Attending: EricG, Gabriele, Xiaoyue
We installed two steel blades with different stiffness. By changing the hanging weight we are leveled the two arms, also the two end mirrors roughly. Leveling the whole stage by a more careful balancing of bearing weight, or does it matter much to the noise issue was left as an open question.
Eric walked me through the control system including the matlab program, emdm interfacing, foton, data viewer, striptool, diagnostic test tool, cymac terminal for signal generation. For every new system, a transfer function should be investigated by sweeping the driving frequency; or we can drive with a range of frequencies and extract the information from the output using Fourier analysis, but the coherence function exhibited a poor correlation (<<1, in a random fashion) between input and output signal when we tried this method.
We went through Eric’s python code for hysteresis analysis. We are driving the system on(+) – off – on(-) – off series with the sign indicating the direction of the driving force. The time interval between consequent actions is half an hour. We set it to run two cycles for each of the three levels of driving voltages.
Gabriele and I set up a rough Michelson interferometer alignment.
Matlab model -- Gabriele
Side view (left) Top view (right)
where the maroon beams are reflected from end mirrors.
We tilted both of the 45 degree mirrors to deviate the reflected beam with an angle from incoming beams to bypass mirror 1(M1), to be detected by photodiode (PD).
Also it should be noted that the two end mirrors (ENDM1, ENDM2) have height difference of 1cm approximately, so we differentiate the optical path lengths of the two arms accordingly.
The alignment procedure is listed briefly as below:
- prepare the first mirror with a horizontal beam using irises.
- prepare a vertical reference using two irises aligned with a home-made plumb bob.
- Align the 45 degrees inclined mirrors for vertical beams.
- Make sure the end mirrors are horizontal by overlapping incoming and reflected beams
- Roughly align the entire setup with beams superimposed
- Tweak the 45 degrees mirrors to separate the beam with a small angle (but large enough to bypass M1)
- Recenter or decenter mirrors to extract the symmetric port
- Install photodiodes and beam dumps
(We may want to order more visible range mirrors / D-cut mirror / D-cut mirror mounts.)
Attending: Eric, Gabriele, Xiaoyue
We overlapped the two arms by first eliminate the fringes as much as possible. However the angular motion of the suspended mirrors kept bringing the fringes in. Then we did finer aligning by maximizing the signal amplitude, making sure a good overlapping is giving magnificent interference (either constructive or destructive). A beating envelope was observed.
Then we installed the system into the chamber. Then we went through the procedures to generate the transfer function for the damping loop. We forgot to turn off the damping which at the beginning raised very strange phase behavior. As people walked around affected the signal a lot, we decided to pump the chamber overnight.
In order to study the current setup better to improve the design of the 2nd version experiment, I did some seismic coupling analysis. The plan is to shake the optical table with a white noise (5V, pre-amplified with a bandwidth 10-1k Hz, input 0.5A, 2V) mini-shaker (B&K type 4810), while the motion of the table is monitored by a 3-axis accelerometer. A full description of the seismic noise picture should include analysis of the coupling from table motion to Mich signal, bench (damped by rubbers) inside the chamber to Mich signal, and we also want to characterize different coupling from bench to different optical elements.
The first and easiest thing I tried is to characterize the transfer function between table vibration and Mich signal. The table was shaken in x, y, and z directions separately, with hopefully three linearly independent measurements of a_x, a_y, and a_z measured for each 1hr shaking. In this way we built matrix [a_xx, a_xy, a_xz; a_yx, a_yy, a_yz; a_zx, a_zy, a_zz] where the additional index indicates the shaking direction. With [e_x, e_y, e_z] for each shaking measured by servo, simply solve [a_xx, a_xy, a_xz; a_yx, a_yy, a_yz; a_zx, a_zy, a_zz][T_x, T_y, T_z] = [e_x, e_y, e_z] will give us the transfer function along x, y and z.
The picture is plotted with coherence between a_ii (where i is the driving direction) and mich signal is larger than 0.8. the result seems to agree with our expectation that the seismic noise transfer function follows the power law trend.
However, the coherence is very bad. I tried increasing the noise power by limiting bandwidth to 10 - 300 Hz and inputing 0.8A 3.0V to the shaker). From the result of the z-drive result, the coherence in low frequency range is improved a lot, so I am going to finish the three-axial analysis. While the last trial of data is fit by 1/f^2, the later trial is better fit by 1/f^3, but this kind of fit is tricky. There are many resonances and it is difficult to judge which fit is the best.
I tried superimposing the two and they are similar where both of them have good coherence.
I also did analysis (keep data with coherence > 0.8) for the coupling from directly the bench motion to optical elements. I mounted another mini-accelerometer on the newport mirror mount and clamp it to the table like what we did inside the chamber.
x has a generally higher level because the accelerometer is mounted along x-direction on the mirror mount. It seems that the transfer function is much smaller than one, which probably indicates a difference in calibration between the two signals. I will at some point mount the accelerometer one next to the other and measure the relative calibration, which should be simply a flat transfer function.
Another problem here is that I got very bad coherence at low frequency. I have no good explanation why there seems to be a high-pass cutoff around 30 Hz, but we definitely need to push the measurement down to 10 Hz.
I got a chance to talk with Norna about the strain range we are in for our maraging steel blades:
We typically load the blades to a stress level of 800 MPa to 1000MPa. The upper value there is approx. 55% of the yield stress which is ~1.9 GPa. The Young’s modulus E = 186 GPa.
—> strain rate = d/dt [ (F sin(wt) + F0) / E ] = (wF/E) cos(wt) —> maximum rate = wF/E = (2 pi 0.125 Hz) (800 counts ~ 1um deflection) / 186 GPa
400 MPa ~ 1mm deflection
4 kPa ~ 1um deflection
—> max rate = 1.689e-08 /second
Also, the triangular shape gives equal stress along the length of the blade when loaded.
In addition, as [1996 Dahmen] "Hysteresis, avalanches, and disorder-induced critical scaling: A renormalization-group approach" shows a relationship between hysteresis and crackle, on page 14 878 they show how a model scaling hysteresis loop area with r, where r is associated with the average avalanche size: A_sing ~ r^(2-alpha) (MFT :alpha =0), I am thinking maybe materials with larger hysteresis loop area would generate crackling noise more “easily”. If this is the case, a good candidate would be the AISI 1085, which is also called music wire; it’s a high carbon steel.
Reference: [1998 Beccaria] "The creep problem in the VIRGO suspensions: a possible solution using maraging steel"
I took the calibration line for the two accelerometers by mounting the small one rigidly next to the 3-axial seismometer and shake to get calib = transfer function G (w/ coh<0.8=NAN). I also solved the problem where we lost information in low frequency range by correcting the frequency axis -- I used wrong sampling frequency because I did not notice that DMPA_IN1 has sampling frequency of 1/4*8192 while the ACCX_OUT channel is 1/2*8192.
After all the debugging, the coupling transfer function looks like:
with resolution of 0.02 Hz, and 2^8 averages (# of hanning windows)
I characterized two different mirror mount configurations -- setup 1 & 2, see figure below -- for comparison. setup2 seemes less robust as expected — as it has an extra post & post-holder joint.
Now the setup is ready for further seismic coupling characterization of different optical elements that we might consider using in the upgraded version of experiment.
I took some measurement for several combinations of opto-mechanics during the weekend:
The structure around 20Hz is unwanted, and we suspect it's due to the resonance of optical bench.
Also, there seems to be a non trivial dependence of the structure there on the post length. For example, the shortest one (0.5”) has a large structure, then there is no data for the 1” one, the 1.5” shows no structure, the 2” is large, the 3" is small again and the 4” is large again. Irene Fiori from Virgo [2013 Fiori] argued that the contact surface between the components might play a role.
In this case we repeat the measurements on the small plate on rubber, instead of shaking the whole table.
Use DTT to have a live view of the changes:
1. test on the rubber plate —> structure at 20 Hz disappears, seems like the 20 Hz is the bench resonance frequency
2. test by tightening clamps —> structure around 1kHz moves to higher frequency
3. test by tightening mirror to post —> structure at high frequency becomes smaller
Below is an example for change#2, where after tightening the clamp, the green ref. curve (power spectrum of ACC#2) shifts to the red one.
The transfer function is smooth and flat, up to 300Hz.
From the latest measurements, it seems that Thorlabs Polaris mirror mount will work better for our purpose:
We suspect the better junction between mirror mount and the post be the explanation for the smoother /flatter transfer function of TP (Thorlabs Polaris) series. Also, there is a trend that shorter post works better for the TP series. NS (Newport Suprema) has a similar trend except for .5’ post, which has more bumpy structures probably due to the poor clamping.
I wired the electronics up according to the satellite amplifier circuit diagram from document LIGO-T040106-01-K.
As the OSEM available have LED SME2470 and PD SMD2420 same as the amplifier is designed for. For simplicity I skipped the voltage regulator part and supply reverse voltage for PD, current for LED using DC voltage supplies. Also, since I am reading Vout uisng a multimeter, no high-current buffer is included in my testing circuit. Another thing to note is that instead of LT1124ACN8 operated at +/- 15V I used OPA604AP operated at +/- 12V, because it's the op amp I found in lab at hand..
I first used a hand-cut aluminum flag, mounted on a translational stage, for calibration. I set reverse voltage as 10V, LED current 35 mA.
By cutting the beam I expected to obtain a symmetric Erf funciton-like Vout vs. flag position data, but as is shown in the figure, trial 2, I got long nonlinear tail for the other half of the data tr, along with the fact that I cannot completely block the light. I trimmed the flag a little bit to make the edge sharper and collected the data as trial 3.
I chose three different fits to analyze the linear behavior range:
linear range (mm)
center V_out (V)
My first guess for the cause of bad shape is the poor quality of my hand-cut flag. Also Gabriele suggested that probably the op amp was saturated at high V_out range.
I changed the flag from the arbitrarily cut square into a slim metallic post, and I decreased the LED current a little bit to ensure the V_out is below 10V to avoid saturation.
In this trial I am able to get a much better — in sense of both symmetry and linear range — response. The maximum linear range I am able to fit is 0.8 mm with a sensitivity of 6V/mm.
I measured the noise for the circuit using SR785, at 10Hz 15 avgs to be 16.14 nVpk2 /Hz ~ 1e-08 m /sqrt(Hz) at .1'' flag position, which is the midway of our linear range. However compared to the noise value of 1e-10 m/sqrt(Hz), tested in LIGO-T040106-01-K, our noise is higher by 2 order of magnitude.
The most probable source of the excess noise is the fact that I am not using a stabilized current supply for the LED. I added in an adjustable voltage regulator LM317T (as I didn't find a precision 10V reference at hand) and it pushed the noise down to 15.92 pVpk2 /Hz ~ 1e-10 m /sqrt(Hz).
Zach designed a wonderful circuit for us, and I wired it up according to the schematics:
For the two OPA140, which I didn’t find in lab I used OP27E instead, and I used two [R = 150, 3W] in series to substitute for [R13 = 270, 1W]. The original PD readout, without the 2-stage whitening, is very low at only 0.166 V with full LED exposure, thus I changed R16, the transimpedance load from 470 to 27k to give a max 9.9V voltage output. The value was determined by a potentiometer but finally substituted with a metal film resistor for noise concern. I also added a 1nF to the feedback of transimpedance for oscillation attenuation.
I re-calibrated the linear range to be 1.143 mm with sensitivity of 5.5V/mm at center voltage of 5.4245 V. Using AC coupling input configuration and measure two channels with channel 2 shorted as a reference, the RMS noises at a mid-way flag position are measured as below in units of m /sqrt(Hz) :
RMS before whitening
The performance is in expectation expect that low frequency range (<1Hz) is behaving weird. I measured the transfer function of one 0.75-75 Hz whitening stage to confirm the noise amplification after two-stage whitening.
To make the analysis more organized I should interface the signal analyzer ASAP..
I measured the typical optical table motion using the wilcoxen accelerometers, and fed it through the transfer function I measured before for the seismic noise estimation.
I also measured the laser intensity noise along with the shot noise. First I opened the chamber and blocked one arm of the beam to decouple the laser noise from other noises that can rise from the asymmetry of Michelson configuration. Also to make sure my data is understandable, I confirmed that the photodiode is not saturated by plotting out the beam power vs. output voltage curve, using a half waveplate + PBS (Thorlabs PBS101A) in front of the fibre input.
Then I used SR785 (interfaced with Q's help) to analyze the laser noises, with the experimental shot noise value extrapolated at high frequency level off floor: mean of the floor RIN_ns = 1.2282e-07/sqrt(Hz). While the incoming beam power P is measured as 0.275 mW we convert to obtain: ns = RIN_ns * P = 1.2282e-07*0.275e-3 = 3.3776e-11 W/sqrt(Hz), which agrees with the theoretical value ns_t = sqrt( 2hvP ) = sqrt(2*6.62e-34 [J*s]*(3e8[m/s]/633e-9[m])*0.275e-3[J/s]) = 1.31e-11 W/sqrt(Hz).
Then I did the unit conversion for laser noises, from V/sqrt(Hz) to m/sqrt(Hz),
DataViewer PDBOUT = 2720 count ~ ocilloscope = 1.50V with 1Mohm termination
Gmich = 1.5e11 count /m
(___ V/sqrt(Hz)) * 1/1.50V*2720 count /(1.5e11 count/m) = (___ )*1.2089e-08 m/sqrt(Hz)
I took laser noises in frequency intervals for finer line-width resolutions. Also it should be noted that I observed 20kHz (and its harmonics) peaks now and then, and I have no clue where they are from -- I got rid of them one time by short-circuiting A of Channel2, terminating all B's with 50ohm caps, but it's not replicable..
I did an Electron Backscatter Diffraction (EBSD, please refer to http://www.ebsd.com for more background information) analysis for the maraging steel (18% Ni Grade 250) blade sample.
To generate this map, BCC and FCC structures were used as the model. It was found that BCC structure is the best fit. Then the high resolution map with pixel size of 0.03 um was taken.
We should use the pole figures as a color key to interpret the map -- it tells us how the grains are orientated in the sample. Since the sample is thin and flat we care only about the Z0 direction, which is the direction normal to the blade surface. For example the greens correspond to grains with zone axis (101) facing up along Z0.
The next step is to choose a good grain with single slip geometry, within which to make a pillar with at least 1 um diameter for compression test.
The goal is to design a damping loop for the newly installed stainless steel blades.
We measured the transfer function for the blade response:
A comparison with the old maraging steel blades measurements can be found in Elog 757 and 587.
We modeled the transfer function and try to compensate the 2nd peak at ~10 Hz using a inverse function drive, however it did not work well. We doubted that the seismic noise is responsible for the problem, because seismic noise can excite the torsion / lateral tilting mode that cannot be damped / controlled by the coil drive, which only takes care of the vertical motion of the blades. To check the guess we took measurement of the coherence function of the seismic signal and the shadow sensor readout while common excitation is on for a sweep sine measurement:
In the Coherence Function measurement Z, Y, X table data correspond to the seismic noises measured by the 3-axial Wilcoxon accelerometer. The Z post data was taken by the seismometer mounted directly on the post.
The high coherence ~10 Hz indicates that we might be able to improve the compensator design with better management of the cables -- now they are hanging and touching freely on the vacuum chamber wall -- i.e. routing the cables such that there is no direct path from chamber motion to motion of the second stack, and closing the lid.
As the small grain size (max ~ 5 um) measured in the last maraging steel sample was skeptical for well annealed steel, I annealed the other non-annealed maraging steel sample under the condition described in E0900023-v12: 450 C for 100 hrs, however in air but not in inert gas atmosphere. I did another EBSD analysis for the self-annealed sample:
Although the data quality is not good mainly because of relatively poor polishing, we should still see that the grain size is actually really large (max ~ 50 um). It indicates that the last sample is not well annealed as it's claimed to be. I plan to double-check by taking a look at the grains of the original non-annealed sample.
On the side I characterized the carbon steel sample:
It should be noted that the Z inverse pole figure (color key) stays the same for all measurements (green 101, blue 111, red 001).
I made a 2D FFT for the EBSD images using matlab
Seems like a rather qualitative analysis. Is there any way you can make a 2D FFT of this so that we can see what the distribution of grain sizes are? What are typical sorts of grain size analysis people do in order to get quantitative comparisons?
where the left one is for the as-received maraging steel sample, right for the self-annealed sample.
and a selected cross-section for direct comparison:
Yet from the plots I can only infer that a more scattered plot is corresponding to a smaller "grain components". May need more study on typical analysis, and here is an EXAMPLE how other people did it.
I did EBSD for Stainless Steel 340:
I also did a grain size analysis in their manager-data software, which directly gives us histogram of grain sizes. It should be noted that different statistics would lead to different results, but still it should allow us to compare the grain information quantitatively between different materials.
Will the tiny modulation bring about crackles is a long lasting question for me. Since driving at force above the pinning barriers is the fundament to generate dislocation slip, I am thinking about using some well-studied material and investigate if, and how the small amplitude perturbation can overcome the threshold with time. My idea is to
1. take some characteristic stress-strain curves -- for literature comparison, basically to make sure my data makes sense
2. load the pillar close to yielding; this may be difficult because the smaller the sample, the more stochastic nature its mechanical property would carry, mainly because of the large statistical fluctuation caused by small ensemble of dislocations.
3. hold the indenter tip at the load, but apply oscillations using a built-in method used for measuring contact stiffness, and look for slip events over time.
I luckily inherited a single crystalline Cu sample. I electropolished the surface using electrolyte consists of 110 mL 85% phosphoric acid, 40 mL nitric acid, 50 mL 99.7% acetic acid, with applied voltage = 1.5V, current = 100 mA, T(heat stage) = 60 C. When reacting the solution gave off terrible yellow smoke and the solution turned from transparent to green and then to blue.. It should be noted that the reacted solution has a much higher temperature than target temperature 60 C because the process is exothermic, but it somehow worked, giving me smooth shiny sample surface. I tried FIBing pillars yesterday but with the current voltage /current I got some pudding-shape pillars... I need to consult people about the right working condition for Cu.
I made a micro-cantiliver out of SS340, single grain. Relocating the EBSD grain map in SEM is tricky, I used a self-defined coords system. However I will put the sample back for a EBSD analysis after making full use of this area:
The cantilever is of size 860 nm * 6 um which mimics the real blade in ratio width : length = 1:7.
I also made a micro-pillar (1 : 2.5 um) in order to compare the nano-pillar compressions to the nano-cantilever bending to see how the signature is different when the strain gradients are present.
Tests will be conducted soon.
From last Thu we are no longer able to lock the Michelson. Today we tried first with 0.5 gain instead of 1, and we added a resonant gain around 10 Hz, where the error signal showed a large peak. This gave us a reasonable lock. From there we measured and fit the plant transfer function and re-designed the compensators for the structures above 100 Hz. Applying the new compensator we were able to lock the Michelson fairly robust, increasing the gain to 2 (unity gain frequency at about 150 Hz)
It should be noted that if we keep increasing the gain to 3, there appeared to be some unstable structure around unity gain frequency. We also tried to increase gain at the other three resonance frequency peaks but it kicked the system to be unstable; we finally decided to use the simplest version of boost. An allipticlowpass filter at 600 Hz was also applied because high frequency resonances were getting unstable.
Now the lock acquisition procedure is:
1. Switch local damping on
2. Engage filters "lock", "notch1810"
3. Ramp up the gain to 0.5
4. Engage “Resgain”, “compensator1/2/3”
5. Ramp up the gain to 2
6. Engage the low pass and additional resonant gains at 30 Hz: “lowpass” and “boost”
We updated the autolocker accordingly. We started a data taking with common driving at 800 counts
Yesterday we vented the chamber and located a secondary beam on SYPD. We pushed it away from the sensing region by re-centering the main beams on both PDs. We were thinking of using iris to block the spurious beam but it clipped the reflection beam. Also we took care of two undamped beams that were dumped on the chamber wall. This helped a lot with the bump feature saw around 400-500 Hz.
After all of these tweaks the lock still worked! We increased the loop gain at ~11 Hz and ~16 Hz and this suppressed the resonance peaks seen in the error signal spectrum. When we were ready to do more adjustment the cables (taped on the wall) fell and we are going to fix it and pick everything up again today.
The data collected during the night were not very good, since the interferometer kept unlocking very often. We can't get any crackle data out of them.
We then tweaked a bit more the interferometer, remeasured and refitted the high frequency compensators. We also cleaned all mirrors. We noticed that the shape of the high frequency structure changed after the cleaning, but they did not change if we moved the beam centering on the end mirrors, by realigning the Michelson to a different point.
We see a strange noise spectrum, in the form of a bump up to 400-500 Hz. This reminds us of spurious interference with a ghost beam. It also seems (but we are not so sure) that the size of the bump changes with the alignment. So, we maybe have some ghost beam interfering with our main beam. We checked that the bump is the same in both AP and SP photodiodes.
We're leaving the autolocker on, to check the lock robustness over night. We also replugged all seismometers, since we suspect that lock losses might eb caused by seismic shocks.
I compressed a pillar (D = 1.1 um, H = 2.5 um, made out of SS304 single grain) using G200 nanoindenter.
Using inflection point I got F_yield = 0.3 mN, and knowing the pillar diameter to be 1 um we can estimate yield stress ~ 0.3 mN / pi (0.55 um)^2 = 316 MPa
However a more conventional definition for yielding point is the “0.2% offset” where people draw a line with slope of elasticity from 0.2% strain, and find the first cross over to be the yielding ~ 0.4 mN/ pi(0.55um)^2 = 421 MPa
I would also love to compare the pillar compression data with the indentation data.
In order to extrapolate yield stress information I need to convert the load vs. depth data to stress vs. strain ones. It involves a better knowledge of the indenter tip, as so far I got contradicting result from projected area function calibration and the tip radius claimed in the spec sheet (max projected area exceeds the claimed tip area). Also I need to learn more about how to find the actual “contact height” which excludes the non-plastic indentation from the machine loading depth.
I used COMSOL to compute the stress distribution on our blades. I set fixed constraint and a boundary load on the block clamp surfaces as demonstrated in the figure. In simulation I used extremely fine free tetrahedral mesh. The first principle stress contour is plotted. We see that we have large amount of blade areas that are bearing stress over 80% of the micro mechanical yielding (~250 MPa).
We were able to collect seven hours of data using driving amplitude 800 counts last night, and the first analysis of the data in a narrow quiet band does not show statistical difference between driving on and off states. We plan to take data with larger driving amplitude. I compared the error signal power spectrums for several candidate amplitudes and there are no distinctive features showing up. Also the system have stayed locked for ~20 mins with common drive amplitude being 1600 counts, so I updated the code and we are going to collect data with double the driving amplitude tonight.
[Gabriele, Xiaoyue] We checked all the mechanical parts received. Although there are some problems, Crackle2 are officially born!
And I updated my wallpaper:
Before we had trouble locking the Michelson for long periods of hours. We found that the problem lies in the autolocker script which checks if the IFo is locked with two conditions: RMS of error signal below threshold, and also RMS of correction below threshold. But the threshold of the correction was set to 1500, which is less than our driving amplitude. Therefore the autolocker at some point believes the IFO is unlocked because the correction gets too large. We increased the correction threshold to 5000 and then it stayed locked without problems.
Thus for the past week we have collected data with driving amplitude of 2400, 3000, 4000, and within certain quiet bands, all of them are showing a sign of non-linear noise being modulated at 2FQ, which agrees with our prediction for a crackling noise due to the fast driving change. We are going to take more data with various of driving amplitudes and see if there's a correlation between the noise and the driving power. For an expedient comparison, I analyzed the three data set in band 548 - 570 Hz.
We believe that the 1FI noise is due to misalignment. It should be noted that analyzing different bands, different hours, will give different results for the 2FQ modulation. Also we should question why the sign of the noise power could flip.
I first double checked if we are driving in a linear range.
Drive Amplitude (counts)
Shadow Sensor Reading (counts)
Oscilloscope Reading of SS output (mV)
Then using Eric's calibration (Elog 601) I calculated 1.97 nm /count for blade A and 1.59 nm /count for blade B. It should be noted that we have set DRVA gain = -1, DRVB gain = -1.19, so the effective driving is (0, 1, 2, 3, 4)k * 1.19 counts.