The low frequency oscillation we mentioned in the previous Log could originate from the creep of the rubber between PZT and the Shim. Because the initial stress caused the creep of the rubber, the Shim relaxed slowly and changed the optical path and caused the low frequency oscillation. This mechanism can explain the phase change between the driving and the signal. Rana recommended to use a spring to replace the rubber. To calculate the spring constant of the spring: Spring constant of the Shim, ks = 3EI/L^3; Amplitude of displacement of PZT ~ A; Amplitude of displacement of the Shim ~ B; the spring constant of the spring ~ k;
k = ks*B/(A-B)
From current dimension, ks ~ 10000 N/m. If we don't want to drive PZT too hard, assume A = 2B; k = ks = 10000 N/m.
We replaced the viton ring of the lid of the chamber with a new ring in hopes of eliminating some leaks. Though the vacuum chamber was pumped down more slowly than before, we expect the new ring to morph after the chamber is pumped down.
We measured the low frequency drive and also concluded from the graphs below that it is responsible for the excess stationary noise in our measurements.
Graphs corresponding to data from July 10 (taken at >2 Torr):
Graphs corresponding to data from July 12 (taken at around 924 mTorr):
We concluded that the excess noise at frequencies above 300 Hz is stationary noise caused by the driving force because the excess noise is present for intermediate frequencies (i.e. 0.15 Hz, 0.25 Hz, 0.35 Hz, 0.45 Hz) as well as the resonance frequencies (i.e. 0.1 Hz, 0.2 Hz, 0.3 Hz, 0.4 Hz).
Furthermore, we realized that switching the vacuum pump off during the data acquisition (1-2min after the start of the measurement) is not a source of excess noise according to the spectrogram:
Today; entered lab at ~09:08. I verified the orientations of the aspheric lenses and blaze gratings relative to the flextures, packaged and then dropped the parts for epoxying to Koji in 40m ~ 11:00. Spent some time between 12:00 and 12:45 finishing the ECDL connections. Everything looked good so I hooked it up to the TED200C controller. After a bit of research, I found out the Steinhart constants for the 10k thermistor;
Plugging these into the Steinhart equation give the actual temperatures from the Tact output on the TED200C (otherwise read as kOhm). According to the spec sheet, the TEC was tested at 250 mA (0.40 V), so not knowing a bunch more, set I_TEC on the TED200C to this limit and inspect the actual TEC current by scanning the Tset (setpoint) and recording the current in the ~ 15 - 25 deg C (attached plot, horizontal line marks room temperature). The diode current driver is hooked up, and everything is on the table as is. Left Crackle ~ 18:30.
Prompted by conversations with Gabriele, we discovered a previously unconsidered systematic effect in the crackle data.
In general, we are trying to use periodicity of the crackling noise to tell it apart from stationary noise, such as shot noise. Since the incident power on the photodiodes when locked at half fringe is constant, I assumed the influence of shot noise on the differential displacement signal would be stationary as well.
But, consider the following:
We induce a common mode drive in the blades. This causes a finite misalignment of the Michelson end mirrors (order of tens of urad), and due to the particular geometry of the setup, the beam spots on the photodiodes move in opposite directions. Thus, the Michelson gain changes with time.
As far as the displacement signal is concerned, this is fine, as we can track the Michelson gain in real time with the calibration line at 1.5 kHz.
However, the shot noise in terms of displacement noise looks like M(t) * s(t), where M is michelson gain in [m/W] and s(t) is the stationary shot noise time series in [W].
My analysis code looks for crackle noise in the form of cos(2f_d t) c(t), so if M(t) has a component varying like cos(2f_d t), it will manifest as apparent crackle power.
In short, it does, and this effect is responsible for the results I've measured thus far.
Our short-term solution will be to rebuild the experiment in a geometry in which the spots move in the same direction, thus hopefully suppressing the change in Michelson gain enough where we can set an upper limit on mechanical crackle below the direct noise floor of the experiment.
To go into more detail, I verified that this was the case in the following manner:
I replaced the time series PD data with random white noise corresponding to the shot noise of the laser power present in the michelson. I then ran it through the identical analysis routines as the real data, while "correcting" the fake data with the same calibration line data as the real data. I.e. simulating absolutely no crackle noise in the experiment, but the existence of the misalignment effect. The "crackle power" found in each simulated case corresponds well to the real data, even reproducing the change in magnitude for different drive amplitudes (since the different drive amplitudes cause different amounts of Michelson gain variation), and for both Maraging Steel and Stainless Steel blades. Here are the plots showing the results of this simulation:
[Rana, Steve, Alastair, Zach, Larisa, Vanessa]
We went over to the old Drever lab (in the room with the Synchrotron) for some sort of vacuum tank/glass bell jar to house our crackle experiment.
The vacuum tank we brought back (currently parked outside the Crackling lab room on a cart) has ~1' diameter and a few glass ports, presumably which we will shine the laser through. This tank is interesting in that it was designed or perhaps originally modified to run on its side instead of standing straight up.
We brought some other items back from the lab as well:
--function generators (x2)
--amps (x2, different kinds)
--lock-in amplifiers (x2 that need function generators, x1 that works on its own)
--tapped aluminium stacks (x2)
We took the SR785 to replace our SR780, which is now in the EE lab(?). Most of the SR560s are also in our lab, as well as one of the function generators and the standalone lock-in amplifier.
Because of the addition of this lab equipment, as well as the newly "cleaned" state of the labroom, we should look into getting some more storage space....specifically: 19" shelves for the Crackling racks, and some NIM racks, both of which Rana informs me we can get from the 40m lab.
Also need to think about acquiring softer rubber stops for separating the two stacks. The black rubber stops we found in the Drever lab are quite hard (presumably made for steel, whereas our stacks are aluminum.
After finding the 3/64'' set screw I surprisingly found the block holes are not tapped! Too bad I didn't even think of this a problem because we specified the importance of the tap holes in communication with machine shops. I talked to the aerospace machine shop and they told me the available tap cannot reach through the hole due a larger diameter to the top -- please see attached drawing for a demonstration. The tapering diameter of the tap is designed to prevent breaking and leaving the tap in the hole during machining. However when I picked it up nobody informed me of this issue... Since the aerospace machine shop will be too slow with re-tapping (Joe is not even back until next Tuesday), I consulted Eddie and Calum for faster solutions. Calum suggested we try the following:
1. We order several 0-80 taps from McMaster and try them out tomorrow morning. If the diameter doesn’t fit we try machining the taps, and then try on some spare aluminum materials to see if it can be applied to the block.
2. If we didn’t work this out I will glue the mirror to the block to continue my experiment. In the meantime, we either talk to Joe about this problem, or we order two new blocks from RDL.
I am suspicious that this is not the true tilt noise, but instead the in-the-loop spectrum as before. Is this corrected for the loop shape an the tiltmeter's mechanical response?
Log of the output power vs current in the 1064 nm (Innolight) pump laser. The crystal temperature was set to 45.5 C, and the current limit is set to 2.1 A
I took a relative intensity noise (RIN) measurement of the ECDL, by feeding the 0th order output of the AOM to the SR785. The RF power driving the AOM was set to 0 dBm. The RIN at 1 Hz is about 3x10-5, which is consistent with informal measurements we took on 08/13. From my understanding this noise looks pretty low, which is good. I will consult with Paco and add more discussion or conclusions, if any.
I took spectra of the resulting signal using the SR785 (Attachment 2). Note that these units are still in V/rtHz, since the signal has not been calibrated to the appropriate units for frequency noise, Hz/rtHz. Finding the calibration term will involve study of delay line frequency discrimination.
Restarted ECDL characterization last Friday. After some lab cleanup, and beatnote amplitude optimization we borrowed Moku Lab from Cryo lab to fast-track phase noise measurements. Attachment #1 shows a sketch of our delayed self-heterodyne interferometer. The Marconi 2023A feeds +7 dBm to a ZHA-3A amplfier which shifts the frequency of the laser in one of the arms using a free space AOM. The first order is coupled back into a fiber beamsplitter to interfere with a 10 m delay line beam.
The 38.5 MHz beatnote was barely detectable before when using PDA20CS2 because at unity (lowest) gain stage, the bandwidth was only 11 MHz... We instead switched to an FPD310-FC-NIR type which has a more adequate high-frequency response. Attachment #2 shows the beatnote power spectrum taken with Moku Lab spectrum analyzer. The two vertical lines indicate (1) the heterodyne beatnote frequency and (2) the "free spectral range" indicating the actual delay in the MZ arms, which is calibrated to = 9.73 m (using 1.46 for n, the fused silica fiber index).
We then tried using the phase meter application on the Moku. The internal PLL automatically detected the 38.499 MHz center frequency and produced an unwrapped RF phase timeseries (e.g. shown in Attachment #3). The MZ interferometer gives an AC signal
oscillating at , i.e. the angular beatnote frequency. The delay (calibrated above) characterizes the response of the MZ relating the RF phase noise spectrum to the optical phase noise spectrum. The RF phase obtained through the phase meter has a fourier transform
So the optical phase spectral density is related to the rf phase spectral density by a transfer function Then, the RF & optical phase power spectral densities are related by or
Then, because the instantaneous laser frequency is , in fourier domain the frequency and phase PSDs are related by the magnitude square of this transfer function like
Following this prescription, we compute an estimate for the frequency noise ASD (square root of the PSD) shown in Attachment #4. The frequency noise estimated by this method has several contributions and *does not* necessarily represent the free-running ECDL frequency noise.
We changed the setup to use a low power amplifier rather than the 5W amp from last time. The updated schematic is in Attachment 2. This is in part because 5W is an overkill to drive a fiber AOM which is known to saturate at 0.6 mW of RF input, but also because working with lower power active elements is easier and considerably safer. We dropped the 5W amp. in Rana's office last Friday, and got a ZHL-3A-sma. This little guy gives a max power output of 29.5 dBm (~890 mW) which should be more than enough while using the Marconi as our source (max output +13 dBm).
We hooked the amplifier to the load (AOM) without any couplers or attenuators in between, powered it with +24 VDC and quickly repeated a scan of the source power level while to see any sign of diffraction in the PDs. The result is in Attachment 2. We were a little bit disappointed that there appeared to be no diffraction, so next we tried scanning the RF frequency (it was nominally at 80 MHz) around and we finally succeeded in seeing some diffraction at 95 MHz! Paco thinks the internal fiber coupling made for the design wavelength (2004 nm) is suboptimal at 80 MHz and ~1.4 um wavelength. Therefore, to couple the 1st order back into the fiber, we need to shift the RF frequency to restore the diffraction angle at the cost of potentially not driving the optimal efficiency. An interesting observation made at the same time we saw 1st order light was that the power seemed to drift very slowly (-1%/min), which may have to do with some thermal drift inside the crystal... Our plan is to make a complete characterization of the diffraction efficiency at 1.4 um, and also investigate the slow intensity drifts as a function of RF input. The goal is not so much to understand and fix this last one, but to be able to operate the setup at a point where things are stable for a low frequency, frequency noise measurement.
When previously trying to characterize the AOM, we had noticed no 1st order diffraction when operating at 80 MHz, but significant diffraction at 95 MHz. This motivated us to take measurements while sweeping across both RF drive frequency and Marconi drive power. For frequency, we swept from 80-120 MHz in steps of 1 MHz. For power, we swept across [3, 0, -3] dBm (3 dBm is max power before saturating AOM). We took our measurements of 0th and 1st order signal using an oscilloscope.
Contour plots of the 0th and 1st order signals can be seen in Attachments 1 and 2, respectively. Peak 1st order diffraction seems to occur at ~106 MHz. Using this AOM for a beat note measurement, the frequency difference would be greater than intended, which could lead to a weaker beat note signal.
*Bonus: Today we moved the ECDL setup off the cryostat table and onto the other table. These measurements were taken after the move.
Should measure the S-matrix using a bi-directional coupler.
Today we tried to pick up from  by repeating the sweep measurements across RF frequency, at 3 dBm (max power). We noticed that the 0th order signal would dip around the expected value, consistent with the plot in . However, there was no signal from the 1st order. Clearly diffraction was occurring as seen by the dip in 0th order, but nothing was coming out of the 1st order port. We spent some time debugging by swapping the photodetector inputs / playing with the PD gains / performing power cycles, but got no insight into the issue.
We suspected the 1st order fiber coming out of the AOM might be damaged, since it loops around fairly tightly. After giving it more slack, we still saw no signal. We wanted to test the fiber, so we took an unused output of the 50-50 beamsplitter and fed it into the 1st order port, effectively running the AOM in reverse. We hooked up the input and 0th order ports to the photodiodes and did not observe any signal. From here we were more convinced that the 1st order fiber may have seen some damage.
For next steps, we can still use the existing fiber setup to take measurements of relative intensity noise (RIN), using the 0th order output of the AOM. I plan to do this in the next few days. Meanwhile, Paco is looking into ordering parts for a free space setup. We found a free-space AOM at 1064nm that seems promising, and we will work to transition the setup accordingly.
In order to transition the ECDL laser noise characterization to a heterodyne setup, we needed to test the AOM (acousto-optic modulator). We wanted to drive the AOM at 80MHz using the Marconi signal generator. Since the AOM has a max driving power of 600 mW, we determined that if we run the Marconi at max output power (13dBm), we saturate the AOM through a variable attenuator and a 5W amplifier. The detailed setup is in Attachment 1.
As we scanned the AOM RF input power, we monitored the mean of the 0th and 1st order power outputs using 2 amplified photodiodes on the scope. Attachment 2 plots the results of the scan; although we noticed the 0th order dropping, we did not see evidence of diffraction in the 1st order. Our suspected theory is that the lost power from the 0th order is due to thermally-driven attenuation inside the AOM (we do not know what is inside the AOM, so this is purely speculative). The next thing we want to try is to add a DC power level to the AOM RF input, but we will double check with Aidan.
I fixed the Z1 PD circuit — it was simply due a poor connection. I also soldered the AP, SP connections. Now everything works out pretty well with the breakout cables.
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.
With Aidan's assistance, I borrowed
for ~ 2 um imaging in the Crackle lab.
- Have been investigating 316 Hz noise in the control signal for the DOPO lock. Here is a list of some things that have been ruled out, mostly electrical:
- EOM power supply --> noise still present in DOPO transmission
- RFPD DC out --> no funky ground loops with scope (also looking at demod signal in different channel), noise still visible in transmission
- RFPD power supply --> noise still visible in transmission...
- Pump laser intensity (upstream pickoff) --> not a great test because pickoff optics are also on the optical table..
- 2 x SR560s --> No effect after bypassing
- Marconi --> same result as with anything in the loop after RFPD demod
- Things left to rule out:
- Fume hood exhaust fan ** highly suspected, my phone's own cheap-o microphone power spectrum shows peaks at 316.5 Hz (!) when near the exhaust fan
- NPRO temp controller fan --> phone audio spectrum shows line noise (60 Hz) mostly, and also 188 Hz... need to test further independently of the fume hood...
In ruling out the 6-axis translation mount on the DOPO cavity, I removed the PPKTP crystal + oven temporarily but still saw the noise. Since the resonator was no longer stable without the crystal, I needed to bring the mirrors closer and realign the output coupler from scratch.
Restored DOPO cavity with crystal, alignment. MM efficiency ~ 35%... still optimizable.
I talked with Zach and I think he is right - there are two modes in the area and I don't think I can excite one without exciting the other (the resolution in my function generator is not good enough). This one was ran at 37.156170 kHz on the drive, with a lock-in at 37.15.
I increased the drive (by rotating the knob) to 37.156570 kHz and we see the following (these are taken while the drive is on):
Where those beats we see happen to be the driven signal. My guess of what's going on is that the beat shown is because of the way the lock-in works (it's close to the drive) and we're driving near the resonance, but not right at it. In this plot, I turned off the driving signal around t=25 - and you can see that the beats go away.
So overall - we're seeing beats because we're driving pretty much not on resonance - so it rings up a little bit, but as it rings down (fast-ish) the drive rings it up again, and it's sort of a push-pull thing I can imagine going on. At some point, if I increased the drive to 1Vpk (instead of 0.5Vpk), these beats would disappear. My guess here is that the resonance was rung up enough that the drive was overpowered, so we didn't see these beats. However, since I can't seem to find the mode exactly... Conclusion - I should run finer sweeps to really pinpoint that resonance. I'll run the sweeps through to morning, work on the thesis until they finish, and then do more ringdowns in the afternoon.
I took the liberty of analyzing Giordon's most recent measurement. It looks pretty good, with an apparent Q of ~1.67 x 107. I think we expect it to be at least this high for a pure FS disc with no coating.
The analysis was done in the following way:
The linear coefficient fit.p1 is -1/tau.
Today, I achieved stability in Simulink for 3DoF, including noise to the hall-effect sensors and the coil's conditioning. We had measured the noise at the ADC to be max 20mV, but that value is amplified by the gain (91) of the HE conditioning boards. So, I included noise of 20/91 mV. I attached the final model and the script. .
I also used vector fitting to find the transfer functions of the coupling between DC1 coil to all sensors. An example of the successful resemblance is shown in the figures below (DC1 coil to W sensor). The figure on the left shows the modelling of the coupling and the deviation between the fitting and the data. The right figure shows a body plot of the modelled and measured transfer function.
I also calculated the amount of cross-coupling and noise inside our system in order to find the allowed gain to avoid any saturation.
Since the OP27 in the coil conditioning board also saturates at 10V, the DAC should provide no more than 400mV; beyond that point, the gain of 25 we introduced in the coils would saturate the OP27.
We had also found the cross coupling to be around 0.01 for two nearby sensors and 0.001 for the third one (in the 3DoF case we ignore all others). If our DAC never exceeds 400mV, cross coupling would get at most 0.0084V (8.4mV) at the ADC.
Similarly, if the coils get at most 10V, the maximum force they provide is 0.02N, which translates to 0.0113m (1.13cm) maximum displacement of the plate. Such displacement would produce 0.1989V at the ADC. Adding noise to these, our signal is only 0.2273V, well below the saturation of the ADC.
Inside the feedback filter, the cross coupling is cancelled down to -60dB (0.001V/V), so only 0.0012V remains, given a 400mV DAC output). The signal is thus 0.2201V. To avoid saturation of the DAC, we can afford a maximum gain of 1.8.
A room temperature ringdown was performed for 4 additional resonant frequencies whose ringdown times were on the order of minutes. The high voltage used was rougly 3.4 kV and 1 V for the AC voltage.
I received the red optics detailed in SUS:474 while I was gone last week. In case you're too lazy to click, they are
I have ordered 2 of each of the following from Tower Optical (ThorLabs' supplier):
I have also ordered 8 rotation mounts and 6 platform mounts from ThorLabs, but I will be using some of them for the iodine setup.
I came into lab last night around midnight or so wanting to run some more measurements - but it seems that when Rana took apart the HV (see previous post) - it wasn't put back together, so it wasn't functional.
Came into lab today, and spent a good amount of time trying to get the GPIB set-up to work (https://wiki-40m.ligo.caltech.edu/GPIB). In the end - it seems like only one of the ethernet hubs in the lab actually works - and it's being taken up by the other group there. So after my attempt to put it online - I tried instead connecting it directly to my Mac. I went into bootcamp, loaded up Windows, ran the exe, set-up an ip address, and then booted back up to my Mac and tried accessing it via telnet -- but that didn't seem to work. I'm not sure what the problem here is.
Apart from that, the lab was rather hot/warm again, and while the air conditioner appeared to be blowing "cold" air - I don't think it was strong enough to cool down the lab at any rate - so I've sorta thrown in the towel for now until I hear back from other people (mostly Rana) about the GPIB and the HV.
Edit: Rana is still working on the HV.
I will update some comments later..
Following up on the data analysis posted by Xiaoyue (see elog 836), I had a closer look at the 50+ hours of data we collected with a driving amplitude of 4000 cts (to be calibrated in meters).
As a first step, I computed the average spectrum of the Michelson error signal for each of the one-hour-long data segments, both those with the low frequency common drive on and off. Then, I compute the minimum of the spectra for each frequency bin, and I used this to whiten all of my spectra. The result is the following plot, which shows for each of the time segments (X axis, binning of 1 hour), the power spectrum normalized to the global minimum (over all 50+ hours):
It's very easy to see that there when the drive is on, the noise in the region between 100 and 500 Hz is clearly larger. Moreover, the noise in this region is not stationary, since it can vary a lot over time, even with the drive off. In some periods, the noise was much larger than the minimum value. The difference of the noise in on and off periods can change a lot over time. All those things are very suspicious, and I tend to conclude that, since the increase of noise in the drive-on period is changing a lot, we're not see in pure crackle noise.
To get a better understanding of what's happening, I selected two drive-on periods (segment 14 and segment 24), the first having very large noise, the second having relatively small noise. I compute a fast spectrogram over the two one-hour-long periods. Non-stationarities are clear visible:
Since it's difficult to tell which are the main frequencies at which the noise varies, I band-passed the Michelson signal between 250 and 295 Hz and computed the RMS in this band as a function of time. I then tok the Fourier transfer of this to look for the main modulation frequencies:
Clearly, segment 14 is much noisier, and the modulation frequency (125 mHz) as well as higher harmonics are very well visible. Segment 24, despite the fact that we were driving with the same amplitude, shows a much lower noise and almost no sign of the driving frequency. Those spectra are not normalized in term of relative noise variation.
Finally, to understand why the noise is changing so much over time, I compared the spectrogram of the one-hour-long periods (the first plot above) with the total RMS (averaged over each hour) of the error signal and the control signal. Since the low frequency gain is not enough to suppress the error signal down to the sensing level, control or error signal RMSs contain the same information:
Clearly, the noise is larger when the RMS of the correction (or error signal) is larger. Most of the RMS of the correction comes from a large seismic peak around 10-12 Hz. It is not clear at this point what is the origin of this noise up-conversion. Here are few hypothesis:
In conclusion, the quality of this data is not very good. But how can we improve it?
I downloaded the hysteresis data and had a first look at it. There are two main things to be addressed.
First, there is the global trend of both shadow sensor signals. Data is still uncalibrated.
[Xiaoyue, Saikanth, Gabriele]
This afternoon we tried to lock the Michelson, but we could only get a very lousy lock, as in the past.
Looking at the z OSEM signals, we can move the blocks by 3.6 microns at DC with an offset of 9000 counts. However, most of the motion we see in the error signals is around 3.5-4 Hz, which seems to correspond to the vertical resonance of the new floated legs. Since we have a whitening with a pole at 0.7 Hz, the actuaton range at 3.5-4 Hz is about 5 times lower. So we are kind of marginal in the actuation range for the present motion.
Tomorrow we'll try two strategies: we can increase the actuation by a factor 5 if we change the output resistor of the coil driver from 270 to 50 ohm, so getting x5 more gain; or we can simply bypass the whitening, at the price of much more high frequency noise (we don't know if this will be a problem)
Armed with the now working current monitors (1696) I got a first look at how actuation noise is modulated. This morning I injected a 95 mHz common mode excitation, with amplitude of 15000 uN (1698). I switched off the filter banks that calibrates the current monitors in MICH meters, since the dynamic range of the resulting signal is too large, generating numerical noise. Therefore the current monitor is calibrated in units of locking force (micro newtons).
Details of the anlaysis and the MATLAB script are attached. In brief, we see a clear increase of actuation noise when the common excitation in on:
Here recall that when the Michelson is locked, the two coils should see the same current, with opposite signs. So the difference signal is just twice the locking control signal, while the sum is ideally zero, and measures any additional actuation noise created by the DACs and coil drivers.
What's interesting is that this actuation noise is definitely modulated by the common mode excitation, as visible in the spectrogram below:
Finally, I performed a standard demodulation analysis using only one half-hour-long segment, and obtained the following modulation components:
Since the current monitors are now working, we could use the signals during our crackling noise runs, and get a better estimate of the modulation components. Then we could multiply the results with the proper actuation calibration to see how the amplitudes compare with the Michelson modulated noise.
Today we started to set up the experiment which will eventually allow us to characterize the noise of the blade spring crackling. The configuration was an analog of the final configuration, where a controlled voltage over a PZT was used as the driving force on the ETMX only.
The first plot, labeled "Spectrum 1" represents the power spectral density plot of the all the noises prevalent in the configuration (i.e., seismic noise, shot noises, fluctuations due to air currents, etc).
"Spectrum 2" is similar, except that the only noise present is 'dark noise', which is the extra signal the PD gets when the laser beams are blocked from hitting it. This 'dark noise' can be thought of as some sort of background noise.
By observation, we can compare the orders of magnitude at which both the sum noise and dark noise curves exist.... Spectrum 1 is around the order of ~10-3 to 10-2 whereas Spectrum 2 is around the order of ~10-5. This confirms that the dark noise occurs within the range of values of the sum noise.
I looked at the last night lock we had (August 5th), reported here, after Xiaoyue realigned and cleaned all the optics.
First of all, there is no more evidence of scattered light:
However, Z1 and Z2 shadow sensors show the same amount of motion as before:
If I use my estimate of the scttered light coupling, I cleary overestimate the noise:
So the conclusion is that the scattered light problem was much smaller in that lock. Maybe this is a result of the optics cleaning, or maybe of a different alignment position. However, we had many large glitches, as visible in the BLRMS plot:
Morevoer, as visible in the first spectrum, the peaks and structures above 80 Hz are much larger in the last lock than in the previous one. Maybe the different alignment brought us to a position where we are close to clipping on a baffle? Or a beam is no more well dumped?
I compared the maraging steel and highC steel (90%YS) blades measurements with the same nominal common driving condition: 0.125 Hz, pk2pk ~ 30 um. The good segments were selected based on stable mean UGF values. We have ~ 20 hrs' good data for both. From the comparison we see very similar noise behavior, suggesting that the noise being modulated are most likely instrumental.
My goal was to have a simple and smart way to reduce the amount of signal sent to the Z_HF coils (path with whitening filter) by offloading part of the force to the Z_LF (low pass at 2 Hz) path.
Here is a solution that seems to work quite well. Inside the real time model I implemented an all-digital feed-back loop which uses the Z_HF signal as input and feed back to itself. The feed-back path includes a simulated version of the low pass (Z1_LP_ and a control filter (Z1_OFFLOAD). When the loop if closed, the HF and LF signals are
z_HF = 1/(1+LP*OFFLOAD) z
z_LF = OFFLOAD/(1+LP*OFFLOAD) z
Since the z_LF is going through an analog low pass, the net effect in term of current in the coil get an additional LP term. The signal after the control filter but before the digital low pass is then sent to the DAC. Therefore, with this technique I can
The results are very good. Here is a comparison of the Z_HF control signal without offloading and with offloading. In the control filter I implemenetd additional high frequency roll-offs, band-stops, and resonant gains at low frequency. The Z_HF signal is slighlty increased at about 10 Hz, due to gain peaking. But this is not important and it doesn't affect the actuator response, since my technique guarantees a sum of exactly 1.
I measured the plant transfer function. It's much better than what I got with my old (three days ago) splitting. Morevoer, this techique also improves the high frequency phase rotation, as visible below. There is small wiggle at about 10 Hz, that might be due to the cross-over in the two paths. Maybe this is due to a smal mis-modeling of the LP filter. It's not a big deal, since I can fit it in the actuator model.
The new calibration model has been loaded.
I added a new button on the main screen to control the offload feature.
The autolocker enables the offloading as the last step in the lock acquisition.
In the past I had the impression that when the blades are damped, there are less glitches.
To check my idea, I created a new low pass filter for the blades, with a corner frequency of 80 Hz. In this way I could keep the damping engaged without adding too much noise above 100 Hz. The following plot shows the displacement noise (calibrated PZT correction) with the PZT locked. The red trace is what happens with blade damping off: the noise shoulder due to the glitches is well visible up to 300 Hz. The blue trace shows what happens with the damping on: the correction is lower at 4 and 14 Hz (blade resonances are damped) and larger below 100 Hz (sensing noise of the shadow sensors). However, there are no more glitches!
The next step was to go back to the PZT correction offload, that luckily I already implemented. The LOCK_PZTOFFLOAD filter bank gain was set to 1e10, and the LOCK_SERV engaged with FM1-2-3-4-7-8. This gives a bandwidth of the offload path of something about 20 Hz, which is just enough to actively damp the two resonances.
The effect on the calibrated PZT correction is shown in the following plot:
Green trace is without damping or offload, blue is with damping on, and red with the offload. There are no more glitches and the noise is good! The bandwidth of the offload path is low enough that there is no need to recalibrate the PSD of the PZT correction above 100 Hz (there might be some phase lag altough).
I added a elliptic low pass at 50 Hz in the offload path, just to further reduce the noise. There is no visible effect on the spectrum.
To conclude, here is a comparison of the displacement noise we got in three different configurations (sorry for the bad MATLAB graphics, but it's not possible to get anything better on the lab workstation). Blue is what we got in the past, before installing the new seismic stack (digital lock). Green is what we got with the new stack and beam injection through the window (digital lock). Finally red is what we got today, with fiber laser injection and PZT lock with offload. I'm almost sure that the increased noise at few hundred Hz is there since the installation of the new plate beam splitter. I hope we'll be able to improve thing with a global realignment.
As we discussed in the meeting today, I set up a Wheatstone Bridge with an AC bias to see if we could make a test of the Crackle demod setup.
I used 5.5k wirewound resistors. Since they're wirewound, I expect almost no excess noise (c.f. Frank's thesis). I used clip probes to take the differential bridge into the A and B inputs of an SR560 set to (A-B) mode, with a gain=1000, and a 10kHz low pass.
I started with a pile of 1% resistors and quickly found a pair that gave a differential bridge voltage of ~0.8 mVpp with a AC bias of 8 Vpp. So the balance is very good (1 part in 10000).
The attached plot shows the differential bridge voltage (I took the SR785 data and divided out by the G=1000 of the SR560). Also plotted is my calculation for the Johnson noise of the bridge.
The drive frequency is ~9.1 Hz. Clearly there is a lot of harmonic distortion at this bridge measurement point.
Q1) How will we measure the excess resistor noise in the presence of this distortion?
Q2) Will there be a similar distortion issue in the blade Crackle measurement?
I upgraded the Resistor Bridge setup and now have pretty good results:
Using a freq bin width of 31 mHz, I find that the residual 2f and 3f peaks are pretty small. Now, I should use the AD734 multiplier chip to square the signal and try out the 2f demod.
I got a few AD587KN (high-precision 10V reference) samples today from AD. I hooked them up to see how much quieter my DC supply would be. The results are pretty good, with the voltage noise reduced by a factor of 5-10 throughout. The first two attachments below are comparisons of the noise in
1. The +12V regulator (MC78M12) alone
2. The AD785KN reference with V_in = +12 V provided by the regulator
3. The same as in 2, only now with an additional "noise reduction" capacitor (a 1-uF capacitor from pin 8 to ground forms a LPF with an internal 4-k resistor, giving a corner frequency of 40 Hz to reduce high-frequency noise),
plotted with the same frequency ranges and settings as those in the previous post.
The reference comes very close to its noise spec of 100 nV/rt(Hz) @ 100 Hz. The only issue is that it seems to have much more line pickup than the regulator (which seems almost completely insensitive to line noise), and this is worsened by the extra capacitor. Attachment 3 is a close-up of the low-frequency spectrum around 60 Hz. I suspect that this will be alleviated somewhat when I move away from the breadboard phase.
I want to rig this up so that I can stabilize the supply voltage to the transimpedance amp and LED, but in order to do so I will need to build a higher-current source using a power transistor, like either of those shown in attachment 4 (the AD587LN is only able to provide <10mA).
Some useful things to remember for the AD734:
The transfer function when wired as a multiplying circuit is: W = ((X1-X2)*(Y1-Y2) / 10V) + Z2
For this to be true the Z1 pin should be wired to the output W, to provide feedback, which isn't shown explicitly on Tara's general multiplying circuit diagram. Also for testing the chip inputs were wired as differential, not with one leg grounded as shown on the GMC diagram.
The 10 V comes from the default division voltage when the denominator control inputs (U0, U1, U2) are grounded. If you want some added offset to the output you can send it to the Z2 pin.
The input impedance is listed as 50k for all X, Y, and Z pins.
We measured the noise with 0V X/Y inputs, it was around 1 mV/rtHz at 10 Hz, as you can see in Tara's earlier post, slightly improving at higher frequency.
The input noise is listed as 1 uV/rtHz from 100 Hz to 1 MHz. The amplifier gain is listed as 72 dB which is ~ 4000x, and we were at the default denominator of 10V so this corresponds to a noise of 1e-3 * 10 / 4000 = 2.5 uV/rtHz at the input, seems reasonable compared to spec sheet. The signal to be squared in the creak setup (the output of the Michelson) will have to be bandpassed first, probably by an SR560, so gain can be applied there to get in over the multiplier noise floor.
As Tara noted the output does rail for signal amplitudes well below the listed maximum input, so we need a better understanding of how to control the gain.
By mingyuan, tara
We figured out the offset problem in AD734 chips, the box for squaring and multiplying signals is finished.
The problem from the previous circuit was that the ground from the signal was grounded with the load ground. This time the load ground is separated from the signal ground, Z2 is grounded to load ground. These corrections fix the offset problem and the maximum allowed input ( was 0.6 V.) Now the input can be up to 10V. The output, Z, is (X1-X2)x(Y1-Y2)/10 as described in the datasheet. Now the chip are connected as shown below.
We are thinking about not using the default denominator (/10) for a multiplying chip (we certainly need it for squaring chips, otherwise the output will rail), because after the signals (from PD and driving voltage) are squared, their dc levels are ~3 V. When the two are multiplied together, the voltage output drops to 3x3/10 = 0.9 V. So if we can have denominator = 1, the signal will be larger. However, we have to understand how the noise in the chip works first. See Mingyuan's entry about input referred noise of the chip ,it is roughly 3 mV/rtHz. If the SNR remains constant regardless of the denominator, we might not need to worry about it.
ADC & DAC
The bits/volts conversion factor is different for our ADC and DAC. Specifically, I measured the voltage output of the ADC and DAC and, by comparing it to the input and output readings--in bits-- of the computer respectively, I found this relationship to be 1.64bit/mV for the ADC and 3.3bit/mV for the DAC.
HE sensors output range
We also measured the output of the HE to fluctuate at most 100mV in response to the movement of the plate. Given that, a small displacement of the plate that produces roughly 30mV would bring approximately a 18bit change in the ADC output. With the already inherent noise and fluctuation of the bits reading, it is therefore difficult to detect small movements of the plate; it is necessary to boost the HE output after subtracting the HE sensors offset.
The HE sensors signal goes a voltage offset and then a high-pass filter. We will adjust our resistors' values only in the first state, so that the voltage offset more accurately corrects the inherent offset of the sensors and amplifies the output even more. Currently, as described in my first research report, the gain was 1; we will now aim for a gain of 50. I calculated the expression for Vout in the voltage offset configuration to be:
Vout=-(R4/R3)Vin + 5* [R2(R4+R3)/R3(R1+R2)].
A gain of 50 would also increase the inherent offset of the sensors, which would now be about (50*2.5)=12.5V; we also need to fix that. I calculated that if we use R4=50*R3 and R1=19.4*R2, we can get the desired gain, while also appropriately correcting for the offset.
Transfer functions saturation
We measured the transfer function of our damping transfer function: (s+Zo)/[(s+Po)(s+P1)] where Zo<Po<P1. We noticed that the voltage source setting of the spectrum analyzer affected our transfer functions. I extracted and plotted the transfer functions for three different voltage sources: 10mV, 100mV and 500mV which are shown in this order below. We are unsure as to why that happens.
I fixed the problem with DAC channel 2 (a bit of solder was shorting one of the DAC output pins with the ground). Now all ADC channels are working, and all DAC channels are qorking too, except for channels 12 and 13, that were already broken.
All componented have been installed on the ADC interface board. Not tested yet.
Today I finished connecting all the STP cables to both ADC/DAC on the CyMAC side and to the two OSEM electronics boxes on the other side. The four cables are running on the floor, against the side wall. The two boxes are under the optical table, on the back side. All cables are crossing the walkway under cable protection, so no tripping hazard.
The following tables lists the connections
Today, we completed the power boards and tested to make sure they work. We had a problem with the LM2991 negative voltage regulator; its tab at the back is connected to the input voltage and should therefore not touch our panel, because it is in this way grounded. We will fix that problem by placing spacors below the power boards.
We also built the connections for our DAC and ADC controllers and designed our DAC & ADC panels so that we can order a company to drill holes for our wires.
To this point, we have to finish the circuits for some of our Hall-effect sensors boards (our missing components arrived) and test all of our circuits to make sure they work as desired. After that, we will move to the second stage of this summer research, taking measurements, debugging problems, improving computer processing, and ultimately successfully isolating the levitated plate up to very low frequencies (starting from 5Hz and hopefully going down to 0.01Hz)