After last night's challenge (or inspiration), we levitated our magnet this morning.  Since the nice Olympus camera is not currently in the 40m, we had to use my less stellar camera, but despite the poor video quality you can still see the magnet returning to its stable equilibrium position.  Once we recover the better camera, we will post new videos.  Also, we haven't yet figured out how to put videos in line in the elog entry, so here are the youtube links:

levitation 1

levitation 2

We adjusted the gain on coil 1 so that the resistance from the pots was 57.1k (maximum gain of 101.2,).

currents from power supply, pre-levitation: 0.08 A and 0.34 A

post levitation: 0.08 A and 0.11 A

note: we're not sure why changing the gain on coil 3 changes the current through the power supply, so we'd like to investigate that next.

This past week, we levitated our small cylindrical magnet (with the flag made from heat shrink).  Though the levitated magnet didn't appear very jittery to the eye, we looked at the PD current on the scope and could see oscillations that corresponded to the flag hitting the sides of the OSEM.  The oscillations were more pronounced as we gently hit/vibrated the lab bench, and by pounding on the bench Rana knocked the levitated magnet completely out of the setup.  So, we're currently working on building a new, stabler mount.  The biggest challenge here is fixing the OSEM in place, but we're experimenting with different optics pieces to see which is the most stable for our purposes.   Jenne taught us how to make through holes using the drill press so we can add slats of aluminum to adjust the height of the OSEM mount.  We also plan to fix some heavy plates to the bottom of our system to decrease its vibration frequency.

We also calculated the transfer function of our circuit, which seems to match the measured frequency response to within a small factor.  We're playing with Rana's Simulink models and are currently modeling our own system to determine what gains we would expect to use and get a better understanding of our circuit.

Once our system is successfully mounted stably, we plan to experimentally observe the effects of changing the gain and integrator by looking at time series measurements of the PD current, as well as using the spectrum analyzer to compare the frequency response of our system at different gain settings.

Some unused optics in the BS chamber were removed. 

After that the beam splitter has been drag wiped. 

So now the BS chamber is waiting for the installation of  the other core optics i.e. PRM, SRM and Tip-Tilts. 

-- removing of unused optics

      There were some unused optics, mainly 1.5 inch optics which had been used for the oplevs in the chamber. 

Kathaine, Shamila (Team Magnet) and Kiwamu took those optics out from the chamber.

And then we carefully wrapped each of them by aluminum foils and put them in some clear boxes.

In fact, before wrapping them, we gently attached lens papers on their HR surfaces such that aluminum foils can not damage it.

Now there are only three 1.5 inch optics in the chamber, and they are supposed to be used for the oplevs.

We didn't remove any of the 2 inch optics and the PZT mirrors because they are still going to be used.

These are the pictures of the BS chamber after we cleaned up them. 

-- wiping of the BS

        Rana and Kiwamu drag wiped the HR surface of the BS by using lens paper with the solvents.

The below is the procedure we did. You can find some details about the wiping technique for suspended optics in this entry.

In this time we could wipe the beam splitter without removing the front earthquake stops because the beam splitter was brought close enough to us. 

(1). put some blocks attaching the edge of the bottom plate of the tower in order to record the original position.

(2).  locked the beam splitter to the frame by screwing the earthquake stops.

(3). made sure if it is really locked by seeing the output signal of the OSEMs in dataviewer. If it's locked successfully, the resonant frequency gets higher and the Q-value gets lower.

(3).  moved the BS tower close to the door in order to reach the beam splitter easily.

(4). inspected the surface by using a fiber light. There were about 10 bright spots on the HR surface.

(5). wiped the surface three times by using the lens paper with Aceton.

(6). wiped it several times with Isopropyl.

(7). inspected the surface again, found there were no big bright spots near the center. Thumbed up 

(8). put the tower back to the original place and released the beam splitter from the earthquake stops.

Another Hamasutu S3399 photodiode was tested with the electronic circuit as described in LIGO-D-1002969-v.

RF transimpedance is 1k although the DC transimpedance is 2k.

The noise level is 25pA/sqrt(Hz) which corresponds to a dark current of 1.9mA or 1.7mA in the independent measurement.

At all frequencies the noise is larger compared to Koji's measurement (see labbook page 4778).

In file idet_S3399.pdf the first point is not within its error bars on the fitted curved. This point corresponds to the dark noise measurement

I made this measurement again. Now it is on the fitted curve. In the previous measurement I pushed the save button a bit too early. The

averaging process has not been ready while I pushed the 'save'  button.

Dark current is 1.05mA and noise is lower than in the previous measurement.

New file are the XXX_v2.pdf files

[Kiwamu / Katrin]

On Wednesday, the green light was locked to the Y arm cavity.

Modulation frequency was changed from 279kHz to 178875Hz. The amplitude was changed from 10Vpp to 0.01Vpp to achieve a modulation index of 0.38. The modulation frequency was changed to minimize AM. With the new modulation frequency the laser light could still locked to the cavity.

The signal of the LO and the photodiode are multiplied by a ZAD-8 mini circuit mixer (Level 7). This mixer requires LO input is +7dBm = 1.4Vpp. Thus we put a 36dB attenuator between the LO and the PZT at the laser. PDH error signal shows lots of peaks that are most likely higher order sidebands. Thus, the next step is to work on the low-pass filter. However the SNR of the error signal has improved with the new modulation frequency. With the old mod. frequency the PDH signal was 4mVpp and the noise floor was 2mVpp.

Phase between the photodiode signal and LO is shifted by about 10 degrees. Step two is to work on a phase shifter.

I inserted several beam blocks and iris on the Y arm Green table. There was/is lots of stray light because a lot of the mirrors are not under an angle of incident of 45°. Some stray light is left since couldn't find an appropriate beam block/dump due to lack of space on the table.

This is a kind of summary of what I have worked on this week.

After all the changes made last week, I could not manage to lock the green light to the cavity, but the PDH error signal looks nicer.....at least something.

Alignment of the light to the cavity:

• DC level of green PD when light is non-resonating 100%
• DC level of green PD when light resonates 75%
• --> Not sure if this alignment is good enough
• In comparision to last week the cavity mirrors seem to move more or my alignment is way worse than last week. The bright spot on ETMY could not be observed for more than let's say a second in the unlocked configuration.

Low-pass filter (LPF)

• The PDH error signal was covered with oscillations of 3.3 kHz, 7.1 kHz and 35 kHz.
• Measured cut-off frequency of the LPF used so far is 35 kHz
• Designed and build a new LPF: second order, cut of frequency of 1.1 kHz (this is just the design value, haven't measured that so far)
• With the new LPF the PDH error signal is free of the above mentioned oscillations.
• Impedance should be checked

PDH error signal

• Signal-to-noise ratio (SNR) could be improved to values between 7.8 and 11.1 (old SNR was 5 to 7)
• Looks more like a PDH signal than with the old LPF (now just derivative of the carrier and the first order sidebands show up)
• Amplitude of the first order sidebands are smaller than the zero order, but are still too high (about 80% of the first order), need to work on the proper value of the LO amplitude an the voltage averager

Phase shift between green PD signal and LO

• Phase shift is about 1MHz
• Tried to find a capacity that compensates the phase shift. This was not successful since the PD frequency changed every now and than by +/- 20 kHz

[Kiwamu, Katrin]

As reported earlier an oscillation around 7kHz is an the PDH error signal. The lower spectrum show that there is a peak from 6-7kHz.

This peak is somehow dependent on the modulation frequency. This means the peak can be shifted to a higher frequency when the modulation frequency is increased (see for comparsion f_mod=279kHz).

If the power supply for the green PD is switched of the peak vanishes. The same happens if the LO is switched of.

On the Green YARM end table the second mirror behind the laser has been exchanged.

Reason: The light is impinging on the mirror under an angle of  about 10 degrees, but the old mirror was coated for angle of incidence (aoi) of 45°.

Thus it was more like a beam splitter. The new mirror is a 1" Goock & Housego mirror which has a better performance for an aoi of 10 degree.

Realignment through Faraday Isolator and SHG cristall as well as 532nm isolator is almost finished.

After all realignment is finished, here are the powers at several positions:

The angle of incidence of light is for some mirrors on the YARM end table different from 45° even though the mirrors are coated for 45°.

The mirrors below are useful if there are plans to replace these mirrors by properly coated ones.

* This is the new mirror as decribed on http://nodus.ligo.caltech.edu:8080/40m/5623

There was a 60 Hz and 120 Hz oscillation on the green PDH photo diode output. After a long search, I could identify that

the source was a broken BNC cable which was connected to the photo diode. I exchanged that BNC cable and the 60 Hz

and 120 Hz are gone :-)

With the new cable the PD output was less noisy so that it was easier to achieve a better alignment of the light to the cavity.

The reflected power could be reduced from 40% to 30%. For perfect alignment the reflected power would be 20%.

The mini circuit power splitter ZFRSC-42S+ used at the YARM has no balanced output as it should have according to the data sheet.

@ 0.05MHz  the amplitude unbalance should be 0.03 dB

A quick measurement shows that there is a LO amplitude dependent unbalance:

So my question is, shall I replace the power splitter just in case it is further degrading?

It is a 4^th order filter with cut of frequency of 120 kHz.

Design

Measurement

Yesterday, I measured the transfer function of the YARM PDH box.

I tested the electronic board and couldn't find a frequency dependent behaviour. So I measured the TF again and it looked nice.

Today's nice measurement could is/was reproducible. I suppose yesterday's measurement is just an artefact.

The electronic board is modified according to Kiwamu's wiki entry http://blue.ligo-wa.caltech.edu:8000/40m/Electronics/PDH_Universal_Box

Btw. The light could be locked to the cavity for ~3min.

I could not improve the locking. So, I checked the transfer function of the PDH box again. The transfer function looks okay if the gain knob is <=2.0.

If the gain knob is >2.0 the 20dB step appears in the transfer function (see elog page 5713). This step is shifted to higher frequencies if the gain is

increased. The PZT drive out was not saturated at any time. Yesterday, I checked the electronic circuit with a gain of 2.0. Thus,  I couldn't find the broken

gain amplifier (AD8336). The amplifier is ordered in will arrive on Monday.

Yesterday, I had the great pleasure to solder a tiny 4 x 4 mm op amp with 16 legs (AD8336).

I figured out that the best and fastest way to do it is

1. to put solder with the soldering iron on every contact of the electronic board (top side)
2. heat the bottom side of the electronic board with a heat gun
3. use a needle to test if the solder is melted
4. if it is melted place the op amp on the electronic board
5. apply some vertical force on the op amp for proper contact and heat for 1 to 2 more minutes
6. done

From time to time the 20 dB jump in the transfer function still occurs. The new AD8336 op amp did not change that issue. I am sure that the op amp was broken,

because the amplitude of the sine did not change when I turned the gain knob.

The above two curves were measured with different input amplitude of the sine from the spectrum analyzer. Nothing changed in between except that there was no

jump when Kiwamu was around. Very strange. Testing the electronic board led to no clue what is happening.

For now, I will just use the PDH box as it is, but one should keep this odd behaviour in mind.

[Katrin,Jenne]

RF photo diodes POP55 and POX11 are installed. The beams are aligned to the photo diodes.

I used 0.7 A/W for the response and 50V/A for POP55 according to elog page #4576.

To install the third RF photo diode we need to order a plano-convex lens with a focal length of 750 or

maybe even better 1000

Today, I could lock the YARM laser for 2h to the YARM cavity. After to hours the output of the servo is saturated. I need to work on thermal feedback to the laser.

It is a nice TEM00 mode and the green light enters PSL table.

Measured with pin-ball machine spectrum analyzer (I forgot the real name, but it is the one that makes sounds like a pin-ball machine), source power10mVp, Lb1005 gain 2.05.

Setup

Input offset of LB1005 is zero

Locking history

On Thursday, Oct 27, lock for 3 min

On Friday, Oct 28, lock up to 18 min, improvements done by

• finding the right adjustment of PI Corner frequency and gain
• better alignment of the light to the cavity
• I used a high-pass filter between LO and LB1005, but no improvement of lock. In contrast, it got worse.

On Monday,Oct 31, careful adjustment of summing box (rear of of LB1005), lock up to 2h, limited by saturated feedback signal --> work on slow control

Some more plots

Slight modification on that model:

• terminated Q_out of Lockins to be able to compile the old model
• assigned other ADC channels to GCY (green YARM)

connector J9B of hardware ADC --> ch1 in software ADC --> GCY_ERR

connector J14 of hardware ADC --> ch11 in software ADC --> GCY_PZT

connector J15 of hardware ADC --> ch13 in software ADC --> GCY_REFL_DC

Channels C1:X05-MADC0_TP_XXX with XXX 2-9, 14-19, 21-27, 29-31 showed digital zeros.

Some of these channels are used in c1scy.mdl, e.g. for OSEM stuff. I guess this is not optimal...

I changed an ADC channel for GCY_ERR and thus recompiled the c1scy model.

while I was not doing anything on the machine.

Plugging in the thermal feedback BNC cable to the laser reduced the DC voltage of the green PDH photo diode from 3.12 V to 1.5V off resonance.

The power emitted by the laser was the same as in the case without that cable. Note LT, i.e. measured crystal temperature, of the laser show a

different value when the BNC is connected, but the manual clearly states that this display does not work properly if a cable is connected to the

slow BNC plug, an offset is added.

The power of the 532nm light behind the SHG oven has been reduced from 1mW to 0.4mW. I changed the crystal temperature such that the power

of the green light is 1mW. With this new temperature setting the laser can be locked again.

Okay, my elog entry was not clear I changed the temperature of the SHG which only changes the conversion efficiency. 

Anyhow, since the laser set temperature and thus the laser frequency has been changed by Zach and I couldn't find a note

of the original laser crystal temperature, my plan is to reset the SHG temperature to the old value, set the laser crystal temperature

around 19°C and do fine adjustment of that temperature by optimising the doubling efficiency. Okay?

63% coupling efficiency into the new fiber collimator (Thorlabs XXXX) and the blue fiber.This should be sufficient for a beat measurement with the PSL laser.

I think the coupling efficiency is not too bad with having no mode matching lenses and no adjustable collimator lens.

252mW in front of the fiber

159 mW fiber output

I measured the power spectrum of channel C1:GCY_SLOW_SERVO1_IN1, which is the PZT driving voltage.

I converted the output to a PSD. Next, I converted counts/sqrt(Hz) to volts/sqrt(Hz) by multiplying with 40 V / 2^16 counts.

Finally, I multiplied it with 5MHz/V for the PZT to end up with Hz/sqrt(Hz).

This corresponds to a cavity length fluctuation of

with lambda = 532nm and a YARM cavity length of 37.757m (elog # 5626).

All in one plot

error signal = signal measured behind the low-pass filter

feedback signal = output of the gain servo, going to the PZT

First of all both signals in V/sqrt(Hz) just in case I mess up the next calibration step.

The 60 Hz line (and its multiple) are a new feature. They show up as soon as the feedback loop is closed. So far, I couldn't find their origin.

For the next calibration step:

• width of a typical error signal, i.e. the frequency band width of the carrier slope, ~1.4 kHz
• height of a typical error signal 182 mV

[Suresh, Katrin]

Measured frequency fluctuation of the beat between PSL and YARM lasers.

Yesterday, it was very tricky to adjust the voltage offset to the slow YARM laser input to achieve the appropriate beat frequency. Today, it was much easier. During measurement beat around 25 MHz. Calibration factor 40 mV per 10 MHz.

[Kiwamu, Katrin]

Red and blue curves: frequency fluctuation of the beat node between PSL and YARM laser.

Green and broen curves: Actuation on ETMY.  In ALS_CONTROL.adl  ETMY filter bank 4 and 5 were switched on. Gain was 0.3

Nice reduction of the frequency fluctuation.

Y axis is in volts^2 per counts. In order to go to MHz/sqrt(Hz) you have to take the square root and then times [20Volts/(2^16)counts]*[10Hz/0.04V].

Started to scan the cavity, but this didn't work. Green light all out of lock. IR beam was badly aligned to cavity. Now, my time is over and I have to leave you.

Thanks, for your help and the nice time.

Motivation:

I got some hands-on-experience on using RF photodetectors and the Network Analyzer from Koji. There were newly purchased RF photodetectors from Electro-Optics Technology, Inc.. These were InGaAs Photodetectors with model no.: 120-10050-0001(ET-3010) and 120-10056-0001(ET-3040). The User Guide for the two detectors can be found here. This is the first time we bought the ET-3010 model PD for the 40m lab. It has an operation bandwith >1.5GHz(not tested yet), much higher than other PDs of its kind. This can be used for detecting the output as we 'sweep' the laser frequency for getting data on the optical cavities and the resonating modes inside the cavity. We just tested out the ET-3040 model today but will test out the ET-3010 next week.

Tools and Machines Used:

We worked on the optical bench right in front of the main entrance to the lab. We put the cables, power chords, etc. to their respective places. We used screws, poles, T's, I's, multimeter, Network/Spectrum Analyzer(along with the moving table), a lab computer, Oscilloscope, power supply and the aforementioned PDs for our testing. We took these items from the stack of tools at the Y-arm and the boxes of various different labelled palced near the X-arm. We moved the Network Analyzer(along with the bench) from near the Y-arm to our workplace.

Procedure:

I will include a rough schematic of the setup later.

We alligned the reference PD(High Speed Photoreceiver model 1611) and the test PD(ET-3040 in this case) to get optimal power output. We had set the pump current for the laser at 19.5mA which produced a power of 1.00mW at the output of the fiber couple. At the reference detector the measured voltage was about 1.8V and at the DUT it was about 15mV. The DC transimpedance for the reference detector is 10kOhm and its responsivity to 1064 nm is around 0.75A/W. Using this we calculate the power at the reference detector to be 0.24mW. The DC transimpedance for the DUT is 50Ohm and the responsivity of about 0.9A/W. This amounts to a power of about 0.33mW. After measuring the DC voltages, we connected the laser input to the Network Analyzer and gave in an RF signal with -10dBm and frequency modulation from 100 kHz to 500 MHz. The RF output from the Analyzer is coupled to the Reference Channel(CHR) of the analyzer via a 20dB directional coupler. The AC output of the reference detector is given at Channel A(CHA) and the output from the DUT is given to Channel B(CHB). We got plots of the ratios between the reference detector, DUT and the coupled refernce for the Transfer Function and the Phase. We found that the cut-off frequency for the ET3040 model was at arounf 55 MHz(stated as >50MHz in the data sheet). We have stored the data using the lab PC in the directory .../scripts/general/netgpibdata/data.

Result:

The bandwidth of the ET-3040 PD is as stated in the data sheet, >50 MHz.

Precaution:

These PDs have an internal power supply of 3V for ET-3040 and 6V for ET-3010. Do not leave these connected to any instruments after the experiments have been performed or else the batteries will get drained if there is any photocurrent on the PDs.

To Do:

A similar procedure has to be followed in order to test the ET-3010 PD. I will be doing this tentatively on Monday.

I am adding the text files with the data readings and paramater settings along with the Bode Plot of the data. I plotted these graphs using matplotlib module with python 2.7.

In continuation with the previous(ET-3040 PD) test.

The ET-3010 PD requires to be fiber coupled for optimal use. I will try to test this model without the fiber couple tomorrow and see whether it works or not.

Summary:

In continuation to the previous test conducted on the ET-3040 PD,  I performed a similar test on the ET-3010 model. This model requires a fiber couple input for proper testing, but I tested it in free space without a fiber couple as the laser power was only 1.00 mW and there was not much danger of scattering of the laser beam. The Data Sheet can be found here

Procedure:

The schematic(attached below) and the procedure are the same as the previous time. The pump current was set to 19.5 mA giving us a laser beam of power 1.00mW at the fiber couple output. The measured voltage for the reference detector was 1.8V. For the DUT, the voltage is amplified using a low noise amplifier(model SR-560) with a gain of 100. Without any laser incidence on the DUT, the multimeter reads 120.6 mV. After alligning the laser with the DUT, the multimeter reads 348.5 mV, i.e. the voltage for the DUT is 227.9/100 ~ 2.28 mV. The DC transimpedance of the reference detector is 10kOhm and its responsivity to 1064 nm is around 0.75 A/W. Using this we calculate the power at the reference detector to be 0.24 mW. The DC transimpedance for the DUT is 50Ohm and the responsivity is around 0.85 A/W. Using this we calculate the power at the DUT to be 0.054 mW. After this we connect the the laser input to the Netwrok Analyzer(AG4395A) and give an RF signal with -10dBm and frequency modulation from 100 kHz to 500 MHz.The RF output from the Analyzer is coupled to the Reference Channel(CHR) of the analyzer via a 20dB directional coupler. The AC output of the reference detector is given at Channel A(CHA) and the output from the DUT is given to Channel B(CHB). We got plots of the ratios between the reference detector, DUT and the coupled refernce for the Transfer Function and the Phase. I stored the data under the directory.../scripts/general/netgpibdata/data. The Bode Plot has been attached below and seeing it we observe that the cut-off frequency for the ET-3010 model is atleast over 500 MHz(stated as >1.5 GHz in the data sheet).

Result:

The bandwidth of the ET-3010 PD is atleast 500MHz, stated in the data sheet as >1.5GHz.

Precaution:

The ET-3010 PD has an internal power supply of 6V. Don't leave the PD connected to any instrument after the experimentation is done or else the batteries will get drained if there is any photocurrent on the PDs.

To Do:

Caliberate the vertical axis in the Bode Plot with transimpedance(Ohms) for the two PDs. Automate the procedure by making a Python script for taking multiple set of readings from the Netwrok Analyzer and aslo plot the error bands.

Using Alberto's paper LIGO-T10002-09-R titled "40m RF PDs Upgrade", I calibrated the vertical axis in the bode plots I had obtained for the two PDs ET-3010 and ET-3040.

I am not sure whether the values I have obtained are correct or not(i.e. whether the calibration is correct or not). Kindly review them.

EDIT: Attached the formula used to calculate transimpedance for each data point and the values of other paramaters.

EDIT 2: Updated the plots by changing the conversion for gettin ghte ratio of the transfer functions from 10^(y/10) to 10^(y/20).

Summary:

I have written a code(a basic one which needs a lot of improvements, but still does the job) for taking multiple measurements from the AG4395A. I have also written a separate code for plotting the data taken from the previoius code along with the error bars upto 1 standard deviation.

Details on How To Operate AG4395A:

1. Under 'Measurement' tab, press the 'Meas' button and select the Analyzer Type (Network Analyzer or Spectrum Analyzer).
2. Then under the same options select which 'ratio' needs to be measured (A/R, B/R or A/B).
3. Then press the 'Format' button to select what needs to be measured (Eg - Log|Mag|, Phase, etc.).
4. In order to measure and see two channels at the same time (Eg - Log|Mag| and Phase), press the 'Display' button and select 'Dual Channel'.
5. Using the 'Scale' button we can set the scale/div or use autoscale and also set the attenuator values of the different channels.
6. The 'Bw/Avg' option gives us an averaging option which averages few sets of data to produce the result. In doing this we lose quiet a lot of data and the resulting plot isn't able to give us the information on the statistical errors.
7. This option also allows us to set the 'Intermediate Frequency' Bandwidth. This basically dictates the sampling rate of the Analyzer. The lower the IF bw, the higher is lesser is the noise (due to less uncertainty in Frequency).
8. The 'Cal' button helps us calibrate the Analyzer to the current connections and signals. This is done because there is usually a difference in the 'cable lengths' for the two channels which introduces an extra phase term depnding upon the rf frequency. The calibration can be simply done by removing the Device Under Test (DUT) and diectly connecting the coaxial cables to the channels. After this the 'Calibrate Menu' allows us to calibrate the response using the short, open and thru methods.
9. Now, under the 'Sweep' tab, the 'Sweep' button allows us to select various sweep options such as 'Sweep Time' (Auto, or set a time), 'Number of Points' (b/w 201-801) and 'Sweep Type' (Linear, Log, List Freq. etc.).
10. Using the 'Source' button we can set the source power in dBm units (Usually kept as -20 to -10 dBm).
11. The Scan Range can be set in a few ways such as using the start and end points or using the center and span range/width.
12. After setting up all of the above, we can take the measurement either from the analyzer itself or using one of the control PCs. The command to download the data from AG4395A is netgpibdata -i 192.168.113.105 -d AG4395A -a 10 -f [filename].

Brief Details on How the 'AGmeasure' command works:

AGmeasure is a python script developed by some of the people who work at 40m. It is set as a global command and can be used from within any directory. The source code is in the scripts folder on the network, or else it can also be found in Eric Quintero's git repository. This command accepts at the very least a parameter file. This is supposed to be a .yml file. A template (TFAG4395Atemplate.yml) can be found in the scripts folder or in Eric's repo. There are some other options that can be passed to this command, see the help for more details.

The Multi_Measurement Script:

This script calls the 'AGmeasure' command repetitively and keeps storing the data files in a folder. Right now, the script needs to be fed in th template file manually at prompt.

The Test_Plotting Script:

This script plots the a set of data files obtained from the above mentioned script and produces a plot along with the errors bands upto 1 standard deviation of the data. The format (names) and total number of text files need to be explicitly known, for now at least.

Attachments:​

1. The output test files and the two scripts.
2. This is the 'Bode Plot' for a data set made using the above two scripts.

To Do:

• Improve upon the two scripts to be as compatible as the AGmeasure function itself.
• Try and incorporate the whole script into AGmeasure itself along with improving upon the templates.
• The above details, with some edits perhaps, can go into the 40m wiki too(?).

Update: Increased the font size in the plot. Added a few comments to the two scripts

To Do: Need to consider the transfer function as a single physical quantity (both the magnitude and phase) and then take the averages and calculate the standard deviation and then plot these results. 

EDIT:

The attachment with the test files and the code now also contains a pdf with all the relations/equations I have used to calculate the averages and errors.

I am leaving a script running on the Pianoso for the night. For this purpose, even the AG4395A is kept on. I'll see the result of the script in the morning (it should be complete by then). Just check so before fiddling with the Analyzer.

Thank you.

In continuation to my previous posts, I have been working on evaluating the data on transfer function. Recently, I have calculated the correlation values between the real and imaginary part of the transfer function. Also I have written the code for plotting the transfer function data stream at each frequency in the argand plane just for referring to. Also I have done a few calculations and found the errors in magnitude and phase using those in the real and imaginary parts of the transfer function. More details for the process are in this git repository.

The following attachments have been added:

1. The correlation plot at different frequencies. This data is for a 100 data files.
2. The Test files used to produce the abover plot along with the code for the plotting it as well as the text file containing the correlation values. (Most of the code is commented as that part wasn't needed fo rhte recent changes.)

Conclusion:

Seeing the correlation values, it sounds reasonable that the gaussian in real and imaginary parts approximation is actually holding. This is because the correlation values are mostly quite small. This can be seen by studying the distribution of the transfer function on the argand plane. The entire distribution can be seen to be somewhat, if not entirely, circular. Even when the ellipticity of the curve seems to be high, the curve still appears to be elliptical along the real and imaginary axes, i.e., correlation in them is still low.

To Do:

1. Use a better way to estimate the errors in magnitude and phase as the method used right now is a only valid with the liner approximation and gives insane values which are totally out of bounds when the magnitude is extrmely small and the phase is varying as mad.
2. Use the errors in the transfer function to estimate the coherence in the data for each frequency point. That is basically plot a cohernece Vs frequency plot showing how the coherence of the measurements vary as the frequency is varied.

In order to test the above again, with an even larger data set, I am leaving a script running on Ottavia. It should take more than just the night(I estimate around 10-11 hours) if there are no problems.

Summary:

The following elog describes the procedure followed for generating a sample simulation for a cavity scan, fitting an actual cavity scan and calculating the relevant paramaters using the cavity scan and fit data.

1. Cavity Scan Simulation:

1. First, we define the sample cavity parameters, i.e., the reflectivitie,transmissivities of the mirrors, the RoCs of the mirrors and the absolute cavity length.
2. We then define a frequency range using numpy.linspace function for which we want to take a scan.
3. We then define a function that returns the tranmission power output of a Fabry-Perot cavity using the cavity equations as follows:  where P_t is the transmission power ratio of the output power to input power, t₁,t₂,r₁,r₂ are the transmissivities and reflectivities of the two mirrors, L is the absolute cavity length, f is the frequency of the input laser, c is the speed of light,  is the gouy phase shift with g₁,g₂ being the g-factors for the two cavity mirrors(g=1-L/R). 'n' and 'm' correspond to the TEM_nm higher order mode.
4. We now obtain a cavity scan by giving the above defined function the cavity parameters and by adding the outputs for different higher order mode('n', 'm' values). Appropriate factors for the HOMs need to be chosen. The above function with appropriate coefficients can be used ti also add the modulated sidebands to the total transmission power.
5. To this obtained total power we can add some random noise using numpy modules random.normal function. We need to normalise the data with respect to the max. power transmission ratio.
6. We can now perform fitting on the above data using the procedure stated in the next section and then plot the two data sets using matplotlib module.
7. A similar code to do the above is given here.

2. Fitting a Cavity Scan:

1. The actual data for a cavity scan can be found in this elog entry or attached below in the zip folder.
2. We read this data and separate the frequency data and the transmission data.
3. Using the peakutils module's indexes function, we find the indices of the various peaks in the data set.
4. These peaks are from the fundamental resonances, sideband resonances(both 11MHz and 55MHz) as well as a few HOMs.
5. Each of these resonances follows the cavity equations and hence can be modelled as Lorentzian within small intervals around the peak frequencies. A detailed description of how this is possible is given here and is in the atached zip folder('Functionsused.pdf').
6. We define a Lorentzian function which returns the follows:  where 'a' is the peak transmission value, 'b' is the 'linewidth' of the Lorentzian and  is the peak frequency  about which the cavity equations behave like a lorentzian.
7. We now, using the Lorentzian function, fit the various identified peaks using the curve_fit function of the scipy module. Remember to turn the 'absolute_sigma' parameter to 'True'.
8. The parameters now obtained can be evaluated using the procedure given in the next section.
9. The total transmission power is evaluated by feeding in the above obtained parameters back into the Lorentzian function and adding it for each peak.
10. We can plot the actual data set and the data obtained using the fit of different peaks in a plot using matplotlib module. We can also plot the residuals for a better depiction of the fit quality.  
11. The code to analyse the above mentioned cavity scan data is given here and attached below in the zip folder.

3. Calculating Physically Relevant Parameters:

1. The data obtained from the fitting the peaks in the previous section now needs to be analysed in order to obtain some physically relevant information such as the FSR value, the TMS value, the modulation depths of the sidebands and perhaps even the linear caliberation of the frequency.
2. First we need to identify the fundamental, TEM₀₀ resonances among all the peaks. This we do by using the numpy.where function. We find the peaks with transmission values more than 0.9(or any suitable value).
3. Using these indices we will now calculate the FSR and the Finesse of the peaks. A description of the correlation between the Fit Parameters and the FSR and Finesse is given here.
4. We define a Linear fitting function for fitting the frequency values of the fundamental resonances against the i^th fundamental resonance. The slope of this line gives us the value of FSR and the error in it.
5. The Finesse can be calculated by fitting the linewidth with a constant function.
6. The cavity length can be calculated using the FSR values as follows: .
7. Now, the approximate positions of the sideband frequncies is given by 11*10⁶%FSR and 55*10⁶%FSR away from the fundamental, carrier resonances.
8. The modulation depth, 'm', is given as  where P_c is the carrier transmission power, Ps is the transmission power of the sideband and J_v is the Bessel Function of order 'v'.
9. We define a function 'Bessel Ratio' using which we'll fit the transmission power ratio of the carrier to the sideband for the multiple sideband resonances.
10. We also check for the Linearity in frequency data by plotting Fitting the frequencies corresponding to peaks in the actual data to ones obtained after fitting.
11. After this we attempt to identify the other HOMs. For this we first determine a rough estimate for the value of TMS using the already known parameters of the mirrors,i.e., the RoC. We then look in small intervals (0.5 MHz) around frequencies where we would expect the HOMs to be, i.e., 1*TMS, 2*TMS, 3*TMS... away from the fundamental resonances. These positions are all modulo FSR.
12. After identifying the HOMs, we take the difference from the fundamental resonance and then study these modulo the FSR.
13. We perform a Linear Fit between these obtained values and (n+m).  As 'n','m' are degenerate, we can simply perform the fit against some variable 'k' and obtain the value of TMS as the slope of the linear fit.
14. The code to do the above stated analysis is given here.

Most of the above info and some smaller details can be found in the markdown readme file in this git repo.

The code to produce a cavity scan simulation and then fitting the data and re-evaluating the initiallt set parameters can be found in this git repo.

The 'CavitScanSimulation' python script now produces a cavity scan with custom parameters which can be easily modified. It also introduces the first TEMs(n+m=0,1,2,3,4) to the laser with power going as (1/(2(n+m)+1))^2 {Selected carefully}. The only care that needs to be taken is that the frequency span should be somewhere near an integral multiple of the FSR so that there are equal number of resonances for all modes and sidebands. This code, as of now also calls the 'FitCavityScan' script which performs the fitting procedure on the data generated above{This data is actually written in a '.mat' file} and generates the Fit parameter data files. The Simulation code then calls the 'CalculatingPhysicalParameters' script which evaluates the data based on the Fit parameters and outputs some physically relevant results like the FSR, Finesse, Modulation Depths, TMS{Current Output is the Estimated RoCs of the two mirrors which isn't something we want directly, so it can be modified a bit to output TMS based on the HOMs}. The scripts do some 'Linearity' checks which might not really be of much significance but can be seen as a reference. Also, the ipython notebook will show all intermediate plots for the actual data and data with custom noise, fit data, FSR fitting, linearity checks, Bessel Ratio plot with mod_depths.

Today, I and Jigyasa connected the Ottavia to one of the unused monitor screens Donatella. The Ottavia CPU had a label saying 'SMOKED''. One of the past elogs, 11091, dated back in March 2015, by Jenne had an update regarding the Ottavia smelling 'burny'. It seems to be working fine for about 2 hours now. Once it is connected to the Martian Network we can test it further. The Donatella screen we used seems to have a graphic problem, a damage to the display screen. Its a minor issue and does not affect the display that much, but perhaps it'll be better to use another screen if we plan to use the Ottavia in the future. We will power it down if there is an issue with it.

It has been working fine the whole day(we didn't do much testing on it though). We are leaving it on for the night.

Ottavia had been left running overnight and it seems to work fine. There has been no smell or any noticeable problems in the working. This morning Gautam, Kaustubh and I connected Ottavia to the Matrian Network through the Netgear switch in the 40m lab area. We were able to SSH into Ottavia through Pianosa and access directories. On the ottavia itself we were able to run ipython, access the internet. Since it seems to work out fine, Kaustubh and I are going to enable the ethernet connection to Ottavia and secure the wiring now.  

I just connected the Ottavia to the Netgear box and its working just fine. It'll remain switched on over the weekend.

Keiko, Kiwamu

We noticed that we have used wrong code for MICH degree of freedom for both of the ELOG entries on this topic (cavity lengths tolerance search). It will be modified and posted soon.

 Keiko, Kiwamu

Length tolerance of the vertex part is about 5 mm.

Sorry for my procrastinating update on this topic. In my last post, I reported that the length tolerance of the vertex ifo would be 2mm, based on Kiwamu's code on CVS. Then we noticed that the MICH degrees of freedom was wrong in the code. I modified the code and ran again. You can find the modified codes on CVS (40m folder, analyzeDRMITolerance3f.m and DRMITolerance.m)

In this code, the arm lengths were kept to be ideal while some length offsets of random gaussian distribution were added on PRCL, SRCL and MICH lengths. The iteration was 1000 times for each sigma of the random gaussian distribution. The resulting sensing matrix is shown as histogram. Also, a histogram of the demodulation phase separation between MICH and SRCL is plotted by this code, as these two length degrees of freedom will be obtained by one channel separated by the demodulation phase. We check this separation because you want to make sure that the random length offsets does not make the separation of these two signals close.

The result is a bit different from the previous post, in the better way! The length tolerance is about 5 mm for the vertex ifo. Fig.1 shows the sensing matrix. Although signal levels are changed by the random offsets, only few orders of magnitude is changed in each degrees of freedom. Fig.2 shows that the signal separation between MICH and SRCL at  POP55 varies from  55 to 120 degrees, which may be OK. If you have 1cm sigma, it varies from 50 degrees to 150 degrees.

Fig. 1 Histgram of the sensing matrix including 3f channels, when sigma is 5mm. Please note that the x-axis is in long 10.

 Fig. 2 Histogram of the demodulation phase difference between MICH and SRCL, when sigma is 5 mm. To obtain the two signals independently, 90 is ideal. With the random offsets, the demodulation phase difference varies from 55 degrees to 120 degrees.

My next step is to run the similar code for LLO. 

 To check the demodulation boards for REFL33 and REFL165, a long cable from ETMY (SUS-ETMY-SDCOIL-EXT monitor) is pulled to the rack on Y side.

(1) A filter just after the RF input and (2) transfer function from the RF input to the demodulated signal will be checked for the two 3f demod boards to confirm that they are appropriate for 33 and 165 MHz.