the DNN reconstruction is performing well for the first attempt.
In the results shown below, I'm using a pre-trained network with parameters that do not match very well the actual data, in particular for the distribution of mirror velocity and the sensing noises. I'm working on improving the training.
I used the following parameters for the Fabry-Perot cavity:
The uncertaint is assumed to be the 90% confidence level of a gaussian distribution. The DNN is trained on 100000 examples, each one a 0.25/8kHz long trajectory with random velocity between 0.1 and 5 um/s, and ending point distributed as follow: 33% uniform on the [-lambda/4, lambda/4] region, plus 33% gaussian distribution peaked at the center with 5 nm width. In addition there are 33% more static examples, distributed near the center.
For each point along the trajectory, the signals TRA, POX11_I and POX11_Q are computed and used as input to the DNN.
Gautam collected about 10 minutes of data with the free swinging cavity, with ALS locked on the arm. Some more data were collected with the cavity driven, to increase the motion. I used the driven dataset in the analysis below.
The ALS signal is calibrated in green Hz. After converting it to meters, I checked the calibration by measuring the distance between carrier peaks. It turned out that the ALS signal is undercalibrated by about 26%. After correcting for this, I found that there is a small non-linearity in the ALS response over multiple FSR. So I binned the ALS signal over the entire range and averaged the TRA power in each bin, to get the transmission signals as a function of ALS (in nm) below:
I used a peak detection algorithm to extract the carrier and 11 MHz sideband peaks, and compared them with the nominal positions. The difference between the expected and measured peak positions as a function of the ALS signal is shown below, with a quadratic fit that I used to improve the ALS calibration
The result is
The ALS calibrated z error from the peak position is of the order of 3 nm (one sigma)
Using the calibrated ALS signal, I computed the cavity length velocity. The histogram below shows that this is well described by a gaussian with width of about 3 um/s. In my DNN training I used a different velocity distribution, but this shouldn't have a big impact. I'm retraining with a different distirbution.
The plot below shows a stretch of time domain DNN reconstruction, compared with the ALS calibrated signal. The DNN output is limited in the [-lambda/4, lambda/4] region, so the ALS signal is also wrapped in the same region. In general the DNN reconstruction follows reasonably well the real motion, mostly failing when the velocity is small and the cavity is simultanously out of resonance. This is a limitation that i see also in simulation, and it is due to the short training time of 0.25s.
I did not hand-pick a good period, this is representative of the average performance. To get a better understanding of the performance, here's a histogram of the error for 100 seconds of data:
The central peak was fitted with a gaussian, just to give a rough idea of its width, although the tails are much wider. A more interesting plot is the hisrogram below of the reconstructed position as a function of the ALS position, Ideally one would expect a perfect diagonal. The result isn't too far from the expectation:
The largest off diagonal peak is at (-27, 125) and marked with the red cross. Its origin is more clear in the plot below, which shows the mean, RMS and maximum error as a function of the cavity length. The second peak corresponds to where the 55 MHz sideband resonate. In my training model, there were no 55 MHz sidebands nor higher order modes.
The DNN reconstruction performance is already quite good, considering that the DNN couldn't be trained optimally because of computation power limitations. This is a validation of the whole idea of training the DNN offline on a simulation and then deploy the system online.
I'm working to improve the results by
However I won't spend too much time on this, since I think the idea has been already validated.
I included the 55 MHz sideband and higher order modes in my training examples. To keep things simple, I just assumed there are higher order modes up to n+m=4 in the input beam. The power in each HOM is randomly chosen from a random gaussian distribution with width determined from experimental cavity scans. I used a value of 0.913+-0.01 rad for the Gouy phase (again estimated from cavity scans, but in reasonable agreement with the nominal radius of curvature of ETMX)
Results are improved. The plot belows show the performance of the neural network on 100s of experimental data
For reference, the plots below show the performance of the same network on simulated data (that includes sensing noise but no higher order modes)
I've begun cleaning the optics that will eventually go back onto the newly installed X-endtable. We decided that First Contact was the way to go (as opposed to methanol drag wiping). Koji demonstrated the application of the (red) First Contact solution onto a 2" mirror - I then proceeded to work on the rest of the optics. We are broadly following the procedure in E1000079 - first one coat of First Contact solution is applied, then a small piece of PEEK is embedded by applying a second layer of solution over it (this will enable us to pull off the First Contact once we are ready - the plan is to do this after roughly placing the optic on the table. As of now, I've finished coating most of the optics that are part of the IR Transmon path - I will continue later in the evening.
The new endtable is almost ready for re-population. Steve just needs to shim the enclosure which will be done tomorrow morning. The game-plan as discussed at the meeting today is to first try and set up the IR Transmon path. This will allow us to verify that the endtable height is such that we can maintain a beam height of 4" everywhere on the table (I suspect we may have to compromise at some poing and do some fine adjustment of 1/4 to 1/2" somewhere though). It will also allow me to define the cavity axis relative to the table, which will be useful to place the green steering optics eventually. Doing this will be challenging though as right now, I can't see any of the arm flashes on the endtable using an IR card. Ideally, we want to somehow lock the X arm and then do the checks mentioned at the endtable, before beginning to put the endtable back together.
I used a pair of tweezers to remove the stray fiber of first contact. As Koji predicted, this was rather dry and so it didn't have the usual elasticity, so while I was able to pull most of it off, there is a small spot remaining on the HR surface of the ETM. We will remove this with a fresh application of a small patch of FC.
I the meantime, I'm curious if this has actually fixed the suspension woes, so yet another round of freeswinging data collection is ongoing. From the first 5 mins, looks positive, I see 4 peaks around 1Hz !
Update 730pm: There are now four well-defined peaks around 1 Hz. Together with the Bounce and Roll modes, that makes six. The peak at 0.92 Hz, which I believe corresponds to the Yaw eigenmode, is significantly lower than the other three. I want to get some info about the input matrix but there was some NDS dropout and large segments of data aren't available using the python nds fetch method, so I am trying again, kicked ETMY at 1828 PDT. It may be that we could benefit from some adjustment of the OSEM positions, the coupling of bounce mode to LL is high. Also the SIDE/POS resonances aren't obviously deconvolved. The stray first contact has to be removed too. But overall I think it was a successful removal, and the suspension characteristics are more in line with what is "expected".
Among the things that we hadn't taken care of yesterday before beginning to look for transmission signals were the polarization of the AUX beam on the AS table and optimizing the PLL feedback. The AUX beam is s-polarized on the PSL table (choice due to availablility of mirrors), and I added a half waveplate in front of the fiber to match it's axes. I placed another half-waveplate at the fiber output and send the reflection port of a PBS cube onto a PDA1CS photodetector. By alternatingly turning the waveplates I minimized the reflected light, giving strongly p-polarized light on the AS table for best results when interfering with the IFO beam. I wiggled the fiber and found no strong dependency of the output polarization on fiber bending. Attachment 2 shows the current layout.
The beat signal between AUX and PSL table is at -20dBm, and I adjusted the PLL gain and PI-corner to get reliable locking behavior. I think it's a good idea to keep the AUX beam on the AS table blocked while it's not in use, and only unblock it when it is phaselocked to avoid a rogue beam with no fixed phase relation to the PSL in the IFO.I blocked the beam after completing this work today.
I used the signal chain that Keerthana, Koji, and I set up yesterday to look for mode flashed of the AUX light in the YARM using the RF beat with the PSL carrier in transmission. To align the AUX beam to the arm the following steps were performed:
This was followed by a sweep over two full FSRs. Attachment #1 shows the trace recorded by the AG4395 using the max data hold setting during the sweep. Essentially the beat between AUX and PSL carrier traced out the arm's transmission curve. At minimum transmission there was still a ~82dB beat on the transmission PD visible.
The YEND QPD is currently blocked and sees no light.
A single channel of this board was stuffed (and other channels partially populated). The basic tests passed, and nothing exploded! Even though this is a laughably simple circuit, it's nice that it works.
HV power supplies:
A pair of unused KEPCO BHK300-130 switching power supplies that I found in the lab were used for this test. I pulled the programmable cards out at the rear, and shorted the positive output of one unit to the negative of the other (with both shorted to the supply grounds as well), thereby creating a bipolar supply from these unipolar models. For the purposes of this test, I set the voltage and current limits to 100V DC, 10mA respectively. I didn't ramp up the supply voltage to the rated 300 V maximum. The setup is shown in Attachment #1.
Need to think more about how to better characterize this noise. An estimate of the required actuation can be found here.
A more careful analysis has revealed some stability problems. I see oscillations at frequencies ranging from ~600kHz to ~1.5 MHz, depending on the voltage output requested, of ~2 V pp at the high-voltage output in a variety of different conditions (see details). My best guess for why this is happening is insufficient phase margin in the open-loop gain of the PA95 high voltage amplification stage, which causes oscillations to show up in the closed loop. I think we can fix the problem by using a larger compensation capacitor, but if anyone has a better suggestion, I'm happy to consider it.
The changes I wanted to make to the measurement posted earlier in this thread were: (i) to measure the noise with a load resistor of 20 ohms (~OSEM coil resistance) connected, instead of the unloaded config previously used, and (ii) measure the voltage noise on the circuit side (= TP5 on the schematic) with some high voltage output being requested. The point was to simulate conditions closer to what this board will eventually be used in, when it has to meet the requirement of <1pA/rtHz current noise at 100 Hz. The voltage divider formed by the 25 kohm series resistor and the 20 ohm OSEM coil simulated resistance makes it hopeless to measure this level of voltage noise using the SR785. On the other hand, the high voltage would destroy the SR785 (rated for 30 V max input). So I made a little Pomona box to alllow me to do this measurement, see Attachment #1. Its transfer function was measured, and I confirmed that the DC high voltage was indeed blocked (using a Fluke DMM) and that the output of this box never exceeded ~1V, as dictated by the pair of diodes - all seemed okay .
Next, I wanted to measure the voltage noise with ~10mA current flowing through the output path - I don't expect to require more than this amount of current for our test masses. However, I noticed some strange features in the spectrum (viewed continuously on the SR785 using exponential averaging setting). Closer investigation using an oscilloscope revealed:
Some literature review suggested that the capacitor in the feedback path, C4 on the schematic, could be causing problems. Specifically, I think that having that capacitor in the feeddback path necessitates the use of a larger compensation capacitor than the nominal 33pF value (which itself is higher than the 4.7pF recommended on the datasheet, based on experience of the ESD driver circuit which this is based on, oscillations were seen there too but the topology is a bit different). As a first test of this idea, I removed the feedback capacitor, C4 - this seemed to do the trick, the oscillations vanished and I was able to drive the output between the high voltage supply rails. However, we cannot operate in this configuration because we need to roll off the noise gain for the input voltage noise of the PA95 (~6 nV/rtHz at 100 Hz will become ~200 nV/rtHz, which I confirmed using the SR785). Using a passive RC filter at the output of the PA95 (a.k.a. a "snubber" network) is not an option because we need to sum in the fast actuation path voltage at the output of the 25 kohm resistor.
Some modeling confirms this hypothesis, see Attachment #2. The quantity plotted is the open-loop gain of the PA95 portion of the circuit. If the phase is 0 degrees, then the system goes unstable.
So my plan is to get some 470pF capacitors and test this idea out, unless anyone has better suggestions? I guess usually the OpAmps are compensated to be unconditionally stable, but in this case maybe the power op-amp is more volatile?
I trained a deep neural network (DNN) to reconstruct MICH and PRCL degrees of freedom in the PRMI configuration. For details on the DNN architecture please refer to G1701455 or G1701589. Or if you really want all the details you can look at the code. I used the following signals as input to the DNN: POPDC, POP22_Q, ASDC, REFL11_I/Q, REFL55_I/Q, AS55_I/Q.
Gautam took some PRMI data in free swinging and driven configuration:
In contrast to the Fabry-Perot cavity case, we don't have a direct measurement of the real PRCL/MICH degrees of freedom, so it's more difficult to assess if the DNN is working well.
All MICH and PRCL values are wrapped into the unique region [-lambda/4, lambda/4]^2. It's even a bit more complicated than simpling wrapping. Indeed, MICH is periodic over [-lambda/2, lambda/2]. However, the Michelson interferometer reflectivity (as seen from PRC) in the first half of the segment is the same as in the second half, except for a change in sign. This change of sign in Michelson reflectivity can be compensated by moving PRCL by lambda/4, thus generating a pi phase shift in the PRC round trip propagation that compensate for the MICH sign change. Therefore, the unit cell of unique values for all signals can be taken as [-lambda/4, lambda/4] x [-lambda/4, lambda/4] for MICH x PRCL. But when we hit the border of the MICH region, PRCL is also affected by addtion of lambda/4. Graphically, the square regions A B C below are all equivalent, as well as more that are not highlighted:
This makes it a bit hard to un-wrap the resonstructed signal, especially when you add in the factor that in the reconstruction the wrapping is "soft".
The plot below shows an example of the time domain reconstruction of MICH/PRCL during the free swinging period.
It's hard to tell if the positions look reasonable, with all the wrapping going on.
Here's an attempt at validating the DNN reconstruction. Using the reconstructed MICH/PRCL signal, I can create a 2d map of the values of the optical signals. I binned the reconstructed MICH/PRCL in a 51x51 grid, and computed the mean value of all optical signals for each bin. The result is shown in the plot below, directly compared with the expectation from a simulation.
The power signals (POP_DC, AS_DC, PO22_Q) looks reasonably good. REFL11_I/Q also looks good (please note that due to an early mistake in my code, I reversed the convention for I/Q, so PRCL signal is maximized in Q instead than in I). The 55MHz signals look a bit less clear...
Then I looked at the spectrum, see Attachment #1. Disappointingly, it looks like the arm PDH servo is dominating the noise, and NOT unsuppressed EX laser frequency noise,. Not sure why this is so, and I'm feeling too tired to debug this tonight. But encouragingly, the performance of the new ALS signal chain looks very promising. Once I tune up the X arm loop, I'm confident that the ALS noise will be at least as good as the reference trace.
I am leaving c1iscey shutdown until this is fixed. So ETMY is not available for the moment.
Random factoid: Trying to print a DTT trace with LaTeX in the label text on pianosa causes the DTT window to completely crash - so if you dont save the .xml file, you lose your measurement.
I made a LISO fit of the measured TF of the daughter board, so that I can digitally invert the daughter board whitening. Results attached. (Inverse) Filters have been uploaded to the ALS X Foton filter banks.
I was going to head out but then it occurred to me that I could do another simple test, which is to try and lock the X arm on ALS error signal (i.e. actuate on MC length to keep the beat between EX laser and PSL fixed, while the EX frequency is following the Xarm length). Comparing the in loop (i.e. ALS) error signal with the out-of-loop sensor (i.e. POX), it seems like POX is noisy. The curves were lined up by eye, by scaling the blue curve to match the red at the ~16Hz peaks. This supports my hypothesis in the previous elog. On the downside, could be anything. Electronics in the POX chain? The demod unit itself? Will look into it more tomorrow..
As an aside, controlling the arm with ALS error signal worked quite well, and the lock was maintained for ~1 hour.
I clamped Bonnie (microphone) to the top of a chamber near the vertex of the arms and placed Clyde (pre-amp) on the table right below (see picture). The cable was laid and Bonnie and Clyde are plugged into port #13 on the ADC. The second cable was plugged into port #14, but it is not connected to anything. I placed the looped up cable on top of the cabinet holding the ADC.
Note: the angle in the photograph is such that we are looking along the y-arm.
Yesterday, I mounted the first PZT in one of the modified mounts, and then glued a 2-inch Y2 mirror on it using superglue.
-The mirror is a 2-inch, Y2 mirror with HR and AR coatings for 532 nm light.
-The AR side of the mirror had someone's fingerprint on it, which I removed (under Manasa's guidance) using tweezers wrapped in lens cleaning paper, and methanol.
-Before gluing the mirror, I had to assemble the modified mount. Manasa handed over the remaining parts of the mounts (which are now in my newly acquired tupperware box along with all the other Piezo-related hardware). I took the one labelled A, and assembled the holder part. I then used one of the new mounts (2.5 inches, these are with the clean mounts in a cardboard box in the cupboard holding the green optics along the Y-arm) and mounted the holder on it.
-Having assembled the mount, I inserted the piezo tip-tilt into the holder. The wedge that the machine shop supplied is useful (indeed required) for this.
-I then cleaned the AR surface of the mirror and the top-surface of the tip-tilt.
-The gluing was done using superglue which Steve got from the bookstore (the remaining tube is in the small fridge). We may glue the other mirror using epoxy. I placed 4 small drops of superglue on the tip-tilt's top surface, placed the mirror with its AR face in contact with the piezo, and applied some pressure for a short while until the glue spread out fairly evenly. I then left the whole setup to dry for about half an hour.
-Steve suggested using a reference piece (I used two small bolts) to verify when the glue had dried.
-Finally, I attached the whole assembly to a base.
Here it is in action in my calibration setup (note that it has not been oriented yet. i.e. the two perpendicular axes of the piezo are for the time being arbitrarily oriented. And maybe the spreading of the glue wasn't that even after all...):
Yesterday, while setting stuff up, I tested the piezo with a 0.05 Hz, 10Vpp input from the SR function generator just to see if it works, and also to verify that I had set up all my electronics correctly. Though the QPD was at this point calibrated, I did observe periodic motion of both the X and Y outputs of my QPD amp! Next step- calibration...
I've done a first pass at trying to arrive at a mode-matching solution for the X-end table once we swtich the lasers out. For this rough calculation, I used a la mode to match my seed beam (with z = 0 being defined as the shutter housing on the current position of the Innolight laser head, and the waist of the beam from the NPRO being taken as the square-root of the X and Y waists as calculated here), to a target beam which has a waist of 35um at the center of the doubling oven (a number I got from this elog). I also ignored the optical path length changes introduced by the 3 half-wave plates between the NPRO and the doubling oven, and also the Faraday isolator. The best a la mode was able to give me, with the only degrees of freedom being the position of the two lenses, was a waist of 41um at the doubling oven. I suppose this number will change once we take into account the effects of the HWPs and the Faraday. Moreover, the optimized solution involves the first lens after the NPRO, L1, being rather close to the second steering mirror, SM2 (see labels in Attachment #2, in cyan), but I believe this arrangement is possible without clipping the beam. Moreover, we have a little room to play with as far as the absolute physical position of the z=0 coordinate is - i.e. the Lightwave NPRO head can be moved ~2cm forward relative to where the Innolight laser head is presently, giving a slightly better match to the target waist (see attachment #3). I will check the lenses we have available at the 40m to see if a more optimal solution can be found, but I'm not sure how much we want to be changing optics considering all this is going to have to be re-done for the new end table... Mode-matching code in Attachment #4...
I've made a first pass at a rack diagram for the 1X1 and 1X2 racks, attached as png.
Gray is old existing boards, power supplies etc. Blue is new CDS computers and IO chassis, and gold is for the Alberto's new RF electronics. I still need to double check on whether some of these boards will be coming out (perhaps the 2U FSS ref board?).
We did the simulation of the stacks by defining a transfer function for one stack (green plot) and another similar transfer function for the other stack.
We simulated the ground motion by filtering a white noise with a low pass filter with a cutoff frequency at 10Hz. (blue plot) (the ground motion for the 2 stacks are completely uncorrelated)
We simulated the electronic white noise for the seismic measurements. (black plot)
We filtered the ground motion (without the measurements electronic noise) with the stack's transfer function and subtracted them to find the mirror response (red plot), which is the target signal for the wiener filter.
We computed the static wiener filter with the target signal (distance between the mirrors) and the input data (seismic measurements = ground motion + electronic noise).
We filtered the input and plotted the output (light blue plot).
We subtracted the target and the output to find the residual (magenta plot).
We didn't figure out why the residual is above the electronic noise only under ~6hz. We tried to increase and decrease the electronic noise and the residual follows the noise still only under ~6Hz.
It also shows that the residues are above the target at frequencies over 20Hz. This means that we are injecting noise here.
We tried to whiten the target and the input (using an high pass filter) to make the wiener filter to care even of higher frequencies.
The residues are more omogeneously following the target.
We also plotted the Wiener filter transfer function without making whitening and with making whitening. It shows that if we do whitening we inject no noise at high frequency. But we loose efficency at low frequencies.
We shouldn't care about high frequency, because the seismometers response is not good over 50Hz. So, instead of whitening, we should simply apply a low pass filter to the filter output to do not inject noise and keep a good reduction at low frequencies.
[Jenne, Kevin, Steve]
We made some progress toward getting the MC's beam profile measured. In the end, no changes were made to anything today, but we're more prepared to go for tomorrow.
What we did:
* Grabbed the scanning slit beam scan from the PSL lab. It's the same kind as we had here at the 40m, so Kevin was able to hook it up to the computer, and confirmed that it works.
* Opened the IOO and OMC chamber doors, and locked the MC. Unfortunately the MC mode was awful in Yaw. Awful like TEM(0,10+). But it still locked.
* Confirmed that the beam went through the Faraday. I looked at the beam before and after the Faraday on a card, and it was the same nasty beam both before and after. So it looks like Zach did a good job aligning the Faraday and everything else. I was going to clamp the Faraday, but I didn't yet, since I wanted to see the nice happy TEM00 mode go through without clipping before risking moving the Faraday during clamping (I don't know how heavy it is, so I'm not sure how much it might potentially move during clamping.)
* Noticed that there is a whole lot of crap on both the OMC and BS tables that's going to have to move. In particular, one of the weights leveling the OMC table is right where I need to put MMT2. Steve suggested putting the optic there, in its approximate place, before doing too much other stuff, since it could potentially affect the leveling of the table, and thus the input pointing to the MC. Unfortunately, to do that I'll need to move the weight, which is definitely going to change things. Sad face. Moving the weight will likely be one of the first things I do tomorrow, so that all 3 profile measurements have the same configuration.
* Before closing up, I tried to align the MC, to get back to TEM00, to no avail. I got as far as achieving TEM11 flashing, along with a bunch of other crappy modes, but didn't get 00. That's also on the to-do list.
What we're going to do:
* Open the chambers, and align the MC to TEM00 (using the sliders on the MC align screen).
* Check with an IR card that the beam goes through the Faraday.
* Clamp the Faraday, reconfirm.
* Remove the weight on the OMC table.
* Place MMT2 on the OMC table in it's approximate final location.
* Realign the MC, and make sure the beam goes through the Faraday. If this doesn't happen smoothly, I may need more instruction since I've never dealt with aligning the Faraday before. What are the appropriate mirrors to adjust?
* Move the PZT flat steering mirror from the BS table to the IOO table. (Thoughts on this? This will change the table leveling, and also includes the trickiness of needing to move the connectors for the PZT.)
* Place a flat mirror on the BS table to route the MC beam out to the BS/PRM/SRM oplev table.
* Measure the mode using the beam scan: on the BS oplev table, on the POX table, and then perhaps by shooting the beam through the beamtube on the ETMY (new convention) table.
* Place MMT1 on the BS table, use flat mirrors to get it out of the chambers, repeat measurements.
* Place MMT2 in the correct position, use flat mirrors to get it out of the chambers, repeat measurements.
All of this may require some serious cleaning-up of the BS table, which is going to be ugly, but it has to happen sometime. Hopefully I can get away with only moving a minimal number of things, in order to get these measurements done.
Another note: Don't trust the PSL shutter and the switch on the MEDM screens! Always use a manual block in addition!!! We discovered upon closeup that hitting the "Closed" button, while it reads back as if the shutter is closed (with the red box around the buttons), does not in fact close the shutter. The shutter is still wide open. This must be fixed.
OK. Don't worry. This is just an initial confusion which we also had for the suspensions a while ago.
The faraday must be clamped. It shakes the table terribly but it is fine. The leveling may change a bit but should be small enough. Otherwise, just tweak the weights. In fact, the faraday has enough large apertures and we hope we don't need to move it again, as far as the MC incident beam is not moved. But if necessary, we don't move the mirrors but move the faraday itself.
Usually the alignment of the MC is taken by MC2/MC3 such that we don't move the refl. But if you think what have moved is the MC1/MC3 (i.e. activity in the IMC chamber), take the alignment of the MC1/MC3.
It is just a matter of time to get TEM00. If you get TEM11, it is already close. If you align for TEM11, it is enough aligned to lock TEM10 or TEM01. Once you got better mode, align for it again. Eventually you will get TEM00.
The leveling may change by moving the optics and the weight again. But once the leveling is recovered by arranging the weights somewhere else,
the pointing must be fine again. If necessary, You can remove two optics for squeezing injection (strange motorized rotating mirror and a mount sticking out from the table to south.)
Yes, we need to move the PZT mirror. For the connection, only Steve can give us the right way to do it. If it is too much hussle, just move only the mirror and ignore the wiring for now.
I will update how the mirrors should be migrated from the table to the table.
Has anyone tried pushing the "reset" button on the Uniblitz driver?
Here is the upadted list http://lhocds.ligo-wa.caltech.edu:8000/40m/Upgrade_09/Optics
I will update how the mirrors should be migrated from the table to the table.
After jumping through few hoops, we have one successful result in diagonalizing the input matrix for MC1, MC2 and MC3.
[Aside - How do you rotate plots in the new elog? It's showing them correctly in the attachments list below the entry, but not in the body of the log :( ]
I tried a round of PRCL ASC Wiener filtering today, but something wasn't right. I was able to either make the cavity motion worse, or completely throw the cavity out of lock. Making it less noisy didn't happen.
I took only 9 minutes of data the other day, since the PRMI didn't want to stay locked while it was daytime. So, this wasn't a whole lot to train on. But, even so, I designed some Wiener filters. The plots with the designs show the calculated Wiener filter ("Wiener") and the result from vectfit ("Fit"). Below the bode plot is the coherence between that witness (seismometer direction) and the degree of freedom (QPD channel). The fits were weighted by the choherence, so you can see that in the areas where the coherence was good, the fit was good. Elsewhere, it's not so great.
Using these filters, and assuming a Cheby1 2nd order lowpass filter at 30Hz, I predicted the following residuals:
After discovering that these filters didn't work, I went rogue and also put in a high pass filter at 0.1 Hz, but that didn't really change anything.
Here is a plot of what happened in Yaw. The Wiener filters' gains were all 0.3 here, which made the cavity motion larger, but not so large that it lost lock. The filters ought to have gains of 1 - the Wiener calculation should figure out the gains appropriately, if I've given it enough information. Here, as in the prediction plots above, red is the reference with the Wiener off, and black is with the Wiener filters on. Black is supposed to be below red, if the filters are working. Blue is the estimate of the angular motion that is being fed forward to the PRM, and you can see that at least the general shape is correct. I do need to figure out what the resonance in the blue trace is from - it's at the same frequency as a peak in the T-240's spectrum (that I didn't save). I suspect the cable might be touching the spaghetti pot on the inside, and making a mechanical short to pot vibrations.
Anyhow, more work to be done. I left the PRMI locked for a while this afternoon, starting at 5:15ish, so I'll see tomorrow how long of a lock stretch I was able to capture for training.
The beginning of my first week was spent at various orientations and safety meetings, some for general SURF and some more specific to LIGO and the lab. In between these I started work.
Jenne and I took out the spare STACIS and took it apart, taking out the circuit boards. I've spent some time looking through the boards and sketching various parts of the board in trying to understand the exact function without any useful technical diagrams (STACIS supplied us only with a picture of the board without components, not all that helpful). I think I now at least understand the basic block diagram of the circuitry: the STACIS geophone signal goes through a preamplifier and filters (the semi-circular board), and converts it into a signal for the PZT stacks. This signal then goes through a high voltage amplifer, and then goes to the five PZTs (3 in the z, one each in the x and y direction). The unit I am looking at has an extension board, which allows us to tap into the signal going into the preamp and the one leaving it. This should allow us to input our own signal instead of the geophone signal, and thereby drive the PZTs ourselves.
My next step, once I get a resistor to replace a burnt one on the high voltage amplifier, is to take a transfer function of the STACIS and see if it is possible to drive the PZT stacks with the cables from the extension board. If that does not work, I'll have to keep tracing the circuit to determine where to input our own signal.
What: Anchal and I measured the XARM OLTF last Thursday.
Goal: 1. measure the 2 zeros and 2 poles in the analog whitening filter, and potentially constrain the cavity pole and an overall gain.
2. Compare the parameter distribution obtained from measurements and that estimated analytically from the Fisher matrix calculation.
3. Obtain the optimized excitation spectrum for future measurements.
How: we inject at C1:SUS-ETMX_LSC_EXC so that each digital count should be directly proportional to the force applied to the suspension. We read out the signal at C1:SUS-ETMX_LSC_OUT_DQ. We use an approximately white excitation in the 50-300 Hz band, and intentionally choose the coherence to be only slightly above 0.9 so that we can get some statistical error to be compared with the Fisher matrix's prediction. For each measurement, we use a bandwidth of 0.25 Hz and 10 averages (no overlapping between adjacent segments).
The 2 zeros and 2 poles in the analog whitening filter and an overall gain are treated as free parameters to be fitted, while the rest are taken from the model by Anchal and Paco (elog:16363). The optical response of the arm cavity seems missing in that model, and thus we additionally include a real pole (for the cavity pole) in the model we fit. Thus in total, our model has 6 free parameters, 2 zeros, 3 poles, and 1 overall gain.
The analysis codes are pushed to the 40m/sysID repo.
Fig. 1 shows one measurement. The gray trace is the data and the olive one is the maximum likelihood estimation. The uncertainty for each frequency bin is shown in the shaded region. Note that the SNR is related to the coherence as
SNR^2 = [coherence / (1-coherence)] * (# of average),
and for a complex TF written as G = A * exp[1j*Phi], one can show the uncertainty is given by
\Delta A / A = 1/SNR, \Delta \Phi = 1/SNR [rad].
Fig. 2. The gray contours show the 1- and 2-sigma levels of the model parameters using the Fisher matrix calculation. We repeated the measurement shown in Fig. 1 three times, and the best-fit parameters for each measurement are indicated in the red-crosses. Although we only did a small number of experiments, the amount of scattering is consistent with the Fisher matrix's prediction, giving us some confidence in our analytical calculation.
One thing to note though is that in order to fit the measured data, we would need an additional pole at around 1,500 Hz. This seems a bit low for the cavity pole frequency. For aLIGO w/ 4km arms, the single-arm pole is about 40-50 Hz. The arm is 100 times shorter here and I would naively expect the cavity pole to be at 3k-4k Hz if the test masses are similar.
Fig. 3. We then follow the algorithm outlined in Pintelon & Schoukens, sec. 184.108.40.206, to calculate how we should change the excitation spectrum. Note that here we are fixing the rms of the force applied to the suspension constant.
Fig. 4 then shows how the expected error changes as we optimize the excitation. It seems in this case a white-ish excitation is already decent (as the TF itself is quite flat in the range of interest), and we only get some mild improvement as we iterate the excitation spectra (note we use the color gray, olive, and purple for the results after the 0th, 1st, and 2nd iteration; same color-coding as in Fig. 3).
We have been discussing how does the parameter estimation depends on the length per FFT segment. In other words, after we collected a series of data, would it be better for us to divide it into many segments so that we have many averages, or should we use long FFT segments so that we have more frequency bins?
My conclusions are that:
1). We need to make sure that the segment length is long enough with T_seg > min[ Q_i / f_i ], where f_i is the resonant frequency of the i'th resonant peak and the Q_i its quality factor.
2). Once 1) is satisfied, the result depends weakly on the FFT length. There might be a weak hint preferring a longer segment length (i.e., want more freq bins than more averages) though.
To reach the conclusion, I performed the following numerical experiment.
I considered a simple pendulum with resonant frequency f_1 = 0.993 Hz and Q_1 = 6.23. The value of f_1 is chosen such that it is not too special to fall into a single freq bin. Additionally, I set an overall gain of k=20. I generated T_tot = 512 s of data in the time domain and then did the standard frequency domain TF estimation. I.e., I computed the CSD between excitation and response (with noise) over the PSD of the excitation. The spectra of excitation and noise in the readout channel are shown in the first plot.
In the second plot, I showed the 1-sigma errors from the Fisher matrix calculation of the three parameters in this problem, as well as the determinant of the error matrix \Sigma = inv(Fisher matrix). All quantities are plotted as functions of the duration per FFT segment T_seg. The red dotted line is [Q_1/f_1], i.e., the time required to resolve the resonant peak. As one would expect, if T_seg <~ (Q_1/f_1), we cannot resolve the dynamics of the system and therefore we get nonsense PE results. However, once T_seg > (Q_1/f_1), the PE results seem to be just fluctuating (as f_1 does not fall exactly into a single bin). Maybe there is a small hint that longer T_seg is better. Potentially, this might be due to that we lose less information due to windowing? To be investigated further...
I also showed the Fisher estimation vs. MCMC results in the last two plots. Here each dot is an MCMC posterior. The red crosses are the true values, and the purple contours are the results of the Fisher calculations (3-sigma contours). The MCMC results showed similar trends as the Fisher predictions and the results for T_seg = (32, 64, 128) s all have similar amounts of scattering << the scattering of the T_seg=8 s results. Though somehow it showed a biased result. In the third plot, I manually corrected the mean so that we could just compare the scattering. The fourth plot showed the original posterior distribution.
I am starting work on the PSL table at the 40m. My goal is to lock the laser coming from the nearby table to the FP cavity and get a measurement of the response to a temperature step on the surrounding can.
I have to mode match the beam to the cavity. Specifically, I have to mode match to the beam coming from the PMC through the EOM to the polarizing beam splitter. Yesterday David and I measured the beam width at various distances (from a particular lens through which the beam traveled), and I fit that data using MATLAB to find the beam's waist size and location. However, I'm not convinced that the fit is any good, since we only took measurements at five spots and they had large error bars.
Here is the fit I obtained using fminsearch. The horizontal beam width measurements were smaller than the vertical width measurements, suggesting that the incoming beam was elliptical. I fit the data for each set of measurements separately and got two waist locations. The red trace is the fit for the horizontal width and the blue represents the vertical width of the beam. Averaging the two fitted waist locations and sizes gives
vert z_0= -1760 mm (waist location)
horiz z_0= -1540 mm (waist location)
vert w_0 = 0.286 mm (waist size)
horiz w_0 = 0.275 mm (waist size)
avg z_0= -1650 mm
avg w_0 = 0.281 mm
Here is the code I used:
I defined the function spotsize.m and then made a function gaussbeam.m that called it with input parameters and returned the least squares error. I then wrote another function twobeamfits.m that ran fminsearch to minimize the least squares error and made the above plot. I've pasted the code below.
function omega = spotsize(z_0, w_0, z)
function sse = gaussbeam(params,xvals,yvals)
%This f'n takes as its inputs
%three parameters (w_0, z_0, and lambda),
%a vector of x-values (distances),
%and an associated vector of y-values (spotsizes),
%It then generates a vector of fitted y-values by applying
%an exponential approach function (single pole), with the given parameters,
%to the x-values.
%It then returns the sum of the squares of the entries of the difference
%between the fitted y-vector and the actual y-vector
fityvals=spotsize(z_0, w_0, xvals);
error=(fityvals - yvals);% .*xvals;
% sse stands for sum of squares error
function [outputs] = twobeamfits(guesses, dists, vert, horiz)
%This f'n takes as its inputs
%two starting guess parameters (w_0 and z_0),
%a vector of distances (x-values),
%and two associated vectors of measured beam radii,
%the radius measured along the vertical axis
%and the radius measured along a horizontal axis (y-values).
%It then calls the gaussbeam f'n for each set of y-values and minimizes its output (sum of squares error)
%using the fminsearch f'n. It outputs the fit parameters it settles on.
%It then plots the input data, the fitted curves, and the residuals
fitvert=spotsize(vertparams(1), vertparams(2), dists);
spoterror=[.1, .1, .1, .1, .1]; %uncertainties, all in mm
fithoriz=spotsize(horizparams(1), horizparams(2), dists);
errorbar(dists, vert, spoterror, 'x')
errorbar(dists, horiz, spoterror, 'r*');
plot(points,spotsize(vertparams(1), vertparams(2), points));
plot(points,spotsize(horizparams(1), horizparams(2), points),'r');
xlabel('Distance z (mm)')
title('Gaussian Beam Fits')
ylabel('Spotsize w (mm)')
legend('Vertical Spotsize','Horizontal Spotsize','Vertical Fit',...
legend('Vertical Fit Residuals','Horizontal Fit Residuals',...
Later on I may repeat some measurements and try to gain more certainty in my fit. In the mean time I will use this beam profile for mode matching.