After having the LN2 dewar refilled, I transferred the newest cantilever (which performed well at room temperature---see CRYO:1332) into the cryostat to make a cryogenic measurement. I had to adjust the clamping block position on the cold plate to put the smooth reflective surface of the cantilever within line of sight of the laser beam, and I think the RTD may have come loose from the block during closeout because it is registering ~100 K after 2 days of cooling.
In any case, I made several-hour measurements at two different amplitudes using the steady state technique, and found a consistent Q of about 5 x 105. This is a bit lower than what is expected given the room temperature performance---when the Glasgow/Taiwain cantilevers showed Q > 105 at room temperature, they almost always had Q 106 at low temperature.
I can think of at least 2 reasons we may be seeing this effect:
I will also re-measure the cantilever at room temperature in the simple chamber, to see if I can recover the result from the other day.
(P.S.: Why do images automatically get reduced now and even when you try to set their size larger upon upload it just magnifies the low-resolution copy? Pooey.)
Over the past couple weeks, I have been iterating on the production process for our cantilevers, trying to get as close to Shiuh Chao's recipe as possible, but with our different design. I will make an entry dedicated to explaining the evolution of the process, but for now I want to happily report that I just measured the most recent sample that I brought over from the KNI today, and its room temperature Q appears to be in excess of 105, which is as good as we have ever seen even for the Glasgow/Taiwan cantilevers.
(on Tuesday, actually)
Here are a couple shots of the cantilever itself. I should note that there are *many* nonidealities with this sample (e.g., it is single-side polished, so the backside is very rough; it was masked using a lo-fi technique that has left the etch pattern slightly wiggly; finally, I feel that the mask can stand to be a bit thicker, as I think we had some etch-through in a few regions that should have been protected), so there is still room for improvement. The second photo here is focused on the reflection of the ceiling, so you can see the surface finish of the protected end regions and the central etched region.
Here is the ringdown. The mode frequency is about 100 Hz, so this tau of 400 s corresponds to Q ~ 1.25 x 105.
The other day me and Chris were trying to make some transfer function measurements using the HP 4395 in the cryo lab. We noticed some noise at lower frequencies. We tried a few things to to get trid of the noise but it was in every measurement we made. We finally hooked up both the R and A inputs to the source using a minicircuits splitter and still saw the noise (see below graph). The noise only appears up to about 200Hz. Our other measurements were made without using the minicircuit splitter so the noise is not coming from that.
Attached updated PDH phasebudget for the LB1005 + pomona box setup currently in use.
Also changed the custom low pass shown in the initial PDH phasebudget with an SLP5. Can swapa freely.
The most gain to be had is in the plant (can either deal with using chris W's AM RF injection idea or by using a fast mod path + EOM).
The phase delay is not the driver (confirmed with conversations with Mike Martin and published JILA paper on the PLANEX lasers)
I do not believe the values written in the diagram for the box between the LB1005 and the current driver.
These need to be confirmed, probably just by taking a transfer function through the LB + driver combo. I suspect I actually used a much smaller capacitor to push the corner frequency of the poles and zeros up.
You want the waveplates to be such that:
Remember that your cavity sweep has significant modulation depth in amplitude, so you will have a hard time minimizing RFAM on the input monitor PD as it will have a ~10-20% amplitude modulation envelope. While you are getting close to correct waveplate angles, it's fine to look at the light reflected from the PBS and the RFAM on the monitor PD during the sweeps. To really fine tune it you may need to turn off the sweep and either detune the cavity from resonance (ok) or block the input beam (better).
Last time I measured the PM depth I found the west laser to be at gamma = 0.13, which is much lower than the expected value of ~0.5. I looked into this today and was able to get gamma back up to 0.5 for the west laser.
The issue was with the waveplates near the EOM. While playing with them to try and reduce the AM, I accidentally reduced the PM depth as well. Lesson learned: when trying to reduce AM, don't adjust the waveplates too far or you'll also lose PM.
I tried again with fitting the correct transfer function. The fit is pretty much the same except with a slightly higher gain and resonant frequency. However, I noticed that the solver wasn't changing the value of Q. In the plot below, I initially guessed 5e7. I tried decreasing the initial guess of Q, but the solver wouldn't change it at all until I got to around 1e5. So as Koji said, there's probably not enough resolution to get a good fit for Q.
With the correct transfer function, I couldn't get the solver to converge anymore with a tau parameter I guess because the function it is trying to fit is slightly more complicated now.
The approach with changing a complex valued function to a 2-dimensional real valued function is what I have been doing for the fitting. I guess I didn't make that too clear in my original post.
EDIT: Evan pointed out to me that the complex pole pair should create a phase lag of 180, not a phase lead. I had used a Hermitian transpose (') instead of a standard transpose (.') on the COMSOL data which flipped the sign of the phase. For the fitted data, there was a flipped sign in the transfer function. It should be: G / (1 + i f / f_res /Q - f^2 / f_res^2). I updated the below plot with this in mind. Changing this didn't affect any of the parameters as both the data and the fitting function had reversed phase.
Wrong: G / (1 - i f / Q - f^2 / f_res^2)
Correct: G / (1 - i f / f_res /Q - f^2 / f_res^2)
Relationship between Q and decay time
There is a way to do the complexfitting by converting C into 2xR
i.e. Conver a data set from
a1 + i b1
a2 + i b2
a3 + i b3
an + i bn
and instead of the complex function f(x)+i g(x), use the 2D fitting function
z(x) = kroneckerDelta(x,1) f(y) +kroneckerDelta(x,2) g(y)
Then the 1D complex fitting is mapped to 2D real fitting.
In any case, your transfer functions might not have sufficient resolution to allow us to do the Q fitting.
I used the matlab function lsqnonlin to do this fitting. This function fits real valued functions so I had it fit both the real and imaginary parts. The first plot is done with tau=0 while in the second I allowed it to solve for tau. I used the DC gain as the initial guess for G, 1e8 for Q, the location of the maximum for f_res and 0 for tau. The version with non-zero tau would not converge on the default settings so I played with the parameters until it converged. Both solvers also ended up giving a warning that the value they converged to might not be a true solution. I tried playing around with the settings of the solver and it ended up giving results that were very clearly off. I might try to play around with it a little bit more later.
The fit with no tau agrees pretty well up until the higher order resonances kick in.
The fit with tau also agrees pretty well in magnitude for the first resonance however the phase is all over the place. As I said, the solver had issues with this so I might try a few things to make it work better.
Between the two fits, G and f_res stayed fairly constant between the 2 as expected. However Q decreased by an order of magnitude in the solution with tau.
Try fitting a function of the form:
The x12 on the resonant EOM circuit is assuredly less than x12 because of lossy RF elements. I would assume x8 is around the true value, which probably makes your measurements of gamma consistent with what you expect.
These measuremets were taken with the cavity close to room temperature.
I went through and calculated what to expect for the PM depth in elog:1319. I calculated a value of 0.78, which roughly agrees with what I have been measuring. However, just now when I measured it I found the west laser gamma had fallen to 0.13 for some unexplained reason. The east laser gamma is still 0.50.
In order to make sure my measurements of gamma in elog:1310 are reasonable, I went through and calculated what we should expect for gamma. The path to the EOM is as follows:
Marconi: +10 dBm
ZFSC 2-4-S+ splitter (port 2): -3.3 dB
VAT-6+ attenuator: -6.0 dB
VAT-10+ attenuator: -10 dB
ZX60-100CH+ amplifier: +36.5 dB
The total output is 27.2 dBm or 7.24 Vpp assuming 50 Ohm resistance.
This then goes into a resonant circuit built by DMass with a voltage gain of 12x (elog:896), leaving us at 86.88 Vpp.
This then goes into a Thorlabs EO-PM-NR-C3 EOM with a half-wave voltage of 350 V for 1550 nm light. So 86.88 V * pi rads / 350 V = 0.78 rads.
This is higher than my measured values of ~0.5. This calculation doesn't acccount for all other causes of attenuation and assumes every device is working perfectly as stated by the manufacturer so the calculated value should be seen as an upper bound.
EDIT: According to DMass' reply, the resonant circuit voltage gain is probably closer to 8x than 12x. This gives 57.92 Vpp going into the EOM which should produce a gamma 57.92 V * pi rads / 350 V = 0.52 rads. This is consistent with the measured values.
I wanted to give a visual outline of the process that we have been using to do silicon fab at the KNI.
Until now, we have been performing this process on individual rectangular sections of Si (recall that we sent two 6" wafers out to be diced a while back---see CRYO:1250). The first and second prototypes (CRYO:1260 and CRYO:1264, respectively) showed some imperfections in both 1) the etch pattern (i.e., the 2D pattern that defines the end blocks of the cantilever) and 2) the etch depth uniformity (i.e., the final surface roughness of the etched region). We suspected that either one or both of these are the result of cleanliness issues while handling the individual rectangles. After talking with Shiuh Chao from Taiwan, it seems that a better option is to perform almost all of the process on an entire wafer, then mechanically scribe out the individual cantilevers just before the main etch. There will be more details on that at the end of this entry.
The following is a photo walkthrough of a test run I did on a practice wafer on Friday. This wafer is just a single-side polish 3" wafer that was given to me by a KNI staff member, and the mask I used (see below) was the one Justin and I made for the individual rectangles. I did not cut the sections out before etching, so this run was never going to make usable cantilevers; instead, I just wanted to test out the "whole wafer at a time" scheme and see how it affected the etch quality. For this, I only chose to etch from the top (polished) side, as opposed to our standard, double-side etch.
Spin and bake
This is the step during which the photoresist is applied to the wafer. Beforehand, the wafer is cleaned using a 1:1:40 solution of ammonium hydroxide, hydrogen peroxide and water.
To date, we have been using a photoresist called ProTEK, which is actually a new-ish product that was designed to eliminate some steps with traditional wet etching (more on that later). To use this, a special primer must first be applied before the actual photoresist. In each case, the wafer is placed on a "spinner", which holds the center of the wafer via vacuum seal, the primer or photoresist is pipetted onto the central region, and then the wafer is spun at 2000 rpm for 1 minute, in our case:
After each application of either the primer or the photoresist on a side, the wafer must be baked on a hot plate. The primer requires a 1-min bake at 110 C followed by a 5-min bake at 220 C; the photoresist requires a 2-min bake only at 110 C. Since, per the standard procedure, the wafer must physically be placed on a hotplate (with a sacrificial wafer in between if so desired), I chose to apply the coatings in the following order:
I felt that was the best way to protect the more crucial top surface. Here are a couple photos of baking. On the left, the bottom side is up with the primer baking (top side is face down on the sacrificial wafer with its already-baked primer protecting it); on the right, the top side photoresist is baking. You can see some thin-film interference from the minute thickness variations.
After both sides are coated with photoresist, the wafer is ready for photolithography. This is accomplished on a Karl Suss MA6 mask aligner machine. This device aligns a photomask to the wafer (with sub-micron precision, if necessary), and then performs controlled UV exposure on the aligned system to define the etch profile.
So far, we have been using a high-resolution transparency print as our mask. This is a common technique in prototyping, and there is a glass blank in the lab that is used to hold the transparency (with scotch tape). The mask is loaded onto a holder and held with vacuum:
The holder is then slid into the machine, and then a drawer underneath holds the wafer, also via vacuum (there are different holders for each wafer size, and there are also adapters to hold smaller chips). The wafer, which is not yet installed, is held within the orange circular region on the plate below:
After loading, various parameters are set, including the contact type (in our case, the mask and wafer are brought into brief contact, then backed off 30 um) and the exposure type (we use 40 seconds of 365 nm exposure at the standard luminosity, which is fixed). Then, a microscope is used to adjust the position of the wafer under the mask via micrometers with 3 degrees of freedom (i.e., X, Y and theta). This is usually a very precise process, but in our case we can actually get by just looking at the alignment by eye. After everything is aligned, the exposure is run. For this, the microscope caddy moves out of the way and the UV source slides in and does its business. Here's a shot of the whole machine:
After exposure, the lithography pattern is only barely visible to the eye under certain light.
To complete the process, the exposed wafer must then be developed to remove the photoresist from the regions where etching is desired. This is done by swashing the wafer in ethyl lactate repeatedly for 10 seconds at a time, blow drying with an N2 gun in between. Four or five cycles is usually enough, and after this is done the pattern is clearly visible:
It is not clear to me what the gunk is in the regions to be etched (these are the central rectangles here). Repeated washing in the developer does not remove it any further, and it may somehow be related to the final etch quality. More on that later.
Now the wafer is ready for etching in KOH. When I did this with Justin, we set up a beaker on a hotplate with a magnetic stirrer, but the KNI has a full immersion etch bench that is much more convenient. The wafer is held in a wafer holder and dipped into the bath, which is heated to around 80 C and pumped to keep flow:
The etch proceeds at a rate of around 50 um/hour, perhaps faster if the solution is at a higher temperature. For this test, I let it run for about 2.5 hours before coming back to pull it out.
After etching, the photoresist must be removed using a piranha etch, which is just a concentrated solution of sulfuric acid and hydrogen peroxide. I think I didn't perform this at a high enough temperature, so in the following pictures there is still some photoresist on the wafer.
As you can see, the 2D etch definition is much better than in the first two prototypes I made with Justin (see the links at the top of this post). That is, the rectangular regions for the blocks at the end and for the thin cantilever section are very well defined, as compared to those previous trials with the individual rectangular pieces of silicon. So, I am concluding that those imperfections were the result of cleanliness/handling issues with the small pieces, and that they will not be present if we work with a whole wafer at a time.
On the other hand, the etch uniformity (final surface roughness) is still very bad. It is about as bad as the first prototype, and actually much worse than the second one (which itself was bad). From the 2nd pair of photos above, you can see that the unetched regions---though discolored from the remaining photoresist that still needs to be removed---have maintained their optical polish, while the etched regions are dull, even in areas that seem macroscopically uniform. This leads me to think that this is a problem with the actual etch process. It's interesting to note that the very-nonuniform-etch areas don't really correspond to the gunky areas I saw immediately post-development (see above).
In the last pair of photos, you can see some regions of the backside that were unintentionally etched. This is probably due to some photoresist having clung to a surface on which it was resting during any part of this process.
The conclusions are thus: 1) Working with a whole wafer solves a lot of problems, and 2) our etch process is not good.
A major caveat is that, apparently, the ProTEK photoresist was expired. It could therefore be that, with fresh ProTEK, we'll be in good shape. However, we may be better off cutting our losses and just going with the traditional oxide/nitride mask. This is the method used by Shiuh Chao's group in Taiwan, which has produced nice cantilevers, and is a straightforward process that I can develop quickly at the KNI. This process is summarized in this PDF:
I have discussed this with Melissa Melendes, the KNI staff member who has been helping me, and we can begin this on Tuesday. There are only two pieces of machinery that I need to get accustomed with to perform this process:
In addition, I'll need to make a new mask (one that has an array of identical cantilever patterns on a single wafer). I can make another transparency, which involves making another image and going to a printshop to have a high-resolution transparency printed, or I can just go ahead and make a nice glass chromium mask, if I know what I want. I'm told this can be done relatively easily using a mask maker at the KNI, though I will need to get some training on it.
For now, I will probably use another practice wafer and test out the oxide/nitride scheme to see how the etch improves. On the plus side, I performed the entire process you see here in a single afternoon by myself, so my proficiency is increasing. It will take a little time to learn to use the machines mentioned above, and having to use them in the process will make the whole fab take a little longer, but not by too much. Stay tuned...
I also re-measured the free-running laser frequency noise using the new driver, and it appears to be exactly the same as measured before with the ThorLabs drivers .
Plots for these last two statements are incoming as soon as I can open Matlab again.
I used the new laser driver to lock each laser to the test PMC and was able to achieve a UGF > 100 kHz in each case :
I also remeasured the laser frequency noise, and it appears not to have improved at all with the new driver :
The increase above 10 kHz for the E laser appears to just be gain peaking. I am somewhat surprised, though, that the noise below 10 Hz has not improved, since we assumed this was from the ThorLabs current drivers. One thing that has not changed throughout these measurements is the use of ThorLabs temperature controllers. Conceivably, this excess low-frequency noise could be from that (in particular, the shape looks like it could be some kind of electronics noise filtered strongly above a few Hz).
I'm not certain it's a problem, since the nosie is good at higher frequencies, but I may at least run some tests to see if this really is where it's coming from.
I spoke too soon yesterday. While we did fix the DC current drive to the laser and everything appeared to be working, I didn't check the actuation path, which in fact was not working.
Rich and I spent some time together again today trying to diagnose the new problem. At first we thought it was a problem with exceeding the acceptable B-E voltage of the main current-drawing transistor, Q1 (schematic at D1200719), so we replaced it and added some diode protection. When the problem didn't go away, Rich kept the board for a while and eventually discovered that there was actually a footprint problem with Q1. He implemented a fix for me and recorded the problem for future versions.
When I got the board back to the lab, it worked as expected (first with a dummy load and then with the real lasers). I locked one laser to the test PMC cavity using feedback to it and achieved a bandwidth of around 100 kHz . I also re-measured the free-running laser frequency noise using the new driver, and it appears to be exactly the same as measured before with the ThorLabs drivers .
I can now do interferometry(!):
Yesterday, we took a look at the diode driver to see what was going on. Earlier, I had tested the driver with a dummy load and still seen some form of oscillation, so I was fairly certain it was something particular to the driver. Rich came over and we did some testing in the lab, and when we narrowed the problem down to the board, we went over to Downs to do some further study.
Rich diagnosed the problem very quickly. There was an oscillation in the low-frequency transistor current drive stage, which was fixed by increasing C35 (schematic at D1200719) from 10 nF to 1 uF.
Today when I came in I found a bunch of ants on top of the cryostat. They were smart enough to realize that water condenses onto cold things and were swarming around the vents on the cryostat.
In the interest of not having to clear ants off the top of the cryostat every time I fill it, I talked with Steve at the 40m and got a bunch of ant traps from him. I placed 3 around the lab, another 3 I left unopened in the desk gaston is on.
The locations I put the traps were: by the door, on top of the tool chest next to the door, and against the wall in the little nook near the phone.
There is liquid inside of them so please try not to knock them over.
These measurements were taken with the cavities at a slightly higher temperature than before. I didn't actually calculate the modematching of the East cavity before taking all the measurements and didn't realize it was so low. It definitely could have been aligned better.
My PM depth still seems abnormally high.
The numbers remained pretty consistent from yesterday. I lowered the power in each beam to see if that would make much effect. My value for RAM depth went up quite a bit for the East cavity, which had the most power in it yesterday. I think this is because with such low power, the dark noise is at a comparable level to the RAM. When blocking the beam, I noticed the AC voltage remained fairly similar.
I also still am measuring anomalously high levels for the PM depth. I'm still not sure why this is.
I've been doing training sparingly at the KNI for the last couple weeks. I got my safety training done relatively quickly and then was granted access to use the facilities.
Since then, I have been receiving training from Melissa Melendes, a facilities manager there, on specific instruments and procedures. These include:
I've been signed off on all these procedures, save for the aligner (which I still need Melissa present for during the first couple runs) and the SEM (which I don't really need yet anyway). So, beginning next week, I'll actually start making some cantilevers using the Si pieces I had diced a while back when I was working with Justin.
My PM depth is much larger than what David thinks it should be (~0.15). I found an old elog post that measured a gamma of 0.17. The carrier voltage was relatively similar to my measurement (1.42 V). However the side band measurement was much smaller (16.2 mV). I'm not entirely sure what's happening here. I made sure that what I was measuring was in fact the sidebands (the signals went away if I turned off the modulation). It doesn't seem like I'm saturating the PDs. I tried playing with the total laser power in the system to see if that changed things but was still getting gammas >0.4.
In order to characterize the state of the setup, David gave me a few questions I should try to answer. In this post I'm going to write my attempts to answer these different questions. In the replies, I'm going to post the measurements I make.
What is the mode matching for each cavity? (should be > 70%, ~80% and 90% are the best we have achieved)
To measure this, I use the reflected light RFPD while sweeping through the 00 resonance. I measure the voltage off resonance (V) and the change between on and off resonance (dV) using an oscilloscope. The modematching is calculated as: dV/V
What is the sideband modulation depth (\Gamma) of each EOM? (measured via transmission peak height)
I use the transmitted light PD for this measurement while sweeping through the 00 resonance and the sideband resonances. I measure the peak voltage at the carrier (V_car) and at the sideband (V_sb) on an oscilloscope. The modulation depth is: gamma = 2*sqrt(V_sb/V_car)
See this for reference. Note that J_1(x)=x/2 for x small.
What is the RFAM in each path? (you want this to be zero, its a function of waveplates by the EOM)
I measure this with the RAM RIN PD. I meaure the DC voltage (V_DC) and the amplitude of the AC voltage (V_AC) on a scope. I set the input impedance of the scope to 50 Ohm as it filters out lower frequency AC signals (the oscilloscope claims it cuts off at 200 kHz). The modulation depth of the AM is: gamma = 1/2*V_AC/V_DC
See this for reference.
What is the voltage offset measured at the error point? (you want this to be zero, adjusted by the offset knob on the LB1005)
To check this, I use the scope to view the error signal from the LB1005 while sweeping through the 00 resonance. I then adjust the voltage offset until the error function is centered on 0 V.
What is the UGF of my loops? (changing power levels and modulation depths on the table mean this can fluctuate a good amount between locks without you noticing - decently complicated to get a transfer function measurement you trust here)
What is the beat frequency at?
Do the DC power levels seen on the RFPD in transmission jive with the depth of the RF signal you see on the PD?
I now have rack power and a nice LIGO power strip (CRYO:1305)---though I only have a single strip-to-chassis cable for now---and I just received my first laser diode driver from Rich & Co., so I figured I'd test it out. Yesterday, I plugged it in and tested it with both lasers, finding that the output power agreed with the current monitor reading according to the datasheet for each head. In the photo below, the DMM is looking at this current monitor channel, which has a scale of 100 V/A (i.e., the shown current is 100 mA).
Today, I wanted to use the PMC setup I've used before (see CRYO:1205) to remeasure the laser frequency noise and see if it is indeed reduced with the new driver. I had problems.
When retweaking the cavity alignment, I couldn't find a clear resonance by ramping either the PMC PZT or the laser current. I was just using the REFL PD at first, which showed some smallish dips that could have been from a misaligned cavity. Then, I borrowed the 1550nm CCD camera and looked in transmission, where I found a pretty-solid-looking TEM00 mode. Oddly, I couldn't align it much better (judging by the HOMs) and I also couldn't get the cavity to flash normally; it had a very persistent TEM00 spot that was not strongly sensitive to current or PMC PZT positioning. Also, the laser power as measured on the REFL PD seemed to have a strong (10-20%), frequency-modulated oscillation on it.
In an attempt to recover the previous state, I switched back to the ThorLabs LDC201C diode controller, and instantly everything was fine again: there were no oscillations in the laser power, and the cavity flashed as expected when either the laser current or PMC PZT were ramped. In both cases, I used the same ThorLabs TED200C TEC controller and the average DC output laser power was the same with either driver (i.e., ThorLabs vs. custom).
I have no idea what's going on. Below are REFL and cavity length actuation traces with each driver (ThorLabs on the LEFT, custom on the RIGHT). Could the laser be running in a multi-mode state with the custom driver? That would seem to explain why I can't get good cavity fringing with it (see the photos below).
Side note on pinouts
In trying to diagnose the problem, I noticed something strange. The LM14S2 butterfly mount specifies that, on the DB9 cable coming in from the diode driver, the laser cathode signal should be on pin 7 and the laser anode signal on pin 3. For the ThorLabs laser current drivers (e.g., LDC201C, ITC502, etc.), which should be directly compatible, the pinout has the laser cathode on pin 7 (check) but the anode on pin 8 (wtf?), while pin 3 is supposed to be the "laser diode ground". I think everything still works because these diodes should have their anodes grounded (this needs fact checking, but the LM14S2 mount is supposed to only work with "anode-grounded" diodes, so it seems standard---I couldn't find anything in the RIO documentation to corroborate this).
So, I believe the above shouldn't matter, but that is one big difference between how the current has been applied by the ThorLabs units up until this point and how it is applied with the custom driver now---the ThorLabs units have laser anode on pin 8 and the custom unit has laser anode on pin 3. All that said, Dmass's lasers are using pin 3 via a custom breakout on the table next to the laser heads, and he appears to have no problem with his lasers.
I added the ability to loop over the support separation. I checked values from .5in to 3.5in. All of these were with L=4", R=1", and at 60 degrees.
The first plot shows each different support separation plotted together. The remaining plots are the bode plots for each individual support separation. Up until aout 10kHz, the transfer functions are pretty much the same besides the slightly different gains at low frequency.
I also committed these changes to the SVN.
After playing around a bit more with Comsol, I realized and fixed some slight mistakes. I added in the phase information. The transitions in phase occur very rapidly and with resolution I was running at I couldn't get any points during the transitions. I used a loss factor of 1e-8 for the silicon (as measured here).
This simulation runs by considering the support points of finite size as fixed constraints.
I'm going to try and check effects of the support positions.
I also uploaded my model to the svn under: /trunk/CryoLab/comsol/cryo_cavity_sagging_transfer_functions/
I installed two Sorensen DC power supplies into the rack today, and I attached one of our new LIGO-style power strips to them. This system will supply +/-18V to our various LIGO-type electronics (e.g., laser current drivers, EOM drivers, ISS, etc.)
This is half of a very nice transfer function plot - See if you can get COMSOL to give you the phase information too and plot that in tandem (e.g. https://en.wikipedia.org/wiki/Bode_plot).
Also, I'm mildly curious how the frequency shifts with support distance. Are you using material parameters for the supports, or treating them as an area of constrained geometry?
I made a COMSOL model to check our assumption that the coupling of vertical motion to the cavity length can be regarded as DC.
I used a prestressed frequency analysis study in COMSOL to evaluate this.
The results are plotted below. The cavity parameters were L=4" and R=1", the supports are at 60º from the horizontal and seperated by 2". Up to about 1 kHz, the response is flat at 308 kHz/g which matches nicely with the number Evan's DC model got. According to a COMSOL Eigenmode analysis of the cavity, the sagging mode is at 6.5 kHz which also agrees with this result.
After talking to Zach on Friday I learned that I need to do much longer averaging on phi/Q measurements. Assuming that the Q of the cantilever is around 1e6, this gives a timescale of around 8 hours. With this in mind I turned on the continuous measurement system for the first mode of the Glasgow cantilever on Friday afternoon around 5 and planned to collect data over the weekend. The mode stayed in lock for around 20 hours. I'm not surprised that I lost the lock as the clamp began to warm up, I usually need to realign optics when the cyrostat makes large changes in temperature. When I came in Monday morning I had completely lost the amplitude signal.
The start time of the plots is at 5pm on Friday. The amplitude set point is 1500.
The average phi was -2.5e-7, and this was after a lot of slow low pass filtering so clearly something is wrong. I also don't know what's going on with the jumps in temperature.
I used a simple model to translate the seismic/boiling noise to the cavity length:
pole with Q=250 at the bounce mode of the platform (2.6 Hz)
60 degree / 2 inch separation point for the supports, giving 300 kHz/g for accel -> length
1/4" uncertainty (pessimistic) in the distance between support points
using this elog: http://nodus.ligo.caltech.edu:8080/Cryo_Lab/863 and those uncertainties, we estimate the coupling to be ~26 kHz/g, aka the common mode rejection is 21 dB.
Attached plots are the seismic noise at the top of the cryostat (measured), and that noise propagated through a Q=250 pole @2.6Hz, as well as a comparison of the beat with the best estimate of seismic noise at platform that we have.
The model does not take into account the voilin modes of the spring, or cross coupling between any of the non bounce modes to vertical platform motion, which will act as mechanical shorts at audio frequencies. I have not calculated where we expect this forest of resonances to be.
I've been trying to model the cavities in the second paper Dmass linked (http://journals.aps.org/pra/abstract/10.1103/PhysRevA.75.011801). I used the same parameters as the open circle trace in their figure 3. There was some ambiguity in how the cut depth is defined, especially in the vertical direction. I assumed a square cross section with sidelength c and one corner at (-R,-R) was removed, with R being the spacer OD. Maybe that's not exactly what they did but it should be fairly close. Their cavity is made out of ULE glass, but I kept mine made out of silicon.
The paper stated that their mesh had ~6000 elements which is about the number that COMSOL gives with an automesh setting of 5 ('Normal'). I looped over the support separation z just as they did to try and replicate the results of figure 3. The result is seen in the first attached figure. There is some qualitative agreement but mine is much less smooth than theirs. The numbers are on the same order as well.
I tried refining the mesh to 3 ('Finer'). The result is shown in the second attachment. The trace is much smoother except the large jump at 10mm.
For these graphs I was using a single point as the support, just as in the paper. I tried changing to a 2.5mm x 2.5mm support. Note that the coordinates are to the center of the square so at z=5mm there is still 2.5mm between the edge of the support and the edge of the spacer. The results are shown in the third and fourth attachments at mesh 5 and 3 respectively. Once again, the finer mesh smooths out the jumps in the trace. However in both of these we see a large change between 5mm and 10mm, just as in the second plot.
Even though the results aren't exactly the same as the paper, I can verify that there is a zero crossing with the slotted supports somewhere in the middle of the range. I'm going to look into what's going weird at 10mm and 5mm. I'll also try changing to ULE glass to see if I can match their results more exactly. Another idea I had is to try to loop over the cut depth to see if I can get similar results to our original support geometry near c=0 and try to see why we only see a zero crossing very close to the edge of our cavity.
We set up the Wilcoxons and rigidly attached them to the top of the cryostat to take 3-axis seismic noise measurements for the following states:
Attached are calibrated plots of the seismic noise and the noise floor of the measurement.
For the noise floor, I bolted wilcoxons to opposite sides of the lid of the cryostat, then looked at their coherence, and did the standard noise = ASD*sqrt(1-coh^2), where coh^2 is what the SR785 calls "coherence"
The fact that this is higher than what we would get in a huddle test where they were bolted to a truly rigid surface is not so surprising, and is a better noise floor to use for the statement "we believe the top of the cryostat is moving this much at these frequencies." Where we have no coherence, it is (obviously) not a good measurement of motion. These measurements were taken with LN2 in the cryostat, which made us use a lower gain setting on the Wilcoxon amplifier (g=10) to not saturate the signals. The SNR might be slightly better than reported for the X and Y (tangential and longitidunal) measurements.
The signal flow is:
Wilcoxon -> amplifier -> SR560(g=1) -> ADC
The calibration used is:
cts/rtHz * 1V/1638cts * 1V/1V * 1V/ampgain * g/10V * 10m/s^2/g
Data all available on the Cryolab svn in /Measurements/Seismic. (x,y,z) are (longitudinal,tangential,vertical)
After cooling down the cryostat to ~90K, I started trying to take continuous measurements for the first two modes of the Glasgow cantilever. However, this time I noticed some coupling between the modes.
In the plot below, the blue trace is the first mode amplitude and the teal trace is the second mode amplitude. At the start I have the first mode locked at an amplitude of 2000, and the second mode is free-running (excited from earlier measurements). At -30 seconds I lower the set point of the first mode to 1000, and we can see that the amplitude of the second mode increases even though it isn't locked. I decrease the first mode amplitude even further at -10s and the same effect happens again.
This continues to happen even after I bandpass filter the drive output (this resolved the issue for the Taiwan cantilever). The effect is much less significant when the second mode is at lower amplitudes, so I usually take Q measurements on the first mode after I reduce the second mode to as low an amplitude as possible.
I tried to realign the optics in order to reduce the clipping/nonlinearity I see at higher amplitudes, but didn't see any significant improvements.
Tonight I am going to do a long Q measurement for the first mode. I ran into some problems trying to do this measurement earlier today, but Zach suggested that I average out the measurement longer by using a slower low pass filer (longer cantilever ringdown tau ---> longer averaging time needed).
I have officially undergone my KNI safety training and am now a lab member. Over the next couple weeks I will do specific process/instrument trianing with both KNI staff and Justin.
I was able to get the continuous measurements working today for the first two modes of the new Glasgow cantilever:
I actually had a lot more trouble setting up the system for the first mode this time (whereas the 2nd mode was significantly more difficult using the Taiwan cantilever). I'm guessing it's because the mode frequency was lower than I'm used to tuning, but I'm not totally sure. As described earlier, I also can't ring the mode up to a very large amplitude without running into nonlinearities.
Tonight I'm cooling the cryostat with LN2 so that I can make cryo measurements tomorrow. Dmass requested that I turn off the pump tonight so that he can do some seismic noise measurements, so I'm also going to be checking out how well the pressure is maintained overnight with the crystat sealed.
Update: Clearly we don't have a good seal. The gauge read ~2e-5 torr while the pump was running, but has now settled to 1.1e-2 torr since I turned off the pump and closed the valve. I'll see how well I can cryopump when I add LN2.
Earlier today I accidentally broke the Taiwan cantilever while switching it out for one of the new Glasgow cantilevers. I had the cantilever in my forceps after removing it from the clamp successfully but brought it down to the table too fast and smashed it.
I have started taking measurements with one of the new Glasgow cantilevers (CRYO:1292). First I took some pictures out of curiosity and to see what the cantilever surface looks like before we handle them:
I think that the surface quality looks pretty comparable to the Taiwan cantilever, but I'm not being at all quantitative.
I also replaced the pressure gauge, since the old gauge wasn't giving accurate readings at low pressures (gauge would get stuck and display 2e-7 torr).
I began the measurement process by looking at the impulse response of the oscillator to find the first couple modes:
It looks like the first three modes are at 66, 417, and 1198Hz. I can easily excite the first two modes, so I'm focused on measuring the quality factor at these resonances. The first mode has a very long decay time (~450s) and starts to get clipped at medium to large amplitudes, so I wasn't able to measure the Q with a ringdown very accurately. I suspect the clipping is due to a bad clamping position, but I'll play with the optics some more to see if I can get better alignment. I measured the decay time of the 2nd mode to be ~80s, so Q=1e5. Pretty comparable to the Taiwan cantilever. This is at room temperature and 2.6e-4 torr. The filtered 2nd mode ringdown is shown below:
I tried to set up continuous measurements on the first two modes to look at Q as the pressure continues to decrease, but got the error message:
Cannot open related display:
when I try to set up the UGF block on the amplitude locked loop stage. It looks like the UGF.adl file in this directory has gone missing! I spent some time trying to fix this but was unsuccessful, so I'll ask around. Hopefully I will be able to take some continuous and cryogenic measurements tomorrow.
Today we went to the 40m and checked our Wilcoxons on their setup with Eric Q. All of our accelerometers appeared to be working normally.
We then went back to the cryo lab and tested some of the parts from the 40m with our setup. We found that our power supply was too low voltage. With the correct power supply, our amplifier and accelerometer worked normally. We found a power supply in the cryo lab that works and returned the parts we borrowed to the 40m.
I returned to my desk to find 4 new uncoated silicon samples sent from Glasgow, thanks to Stuart Reid and Iain Martin. We'll toss these into the Q setup and see how they compare to the Taiwain cantilever (which has almost the same mechanical design, but was made in a different facility using a different recipe).
This post will serve as a log of when the cryostat is refilled with LN2.
The cryostat was not refilled and came back to room temperature over 8/12-8/17. Refilling on the 8/18 brought the cold plate back down to <90K. On 8/19 it was not filled again and went back up to ~200K before being cooled down the next day.
On 8/29 the LN2 ran out and was not refilled until Monday 8/31. The cold plate reached 217K before being cooled down. The two cavities reached 132K.
We've been trying to use the Wilcoxon accelerometers to measure the seismic noise in the cryo lab. We were able to see a signal from a shaker next to the Wilcoxon, however we could not see any seismic noise at low frequencies.
We went through and checked all the channels on the Wilcoxon amplifier. Of the 10 channels, we found 4 of them to be completely bad. Channels 4 and 8 looked ok. 9 and 10 had similar sensitivity to 4 and 8 but had a higher noise floor. 2 had the same noise floor as 4 and 8 but lower sensitivity.
We also found that the gain switch on the amplifier is bad. Flipping it to gain 10 increased the signal by ~5x but the noise floor by ~20x.
We tested a different cable and found similar results between the two. We also tried 5 different Wilcoxon accelerometers and saw fairly similar results across the board. There was a difference of ~40% between the least and most sensitive aceelerometer. The two most sensitive accelerometers are the ones labeled A and D. However they both still could not see any seismic noise.
We then tried using some of the tiny Kistler accelerometers. The Kistlers saw what looked to be seismic noise, even though the Wilcoxons are rated 10x more sensitive.
Tomorrow we will be going to the 40m to try out our Wilcoxons on their amplifier to try and determine where the fault is.
Added in DMass' notes.
The turbo was touching the chair by the workstation and very easy to kick the power button. I closed the sifi vacuum,. turned off the pump, and moved the pump back towards the table.
It seemed to be in the bad location because of ground flatness (lack thereof), so I shimmed it up with some aluminum foil.
No data was being written to frames / test points were broken for the X1CRY model. We restarded the daqd and ran the startallmodels script on cymac1.
There are still many red lights and error indications on the medm master screen which we could not resolve.,
The timing error (x4000) is one of the problems.
Today I was able to get the NDS client working in MATLAB with Chris' help. This allows us to fetch online and offline data from the server and perform separate analysis afterwards. The motivation behind this is to eventually develop a fully automated measurement system where we load the cantilever sample into the cryostat, add LN2, and run the MATLAB scripts to measure the Q of several modes as a function of temperature.
I have been consulting this guide: https://www.lsc-group.phys.uwm.edu/daswg/projects/nds-client/doc/manual/index.html
I made a couple plots using data from when I cooled the cryostat down last week to test out grabbing data from different channels. These are plots of the temperature, RMS fundamental mode amplitude, and Q for 6 hours. Clearly I need to do more low pass filtering on the Q data, since the quality factor should never be less than zero. The amplitude set point was c = 500.
Today I was able to successfully perfom continuous Q measurements on the first and second modes of the Taiwan cantilever simultaneously for the first time. The results and system parameters are shown below:
All measurements were taken with a 150V bias voltage on the ESD. These results should be compared to the ringdown and individual continuous measurements I took earlier today:
These simultaneous measurements look very consistent with what I have measured in the past.
I think that there were 3 important parameters that I needed to change in order for this measurement system to work correctly. The first change was doing more aggressive low pass filtering at the RMS stage. Previously this stage was being low pass filtered at 500 or 1000 Hz, which resulted in rapid amplitude oscillations appearing on the drive signal. This was especially troublesome when I was trying to take continuous measurements on the second mode. I moved the low pass filter down to 50Hz and the results were much better. The second change was tuning the phase offset at the sinphase/differentiation stage. Rather than using the 90 degree phase shift, I played with other phase offsets. I settled on a 120 degree shift for the first mode and a 55 degree shift for the second mode by implementing other filters at this stage. I suspect that the original 90 degree shift wasn't optimal due to other accumulated phase shifts throughout the system. Regardless, the phase margin for each mode appears to be better now. The third change was bandpass filtering the output of each drive signal around the resonant mode frequency. Previous PSDs of each drive are shown below:
The MODERINGER and MR1 channels are used for driving the fundamental mode and second mode respectively. Although the peaks are where they should be at 106Hz and 663Hz, I was worried that a significant amount of energy might transferred to the wrong mode by each drive. After bandpass filtering, the outputs look like this:
Once I made these changes I saw much less coupling between modes than before (CRYO:1283). For example, I can now drive one mode and see that the other mode remained unexcited.
In order to check for coupling in the new system, I would place both modes in lock then let one mode ring down and look at the loss of the still-locked mode. For the traces below:
Blue = 1st mode amplitude
Cyan = 1st mode loss (Q^-1)
Green = 2nd mode amplitude
Red = 2nd mode loss
Yellow = cryostat temp. (not important for these experiments)
In the plot below I had previously locked both modes. I let the 1st mode ring down at t = -2 minutes and look at the effect on the 2nd mode. The 2nd mode loss changes slightly (~20%) but returns to the correct value when the 1st mode decays completely. We can also see that the 1st mode decays naturally, even though the 2nd mode is still being driven.
I repeated the experiment, this time ringing down the 2nd mode and looking at the loss of the 1st mode. I let the 2nd mode ring down at t = -1 minute We can also see that the 2nd mode has a much lower Q since it decays much faster. Again the loss only changes slightly and returns to the correct value when the 2nd mode has decayed away.
I also checked the robustness/speed of the system by putting both modes in lock and then exciting the cantilever by hitting the table and cryostat with a screwdriver. At t = -2 minutes I hit the table. We can see that both modes are temporarily excited, but are quickly driven back to the amplitude set point. The calculated loss of each mode take much longer to settle, but do eventually return to their steady state values. This is a good sign, in previous systems I had occasionally been in a semi-stable regime where an external input (like a screwdriver) could rail the drive output.
I took the first cryo measurements using the Taiwan cantilever on Friday (7/31/15). The cryostat had reached a stable temperature of 97K. I performed two continuous measurements of the first mode--- the Q is large enough in this regime that ringdowns start to become impractical.
These are fairly close results to previous measurements (CRYO:1267) and I think that any improvements are due to improved clamping. We noticed in previous setups that the the upper SS plate wasn't flush with the bottom, so we inserted a si shim. The clamping looks much more even now:
I also noticed that the measurement looked much better at the higher amplitude set point. After playing around with the set point for a while, I think that the best set point is around 50-70% of the amplitude when the displacement signal begins to look nonlinear.
The most interesting result from this experiment was that the second (663Hz) mode's Q decreased dramatically at the lower temperature. I couldn't make a continuous measurement on the mode but I estimated the time constant tau to be ~2s with a ringdown, so the Q is ~4,200. This is almost an order of magnitude worse than previous measurements (CRYO:1278). I talked to Nic about the disparity on Friday and he suggested that the clamping may have changed due to clamping materials' different thermal expansion coefficients. It seems strange to me that second mode would suffer from cryogenic clamping changes so much more than the fundamental mode, so there is clearly some work to be done thinking about these effects.