NAOJ GW Elog Logbook 3.2
When the "noisy measurement" lock was performed I forgot to check if the error signal was at 0 ...
Participants : Eleonora, Emil, Yuhang
We performed 3 new losses measurements using the "lock-unlock" techique.
The IR reflected power can be seen in fig "23to26.pdf".
To extract the losses value for the measurement made on April 23d 2018 I only extracted the firsts values to avoid the noisy part of the signal.
The April 26th measurement was really noisy. However, 3.69% of the power were coupled to the FC 1st order mode and 2.49% with the 2nd order.
In order to better investigate the source of this noise, we will add a beam splitter and a photodiode on the IR injection path in order to see if there is any coupling between the laser power fluctuations and the IR reflected power or if we should investigate other sources.
It also seems that the IR reflected power fluctations are higher when the frequency of the AOM is such that the IR 0 order mode is resonant in the FC.
However, if we change slightly this frequency, the fluctuations seems to disappear.
We will install a camera on the IM viewport where a 2" mirror was installed to see if we can extract some informations about the scattered light.
The computation of the 3 measurements can be seen on "23to26meas.png".
The noisy measurement leads to the huge error bar.
When the "noisy measurement" lock was performed I forgot to check if the error signal was at 0 ...
After change the new servo, we tried a lot to make it work well. Now we can get a stable operation by using this new loop. So it's time to characterize our new locking.
The green calibration factor was got in this way:
1.Measure the ratio between the point before servo(Y) and the point after servo(X). Actually the second point is PZT monitor, so we need to multiply PZT monitor by 100 to get X.
2.According the loop flow chart, we can present Y/X by using transfer function of plant and filter. And we know the laser will actuate with 10^6 V/Hz. The SHG gives a factor of 2. We also measured the open-loop transfer function and we call it G. You can refer to attached picture 1, the blue line is Y/PZTmonitor. We can see from the phase, only high frequency has good shape. So we trust only high frequency and we use it for the calculation afterwards.
3.Now we can get the the correction of PZT(in other word, the slope of error signal). The unit of it is V/Hz. The equation to get it is K=(Y/(X*100))*(1+abs(rho(G)*e^(-iphi(G))))*sqrt(1+f^2/f_0^2)/10^6/2
The result is calibration factor(green)=1/K=552 Hz/V.(Here f is frequency, f_0 is the pole of filter cavity)
The infrared calibration factor was got in this way:
1.We give a tri-angular modulation for AOM, it is pk-pk 4000Hz, T 5s. This means 1600Hz/s.
2.We save the error signal of infrared, we calculate the pk-pk of this error signal. Then we divide it by their corresponding time. Let's say the result is slope(V/s). The calibration factor is 2*slope(V/s)/1600(Hz/s)
The result is calibration factor(infrared)=13.33 Hz/V
Finally, we get the error signal.
Participant: Emil, Eleonora, Marc, Yuefan,Matteo
Yesterday, We used the green light to test the Mach-Zehnder. After giving a ramp to its PZT, we can get the picture shown as below. After adjusting, we can maximize it to this case shown in the picture. The contrast is 4.04/4.72=85.6%
We discussed about the possible interaction between the SHG control loop and the Filter Cavity control loop to explain the 6.56 kHz oscillation at the error signal of the FC control loop.
If noise appears on the SHG control loop, the power level of the green beam will vary.
The gain of the FC control loop is power beam dependent and can vary.
As the FC control loop is controlled to 0 crossing of the error signal, a variation of gain has a 2nd order influence.
But if the mixer produces an offset, this influence increases with the level of this offset.
Things to do:
0) Measure the FC loop offset (at EPS1 divided by 26.5)
1) Inject a DC into PERTURB to see the influence on the oscillation
2) Measure noise in SHG without and with FC control loop
3) Match the impedance (50 Ohm) at output of the LP filter (set at the output of the FC demodulation miser)
4) Measure LO and RF levels on FC demodulation mixer
5) Remove cables between LP filter and the input of the Stanford Research SR560 amplifier (connect directly Mixer, filter and SR560 without cable)
The gain of the input gain G1 has changed and is set to G1 = 5.1
So the output EPS1 (AC2) shows the input signal with a gain G4 = G1 * G2 = 5.1 * 5.2 = 26.5
If you measure the offset at EPS1 output, it should be divided by 26.5 to obtain it at the input (Detect Sig).
Remark:
The attenuator "Gain Piezo" has an effect on the dynamic of "Piezo Sig" output.
For instance, if "Gain Piezo" is set to position 0.7 as currently (on 10 max), the dynamic will be:
D = +/- 0.7/10 * 14 * 10 = +/- 10V
(Gain Ampli HT = 10)
The sample we are going to measure is 0.5mm thick and 2inches diameter large. Our mount has a grub screw that is not able to secure such a thin sample. So I had to add a thick ring behind the sample. I did a mounting test with a "not for use" (not polished) sapphire piece with the same dimensions as the sample. I add a ring (which is the 1.5-to-2 inches adaptor), leaned the ring on the sample, and fixed the ring with the grub screw. The ring doesn't push the sample, it only touches it. This reduces the risk of breaking the sample.
In order to test the IR probe on the LMA samples I previously cleaned them and applied the first contact.
I checked the crystalline coating sample (the one on silica substrate) under a powerful green light. I carefully blew some spray air on it to remove the dust and the best I could do is showed in the picture.
To check which side is the coated one, I put the sample on a clean tissue on the table, and I looked at the shadow below the border of the coating. We the shadow is larger, the coating faces up.
I calculated the ratio between the absorption measured at LMA and at NAOJ.
Since the maps were not exactly overlapping, the ratio showed the same structure of the absorption maps.
This is because the center of the mirror in the two systems has some mismatch.
To find the best overlap of the maps, I calculated the ratio in a loop where at each iteration the two maps were shifted with respect to each other.
I calculated the standard deviation of the ratio map and I found a minimum of the standard deviation for a shift of 0.6mm along X and -0.6mm along Y
the ratio is 3.0 +/- 0.8 (average and std on the map)
I plot also a histogram of the ratio
Previous values:
L1 = L2 = 100 microH (L1 and L2 are in parallel)
R25 = 390 Ohms in parallel with 270 Ohms = 160 Ohms
fc = 370 kHz (Cpiezo = 3.7 nF)
Q = 0.73
New values:
L1 = L2 = 680 microH (L1 and L2 are in parallel)
R25 = 390 Ohms
fc = 142 kHz (Cpiezo = 3.7 nF)
Q = 0.78
We tested the open loop TF. The oscillation at 300kHz disappeared.
We succeed in adjusting a unity gain frequency above 20 kHz.
We noticed that sometimes, an oscillation at about 6.5 kHz appeared. It does not seem to be due to an instability servo loop because the gain margin at this frequency is about 10dB.
We noticed also an oscillation at 10kHz with the signal analyser HP 35670 which is very stable (exactly 10.000 kHz) and does not vary with the servo gain.
We will continue to investigate about the 6.5 kHz spurious oscillation in order see if its frequency varies with the servo gain.
After the failed attemp to stably lock the cavity with the new servo (reported here), Pierre has modified the servo by shifting the differentatior. This was done in order to mitigate the effect of the piezo resonances:
Changes:
-zero : 32.8 kHz -> 88 kHz
-pole : 732 kHz -> 380 kHz
We have tried to lock the cavity with this modified servo. Here what we observed:
1) Thurday evening and Friday afternoon we could stably lock the cavity with the new servo (gain between 4 and 5). It corresponds to a UGF of about 14 kHz and with a large phase margin of 55°. In this configuration the error signal is much smaller than with the old servo.
The comparison between the spectrum of the error signal with the new and the old servo is plotted in pic 1 and seems remarkable. (About a factor 7 in the rms)
The calibration used is 385 Hz/V (as here). We found a rms of 140 Hz for the old servo which is compatible with the previouse observation.
2) Friday morning and sometimes in the afternoon the servo showed a strong oscillation at about 300 kHz (similar to that observed before Pierre's modification). We remarked that the oscillation is sometimes triggered when the lock is reacquired. (During the long lock of yesterday and this afternoon the cavity mirrors were very stable, while this morning when we observed the oscillation they were moving more).
3) With the new servo, we have masured the openlooop TF at high frequency and we have observed the presence of many peaks between 60 kHz and 300 kHz, some of them (in particular that at 300 kHz) have amplitude close to 1 and small phase margin. The origin of this peak is not clear (Piezo resonances?, structure in the optical TF?). Pic. 2-3 show the open loop tf between 40khz and 400 kHz and betwenn 10 kHz and 1MHz, respectively
The TF at high frequency has been aquired with the network analyzer from which we cannot save the data. I have manually extracted the data from the first TF (40-400kHz) of that in order to try to fit them.
They can be found here
NEXT STEP
We are currently studying a modification of the servo in order to improve the stability.
We have done a more precise measurement of the open loop TF (with the old servo) between 70 kHz and 170 kHz. (See attached pdf).
Data can be found here:
https://drive.google.com/drive/folders/1HrR6Bq3lwTRyxw1Q6pXoPU0TxDqfFtRs?usp=sharing
(AMP2.CVS and phase2.CVS)
We have also recorded the error signal spectrum with the new servo. The shape changes quite a lot when changing the gain from 4 to 5. (see pic 1 and 2)
We also recorded the error signal in time (gain 0.7) where an oscillation at about 285 kHz is visible. (pic 3)
Plot the rectangular maps along the XZ and YZ planes.
Plot the small maps 1cm-diameter, resolution 0.1mm, along the axis of the substrate every 5mm.
Plot the 3D overview of the substrate absorption.
[Pierre, Matteo L., Yuhang, Eleonora]
In the past days we have tried to lock the cavity using the new servo, with an increased bandwidth. The differences between the old and the new servo are reported in entry #736.
Unfortunatley we didn't succeed in improving the lock perfomances.
We menaged to lock the cavity but the error signal shows a strong oscillation and the transmitted power is much lower than the peak observed during a scan of the cavity:
- If we increase the gain the situation doesn't change (see video here) and the UFG which has been found at about 4 kHz doesn't increase.
- If we reduce the gain, the trasmitted power increases slightly but at some point the lock becomes less stable. (see video here)
We suspected the the loop instability can be caused by the piezo resonances, which according to Matteo L's experience (entry #737) cannot be modeled as a simple pole and could have a stonger impact on the loop stability after the servo modification.
In order to better characterize such resonances we tried to measure the openloop TF (with the old servo) at higher frequency.
We found in TAMA a network analyzer which goes from 10 kHz to 150 MHz (see second pdf attached) and performed the measurement up to 200 kHz with a swept sine.
The results are plotted in the attached picture (top plot). Since we were not able to extract the data from the instrument, we had no other option than to extract them from the picture (bottom plot).
These data and the matlab script to plot them can be downloaded from this link.
https://drive.google.com/drive/folders/1HrR6Bq3lwTRyxw1Q6pXoPU0TxDqfFtRs?usp=sharing
We will try to fit them and see if it is possible to extract usefull information about the piezo resonances.
We have done a more precise measurement of the open loop TF (with the old servo) between 70 kHz and 170 kHz. (See attached pdf).
Data can be found here:
https://drive.google.com/drive/folders/1HrR6Bq3lwTRyxw1Q6pXoPU0TxDqfFtRs?usp=sharing
(AMP2.CVS and phase2.CVS)
We have also recorded the error signal spectrum with the new servo. The shape changes quite a lot when changing the gain from 4 to 5. (see pic 1 and 2)
We also recorded the error signal in time (gain 0.7) where an oscillation at about 285 kHz is visible. (pic 3)
Following the discussion we had offline, I upload a measurement that was done few years ago when I was in the Padova group. The measurement is a characterization of the laser PZT gain as function of the frequency.
The laser is a 1W Mephisto laser from Coherent.
[Yuhang, Matteo L., Eleonora]
We have summarized the lock/unlock losses measurement done in the past and plotted them together (pic 1, 2).
We analyzed 11 set of data.
Each measurement is done taking a set of lock/unlocks and computing the reflectivity as the ratio between the mean of two consecutive lock and unlock period.
The error has been computed propagating of the error of each value of the ratio (taken as two time the standard deviation)
Since for each set we have many lock/unlock we have done a weighted mean of the refelctvities found like this:
and for the uncertainty we have used:
Below the results are reported:
| losses (ppm) | relative error |
| 45.4 +/- 10.5 | 0.23 |
| 43.4+/- 14.4 | 0.33 |
| 48.9+/- 23.9 | 0.48 |
| 60.4+/- 12.8 | 0.21 |
| 45.6+/- 10.0 | 0.22 |
| 58.7+/- 11.4 | 0.19 |
| 47.9+/- 6.7 | 0.14 |
| 74.2+/- 8.9 | 0.12 |
| 52.4+/- 12.2 | 0.23 |
| 58+/- 8.0 | 0.14 |
| 38+/- 10.2 | 0.27 |
The mean of these measurements gives a reflectivity of 0.856, corresponding to a about 53 ppm of losses. (I'm not sure about the best way to compute the error on this number)
The data and the matlab code for the analyisis can be found here:
https://drive.google.com/open?id=1QW5Ym1lkgNS5FvIgFqtM6UC7fXNnXmym
* INPUT LP Filter: 36kHz
* OUTPUT 2nd order LP filter: 120 kHz - Q = 0.79
* OUTPUT LP filter: 155 kHz
* pole (LP filter R54-C54): 145 kHz
* Integrators:
- 1/f^4 : 4 zeros @ 1.55kHz
- 1/f : 1 zero @ 145 Hz
=> New servo: newservo.jpg
* INPUT LP Filter: 675kHz
* OUTPUT 2nd order LP filter: 375 kHz - Q = 0.74
* OUTPUT LP Filter: 330 kHz kHz
* pole (LP filter R54-C54): 660 kHz
* Integrators:
- 1/f^4 : 4 zeros @ 2.7kHz
- 1/f : 1 zero @ 145 Hz
* Differentiator (added compared to the old version):
- zero: 33 kHz
- pole: 725 kHz
Following the discussion we had offline, I upload a measurement that was done few years ago when I was in the Padova group. The measurement is a characterization of the laser PZT gain as function of the frequency.
The laser is a 1W Mephisto laser from Coherent.
Yesterday I measured power after the first BS on in-air bench. They are 16.84mW and 601.5mW seperatly. This means the ratio is 36:1 of this 2-inch BS.
And I also measured the power going into SHG, which is 413.3mW.
[Eleonora, Matteo L.]
In order to investigate the fluctuations of the IR reflected power during the lock-unlock measurement, we have plotted the histogram of the data both for a lock and for an unlocked period.
We observe that for the unlocked period the noise seems to be gaussian as we expected assuming that it is domated by input power fluctuations.
On the other hand the fluctuations during the locked period dosen't seem to be gaussian and shows a "longer tail' on the right side. This is compatible with fact that the mechanisms explaining such fluctuations (in addition to the input power one), that is misalignments and lock accuracy, are expected to act only increasing the reflected power.
We don't know which is the best distrution to use to fit the locked data. Up to now they have been treated as if they were gaussian.
The last plot shows the contour of the normalized histogram for different set of lock/unlock taken during the same measurement.
I have been doing a simulation of TAMA optical bench using OptoCAD. Here attached interim results. It has not been completed. You can convert an attached text file into a fortran source code by changing .txt to .f90 for eample (depending on your environment). For some unknown reason (probably a problem of windows OS), I couldn't divide code into multiple files (like a main program and some external files beside it) as is a common method to gain readability of a long code. Consequently, the source code got complete mess. Basically it is just a list of optical component so you caan just add components which will be placed later on. For a green beam part at least it is consistent to the actual situation. For an IR beam part it should be changed afterwards.
alignment of the imaging unit:
put the surface reference and aling the IU in order to have the blade sharp image on the pd. Do a scan and move the z axis to the central peak maximum Maximize the AC/DC signalas goog as possible. Do again the scan (see first screenshot). The imaging unit position is 65.5mm, set exactly at the distance that have to be moved to measure the 154mm thick kagra sapphire. To measure the substrate we have to move the IU to 0mm.
Calibration: bulk reference
pump power=32mW, DC=4.1V, IUposition=65.5mm, AC=60mV (see second screenshot)
Maps of KAGRA substrate shinkosha#7: 130mm diameter, 1mm resolution, z_stage=110mm,70mm,35mm
plot the maps with the same color scale
