To pick off adequate laser power for our PD QE enhancement experiment, the first HWP in front of the laser was rotated.
The inititial angle of the first HWP was 48 degree.
For measuring the laser power, some optics were aligned as shown in the following figure using a CCD camera.
In this figure, the beam dump #1 is placed for dummping the laser for the other expetiment that is made on the same optical bench as the PD QE experiment, and the Irises are placed for dumping unnecessary light.
I plan to place HWPs and PBSs additionally and to measure the polarization and the laser power at the beginning of next week.
I prepared some basic optics for a PD QE enhancement experiment.
Specifically, two half wave plates, a PBS, a BS, a PD mount, and a stage for the PD mount are prepared.
The PD mount has a glued connector for PDs for replacing them easily.
The sage for the PD mount has three micrometers for moving PDs accurately to three axes.
A male pin assignment for a DC power supply of a circuit for the PD is confirmed.
As shown in the following image, #1 pin, #2 pin, and #5 or #9 pin should be connected to +15 V, -15 V, and GND, respectively.
In addition, for aligning the optics, a CCD camera and a lens for the camera are also prepared.
All things are placed on an optical bench without being aligned.
I will align the optics and test the PD circuit and the camera with laser light.
As noticed by Kate a few times last year, the north side of the lab has hot air comiing out of the HEPA vents and the south side has cold air. This seems to be a problem with the setpoints for the sensors or the hot water actuators.
Let's remember to call physical plant after the current roof leaking situation settles down.
Alessandra and I have constructed the IP at the 40m.
The lowest resonant freq I could obtain was 132mHz when 1613g additional mass is placed on the top plate.
It is very tilt sensitive and the bottom plate has three screws to adjust the leveling.
Final parameters estimate
Using the method described in the previous entry, I measured the spring constant () of three inverted pendulums with different flexure dimentions. The flexures where all in 302/304 stainless steel and had a 3.2 cm length, while their diameter was different:
1) Diameter: 0.98 mm
: 0.295 Nm
2) Diameter: 1.40 mm
: 1.188 Nm
3) Diameter: 1.99 mm
: 1.507 Nm
Using those values for the sping constant I calculated the value needed for the top mass of the final IP to reach the desired 40 mHz resonant frequency.
In order to do this I used the resonant frequency expression in elog entry 2004 with . Let's see why.
If we have a single flexure structure of height and we apply a force F on top as in picture:
in the steady-state the torque equation is:
thus, using , we obtain:
If we have a double flexure symmetric structure of height where the top part can only roll (as in our final IP) and we apply the same force F as in picture:
In the steady-state the torque equation is:
As I said in a previous entry, a double flexure three-legs IP with spring constant is equivalent to a double flexure one-leg IP with spring constant . As the sping constant for a double flexure symmetric IP is the double of the spring constant of a single flexure IP (wich is the one measured) we obtain that the sping constant of our IP is .
I obtained that the values for the top mass needed to reach a resonant frequency of 40 mHz in the three cases above are:
The case 1 can be excluded because the rod is too narrow and buckling would certainly occur. The other two cases are acceptable.
A test to verify if this model is correct will be done on a prototype three-legs IP.
Spring constant and resonant frequency
In order to verify my calculations for the IP resonant frequency and Comsol results some experimental test has been done at the 40m lab.
With the help of Koji I built an inverted pendulum as in picture below:
It is made of a single flexure in stainless steel of 3.2 cm length and 0.98 mm diameter, a pin-vise and a top alluminium mass.
In order to measure the resonant frequency of the IP we used a LED light and two photosensors. The LED light hit the alluminium mass as in picture and the reflected light was detected by the photosensors. We could read the photosensors output on an oscilloscope:
As we made the alluminum mass oscillate by appliyng a small force on the top mass, we could read the mass displacements on the oscilloscope and measure the resonant frequency.
Expected resonant frequency, calculated with an analytical model and the use of Comsol (as explained in a previous elog) was 3.58 Hz while measured was 2.56 Hz.
To test if there was an error in Comsol estimate of the IP spring constant () I measured it. The set-up used is shown in picture below:
I measured the displacement of the top mass as it was subject only to the weight force and deduced . The value expected from Comsol was 0.504 Nm while measured was 0.263 Nm. So probably the material used on Comsol is not exactly the same stainless steel we're using. This means that previous models on Comsol can't be trusted.
Using the measured I calculated the resonant frequency and it resulted 2.50 Hz (measured 2.56 Hz), which is a good result, considering the approximations made in the analytical model to describe the IP structure.
Inverted pendulum Q factor
As we can see from the oscilloscope picture above, the IP is subjected to damping, which is mostly structural damping. In order to calculate this damping we can approximate our IP impulse response by:
the times at which the peak amplitude occurs are given by:
From these expressions we obtain that
Thus, measuring the amplitude of the oscillations peaks I could deduce Q, which results:
Yesterday some measurements where taken to see how the termal enclosure's temperature stabilzes.
I took measurements for decreasing temperature: Initial temperature was 23 C and target temperature was set to 22 C. Results are shown in this plot:
Koji took measurements for increasing temperature using the continuous data acquisition. Initial temperature was 22 C and target temperature was 23 C. Here are the results:
This work was done at the 40m.
Alessandra and I jiggled the PID parameters in order to try some temperature stabilization. But the temperature kept going below the set temp and we were confused.
On Thursday (yesterday):
Alessandra and I succeeded to stabilize the box temperature. We used the PID setting of 250 250 0. Previously, the control gain was way too low and the final temp had significant deviation from the set temp. Now with the max I gain, the controller squishes the DC deviation better.
In order to try to take the continuous temperature measurement, I picked up the Rapsberry Pi at the Yend.
It has the IP of 192.168.113.166 accoding to the log http://nodus.ligo.caltech.edu:8080/40m/8745
Initially I could not login to the host. After struggling with the HDMI cable and connected the display/keyboard/mouse to the host, I found that the user name is not "controls" but "pi". How can I know!
I could manage to change the password to the nominal 40m controls' one, and also created "controls" account by "adduser" command.
After played with Gautam's code a bit, I understood how to acess to the serial port.
- python library "serial" is installed only for python3.
- In order to use the USB port, the user must be in "dialout" group
I made a little bit of coding to have constant but slow sampling rate. Now I started to log the temperature data with the rate of 10sec.
This program changes the set temp from 22degC to 23 degC and continuously take the data.
controls@raspberrypi ~ $ cat 150821_222610.log
1440221170 21.9 : 08/21/15 22:26:10
1440221180 21.9 : 08/21/15 22:26:20
1440221190 21.9 : 08/21/15 22:26:30
1440221200 21.9 : 08/21/15 22:26:40
1440221210 21.9 : 08/21/15 22:26:50
1440221220 21.9 : 08/21/15 22:27:00
1440221230 21.9 : 08/21/15 22:27:10
1440221240 21.9 : 08/21/15 22:27:20
1440221250 21.9 : 08/21/15 22:27:30
1440221260 21.9 : 08/21/15 22:27:40
1440221270 21.9 : 08/21/15 22:27:50
controls@raspberrypi ~ $ cat 150821_222802.log
1440221290 21.9 : 08/21/15 22:28:10
1440221300 21.9 : 08/21/15 22:28:20
1440221310 22.0 : 08/21/15 22:28:30
1440221320 22.0 : 08/21/15 22:28:40
1440221330 22.0 : 08/21/15 22:28:50
1440221340 22.0 : 08/21/15 22:29:00
1440221350 22.0 : 08/21/15 22:29:10
1440221360 22.1 : 08/21/15 22:29:20
1440221370 22.1 : 08/21/15 22:29:30
1440221380 22.1 : 08/21/15 22:29:40
1440221390 22.1 : 08/21/15 22:29:50
1440221400 22.1 : 08/21/15 22:30:00
Unfortunately this program stopped when I logged out. It was fixed by running the command via nohup (no hangup):
nohup ./TC200scan.py &
The previous attempt injected the heat to the system, I'll let the system cooled down for several hours and then run the step rise to log the data.
BTW: TC200 doesn't allow us to observe the data below 0.1 degC level. The other temp controller we brought from WB read the thermister resistance with the precision of 0.001 Ohm.
Thermal enclosure tests
Some tests have been done to see how the thermal enclosure behaves.
- The first was made on Monday by Megan and Koji.
Inside the thermal enclosure there are two heaters on opposite sides and they are connected to the temperature controller box.
In order to determine the behavior of the enclosure, the target temperature was set to 35 °C, and measurements of the temperature where taken starting from room temperature (20.1 °C) using a thermistor attached near to one of the heaters.
Results are shown in this plot:
The fit was made with:
and fit results are:
We see that the temperature of 35 °C is not reached. That is probably due to leakage: the equilibrium temperature is reached when the given heat and leakage heat balance.
- Yesterday I measured values of decreasing temperature starting from 24.3 °C. Results are shown in this plot:
- Today we wanted to choose the target temperature at 23 °C, which is at the middle of the two equilibrium temperatures (25 °C with the heater on and 20 °C with the heater off), reach the linear control range, and test the closed loop response by changing the setpoint by 1 °C.
Unfortunately what happened is that in about four hours the temperature reached 23.8 °C and kept increasing. So we tried to use different approaches to reach a constant temperature of 23 °C.
Parameters for the new shape of the IP
The final shape for the IP is made of three legs having a block on top. To make the calculations simpler I considered a one-leg structure as following:
Sizes for the different parts composing the IP are:
The three cylinders are made in Steel AISI 4340.1 (density: 7850 kg/m^3) while the two blocks are in aluminum (density: 2700 kg/m^3).
The resonant frequency for this structure is given by:
Where is the spring constant and the moment of inertia of the structure.
Moment of inertia
depends on the axis of rotation chosen:
- For an axis perpendicular to and as in picture
We are interested in calculating the resonant frequency for a three legs structure.
In order to do this we can think of a one-leg IP of lenght as a mass on a spring of constant . The relation between the IP spring constant, ,and is:
Now we can think of the three legs of our IP as three springs in parallel, which are equivalent to a single spring of constant and consequently the three legs-IP can be studied as an analogous one-leg IP of spring constant .
Using Comsol (as explained in a previous entry) I calculated and obtained:
Top mass values
From the two plots we can deduce that a resonant frequency of 40 mHz is reached for in both cases.
Anyway, using a fixed mass on top of the structure there will be a small difference between the resonant frequencies in the two directions of oscillation due to the difference between the two moments of inertia.
Link to a block diagram to aid in the setup of the PDH loops TTFSS_Fieldbox.pdf
Attached is my final (?) version of the layout for the seismometer's Michelson.
Yesterday (08/11/15) Koji helped me get some light through the fiber that will eventually bring light to the seismometer's Michelson. A fiber illuminator was attached on the output end of the fiber, and this produced a beam bright enough to see on the input end of the fiber. This beam was aligned on all of the optics between the fiber and the premode cleaner. The laser was then turned on, and the IR beam was then aligned from the PMC to the fiber. Both beams could be seen on the detector cards, so we were able to co-align the two beams through many small adjustments. Once the beams were co-aligned, the illuminator was taken off of the output end of the fiber, and the fiber was replaced into its mount. Then, using a power meter, we were able to take readings on either end of the fiber to see how much of the light was actually making it through the fiber. Before the fiber, the beam was at ~64mW, and after the fiber, the beam was at ~18mW, which is about 28% throughput.
After getting some light through the fiber, we set up the beam scan CCD in front of the output end of the fiber. A long rail was fastened to the table parallel to the beam, so that the CCD could slide in a straight path down the table (see Attachment 1).
After making sure the beam spot remained on the CDD's face over the whole length of the rail, the width of the beam was recorded at every inch interval down the length of the rail. Measuring the distance from the fiber in inches was convenient, because the holes in the table are placed at one-inch intervals. The value shown by the beam scan software is the Gaussian diameter of the beam (the point at which the beam intensity is ~13.5% of its peak value), so when plotting the data the recorded value was divided by 2 to give the Gaussian radius. Attachment 2 is the plot of the beam profile, beam radius as a function of distance from the fiber's collimating lens. The plot shows the clear dispersion of the beam as it gets further away from the beam.
The next beam scan that was done was after a lens that is upstream from the input of the fiber. The setup to do this scan was similar, but I used a ruler rather than the larger rail used in the previous scan (see Attachment 3).
Attachment 4 shows this beam's profile.
This part of the beam may need to be scanned further out than just 12", and that can be done next. Another task is to measure the Y values of the beam as well. The next step for the exisitng data is to fit a Gaussian to them, which will give the size of the waist and the position of the waist. These values can then be used in a la mode to find the optimal lens placement to maximize the amount of light that makes it through the fiber.
Here are the breadboard and IP top mass dimentions resulting from measurements on the objects.
The objects are presented in a top view and the bottom part is the thickness. The "o" sign on top left is actually present on the objects to distinguish their dimentions.
Koji gave me some suggestions and changes to my first Michelson layout diagram, so in this second one I have implemented them:
Edit to the image: The base of the photodetector should be either a BA1S or a BA1V.
Since Kate had the breadboard for the top of the seismometer's rhomboid machined, I was able to make a diagram of the layout for the Michelson (see attached image).
All of these components are in the lab now, so I can start making this layout right away. Let me know if anyone has suggestions, changes that need to be made, etc.
Today I finished attaching the bottom of the thermal enclosure. See images:
Attachment 1: The bottom of the enclosure before the foam and feet are put on (the enclosure is sitting on its head in this photo). There are two holes per corner brace that fasten the brace and the aluminum to the frame, and one hole drilled and tapped for the feet to go through.
Attachment 2: The feet and the foam attached to the bottom of the frame.
Attachment 3: The feet screwed in to a proper height, secured with lock nuts on the other side of the aluminum, and the edges of the foam sealed up.
Attachment 4: The enclosure sitting on its feet!
Attachment 5: The threaded part of the foot on the inside of the enclosure. If this ends up getting in the way of any seismometer components, it can be cut down later.
Attachment 6: One of the feet on the floor. I adjusted the height such that the base of the foot is flush with the foam, but if other heights are needed all of the feet are adjustable.
Progress today on the seismometer's thermal enclosure:
Attachment 1: The enclosure with newly-taped corners. If there were slight gaps between sheets of foam, I stuffed them with smaller pieces of foam before taping over them.
Attachment 2: The aluminum corner brace, with the foot through its hole.
Attachment 3: Side view of the brace and foot. In the actual setup the locking nut will be above the brace, allowing for the height of each foot to be individually adjusted.
IP parameters for the 40 mHz resonant frequency
With reference to a previous entry, in order to make the IP have a resonant frequency of 40 mHz I changed the bottom cylinder parameters (since depends on the bottom cylinder).
I made and assume the following values:
: (1.0; 0.9; 0.8; 0.7) mm
: (0.03; 0.025; 0.02; 0.015) m
while changing correspondingly to make the total lenght of the IP (0.4123 m) constant.
Using Comsol, I determined and deduced for each combination of and :
We can see that the lowest resonant frequency reached is with and .
In this case k results .
Chosen those parameters for the bottom cylinder, we can increase the mass of the sphere to reach a lower resonant frequency.
I made the mass of the sphere vary between 1.00 kg and 1.16 kg (for bigger masses the resonant frequency becomes a complex number and there are no oscillations) and obtained:
Thus a resonant frequency is reached for . In this case we also have:
For these values we have to take care about buckling of the bottom cylinder. Comsol allows the study of linear buckling and returns the Critical Load Factor, which is the ratio of the buckling loads to the applied loads. In our case Comsol returns:
As for CLF=1 buckling is expected, we are very near to the critical point.
FB0 was unresponsive from the network. I am trying a hard reboot of it.
In a previous entry I described the setup used to build the QPD calibration curve and the method used to take measurements.
Here I show the results of our measurements and calculate the Volts/displacement ratio and the laser's beam radius.
X axis calibration
The errorbars on the plot where estimated by looking at the fluctuations of the voltage output.
The fit in the linear region with the function
where gives us the Volts/displacement ratio.
The fit with the function:
The QPD's X output is a voltage given by:
where is a constant, while is the difference between the power on the right and left side of the QPD. Thus:
where is the total power transmitted by the beam, is the distance from the beam's center to the QPD center, is an offset and is the beam radius.
From the expression above and the fit's results we obtain:
Y axis calibration
where gives us the Volts/displacement ratio.
The expression for the QPD's Y output is analogous to the one for the X axis:
From the fit results we obtain:
The Volts/displacement ratios obtained here will be used to measure the resonant frequencies of the rhomboid motion.
Today I did the first test of the new 6" x 24" heaters from McMaster-Carr. I wired them in series, and connected the two leads directly into the TC200 temperature controller. The setup for testing them was a stack of foam, a sheet of aluminum siding, the heater, and then another piece of foam. Since there is currently no way to get temperature data directly from the TC200 controller yet, for this initial test I just took a temperature reading every 30 seconds as the setup was warming up to the set temperature.
Starting from 23.7oC, the setup took 83.5 minutes to first make it to 35oC. The time constant is the time that it takes for a system to reach 1-(1/e) (about 63.2%) of its final asymptotic value, so the time constant of this data, assuming an ideal (1 - e^(-t)) curve, was calcuated to be 25 minutes. The attached plot shows the raw data, and overplotted is an exponential temperature curve with a time constant of 25 minutes (a relatively good fit for values in the center of the range).
The section of aluminum siding used in this test is much smaller than the whole enclosure, so if this controller were used to drive these heaters on the sull-size enclosure, the time constant would be very, very long. So for bringing the whole enclosure up to temperature, a bigger power source will be needed.
Attachment 1: The setup for the heaters. My laptop + a textbook were used to weigh the foam down.
Attachment 2: The plot described above.
Calculation of the inverted pendulum spring constant
To calculate the IP spring constant I used an analytical model and Comsol.
I assumed the inverted pendulum to have the following shape:
By applying a force F on the top of the sphere (as in picture) and measuring the displacement of the IP it is possible to deduce the spring constant:
The equation of motion (without gravity) is:
Where I is the moment of inertia of the IP.
In steady-state we have:
Applying a small-angle approximation:
I modeled the IP in Comsol, calculated and deduced .
The IP is made in Steel AISI 4340.1 (density: 7850 kg/m^3) and the values I used are:
applying a force we obtain a displacement
Calculation of the inverted pendulum resonant frequency
Knowing the IP spring constant we can calculate the IP resonant frequency using the following analytical model.
The equation of motion is:
using the small-angles approximation we obtain:
And the resonant frequency is
Where moment of inertia I is:
By plotting the expression above we can see that decreases as increases, as expected. We can also see that the spherical mass on top of the inverted pendulum, , should be about 8.99 kg to reach the desired resonant frequency of 40 mHz.
This value is not realistic, but in order to reach the 40 mHz resonant frequency we can also change the bottom cylinder parameters and make k smaller.
Note: to make increase I made increase keeping the total length of the IP constant.
Today I added the two DB 25 punches into the last side panel of the seismometer enclosure. These will be used to get the electronics wires from inside the enclosure to outside.
I've ordered some thermal paste (should show up at the 40m on Wednesday) for the thermistors and 2 silicone heaters for the panels. The silicone heaters are from McMaster (picked by Megan) and should allow us to deliver ~15 W of heat to the panels if we wire them in series.
The heat capacity of Aluminum is ~0.9 J/g/K or 45000 J/K for a 50 kg chunk. With no heat loss, that means it ought to take (45e4 J)/(15 J/s) ~ 9 hours to heat up the whole thing. Which is OK for maintaining the temperature, but pretty painful from the standpoint of initial warm up.
Perhaps we ought to just use the power supply we used for the reference cavity heaters. That one is too noisy for any kind of precision measurement, but ought to let us test the time constants of the box.
Today I built a miniature thermal enclosure in order to test the temperature controller box. I found a small aluminum box and surrounded it with scrap pieces of foam.
I soldered extension wires to the leads of the thermistor and the heater, and to these extension wires I soldered small pieces of resistor wire that fit into the main output connection on the back of the controller. The heater was then adhered to the inside of the aluminum box (via its own sticker-back), and the thermistor was attached near the heater via masking tape.
I set the target temperaure to 35oC, and adjusted all the necessary parameters on the controller. The initial test was the heater inside the box, with foam only beneath the bottom of the box. In this setup, it took about about 25 minutes to equilibrate. The next test was with the box completely enclosed with foam, and held up from the desk by a glass dish. This equilibrated more quickly, reaching the specified temperature after about 15 minutes.
After the warm-up time, the temperature of the box tends to overshoots the set 35oC target, before settling down to the target temperature. I'm working on using the USB interface of the controller so that I'll be able to have plots of the temperature of the enclosure as a function of time.
Attachment 1: The cable I made, with the connections to the controller at one end, and the heater and thermistor at the other end.
Attachment 2: The first test of the control system.
Attachment 3: How the heater and the thermistor are fastened to the inside of the box.
Attachment 4: The second, more quickly equilibrating test where the aluminum box is surrounded by foam.
As described in a previous log, CMRR of the setup will determine if the suppression we have provided is adequate. But, in the last log I considered ideal PDs which are perfectly matched and the CMRR of the setup as a whole was limited by the differential amplifier used. But, in reality we can never match PDs so close to each other! This was pointed to me by Rana and Zach. Rana also suggested that we should take a look at the coherence of the output of the PDs for the unsuppressed case and estimate the CMRR of the PDs and the transimpedence amplifier through that. I am wroking out the math for this to convince myself that this measurement would indeed give us what we want.
As mentioned in a previous eLog, due the inconsistency observed, I decided to measure the Free running RIN and supressed RIN again. I present the results below. A few things are bothering me though:
1)The peak at 25kHz has been supressed! How? UGF is around 10kHz!
2) The supression is more almost 2 orders(40dB) at 100Hz. Expected supression about 30dB.
The splicing has resulted a sudden jump at 100Hz, but I think thats nothing to be worried about, as expected we get an a little more than 1 order of suppression, in the bandwidth of interest from 3Hz-10kHz. Also, I think I figured out what went wrong last time. I had the spectrum analyzer in the DC coupled mode when I was measuring the free running RIN of the laser, where as for the suppressed case I was using AC coupled mode of spectrum analyzer, I think that could possibly be the reason for the inconsistency observed in my previous measurement.
I did not note this inconsistency. I will take new measurements. I am wondering what error on my part could have caused this to happen.
something seems bogus here...the suppression at 1 Hz is much more than the open loop gain. usually this is mathematically impossible...
- The power supply was TEMMA triple power supply with dual 30V supplies and a fixed 5V supply. This was a long loan from ATF to the OMC lab.
- The 4ch color oscilloscope is a loan from the OMC lab to ATF. ATF seemed to have only one oscillocscope that is what Arjun is using.
- During the calibration, the suspension was stopped by the stoppers. Also we added a mass at the bottom so that the suspension is further stabilized by the increased pressue to the stoppers.
Yesterday afternoon Koji and I made some measurements to determine the QPD calibration curve.
We used a power supply with a potential difference of 18 Volts as input for the QPD and we looked at the X and Y outputs of the QPD using an oscilloscope. We first centered the beam on the QPD, then we moved the QPD from left to right in a 3 mm range along the horizontal axis using a micrometer, and, in this range, we took 30 measurements of the QPD X output using a digital multimeter. Then we repeated the procedure moving the QPD along the vertical axis and took 30 measurements of the QPD Y output.
I'm going to plot the measurements and to determine the Volts/displacement ratio.
Today, I implemented the intensity servo and characterised it using the voltage injection method to calculate its loop gain. I also compared it with the simulations for the same that I performed on LISO. I have attached the figures below. I also completed the circuit I made to measure the differential signal of the PDs(its just a voltage regulator setup with a AD620 with a gain of 100), but I could not characterize or take measurements using that. I will do that tomorrow.
1) RIN with and without feedback( both in-loop and out-of loop). The gain for this loop was set at 200, this was to compensate the -16.5dB loss in the remaining setup(AOM, RF function generator etc).
2) Open loop gain Transfer function- simulated and measured.
I am still stuck on how to measure the difference in the reponse of the two transimpedence amplifiers on the photodiode readout board, I have a few ideas, I am assessing their validity.
Some supplimental info on Alessandra's entry
0. Suspension stopper: In order to make the work on the suspension easier, I made simple suspension stoppers.
1. Oplev layout: We decided to put all of the input-output optics on a single triangle platform so that the optical lever angle become small. However, this was a challenge as the x-z stage for the QPD calibration is bulky... Once the calibration is done, the stage can be replaced with a pole.
2. The laser: The bare outputs of the laser diodes are too dirty for the optical lever measurement. We decided to use a fiber pigtail laser as the mode quality is excellent.We needed to setup a collimation optics. I brought a bunch of fiber coupling optics including an aspherical collimation lens with f=10mm. It was adjusted to have the focus at ~1m from the collimator. The beam radius looked like ~0.5mm. Allessandra will check this this afternoon.
3. The reflection mirror: Since the beam height on the laser platform determines the optical height at the rhomboid that is higher than the middle plate of th rhomboid, we needed to use an optical mounts on the middle plate. In fact we installed two (almost) identical mirror assemblies for counter balancing. This actually made the rhomboid unstable as the center of mass became higher than the clamping point. We decided to add a balast mass at the bottom of the rhomboid. This also work as a tilt adjuster. The balast mass was attached to the plate using a double sided tape. As a result, we recovered a stable condition (positive spring constant) of the pendulum, however, the tilting (pitching) frequency is now not precisely tuned. Maybe this is what Alessandra can work on after the QPD calibration?
Today me and Koji set up the sensors to mesure the rhomboid motion as shown in the attachments.
We are using a fiber-coupled laser and a QPD. The QPD can be calibrated: we are going to determine the calibration curve to obtain the Volts/displacement ratio.
Attachment 1:scheme of the optics used.
Attachment 2, 3: picture of the system. We put an additional mirror on the rhomboid to balance the one we needed to sense motion.
We also put a mass on the bottom surface of the rhomboid to balance it.
Today evening I implemented the intensity servo, but I couldnt characterize it properly, which would be my first task tomorrow morning. Also, I have made a small circuit consiting of AD620 to analyze the differential signal and see the amount of common mode supression that I obtain. One thing to note is that, gain of the servo will have to be increased 30 to 300, because the remainig loop(AOM, MArconi FG etc) has a flat magnitude response of ~-20dB, to compensate for that we will have to increase the gain.
Also, another thing is to consider is that, there could be some differential signal due to the fact that the the transimpedence amplifiers for the two photodiodes are not exactly identical and this could cause some additional differential signal. I am currently thinking of a method to characterize and measure that difference.
This afternoon I finished putting together three of the four sides of the thermal enclosure. I will leave the fourth side off until I use the die cut to make a hole for the 15- or 25-pin connector for all the electronics inside the enclosure. I also won't tape the corners of the base until I know that they will be staying on the frame for an extended period.
On each of the three sides, I was able to make 12 of the 14 connections. I used washers as needed; if the bolt held fine, I skipped a washer, and if the bolt started to snap the threads in the foam's paper backing, I put a washer in. There are washers on approimately half of the connections. By the last side I put on, I had made a process for getting the connections made, so it became not quite so time-consuming as when I started.
Attachment 1: The inside of the enclosure with three of the four sides attached.
Attachment 2: The enclosure with the lid on top. The lid fits very well; eventually when we attach it while the interferometer is running we can tape the seam between the lid and the rest of the enclosure.
Rana came up with the following intensity suppression servo- A simple first order bandpass filter to supress noise in the band witdth of interest from ~1Hz to 3kHz. The pole and zero are at the same frequency of 300Hz and a gain of 30 at 300Hz. Following are some simulations as to how the closed loop transfer will look. This inturn is also a test for the stability of the closed loop. Additionally, I also measured the TF of the remaining loop( ie the MArconi FG, AOM and photodiode put together) Take a look at the attached images
1) TF of remaining loop(AOM plus Function generator).
2) TF of the designed servo.
3)Magnitude and phase response of the open loop gain.
4) TF of the closed loop will require the responsivity of the photodiode, I am not aware of this value for the photdiode I am using, as soon as find that value I will attach the closed loop reponse as well.
(The sudden phase jmp is because in LISO angles go from -180 to +180 degrees.)
I was able to deduce the answers for a few questions I was working on. The factor that will limit how well we ca subtract two signals is limited by the amplifier we use and it Common Mode Reduction Ratio(CMRR). Some calculations to support my point:
Output of any amplifier is given as : , where is the differential gain and is the common mode gain. CMRR is defined as in dB.
Consider a generic differential amplifier(like AD620) it has a CMRR of 100dB() for a gain of 100. The common mode noise is at and the noise we wish to detect is at ie around the shot noise limit. Lets say the gain of this differential amplifier is 100, then that would mean that the gain associated with the common mode noise would be as CMRR is 100dB. So the final output of the amplifier would be that is the common mode would be 1% of the total output and this is not very good, by doing a intensity suppression we can improve our ability to subtract by another order or two depending on our servo design. This is the idea behind doing a intensity supression, so that at our output we have negligible common mode component, which comes from our readout amplifier which has finite CMRR.
This morning I put one of the walls of the thermal enclosure onto the frame. Pictures below:
Attachment 1: The side of the thermal enclosure attached to the frame. The second bolt down on the left side wasn't connected because the nut's spring lost its grip and slid down the track (after the bolts on either side had been tightened). I added washers to three of the four corners to relieve some stress on the foam, and will find more of that size washer so that all the connections can have one.
Attachment 2: The view down the top of one of the beams. When the bolt is tightented, the nut's springs aren't enough to hold it in place and it rotates slightly. This means that if the bolt is removed, the nut is likely to slide down the track. The connection is good, but this means that the removability of the side panels is more difficult than anticipated.
Attachment 3: The tape on the corners of the lid is coming undone! It doesn't stick well to the foam's paper backing; I will either glue this tape down or find some other tape that adheres better.
I will put two more sides of the enclosure on like this one, and leave the last one off until I am able to use the punches to make holes in the aluminum sheeting for the electronics wires to go through.
The previous eLog I had described, the way I tried to supress intensity noise is a adhoc method. So after a discussion with Rana, I realised the parameters that needed to be considered while designing the sero and it was also pointed that my filter itself was unstable, which I overlooked yesterday.
Things to keep in mind while designing the servo:-
1) Why do we need intensity a servo if finally we calculate the diffrential signal, won't it get rid of the laser noise, as its common mode? What dictates the subtraction efficiency one can have is such a subtraction?
2) What would this efficiency be in the 'ideal' and 'non-ideal' scenarios?
3) This subtraction efficiency would inturn dictate how much gain one needs for the servo.
A simple filter design with a modest gain was suggested by Rana, I am convincing myself how it will help get better subtraction efficiencies.
Yesterday I began to contruct the thermal housing for the seismometer. I cut foam panels for the four sides of the frame, the four sides of the lid, and the top of the lid. I then assembled the aluminum sheets making up the lid via hinges. I dropped the spring-loaded nuts into the McMaster-Carr posts, and began to fasten the sides of the lid, foam included, to the posts. I discovered that even though the nuts are spring-loaded, they still have a tendency to move quite a lot when you are trying to get the bolt to find them in the track. And once one pair is fastened, it closes off the whole line such that you can't see if you're putting the bolt in the right place to meet the nut. It was also more difficult than expected to have the nut pass through the foam as well as the aluminum sheeting. Nonetheless, I assembled the whole lid save the foam panel on the top face. See photos below:
Attachment 1:The top face of the lid and its four side panels, connected by hinges.
Attachment 2: Two of the sides connected to the corner posts; six bolts per face.
Attachment 3: All four of the sides secured up.
Attachment 4: The day's final product, right side up, with the corners sealed up with aluminum tape.
Attachment 5: The lid upside down, so you can see the foam sealing around the corners.
Problems & Potential Solutions
The first two sides that I brought up to the posts went fairly easily. However, I was only able to secure 8 of the planned 12 nut/bolt connections on the remaining two sides (the 8 corners of the two faces).
For assembling the rest of the housing (the non-lid part), I want to try and find a way to more securely keep the spring-loaded nuts in place. Assembly would be much easier if the nuts were more stable in the tracks. Also, I will find some washers to put between the bolts and the foam. I tested this on one connection, and it helps the bolt from breaking through the foam after many fasten/unfasten attempts. Lastly, I want to perhaps adhere the foam to the centers of the aluminum panels as well. This would serve the dual purpose of keeping the foam from bowing out from the aluminum, and keeping the holes in the foam aligned with the holes in the aluminum if (when) the side is removed from the rest of the frame.
The plot in the previous eLog was all mixed up, hence I am attaching another plot for the relative voltage noise observed in the photodiodes.I increased the number spans of measurement from 3(100Hz, 1kHz and 50kHz) to 6(100Hz,1kHz,3kHz,10kHz,25kHz and 50kHz). The plot this time is much cleaner then the jaggered one I got yesterday.
First, the relative voltage noise plots for the 2 PDs, the very noise at low frequency(~500mHz) is becuase the spectrum analyzer was set in the DC coupled mode and the Pds were biased at 1V, thats what is being seen there.
I have been thinking on the intensity noise suppression, suggestions from Zach,Rana and Gabrielle were extremely helpful in this regard. What I have in mind is a AC coupled feedback loop, AC coupled because if we have a high Gain at DC, we will have to prodive an additional stable reference to the circuit so the the DC power coming from the laser is not suppressed. Additionally, if we went with DC coupled feedback, we would have to change the reference everytime we change the power going into photodiodes and making a tuneable reference is easy. Rather we could ignore the DC drift of the laser. Our region of interest would be to know the excess noise in photodiodes beyond 10Hz and upto a 1000Hz. So we could provide very high gain in this region and supress these fluctuations in the laser. This is precisely what did today.I used the outputs of one of the PDs and amplified it using 2 SR560's and fed this back to the modulation port of Marconi FG which drove these to supress the intensity flcutuation in the other PD. The schematic is shown is shown below:-
As mentioned before, I assumed our region of interest to be 1Hz to 1000Hz and owing to the fact that its AC-coupled feedback, I used to bandpassed filter configurations in SR560's. In the first one I used a bandpass with cutoffs 0.3Hz and 1KHz with a roll-off of -6dB/octave and a gain of 20, anymore gain overloads this amplifier. This was cascaded with another SR560, with a bandpass configuration of 1Hz to 100Hz. The gain in this was incresed slowly in steps from 100 to 1000.The total gain in the region of interest being 10,000 Anymore gain and this SR560 gets overloaded. It is very importnant to keep an eye out for large fluctuations, as these immidiately overload the amplifiers, making the whole loop crazy and one has to reduce the gain first and then re-stablize it. Also the power output of the Marconi FG must be kept low as a large amplified feedback signal could harm the AOM which has a input power limit of 2W. In the end I was able to achieve around 2 orders of supression! See associated images below for the configuration that seemed to be stable for quite some time(~1hr and counting).
The final suppressed noise spectrum is presented below.
My plan next is to simulate and design this loop more efficiently, probably by adding a few boost stages. With -15V to 15V rails in opamps I should be able to give this feedback loop even more gain and maybe supress the fluctuations by another order or so. Once I simulate the circuit I can probably start putting it together, also in my cicuit I will have to give a port for adding the modultaion, this could be done using a summing amplifier.
Today, in the process of designing a intensity control servo I took some noise readings of the PDs and also characterized how the modulation function in the Marconu FG works, as it would this would be essential in the process of desigining a efficient feedback loop.
Firstly, the alignment of PDs was off, so I had to correct them, which took me more time then it should have, but I finally got it done. Next, I moved on to taking noise readings to measure the 'free running' laser noise, but as it was pointed out to me, this plot in itself is meaningless until the power at which it was taken is specified or in other words the quantity of use would be which is also called the Relative Intensity Noise(RIN). What I measured was the Voltage noise in the PDs for a fixed Bias voltage( set using the power control of the laser). I calculated them for different bias voltages and the plot is shown below, the wierd shape is because I tried to splice three dfferent spans and it did ot combine as smoothly as I expected. I took noise at 3 different spans(100Hz, 1kHz and 50kHz) and combined them using splice.m program written by Koji. The change in the voltage noise with the bias voltage can be seen very evidently . We could then use the voltage noise at 1V as a measure of RIN . Again the plot looks wierd becasue of the splice function I used, I will post a better plot when I take another set of readings, in my next log. This plot tells us approximately how much of RIN is there and how much suppression would be needed in our servo. Additionally, I also measured the dark noise but they really wierd after splicing, so I will post those as well in my next log.
The marconi RF function generator I am using has a modulation input which can be used to control the power going into the AOM which would inturn control the power in the main beam, this is my plan in implementing the intensity feedback. So, I studied the AOM and how it responds to imput modulations of different kinds, this is what I learnt:-
Today we were able to get the servo running which we described in the previous eLog. The servo locked beautifully and the instabilities other wise observed without the zero we specifically added was gone. There was small change that had to be made, the servo had the wrong sign which we very took care of. So, just for the sake of completeness, I am attaching the TF of the inverted and the non- inverted servo. Also, I am attaching the corrected schematic. I coudn't take a snap of how the lock was before and after we introduced the our servo( I will make sure its in the next log).
Addititonally, we assembled koji style beam dumps onto our setup, but the alignment was such that we couldn't place the third beam dump for the reflection coming from the bea splitter. So we may have to realign the beam splitter and then re-align the PDs as well. Its not as tedious as it sounds and we should be done with it tomorrow.
The only thing that would now remain would be to design and implement the servo for intensity suppression, what makes it ore difficult is that we need to include a very quiet reference in the circuit and we are brainstroming over it. Also, find attached a image of the actual servo we built. Also, I have attached the LISO simulation code.
#---------------Frequency tracking control servo---------------
#stage-1- non-inverting gain stage,G=30
r r1 1k n1 gnd
r r2 32.8k n1 n2
op u1 lt1128 nin n1 n2
#stage-2, Low pass filter pole=10Hz, zero=500Hz
r r4 2k n2 n3
I estimated what the inverted pendulum leg's spring constant (K) should be using some realistic/desired parameters.
Me and Kate assumed the inverted pendolum made of a cylindrical steel leg of radius 0.5 cm and lenght 0.42 m, and a point mass of 1 kg. With a resonant frequency of 40 mHz we obtain:
Yesterday I tested one of the heaters that will be used to warm the seismometer housing. I soldered wires onto the heater leads, finished with shrink tubing, and then hooked them up to a power supply. The power supply was set to the max power output that our new temperature controller can provide, which is 18W = (750 mA)(24 V). After the system equilibrated, the small frame piece we were using for the test was at 37oC. This power output was no trouble for heater, other than its adhesive paper backing starting to cook (this backing will be gone once the housing is assembled).
Clarification: the heaters are going to go inside on the aluminum sheets, not between the aluminum and the insulation on the outside. When they're on the inside, we don't have to worry about the heaters burning or melting the foam, and routing the heater wires through the side of the box becomes easier. Thanks to Rana for clearing this up for me.
Lastly, yesterday I drilled the last holes in the aluminum sheeting. These will allow hignes to connect the sides of the lid to the top face of the housing.
Attachment 1: The setup used to test the heater. The heater is the small orange strip laying on the yellow kevlar band, and the silver box on top of the heater is a small piece of the supports that make up the frame. The power supply is on the left, and the thermocouple used to check the framing's temperature is on the right. The power supply reads 25.1V and 0.81 A, and the thermocouple reads 37.1oC.
Attachment 2: Koji and I were wondering where the heater's bad smell was coming from... the paper protecting the heater's adhesive started to burn.
Attachment 3: The new holes that I drilled in the aluminum sheeting yesterday are the smaller ones in the center, that come in sets of two.
Here are the final drawings for the upper clamp.
Assem1 - Sheet1.pdfTop_Plate2.pdfclamping_plate.pdfPIn.pdf
I have attached some pictures of the PCB required to make digital measurement for the seismometer.