NAOJ GW Elog Logbook 3.2
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
Loss measurement 28/03/18
Reflectivity: 89%+/- 2.5% => Losses: 44 +/- 12 ppm
Mismatching/misalignement considered in the estimation: 11% (worse than usual)
New did a new measurement of RTL with lock/unlock.
Reflectivity 84% +/- 2% => Losses 63±12 ppm
We considered that 7% of the input light is not coupled into the cavity.
We have measured the spectrum of the piezo correction, through the channel PZT mon.
In the plot we took into account the factor 100 of attuation of the channel PZT MON and we used the calibration 2 MHz/V.
The spectrum looks similar to that we measured in july. We fitted it with the curve 7.5 kHz/f, which is compatible with the expected free running laser noise.
I attach the .txt file with data not calibrated.
In order to increase the statistic yesterday we repeated the measurement of the round trip losses, with the lock unlock technique.
Since we did it in two different moments of the day the alignement conditions were likely to be different.
| reflectivity | losses | |
| #1 | 0.87±0.02 | 50±13 |
| #2 | 0.80±0.03 | 81±16 |
The reflectivity has been computed by taking the mean of the time series between a lock and an unlock period. The error is computed as the progagation of the standard deviation of these two set of data.
We estimated that 7% of the input light does not couple into the cavity.
Last week we measured the bandwidth of cavity. By using this data, we also did the extrapolation and got the losses.
We considered all the losses come from the increase of end mirror transmissivity. Then we did like this:
- Fix r1 as sqrt(1-T1) and T1=0.136%.
- Use the Airy distribution to fit EM transmission and get R2.
- Losses is calculated as 1-R2-T2. T2 is set as 3.9ppm.
| Velocity | Bandwidth | Finesse | Losses | r2 |
| 200Hz/s | 119Hz | 4191 | 134 | 0.999931 |
| 400Hz/s | 114Hz | 4355 | 78 | 0.999959 |
| 80Hz/s | 115Hz | 4312 | 92 | 0.999952 |
After measuring the Tama-mirror-size sapphire substrate Sample2 (see elog entry 678), I measured the Sample1. I upload the maps of Sample1.
I plot the maps of the small sapphire sample we measured.
