I was able to measure the sensing matrix in the PRMI configuration.
The results will be posted later.
Elog re: Friday's work
Adjusted PZT2 so we're hitting the center of PR2.
Noticed that the beam centering target is too low by a few mm, since the OSEM set screw holes that it mounts to are lower than the center line of the optic. This meant that while we were hitting the center of PR2, the beam was half clipped by PRM's centering target. We removed the target to confirm that the beam is really centered on PR2.
Checked the beam on PR3 - it looked fine. There had been concern last week that PR2 was severely pitched forward, but this turns out to be an effect of the PRM centering target being too low - shoot the beam downward to go through the hole, beam continues downward to hit the bottom of PR2, so beam is falling of the bottom of PR3. But when we actually centered the beam on PR2, things looked fine on PR3.
Checked that the beam approximately goes through the beam splitter. Again, the targets are too low, and these 45 deg targets' holes are smaller than the 0 deg targets, so we don't see any beam going through the target, since the beam is hitting the target higher than the hole. The beam looked left/right like it was pretty close to the hole, but it was hard to tell since the angle is bad, and I'm not infinitely tall. We should check again to make sure that the beam is going through properly, and we're not clipping anywhere. I'll need help from a height-advantaged person for this.
Checked that the beam is hitting the center of the ITMY, as best we can see by using an IR card at the back of the optic. We didn't try reaching around to put a target on the front side.
We were debating whether it would be worth it to open ETMY this week, to check that the beam transmitted through the BS hits the center of ETMY.
We also took a quick look around the AS optics, but since that depends on BS/ITMX alignment, we weren't sure how to proceed. We need a plan for this part. All suspended optics were restored to their last good alignment, but we haven't tried locking MICH or anything to confirm that the alignment.
To do list: Check no clipping on ITMY table of beam between BS and ITMY, clipping on POY optics. Also, oplev is clipping on cable holder thing on the table - this needs to be moved. .....other?
I wanted to try common/differential ALS Friday evening. I tried ALS using the LSC servo but this was not successfull.
The usual ALS servo in the ALS model works without problem. So this might be coming from the shape of the servo filter.
The ALS one has 1:1000 filter but the LSC one has 10:3000. Or is there any problem in the signal transfer between
ALS and LSC???
Slow offset -0.302V
TRX=1.18 / TRY=1.14, XARM Servo gain = 0.25 / YARM Servo gain = 0.10
- Green Xarm:
GTRX without PSL green 0.562 / with PSL green 0.652 -> improved upto 0.78 by ASX and tweaking of PZTs
Beat note found at SLOW OFFSET +15525
Set the beat note as +SLOW OFFSET gives +BEAT FREQ
- Green Yarm:
GTRY without PSL green 0.717 / with PSL green 1.340
Beat note found at SLOW OFFSET -10415
Set the beat note as +SLOW OFFSET gives -BEAT FREQ
- BEAT X -10dBm on the RF firstname.lastname@example.orgMHz / Phase tracker Qout = 2300 => Phase tracking loop gain 80 (Theoretical UGF = 2300/180*Pi*80 = 3.2kHz)
- BEAT Y -22dBm on the RF email@example.comMHz / Phase tracker Qout = 400 => Phase tracking loop gain 300 (Theoretical UGF = 2.1kHz)
Transfer function between ALSX/Y and POX/Y11I @560Hz excitation of ETMX
POX11I/ALSX = 54.7dB (~0deg)
POY11I/ALSY = 64.5dB (~180deg)
ALSX[cnt]*19230[Hz/cnt] = POX11I[cnt]/10^(54.7/20)*19230[Hz/cnt]
= 35.4 [Hz/cnt] POX11I [cnt] (Hz in green frequency)
35.4 [Hz/cnt]/(2.99792458e8/532e-9 [Hz]) * 37.8 [m] = 2.37e-12 [m/cnt] => 4.2e11 [cnt/m] (c.f. Ayaka's number in ELOG #7738 6.7e11 cnt/m)
ALSY[cnt]*19230[Hz/cnt] = POY11I[cnt]/10^(64.5/20)*19230[Hz/cnt]
= 11.5 [Hz/cnt] POX11I [cnt] (Hz in green frequency)
11.5 [Hz/cnt]/(2.99792458e8/532e-9 [Hz]) * 37.8 [m] = 7.71e-13 [m/cnt] => 1.3e12 [cnt/m] (c.f. Ayaka's number in ELOG #7738 9.5e11 cnt/m)
[Rana / Kiwamu]
Last Friday we did several things for MC :
- aligned the incident beam to MC
- increased the locking gain by 6 dB and modified the auto-locker script accordingly
- improved the alignment of the beam on the MC_REFLPD photo diode
In the beginning of the work, we wanted to know what RF frequency components are prominent in the reflection from MC.
Since the WFS circuits are capable for two RF notches, we wanted to determine which frequencies are appropriate for those notches.
So for the purpose we tried searching for unwanted RF components in the reflection.
However during the work, we found several things that needed to be fixed, so we spent most of the time for improving the MC locking.
- Alignments of the incident beam
At the beginning, the reflection from MC was about 2.2 in C1:IOO-REFLDC and the lock of MC had been frequently unlocked.
This situation of high reflection seemed to be related to a work done by Suresh (#4880).
Rana went to the PSL table and tweaked two input steering mirrors in the zig-zag path, and finally the reflection went down to ~ 0.8 in C1:IOO-REFLDC.
This work made the lock more robust.
- Change of the locking gain
After the alignment of the incident beam, we started looking at the time series of the MC_REFLPD signal with an oscilloscope as a start point.
What we found was a significant amount of 30 kHz components. This 30 kHz oscillation was thought be a loop oscillation, and indeed it was so.
We increased the loop gain by 6 dB and then the 30 kHz components disappeared successfully.
So the nominal locking gain of MC is now 11 dB in C1:IOO-MC_REFL_GAIN. The auto locker script was also modified accordingly.
- RF components in the MCREFL signal
After those improvements mentioned above, we started looking at the spectrum of the MCREFL PD using the spectrum analyzer HP8590.
The 29.5 MHz component was the biggest components in the spectrum. Ideally this 29.5 MHz signal should be zero when MC is locked.
One possible reason for this big 29.5 MHz signal was because the lock point was off from the resonant point.
We tweaked the offset in the MC lock path using a digital offset, C1:IOO-MC-REFL_OFFSET.
We found an offset point where the 29.5MHz signal went to the minimum, but didn't go to zero.
(works to be done)
So it needs some more works to investigate the cause of nonzero 29.5 MHz signal as well as investigation of what RF components should be notched out.
A good start point would be writing a GPIB interface script such that we can get the spectra from HP8590 without any pains.
Gautam will soon follow up with detailed analysis, but here is a brief summary of some of our activities and findings.
Please note that there is a long BNC cable still laid out from the IOO rack area to the X end table; watch your step!
I took several measurements today using the revised PLL scheme of using the Marconi just as an LO, and actuating on the Laser PZT to keep the PLL locked (I will put up a sketch soon). On the evidence of the attached plots (spectra of PLL control signal), I guess we can conclude the following:
Attachment #2: Measured OLG of PLL for the PSL+X and PSL+Y combinations. The UGF in both cases looks to be above 100 kHz, so I didn't do any calibration for the spectra attached. The gain on the SR560 was set to 200 for all measurements.
Attachment #3: Measured spectra of PLL control signal for various diode currents, with one reading from the PSL+Y combination plotted for comparison. When we took some data last night, Eric noted that there was a factor of ~6 increase in the overall frequency spectrum level at higher currents, I will update the plots with last night's data as well shortly. I found it hardest to keep the PLL locked at a diode current of 2.00 A across all measurements.
Attachment #4: Measured spectra of PLL control signal at two different crystal temperatures. There does not seem to be any significant dependance on temperature, although I did only do the measurement at two temperatures.
Attachment #4 Attachment #1: All the data used to make these plots (plus some that have yet to be added to the plots, I will update them).
Unrelated to this work:
When I came in this afternoon, I noticed that the PMC was unlocked. The usual procedure of turning the servo gain to -10dB and playing around with the DC output adjust slider on the MEDM screen did not work. Eric toggled a few buttons on the MEDM screen after which we were able to relock the PMC using the DC output adjust slider.
Multiple realtime processes on c1sus are suffering from frequent time outs. It eventually knocks out c1sus (process).
Obviously this has started since the fiber swap this afternoon.
gautam 10pm: there are no clues as to the origin of this problem on the c1sus frontend dmesg logs. The only clue (see Attachment #3) is that the "ADC" error bit in the CDS status word is red - but opening up the individual ADC error log MEDM screens show no errors or overflows. Not sure what to make of this. The IOP model on this machine (c1x02) reports an error in the "Timing" bit of the CDS status word, but from the previous exchange with Rolf / J Hanks, this is down to a misuse of ADC0 Ch31 which is supposed to be reserved for a DuoTone diagnostic signal, but which we use for some other signal (one of the MC suspension shadow sensors iirc). The response is also not consistent with this CDS manual - which suggests that an "ADC" error should just kill the models. There are no obvious red indicator lights in the c1sus expansion chassis either.
We had another crash of c1sus and Gautam did full power cycling of c1sus. It was a sturggle to recover all the frontends, but this solved the timing issue.
We went through full reset of c1sus, and rebooting all the other RT hosts, as well as daqd and fb1.
Kira informed me that she was having trouble accessing past data for her PID tuning tests. Looking at the last day of data, it looks like there are frequent EPICS data dropouts, each up to a few hours. Observations (see Attachment #1 for evidence):
It is difficult to diagnose how long this has been going on for, as once you start pulling longer stretches of data on dataviewer, any "data freezes" are washed out in the extent of data plotted.
I have been experiencing frequent crashes of DTT on pianosa in the past few weeks. This is pretty annoying to deal with when trying to characterize the interferometer loops. I attach the error log dumped to console. The error has to do with some kind of memory corruption. Recall that we aren't using a GDS version that is packaged with the SL7 lscsoft packages, we are using a pretty ancient (2.15) version that is built from source. I have been unable to build a newer version from source (though I didn't spend much time trying). pianosa is the only usable workstation at the moment, but perhaps someone can make this work on donatella / rossa for general improvement in quality of life.
Below are revised design parameters for the Stewart platform based on ground motion measurements.
The goal is that the actuators should be able to exceed ground motion by a healthy factor (say, two decades in amplitude) across a range from about .1 Hz to 500 Hz. I would like to stitch together data from at least two seismometers, an accelerometer, and (if one is available) a microphone, but since today this week I was only able to retrieve data from one of the Guralps, I will use just that for now.
The spectra below, spanning GPS times 1010311450--1010321450, show the x, y, and z axes of one of the Guralps. Since the Guralp's sensitivity cuts off at 50 Hz or so, I assumed that the ground velocity continues to fall as f-1, but eventually flattens at acoustic frequencies. The black line shows a very coarse, visual, piecewise linear fit to these spectra. The corner frequencies are at 0.1, 0.4, 10, 100, and 500 Hz. From 0.1 to 0.4 Hz, the dependence is f-2, covering the upper edge of what I presume is the microseismic peak. From 0.4 to 10 Hz, the fit is flat at 2x10-7 m/s/sqrt(Hz). Then, the fit is f-1 up to 100 Hz. Finally, the fit remains flat out to 500 Hz.
Outside this band of interest, I chose the velocity requirement based on practical considerations. At high frequencies, the force requirement should go to zero, so the velocity requirement should go as f--2 or faster at high frequencies. At low frequencies, the displacement requirement should be finite, so the velocity requirement should go as f or faster.
The figure below shows the velocity spectrum extended to DC and infinite frequency using these considerations, and the derived acceleration and displacement requirements.
As a starting point for the design of the platform and the selection of the actuators, let's assume a payload of ~12 kg. Let's multiply this by 1.5 as a guess for the additional mass of the top platform itself, to make 18 kg. For the acceleration, let's take the maximum value at any frequency for the acceleration requirement, ~6x10-5 m/s2, which occurs at 500 Hz. From my previous investigations, I know that for the optimal Stewart platform geometry the actuator force requirement is (2+sqrt(3))/(3 sqrt(2))~0.88 of the net force requirement. Finally, let's throw in as factor of 100 so that the platform beats ground motion by a factor of 100. Altogether, the actuator force requirement, which is always of the same order of magnitude as the force requirement, is
(12)(1.5)(6x10-5)(0.88)(100) ~ 10 mN.
Next, the torque requirement. According to <http://www.iris.edu/hq/instrumentation_meeting/files/pdfs/rotation_iris_igel.pdf>, for a plane shear wave traveling in a medium with phase velocity c, the acceleration a(x, t) is related to the angular rate W'(x, t) through
a(x, t) / W'(x, t) = -2 c.
This implies that |W''(f)| = |a(f)| pi f / c,
where W''(f) is the amplitude spectral density of the angular acceleration and a(f) of the transverse linear acceleration. I assume that the medium is cement, which according to Wolfram Alpha has a shear modulus of mu = 2.2 GPa and about the density of water: rho ~ 1000 kg/m3. The shear wave speed in concrete is c = sqrt(mu / rho) ~ 1500 m/s.
The maximum of the acceleration requirement graph is, again, 6x10-5 m/s2 at 500 Hz.. According to Janeen's SolidWorks drawing, the largest principal moment of inertia of the SOS is about 0.26 kg m2. Including the same fudge factor of (1.5)(100), the net torque requirement is
(0.26) (1.5) (6x10-5) (100) pi (500) / (1500) N m ~ 2.5x10-3 N m.
The quotient of the torque and force requirements is about 0.25 m, so, using some of my previous results, the dimensions of the platform should be as follows:
radius of top plate = 0.25 m,
radius of bottom plate = 2 * 0.25 m = 0.5 m, and
plate separation in home position = sqrt(3) * 0.25 m = 0.43 m.
One last thing: perhaps the static load should be taken up directly by the piezos. If this is the case, then we might rather take the force requirement as being
(10 m/s2)(1.5)(12 kg) = 180 N.
An actuator that can exert a dynamic force of 180 N would easily meet the ground motion requirements by a huge margin. The dimensions of the platform could also be reduced. The alternative, I suppose, would be for each piezo to be mechanically in parallel with some sort of passive component to take up some of the static load.
The schematic of the homodyne configuration is shown below.
Following are the list of components
One set of fiber is now kept along the arm of the interferometer
Fiber coupled (3 No's)
Free space ( 2 No's)
The frequency source was fixed. The IMC LO level was adjusted.
IMC is locked => OLTF measured UGF 144kHz PM 30deg.
The trouble we had: the 29.5 MHz source had an output of 6 dBm instead of 13 dBm.
The cause of the issue: A short cable inside had its shield cut and had no connection of the return.
- The frequency source box was dismantled.
- The power supply voltages of +28 and +18 were provided from bench supplies.
- The 29.5 MHz output of 5~6 dBm was confirmed on the work bench.
- The 11 MHz OCXO out (unused) had an output of 13 dBm.
- Once the lid was opened, it was immediately found that the output cable for the 29.5 MHz source had a sharp cut of the shield (Attachment1).
- OK. This cable was replaced. The output of 13 dBm was recovered.
- But wait. Why is the decoupling capacitor on the 29.5 MHz OCXO bulging? The polarity of the electrolytic capacitor was wrong!
- OK. This capacitor was replaced. It was 100 uF 35 V but now it is 100 uF 50 V.
- I further found some cables which had flaky shields. Some of them were twisted. When the panel cable s connected, the feedthroughs were rotated. This twists internally connected cables. Solder balls were added to the connector to reinforce the cable end.
- When the box was dismantled, it was already noticed that some of the plastic screws to mount the internal copper heat sinks for ZHL-2's were broken.
They seemed to be degraded because of the silicone grease. I didn't try to replace all as it was expected to take too much time, so only the broken screws
were replaced with steel screws with shoulder washers at the both side of the box.
- After confirming the circuit diagram, the box was returned to the rack. The 29.5 MHz output of 13 dBm there was confirmed.
One of the main draw backs of the measurement was the polarisation was not aligned properly in the setup. So, then the next step was to identify the polarisation at different locations in the beam path and to maximise the polarisation to either S or P component.
So, we introduced HWP at the input beam path after isolator as shown in attachment #1. Also, the polarisation was tested at positions P1, P2, P3, and P4 shown in attachment #1 by placing a polarisation beam splitter at these locations and then by observing the transmitted (P component) and reflected light (S component) using power meter.
The observations at different locations are as the follows
These observations show that the P and S components are almost equal, and this is not a good polarisation arrangement. At this point, we also had to check whether the incoming beam is linearly polarised or not.
To test the same, the PBS was placed at position P1 and the P and S components were observed with power meter as the HWP is rotated.Attachment # 2 shows the results of the same, that is the variation in P and S component as the HWP is rotated.
This result clearly shows that the input beam is linearly polarised. The HWP was then adjusted such that the P component is maximum and coupled to the MZI. With this orientation of HWP, the polarisation observed at different positions P1, P2, P3, and P4 are as follows.
This shows that the polarisation is linearly polarised as well as it is oriented along the P direction (parallel to the optical table).
We have the polarisation maintaining fiber (PM 980) as the delay fiber. The polarisation of the light as it propagates through a PM fiber depends on how well the input beam is coupled to the axis (slow or fast) of the fiber. So, the next task was to couple the light to one of the axes of the fiber.
The alignment key on the fiber is a good indication of the axis of the fiber. In our case, the alignment key lines up with the slow axis of the fiber. We decided to couple the light to the fast axis of the fiber. Since the incoming beam is P polarised, the output fiber coupler was aligned such that the fast axis is parallel to optical table as possible.
A PBS was then introduced after the fiber output collimator . There is a HWP (marked as HWP2 in attachment 1) in front of the input coupler of the fiber as well. This HWP was then rotated and observed the P and S component from the PBS that is now placed after the output coupler with a power meter.The idea was , when the light is coupled to the fast axis of the fiber, we will see the maximum at the P componet at the output
Attachment # 3 shows the observation.
In this way I tried to find the orientation of the HWP2 such that the P component is maximum at the output. But I was not succeeded in this method and observed that the output was fluctuating when the fiber was disturbed. One doubt we had was whether the fiber is PM or not . Thus we checked the fiber end with fiber microscope and confirmed that it is PM fiber.
Thus, we modifed the setup as shown in attachement # 4.The photodetector (PDA55) was monitoring the S component and the output of the detector was observed on an oscilloscope. We rotated the HWP2 such that the S component is almost minimum. At the same time, we were disturbing the fiber and was observing whether the output is fluctuating. The HWP2 angle was tweaked around the minimum of S component and observed the output with disturbing the fiber. This way we found the orientation of HWP2 such that the light is coupled to the fast axis of the fiber and the output was not fluctuating while we disturb the fiber. We tested it by heating the fiber with a heat gun as well and confirmed that the output is not fluctuating and thus the light is coupled to the fast axis of the fiber.
The alignement was disturbed after the replcement of the beam splitter. We tried to get the alignment back . But we are not succeeded yet in getting good interfernce pattern. This is mainly because of poor mode matching of two beams. We will also try with the spooled fiber.
From the earlier results with homodyne measurement,the Vmax and Vmin values observed were comparable with the expected results . So in the time interval between these two points, the MZI is assumed to be in the linear region and I tried to find the frequency noise based on data available in this region.This results is not significantly different from that we got before when we took the complete time series to calculate the frequency noise. Attachment #1 shows the time domain data considered and attachment #2 shows the frequecy noise extracted from that.
As discussed, we will be trying the heterodyne method next. Initialy, we will be trying to save the data with two channel ADC with 16 kHz sampling rate. With this setup, we can get the information only upto 8 kHz.
We repeated the homodyne measurement to check whether we are measuring the actual frequency noise of the laser. The idea was to repeat the experiment when the laser is not locked and when the laser is locked to IMC.The frequency noise of the laser is expected to be reduced at higher frequency (the expected value is about 0.1 Hz/rtHz at 100 Hz ) when it is locked to IMC . In this measurement, the fiber beam splitter used is Non PM. Following are the observations
1. Time domain output_laser unlocked.pdf : Time domain output when the laser is not locked. The frequency noise is estimated from data corresponds to the linear regime. Following time intervals are considered to calculate the frequency noise (a) 104-116 s (b) 164-167 s (c) 285-289 s
2. Frequency_noise_laser_unlocked.pdf: Frequency noise when the laser is not locked. The model used has the functional form of 5x104/f as we did before. Compared to our previous results, the closeness of the experimental results to the model is less from this measurement. In both the cases, we have the uncertainty because of the fiber length fluctuation. Moreover, this measurement could have effect of polarisation fluctuation as well.
3.Time domain output_laser locked.pdf :Time domain output when the laser is locked. Following time intervals are considered to calculate the frequency noise (a) 70-73 s (b) 142-145 s (c) 266-269 s.
4. Frequency_noise_laser_locked.pdf : Frequency noise when the laser is locked
5. Frequency noise_comparison.pdf : Comparison of frequency noise in two cases. The two values are not significantly different above 10 Hz. We would expect reduction in frequency noise at higher frequency once the laser is locked to IMC. But this result may indicate that we are not really measuring the actual frequency noise of the laser.
The new ZKL-1R5 RF amplifier that Steve ordered arrived yesterday. I installed this in the frequency divider box and did a quick check using the Fluke RF signal generator and an oscilloscope to verify that both the X and Y paths were working.
I've now installed the box in the 1X2 rack where the olf "RF amplifiers for ALS and FOL" box used to sit (I swapped that out as I needed the L brackets on that chassis to mount mine, see Attachment #1 for the new layout). The power cable that used to power the old chassis was available, but the connector was of the wrong gender, so I had to switch this out. After verifying that I was getting the correct voltage (+15V), I connected it to the chassis.
I then did a quick check with the Fluke generator to make sure that all was working as expected - Eric had set up some ADC channels for me earlier today in the C1ALS model, and I copied over my frequency counting module from C1TST into C1ALS, and recompiled the model. The RF generator was set to generate a 25MHz signal at -20dBm, which I then split using an RF power splitter between the X and Y arms. I then checked the output using dataviewer - I recovered an output frequency of ~27.64 MHz with a jitter of ~0.02 MHz with a 20Hz low-pass filter in place (see Attachment #2), which looks consistent with the systematic error inherent in the zero-crossing counting algorithm and random fluctuations I had observed in my earlier trials, discussed here. But a more systematic investigation needs to be carried out in this regard. The interfacing between the hardware and software seems to be working alright though. I've left the RF generator near the 1x2 rack for now, though its powered off.
The mode cleaner unlocked quite a few times while I was working but looks stable now.
I carried out some more tests on the digital frequency counting system today, mainly to see if the actual performance mirrors the expected systematic errors I had calculated here.
Setup and measurement details:
I used the Fluke 6061A RF signal generator to output an RF signal at various frequencies, one at a time, between 10 and 70 MHz. I split the signal (at -15 dBm) into two parts, one for the X-channel and one for the Y-channel using a mini-circuits splitter. I then looked at the input signal using testpoints I had set up within the model, to decide what thresholds to set for the Scmitt trigger. Finally, I averaged the outputs of the X and Y channels using z avg -s 10 C1:ALS-FC_X_FREQUENCY_OUT and also looked at the standard deviation as a measure of the fluctuations in the output (these averages were taken after a low-pass filter stage with two poles at 20Hz, chosen arbitrarily).
I carried out some further diagnostics and found some ways in which I could optimize the zero-crossing-counting algorithm, such that the error in the measured frequency is now entirely within the expected range (due to a +-1 clock cycle error in the counting). We can now determine frequencies up to ~60 MHz with less than 1 MHz systematic error and <10 kHz statistical error (fluctuations after the 20 Hz lowpass). This should be sufficient for slow control of the end-laser temperatures.
The conclusion from my earleir tests was that there was possibly an improvement that could be made to setting the thresholds for the Schmitt trigger stage in the model. In order to investigate this, I wanted to have a look at the 64K sampled raw input to the ADCs. Yesterday Eric helped me edit the appropriate .par file for viewing these channels for c1x03, and for an input frequency of 70MHz (after division, ~4.3 kHz square wave), the signal looked as expected (top left plot, attachment #1). This prompted me to check the counting algorithm again with the help of various test points I had setup within the model. I found that there was a tendency to under-count the number of clock-cycles between zero-crossings by more than 1 clock cycle, due to the way my code was organized. I fixed this and found that the performance improved dramatically, compared to my previous trials. With the revised counting algortihm, there was at most a +-1 clock cycle error in the counting, and the systematic error between the measured and requested RF frequencies is now completely accounted for taking this consideration into account. The origin of this residual error can be understood by looking at the top right plot in Attachment #1 - presumably because of the effects of some downsampling filter, the input signal to the Schmitt trigger isnt a clean square wave (even at 4kHz) - specifically, the time spent in the LOW and HIGH states of the Schmitt trigger can vary between successive zero crossings because of the shape of the input waveform. As a result, there can be a +-1 clock cycle error in the counting process. Attachment #2 shows this - the red and blue lines envelope the measured frequency for the whole range investigated: 10-70MHz. Attachment #3 shows the systematic error as a function of the requested frequency.
If there was some way to bypass the downsampling filter, perhaps the high-frequency performance could be improved a little.
Earlier today, the front panels for the 1U chassis I obtained to house the Wenzel dividers + RF amplifiers arrived, which meant that finally I had everything needed to complete the assembly. Pictures of the finished arrangement attached.
Summary of the arrangement:
Once I figure out the problem with this amplifier/replace it, the box is ready to be installed.
I'm working on setting up a moving-average in the custom C code block that counts the zero crossings to see if this approach is able to mitigate the glitchy frequency readout due to mis-counting by one clock cycle between successive zero crossings. I'm storing an array the size of the moving average window of frequency readouts at each clock cycle, and then taking the arithmetic mean over the window. By keeping a summing variable that updates itself each clock cycle, the actual moving average process isnt very intensive in terms of computational time. The array does take up some memory, but even if I perform the moving average over 1 second with 16384 double precision numbers stored in the array, its still only 130 kB so I don't think it is a concern. Some tests I've been doing while tuning the code suggest that with a moving average over 16384 samples (i.e. 1 second), I can eliminate glitches at the 1Hz level in the frequency readout for frequencies up to 5 kHz (generated digitally using an oscillator block). Some tuning still needs to be done, and the window could possibly be shortened. I also need to take a look at the systematic errors in this revised counting scheme, preferably with an analog source, but this is overall, I think, an improvement.
On a side note, I noticed some strange behaviour while running the cds average command - even though my signal had zero fluctuations, using z avg 10 -s C1:TST-FC_FREQUENCY_OUT gave me a standard deviation of ~1 kHz. I'm not sure what the problem is here, but all the calibration data I took in earlier trials were obtained using this so it would be useful to perform the calibration again.
I made some changes to the c1tst model running on c1iscey in order to test my algorithm for frequency counting. I followed the steps listed in elog 8909 to make, install and start the model.
I need to debug a few things and run some more diagnostics so I am leaving the model in its edited version (Eric had committed it to the svn before I made any changes).
I have been working on setting up a frequency counting module that can give us a readout of the beat frequency, divided by a factor of 2^14 using the Wenzel frequency dividers as described here. This is a summary of what I have thus far.
The algorithm, and simulink model
The basic idea is to pass the digitized signal through a Schmitt trigger (existing RCG module), which provides some noise immunity, and should in theory output a clean square wave with the same frequency as the input. The output of the Schmitt trigger module is either 0 (for input < lower threshold value) and 1 (for input greater than the high threshold value). By differencing this between successive samples, we can detect a "zero-crossing", and by measuring the time interval between successive zero crossings, we can take the reciprocal to get the frequency. The last bit of this operation (i.e. measuring the interval) is done using a piece of custom C code. Initially, I was trying to use the part "GPS" from CDS_PARTS to get the current GPS time and hence measure intervals between successive zero-crossings, but this didn't work out because the output of GPS is in seconds, and that doesn't give me the required precision to count frequency. I tried implementing some more precision timing using the clock_gettime() function, which is capable of giving nanosecond precision, but this didn't work for me. So I am now using a more crude way of measuring the interval, by using a counter variable that is incremented each time a zero-crossing is NOT detected, and then converting this to time using the FE_RATE macro (=16384). In any case, the ADC sampling rate limits the resolution of frequency counting using zero-crossing detection (more on this later). Attachment 1 shows the SIMULINK block diagram for this entire procedure.
Testing the model
I implemented all of this on c1tst, and followed the steps listed here to get the model up and running. I then used one of the DB37 breakout boards to send a signal to the ADC using the DS345 function generator. Attachment 2 shows some diagnostic plots - input signal was a 2.5Vpp (chosen to match the output from the Wenzel dividers) square wave at 2kHz:
The right column pointed me to the limitations of frequency counting using this method - even though the input frequency was constant (2kHz), the counter variable, and hence the frequency readout, was neither accurate nor precise. But this was to be expected given the limitations imposed by ADC sampling? We only get information of the state of the input signal once within each sampling interval, and hence, we cannot know if a zero crossing has occurred until the next sampling interval. Moreover, we can only count frequency in discrete steps. In attachments 3 and 4, I've plotted these discrete frequencies which can be measured - the error bars indicate the error in the frequency readout if the counter variable is 1 more or less than the "true" value - this can (and does) happen if the high and low times of the Schmitt trigger are not equal over time (see top left plot in Attachment 2, its not very obvious, but all the "low" times are not equal, and so, the interval between detected zero crossings is not equal). This becomes a problem for small values of the counter variable, i.e. at high input frequencies. I was having a look at the elogs Aidan wrote some years ago for a different digital frequency counting approach, and I guess the conclusion there was similar - for high input frequencies, the error is large.
I further did two frequency sweeps using the DS345, to see if I could recover this in the frequency readout. Attachments 5 and 6 show the results of these sweeps. For low frequencies, i.e. 100-500 Hz, the jitter in the readout is small (though this will be multiplied by a factor of 2^14), but by the time the input frequency gets up to 2kHz, the jitter in the readout is pretty bad (and gets worse for even higher frequencies.
Some refinements can be made to the algorithm, perhaps by introducing some averaging (i.e. not reading out frequency for every pair of zero crossings, but every 5) which may improve the jitter in the readout, but I would think that the current approach is not very useful above 2kHz (corresponding to ~30MHz of pre-divider frequency), because of the limitations shown in attachments 3 and 4.
I definitely think lowpassing the output is the way to go. Since this frequency readback will be used for slow control of the beatnote frequency via auxillary laser temperature, even lowpassing at tens of Hz is fine. The jitter doesn't mean its useless, though.
If we lowpass at 16Hz, we're effectively averaging over 1024 samples, bringing, for example, a +-2kHz jitter of a 6kHz signal as you post down to 2kHz/sqrt(1024) ~ 60Hz, which is 1% of the carrier. This seems ok to me.
I was going to suggest using a software PLL, but perhaps averaging gives the same result. The same ADC signal can be fed to multiple blocks with different averaging times and we can just use whichever ones seems the most useful.
I've made quite a few changes in the software as well as the hardware of the digital frequency counting setup.
Eric helped me test the new setup by doing an arm scan through an IR resonance by ramping the ALS offset from -3 to +3 with a ramp time of 45 seconds. The data was acquired with the window size of the moving average set to 4096 clock cycles, and a 2 Hz low pass IIR filter before the frequency readout. Attachment 1 shows a plot of the data, and a fit with a function of the form trans = a/(1+((x-b)/c)^2), where a = normalization, b = center of lorentzian, and c = linewidth (FWHM) of the peak (the fitted parameter values, along with 95% confidence bounds are also quoted on the plot). In terms of the data acquisition, comparing this dataset to one from an earlier scan Eric did (elog11111) suggests that the frequency counting setup is working reasonably well - at any rate, I think the data is a lot cleaner than before implementing the moving average and having a 20Hz lowpass IIR filter. In any case, we plan to repeat this measurement sometime next week during a nighttime locking session. It remains to calculate the arm loss from these numbers analogous to what was done earlier for the X arm.
Calculation of loss:
Fitted linewidth = 10.884 kHz +/- 11Hz (95% C.I.)
FSR of Y arm (from elog 9804) = 3.9468 MHz +/- 1.1 kHz
=> Y arm Finesse = FSR/fitted linewidth = 362.6 +/- 0.5
Total round trip loss = 2*pi/Finesse = 0.0173
It is a nice scan. I'm still thinking about the equivalence of the moving average and the FIR low pass that I have mentioned in the meeting.
I'm confused by the plot. The bottom axis says "green beat frequency".
If you scan the IR laser frequency by df, you get 2*df shift of the green beatnote. You need to have this factor of two somewhere.
If you are looking at the IR beat freq, just the label is not correct. (I believe this is the case.)
Accepting the rather-too-low finesse of 363 (nominally 450), the total round trip loss is said to be 0.0173.
If we subtract the front transmission of 1.38% (and ignoring the transmission loss from the ETM),
the round trip loss is 3500ppm. Is this compatible with the following elog?
In fact, I'm afraid that the loss number in the above elog 11111 was not correct by a factor of 10.
Then, if so, can we believe this high loss number? (Nominally we expect ~100ppm loss per round trip...)
Sorry for the confusion - I did mean Green beat frequency, and I had neglected the factor of 2 in my earlier calculations. However, the fit parameter "c" in my fit was actually the half-width at half maximum and not the full width at half maximum. After correcting for both these errors (new fit is Attachment #1, where I have now accounted for the factor of 2, and the X axis is the IR beat frequency), I don't think the numbers change too much. It could be that the frequency counter wasn't reading out the frequency correctly, but looking at a time series plot of the frequency counter readout (Attachment #2), and my earlier trials, I don't think this is the case (38 MHz is a frequency at which I don't expect much systematic error - also, the offset was stepped from -3 to 3 over 45 seconds).
The revised numbers:
Fitted linewidth = 2*c = 10.884 kHz +/- 2 Hz (95% C.I.)
I've made a few more changes to the frequency counting code - these are mostly details and the algorithm is essentially unchanged.
The other thing that came up in the meeting last week was this issue of the systematic errors in the measured frequency, and how it was always over-estimating the 'actual' frequency. I've been investigating the origin of this over the last few days, and think I've found an explanation. But first, Attachment #1 shows why there is a systematic error in the first place - because we are counting the period of the input signal in terms of clock cycles, which can only take on discrete, integer values, we expect this number to fluctuate between the two integers bounding the 'true value'. So, if I'm trying to measure an input signal of 3000Hz, I would measure its period as either 5 or 6 clock cycles, while the "true" value should be 5.4613 clock cycles. In attachment #1, I've plotted the actual measured frequency and the measured frequency if we always undercounted/overcounted to the nearest integer clock cycles, as functions of the requested frequency. So the observed systematic error is consistent with what is to be expected.
The reason why this doesn't average out to zero is shown in Attachment #2. In order to investigate this further, I recorded some additional diagnostic variables. If I were to average the period (in terms of clock cycles - i.e. I look for the peaks in the blue cuve, add them up, and divide by the number of peaks), I find that I can recover the expected period in terms of clock cycles pretty accurately. However, the way the code is set up at the moment, the c code block outputs a value every 1/16384 seconds (red curve) - but this is only updated each time I detect a zero crossing - and as a result, if I average this, I am in effect performing some sort of weighted average that distorts the true ratio of the number of times each integer clock-cycle-period is observed. This is the origin on the systematic error, and is a function of the relative frequency each of the two integer values of the clock-cycle-period occurs, which explains why the systematic error was a function of the requested frequency as seen in Attachment #1, and not a constant offset.
At the frequencies I investigated (10-70MHz in 5MHz steps), the maximum systematic error was ~1%.
Is there a fix?
I've been reading up a bit on the two approaches to frequency counting - direct and reciprocal. My algorithm is the latter, which is generally regarded as the more precise of the two. However, in both these approaches, there is a parameter known as the 'gate-time': this is effectively how long a frequency counter measures for before outputting a value. In the current approach, the gate time is effectively 1/16384 seconds. I would think that it is perhaps possible to eliminate the systematic error by setting the gate time to something like 0.25 seconds, and within the gate time, do an average of the total number of periods measured. Something like 0.25 seconds should be long enough that if, within the window, we do the averaging, and between windows, we hold the averaged value, the systematic error could be eliminated. I will give this a try tomorrow. This would be different from the moving average approach already explored in that within the gate-time, I would perform the average only using those datapoints where the 'running counter variable' shown in Attachment #2 is reset to zero - this way, I avoid the artificial weighting that is an artefact of spitting out a value every clock cycle.
I checked the BK precision 1856D manual. I found that although this frequency counter can measure upto 3.5GHz, it has 2 separate input channels to measure two range of frequencies.
One input to measure between 0.1Hz to 100 MHz and the other to measure between 80MHz to 3.5GHz. Our beat frequency desirable range is <100MHz for stable ALS. Also, the beat PD response falls off beyond ~150MHz . Should we be happy with this frequency counter and use it in the 0.1Hz-100MHz range or look for one with a better measuring range?
P.S. Right now we are using the spectrum analyzer in the control room set to frequency range from 10MHz - 140 MHz for beat note search.
So, I actually took these measurements last week, but I didn't get around to making nice plots and things until now. I figured the time while I wait for the spectrum analyzer to do its thing was a good time.
Having been unable to locate the SR785 and also unsure how to connect it to a computer speaker (and also unable to find a free one), I downloaded a demo of a function generator onto my computer and just used that. (Same thing I used to do the swept sine that created the frequency power response plots I posted last week.) I set the program to a number of different frequencies and had the other end of the cable hooked into the oscilloscope to see a) if I could pick out the frequency and b) see how the magnitude of the microphone output varied with the frequency.
The first set of measurements I took, I didn't realize that I could increase the output power of the function generator. Because the generated sound at the default setting was relatively quiet, the oscilloscope traces were pretty chaotic, so I usually froze the trace so that I could look at it better. I ended up with a lot of weird jumps in the magnitude, but I later realized that there was a lot of beating going on at some frequencies, and the amplitude changes were probably much more drastic for the -20 dB sounds than the 6 dB sounds, since it was closer in amplitude to the surrounding noises. So, I've included that data set in my plots for the sake of completeness, but I'm pretty sure that it is useless.
Once I realized I could increase the power output for the signal generator, I took a set of data with and without the voltage divider at 6 dB. There was a cluster of frequencies that showed significant beating around 1700-3000 Hz in the data WITH the voltage divider, but I did not see any clear beating in the data WITHOUT. In the plots, I simply plotted up the highest and lowest amplitudes I measured for the frequencies with significant beating, since it was obviously hard to tell what the amplitude would have been without any background noise. In the w/o volt. div. set, although I didn't see any obvious beat patterns, the measured amplitudes did jump slightly at the frequencies that showed beats with the voltage divider. So, perhaps I was just not seeing them, but they influenced my amplitude measurements? I'm not sure if it would be possible for the voltage divider itself to cause beat frequencies.
(Note: the amplitudes measured were from zero to peak, as the oscilloscope I was using wouldn't show a big enough vertical range to easily measure the peak-to-peak voltage difference.)
I've attached two plots of my measurements. One has a regular x-scale and includes all the measurements. The second has a logarithmic x-scale and omits the 20 Hz points. I had some troubles being able to pick out the 20 Hz signal on the oscilloscope... I don't know if my computer speakers just don't work well at that frequency or what, but either way, those points seemed highly suspect, and omitting them from the log plot allowed me to spread things out more.
One thing I'm not sure about is the 3000 Hz point. It was one of the ones with a beat frequency (~130 Hz), and the amplitudes were pretty low. The corresponding point from the non-voltage-divider data set is also low. So, I'm not sure what's happening there.
The one thing that I do think is quite clear is that the 1000 Hz drop-off in power when the microphone is connected to the ADC has nothing to do with the voltage divider. Beat issues aside, the shapes are very similar (pay no attention to the absolute scale... obviously, the voltage responses with and without the voltage divider were very different, and I just scaled them to fit in the same plot).
Update: Jenne pointed out that I was not absolutely clear about the voltage scale in my plots. The GREEN and BLUE points are on a mV scale, and the RED points are on a 10mV scale. I should probably redo the plots in Matlab in eventuality, since Excel is hard to use if you want to do anything that is not extremely basic with your plots, but this was my solution for the time being. So, the fact that the RED points, which are the data taken WITHOUT the voltage divider, are lower than the GREEN ones does not in any way indicate that I measured lower voltages when the voltage divider was not used.
Also, a to do list:
- Many of the beat frequencies I picked out were veeeeery slow, indicating that something is going at a frequency that is very close to the arbitrary frequencies I chose to sample, which is a little strange. That, combined with the fact that I saw clear beats with the voltage divider but not without leads me to believe that it may be worth investigating the frequency response of the voltage divider itself.
- Redo the measurements near the anomalous 3000 Hz point with a higher density of sampled frequencies to try to see what the heck is going on there.
I finished the polishing in the scripts/FOL directory, this is the current status and this post replaces my two previous posts on the subject:
Unfortunately the order placed for beam samplers last week did not go through. These will be used at the X and Y end tables to dump the unwanted light appropriately. Since they will not be here until Tuesday, I revised the timeline for FOL related activities accordingly.
Attached is the timeline for Frequency Offset Locking related activities. All activities will be done mostly in morning and early afternoon hours.
I finished assembling the frequency generation unit for the upgrade. I tested it through to check that the power levels are as expected at the various connection (see attached png, showing in black the design power values, and in red the measured ones).
Because of some modifications made on the design along the construction, I have to recalculate the SNR along the lines.
I can now start to measure phase noise and distortion harmonics.
A document with a description of the design and the results of the characterization measurements will be available in the end.
Here are the results of my phase noise measurements on the 7 outputs of the Frequency Generation Box. (BIN=95L applied by DTT). See attached pdf for a higher definition picture.
The plot shows that the phase noise of the 11 MHz outputs (Source, EOM modulation signal, Demodulation signal) is as low as that of the Marconi. The Marconi is limiting my measurement's resolution.
The mode cleaner signal's oscillator (29.5 MHz output, blue trace) is higher than the 11MHz above 1KHz.
The 55MHz signals have all the same phase noise (traces overlapped), and that is higher than the 11 MHz ones from about 100Hz up. i don't know what's going on.
I need to use the spare 11MHz Wenzel crsytal to have a better reference source for the measurement.
I measured the amplitude noise of the source outputs and the EOM outputs of the Frequency Generation box.
the setup I used is shown in this diagram:
(NB It's important that the cables from the splitter to the RF and LO inputs of the mixers are the same length).
The results of the measurements are shown in the following plot:
1) both Crystals (29.5MHz and 11MHz) have the same noise
2) the 55MHz source's noise is bigger than the 11 MHz (~2x): the frequency multiplication and amplification that happen before it, add extra noise
3) the noise at EOM outputs is ~2x bigger than that of the relative sources
When I have the chance, I'll plot the results of my calculations of expected noise and compare them with the measurements.
I uploaded all the material about the RF frequency Generation Box into the SVN under the path:
I structured the directory as shown in this tree:
I'm quickly describing in a section of the Rf system upgrade document with LIGO # T1000461.
I completed a LIGO document describing design, construction and characterization of the RF System for the 40m upgrade.
It is available on the SVN under https://nodus.ligo.caltech.edu:30889/svn/trunk/docs/upgrade08/RFsystem/RFsystemDocument/
It can also be found on the 40m wiki (http://lhocds.ligo-wa.caltech.edu:8000/40m/Upgrade_09/RF_System#preview), and DCC under the number T1000461.
The freq fluctuation of the beat note has been measured with the following condition
- The output of the freq divider is already calibrated to have the unit of MHz.
- The transfer function between the analog PFD channel and the digital PFD output was measured to be -23dB = 0.7.
The gain of the XARM-FINE channel was changed to 0.7 such that the output is calibrated in MHz.
- I have not checked the analog noise level of the analog PFD path. We may need more whitening gain (by icreasing the gain of SR560).
- The analog PFD is always better than the digital PFD above 20Hz.
- Both the digital and analog PFD showed good agreement below 20Hz.
Note the measurement was not simultaneous.
- When the arm is locked with the ETMX being actuated , the fluctuation of the arm length must be stabilized by a huge factor
(~10^5 according to Kiwamu's entry) However, we only could see the stabilization factor of 30.
As this residual is the difference of the freq noise felt by the IR and the green,
this is a real issue to be tackled.
- The RMS fluctuations of the arm with and without the IR beam being locked are 2MHz and 0.1MHz,
which correcponds to the arm length motion of 250nm and 13nm, respectively.
Ed: I had to use 532nm in stead of 1064nm. The correct numbers are 130nm and 7nm.
- Without the IR locked, The typical peak-to-peak fluctuation of the beat freq was 10MHz.