NAOJ GW Elog Logbook 3.2
According to the fit the decay time is 0.3msec that is a factor of 10 smaller than the cavity decay time.
For the purpose of getting a better estimation of cavity bandwidth, we want to fit the transmission of End Mirror.
I tried three model, including gaussian function, generalized normal distribution and airy pattern function. However, none of them seems fit very well. Before proceeding to next step, I would like to ask for some suggestions.
Constant velocity assumption may be wrong? I'm not very clear. I can try with some acceleration or the combination of erf and exp as you suggested.
Trying to understand why the best fitting function is not a erf function (given the hypothesis that the beam is cut at constant speed): maybe the exponential decay we see in the data is dominated by the electronics ? one can also try to fit with a function erf + exp.
Yesterday the clean booth in TAMA central area has been installed. Currently we are working to reorganize the area inside it and reconnect the electronics.
At the link below you can find pictures taken to the optical table rack before we disconnect everything. They may help the repristination activity.
https://drive.google.com/open?id=1XDv4P4gmAJMNsEKLoFNGZLUkMw5nT9kr
According to the esponential fit, the decay time of the "hand cut" is about 0.6 ms which is roughly a factor 5 smaller than the expected decay time of the cavity. We will take some more measurements in order to check the dispersion of such value.
To measure cavity decay time, we are currently just cutting beam by bending a IR card and releasing it towards beam path. This method is not ideal and affect a signal. Since we don't have enough channels on oscilloscopes to conduct measurements at the same time, we cannot distinguish genuine cavity decay time and effect of not-ideal cutting method. Thus I tried to fit a signal obtained by cutting beam by hands. Data is attached as a txt file. Note that this data dosen't contains any effect other than cutting beam.
Two different functions are used for fitting; an error function (erf) and an exponential function. An erf is obtained by integrating a gaussian function. This seems plausible given a laser intensity transverse distribution is typically a gaussian. These functions are shown in a figure attached with resulting fitting parameters. I assumed a constant velocity to cut beam (IR card go across beam crosssection with a constant velocity).
From this calculation, exponential deccay is more fit.
Python codes used is also attached (please change .txt to .py if you try).
According to the esponential fit, the decay time of the "hand cut" is about 0.6 ms which is roughly a factor 5 smaller than the expected decay time of the cavity. We will take some more measurements in order to check the dispersion of such value.
Trying to understand why the best fitting function is not a erf function (given the hypothesis that the beam is cut at constant speed): maybe the exponential decay we see in the data is dominated by the electronics ? one can also try to fit with a function erf + exp.
Constant velocity assumption may be wrong? I'm not very clear. I can try with some acceleration or the combination of erf and exp as you suggested.
According to the fit the decay time is 0.3msec that is a factor of 10 smaller than the cavity decay time.
Actually, there is a factor 2 to take into accunt in the definition of the decay time we used, that is P = P0*exp(-2*t/tau)
(see https://www.osapublishing.org/oe/abstract.cfm?uri=oe-21-24-30114 )
So the decay time from the "hand cutting" fit should be: 2/tau = 3149 => tau = 0.6 ms. Anyway, since I used this definition also for computing the filter cavity decay time (about 2.7ms) if I'm not wrong we have a factor 5 of difference between the two, in any case.
We measured the cavity bandwidth and error signal for IR with three different velocity of frequency scan. In this case, we can give a reasonable estimation of the calibration factor of IR. The result is 180.7 +/-5 Hz/V. We didn't consider error of invidual measurement, the standard deviation only comes from these three measurements results.
| velocity | bandwith | calibration |
| 200Hz/s | 106Hz | 176Hz/V |
| 400Hz/s | 112Hz | 186Hz/V |
| 80Hz/s | 108Hz | 180Hz/V |
For a better parameter estimation, we will fit these measurment result.
As pointed out by Matteo B., the spectrum in the entry693 was not correct. After some investigation, we found the problem comes from the conversion of .DAT file.
After solving this problem, we compared the spectrum of green and infrared error signal, taken with different value of loop's UGF(10kHz and 18kHz). Now we are using UGF as 18kHz.
In the attached plot there are calibrated spectrum. The calibration factor we are using for green is 385Hz/V, for infrared is 180Hz/V.
We also multiplied a factor to make green and infrared superpose. We can see from the attached plot that green and infrared have the same trend at high frequency. This is in agreement with the fact that after 1.4kHz we should also see the effect of the green cavity pole.
The .txt files attached are not calibrated.
Participants: Eleonora, Matteo L, Yuefan
We did a preliminary try to implement the dithering technique to keep the beam direction aligned with the cavity axis by acting on BS pitch and yaw.
We started with yaw:
1) We inject a sine perturbation in BS yaw with frequency 10 Hz and amplitude 3mV.
2) We acquired the transmitter green power in labview using one of the spare channel of the "telescope" ADC board.
3) We demodulated it by multipling it for a sine with the same frenquency and filtered it with a lowpass (butterworth 4th order, cutoff frequency 1 Hz)
4) We filtered the error signal with another lowpass (butterworth 1th order with cut off frequency at 0.01 Hz and adjustable gain).
5) We summed the correction signal to the "manual offset" in the yaw local control loop which is usually set by hand during the manual alignement procedure.
In Pic. 1 there is an "explained" scheme of the labview frontpanel, in Pic. 2 there is the block diagram of the vi.
The attached video shows the effect of the loop when we change the manual offset of BS yaw. The starting position is 0.02. We change it to 0.01 and to 0.
(See Pic.1 for a reference of the different controls and graph shown)
It seems that the loop is somehow able to bring back the offset to a position which makes the transmitted power less sensitive to the modulation. We need to check the long term performances and implement the same loop on the other degree of freedom.
DEMODULATION PHASE ISSUE
We tried to adjust the demodulation frequency by adding a tunable phase difference between the signal sent to the BS and the one used for the demodulation. With the loop open, we tried to change the demodulation phase in order to maximize the error signal but we couldn't see any change. We suspect that there is a problem with the reset of the subvi used to generate the sine wave. We might have found a solution that we will try soon. Anyway for the moment the demodulation phase is not optimized.
Link to the video in mp4 format.
https://drive.google.com/file/d/178Y6unT0S023VQCVl7pdYEdYgbTta22U/view?usp=sharing
Today, We try to use a way to measure the decay time of our filter cavity. The way is to cut the incident laser mechanically. By taking the data of oscilloscope, I used this function to fit
y=np.exp(-t/a1)+np.exp(-t/a2)
The reason I use this function is we have two decay mechanisms. One is mechanical cutting, the other is cavity decaying. The fitting result is a1=0.000326, a2=0.0025. This means the cutting time is 0.000326s and cavity decay is 0.0025s.(See attached Fig 1)
I've compared the error signals measured in the entry 690 with the new ones. There is something strange: now the error signal for the IR is 10 times smaller than before.
PARTICIPANTS: Yuhang, Yuefan, Eleonora
In the past days we have monitored the cavity round trip losses. We computed them from the cavity reflectivity with the tecniques described here.
In the actual setup the losses are measured using the IR reflected beam, sensend by a TAMA fotodiode. The reflected beam is filtered whith a bandpass filter in order to get rid of the residual green and it is focused on the photodiode using a 2 inch lens with f = 30 mm. (See first attachment for the setup scheme)
With this setup we have found that the reflectivity (ratio between reflected power in lock and out of lock) changes from day to day and takes values between 0.88% and 0.82%. It corresponds to a variation in the RTL between 40 ppm and 75 ppm.
The change can be due to the different alignment condition (the beams impinges on different points of the mirror which scatter differently) and/or to some other factor affecting the measurement and not yet understood.
In the attached plotes there are some measurments from the last days. Unfortunately not all the measurements from which we deduce the RTL variation reported before have been recorded.
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.
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.
Loss measurement 28/03/18
Reflectivity: 89%+/- 2.5% => Losses: 44 +/- 12 ppm
Mismatching/misalignement considered in the estimation: 11% (worse than usual)
Yesterday, we did some characterization of our filter cavity.
1. Open Loop Transfer Function: The unity gain frequency is 10kHz and the phase margin is 39 degree. Actually this is not the practical case, we changed the gain of our loop. And we suspected this is because of the increase of circulating power.(Fig 1)
2. Calibration: We measured the calibration of green and infrared again. The calibration factor is similar with before.(Fig 2)
3. Error signal noise spectrum: We plot out the direct measurement and calibrated one together.(Fig 3 and 4)
You can use the data attached. They are not calibrated.
ger25k6 is green error signal with highest frequency 25600Hz(calibration factor is 2.6e-3V/Hz).
ier25k6 is infrared error signal with highest frequency 25600Hz(calibration factor is 6.3e-3V/Hz).
ol51k2 is open loop transfer function with highest frequency 51200Hz.
I've compared the error signals measured in the entry 690 with the new ones. There is something strange: now the error signal for the IR is 10 times smaller than before.
In order to reproduce the "Pacman" shape seen in the reflected beam (see #entry 687), I have made a simulation of the cavity using the FFT code OSCAR.
https://fr.mathworks.com/matlabcentral/fileexchange/20607-oscar?requestedDomain=true
The shape is more or less reproduced with a mismatching of 4% and a misalignemnt of 5microrad of the end mirror.
I attach the plot of the fields and the script used (it needs the code OSCAR to be used), which can be useful also for other applications.
I also attach the txt file here. It has not been calibrated yet. The calibration factor I used here is 2.6e-3 V/Hz(for green), 170Hz/V(for infrared).
Yesterday at some point the lock was disturbed by some spikes affecting the BS local control signals. The problem could be temporarily solved by switching off and on the laser.
In the past weeks we observed in two ocassions glitches affecting the error signals of the end mirror local controls.
When the control loops are open, the glitches look like "jumps", affecting simultaneusly both pitch and yaw.
They are quite frequent and in most of the cases they cause the unlock of the cavity. In both cases the problem was solved by switching off and on the ADC in the end room.
Participants: Yuhang, Yuefan, Tomura, Raffaele, Eleonora
In the past days we have worked in order to improve the IR alignment.
As a first thing we placed a camera on the optical bench to look at the IR reflected beam and we tried to maximized the trasmitted power while monitoring the shape of the reflected beam. According to our understanding, in reflection we should see the superposition of the resonant TEM 00 (dephased of 180 deg after it is reflected by the cavity) and the HOM due to misalignement/mismatching which are promplty reflected.
The procedure to align the cavity both for green and IR is the following:
1) Adjust BS position to center the beam on the end mirror (reference on the end camera screen)
2) Align the cavity for the green beam by moving input and end mirror to maximize the transmitted power
3) Move the last two steering mirror for the IR on the bench to maximize IR trasmitted power
4) While aligning the IR we take care that it is always centered on the resonance by looking at the error signal and adjustig the AOM frequency to null its offset.
During in this activity we realized that the alignement improvement was limited by the position of the last IR steering mirror on the bench. So we have shifted it after carefully taking some references in order not to loose the alignment. After this change we were able to improve the IR transimitted power from about 2.5 up to more than 3.5 V
Currently in the best alignement condition we have about 1.8 V of transmitted power for the green and 3.8 for the IR.
The attached video shows the reflected and the trasmitted IR beam when we change the alignment condition in pitch and yaw by moving the steering mirror on the bench. In the case of strong misalignement the presence of first order modes becomes evident. Anyway also in the best aligment condition (about 95 %) there is still a small black dot in reflection.
The oscilloscope in the video shows the transmitted power (yellow line) and the IR error signal (blue line).
After this change in the alignement we have verified that the IR beam in refection was not touching a side of the viewport. (See entry #659 related to this issue )
In order to calibrate the IR error signal we have scanned the resonance by adding a modulation to the AOM around the resonance driving frequency.
We choose a triangular wave, with period 50 mHz and amplitude of 2 kHz (which corresponds to 1 kHz for the IR). This means that the resonance is crossed with a constant speed of of 200 Hz/s.
In the first attached picture, the IR transmission and the error signal are shown during a crossing of the resonance. The x axis has been calibrated in Hz using the computation reported before.
The FWHM of the trasmission is about 116 +/- 4 Hz, corresponding to a finesse of 4310 +/- 150, which is comparable with the design and the previous measurements.
The correspondig PDH has been used to calibrate the IR error signal, finding a value of about 170 +/- 20 Hz/V
The second plot shows the calibrated IR error signal, when the cavity is on resonance. The RMS is about 4.4 +/- 0.5 Hz.
In the third plot, I have merged and calibrated the spectra of the error signal recorded with the spectrum analyzer in two different frequency regions (from 1Hz to 100 Hz and from 100 to 51kHz) and I have computed and plotted the rms. As expected it is in agreement with that found from the time series.
According to the plot, the high frequency (above 100 Hz) seems to contribute with 3.5 Hz to the total rms. The remaing (about 1 Hz) is accumulated below. The contribution of the suspension resonances in the region from 1 to 10 Hz is visible and seems to be about 0.5 Hz.
The origin of the peak at 12 kHz and the quite complex shape of the signal are not very clear to me.
Next step will be to comprare this spectrum with that of the green error signal in order to investigate the role played by the IR pole.
