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ID Date Author Type Category Subject
1994   Tue Aug 4 16:13:03 2015 AlessandraMiscSeismometerIP parameters

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 $k$ depends on the bottom cylinder).

I made $r_1$ and $l_1$ assume the following values:

$r_1$: (1.0; 0.9; 0.8; 0.7) mm

$l_1$: (0.03; 0.025; 0.02; 0.015) m

while changing correspondingly $l_2$ to make the total lenght of the IP (0.4123 m) constant.

Using Comsol, I determined $k$ and deduced $f_{IP}$ for each combination of $r_1$ and $l_1$

We can see that the lowest resonant frequency reached is $f_{IP} = 0.31\hspace{0.2cm} Hz$  with  $r_1=0.7\hspace{0.2 cm}mm$  and  $l_1=0.03\hspace{0.2 cm}m$.

In this case k results $k=4.69\hspace{0.2 cm} Nm$.

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 $f_{IP}=40\hspace{0.2 cm}mHz$ is reached for  $m_3=1.159\hspace{0.2 cm} Kg$. In this case we also have:

$r_3=0.0328\hspace{0.2 cm} m$

$l_2=0.3168\hspace{0.2 cm}m$

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:

$CLF=1.025$

As for CLF=1 buckling is expected, we are very near to the critical point.

1993   Tue Aug 4 10:43:21 2015 AidanComputingGeneralFB0 unresponsive. Rebooting.

FB0 was unresponsive from the network. I am trying a hard reboot of it.

1992   Fri Jul 31 15:21:19 2015 AlessandraMiscSeismometerQPD calibration

QPD calibration

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

• In the following plot the X axis QPD calibration curve is shown and a fit in the linear region is made:

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

$f(x)=ax+b$

returns:

$a=(2.34\pm{0.02})\hspace{0.2cm}V/mm$

$b=(-10.942\pm{0.004})\hspace{0.2cm}V$

where $a$ gives us the Volts/displacement ratio.

• The following plot shows the fit of the QPD calibration curve with the error function

The fit with the function:

$f(x)=a_1+b_1\cdot{erf(c_1x+d_1)}$

returns:

$a_1=(0.252\pm 0.007)\hspace{0.2cm}V\\ b_1 = (1.961\pm 0.009)\hspace{0.2cm} V\\ c_1 =(1.236\pm0.007) \hspace{0.2cm}\tfrac{1}{mm}\\ d_1 =-5.94\pm 0.04$

$%u200Ba_1=0.2517 \hspace{0.2cm}V\\ b_1 = -1.961\hspace{0.2cm} V\\ c_1 =-1.236 \hspace{0.2cm}\tfrac{1}{mm}\\ d_1 =5.939$$%u200Ba_1=0.2517 \hspace{0.2cm}V\\ b_1 = -1.961\hspace{0.2cm} V\\ c_1 =-1.236 \hspace{0.2cm}\tfrac{1}{mm}\\ d_1 =5.939$

The QPD's X output is a voltage given by:

$\Delta{V}=\alpha(P_{right}-P_{left})$

where $\alpha$ is a constant, while $P_{right}-P_{left}$ is the difference between the power on the right and left side of the QPD. Thus:

$\Delta{V}=\alpha P_{0}\cdot{erf\left(\frac{\sqrt{2}(x-x_{0})}{w_x} \right )}$

where $P_0$ is the total power transmitted by the beam, $x$ is the distance from the beam's center to the QPD center, $x_{0}$ is an offset and $w_x$ is the beam radius.

From the expression above and the fit's results we obtain:

$w_x=1.14 \hspace{0.2 cm} mm\\ x_0=4.81 \hspace{0.2cm} mm$

Y axis calibration

• Linear region fit

The fit with the function:

$f(x)=px+q$

returns

$p=(2.89 \pm 0.03)\hspace{0.2cm}V/mm$

$q=(-28.647\pm0.003)\hspace{0.2 cm} V$

where $p$ gives us the Volts/displacement ratio.

• Error function fit

The fit with the function:

$f(x)=a_2+b_2\cdot{efr(c_2x+d_2)}$

returns:

$a_2=(0.041\pm 0.007)\hspace{0.2cm}V\\ b_2 = (2.005\pm 0.008)\hspace{0.2cm} V\\ c_2 =(1.311\pm 0.008)\hspace{0.2cm}\tfrac{1}{mm}\\ d_2 =-13.02\pm 0.08$

The expression for the QPD's Y output is analogous to the one for the X axis:

$\Delta{V}=\alpha P_{0}\cdot{erf\left(\frac{\sqrt{2}(y-y_{0})}{w_y} \right )}$

From the fit results we obtain:

$w_y=1.08 \hspace{0.2 cm} mm\\ y_0=9.93 \hspace{0.2cm} mm$

• Observation: Both $w_x$ and $w_y$ are compatible with the beam spot size we observed in laboratory.

The Volts/displacement ratios obtained here will be used to measure the resonant frequencies of the rhomboid motion.

1991   Thu Jul 30 16:35:00 2015 MeganMiscSeismometerInitial test of new heaters

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.

Attachment 1: IMG_5407.jpg
Attachment 2: temp_data_theory.jpg
1990   Tue Jul 28 16:32:38 2015 AlessandraMiscSeismometerIP spring constant and resonant frequency

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:

$-k\theta +(l_1+l_2+2r_3)Fcos\theta=I\ddot{\theta}$

Where I is the moment of inertia of the IP.

$-k\theta +(l_1+l_2+2r_3)Fcos\theta=0$

Applying a small-angle approximation:

$cos\theta\simeq1 ;$

$\theta\simeq\frac{x}{l_1+l_2+2r_3}$

we obtain:

$k=\frac{(l_1+l_2+2r_3)^2F}{x}$

I modeled the IP in Comsol, calculated $x$ and deduced $k$.

The IP is made in Steel AISI 4340.1 (density: 7850 kg/m^3) and the values I used are:

$r_1=0.001 \hspace{0.2cm} m; \hspace{1 cm} l_1=0.03 \hspace{0.2cm} m$

$r_2=0.005 \hspace{0.2cm} m; \hspace{1 cm} l_2=0.32 \hspace{0.2cm} m$

$r_3=0.0312 \hspace{0.2cm} m$

applying a force $F=1\hspace{0.2cm}N$ we obtain a displacement $x=0.005493 \hspace{0.2cm}m$

and $k$ results:

$k=30.96 \hspace{0.2 cm} Nm$

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:

$-k\theta+m_1g\frac{l_1}{2}sin\theta+m_2g(l_1+\frac{l_2}{2})sin\theta+m_3g(l_1+l_2+r_3)sin\theta=I\ddot \theta$

using the small-angles approximation we obtain:

$I\ddot \theta+[k-m_1g\frac{l_1}{2}-m_2g(l_1+\frac{l_2}{2})-m_3g(l_1+l_2+r_3)]\theta=0$

And the resonant frequency is

$f_{IP}=\frac{1}{2\pi}\sqrt{\frac{k}{I}-\frac{g}{I}[m_1\frac{l_1}{2}+m_2(l_1+\frac{l_2}{2})+m_3(l_1+l_2+r_3)]}$

Where moment of inertia I is:

$I=\frac{1}{4}m_1r_1^{2}+\frac{1}{12}m_1l_1^{2}+m_1(\frac{l_1}{2})^{2}+\frac{1}{4}m_2r_2^{2}+\frac{1}{12}m_2l_2^{2}+m_2(l_1+\frac{l_2}{2})^{2}+\frac{2}{5}m_3r_3^{2}+m_3(l_1+l_2+r_3)^{2}$

By plotting the $f_{IP}$ expression above we can see that $f_{IP}$ decreases as $m_3$ increases, as expected. We can also see that the spherical mass on top of the inverted pendulum, $m_3$, 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 $m_3$ increase I made $r_3$ increase keeping the total length of the IP constant.

Attachment 1: foto_IP.jpg
1989   Mon Jul 27 16:15:24 2015 MeganMiscSeismometerDB 25 Punches

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.

Attachment 1: IMG_5402.JPG
1988   Fri Jul 24 17:59:39 2015 ranaMiscSeismometerMini thermal enclosure test

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.

1987   Fri Jul 24 15:55:05 2015 MeganMiscSeismometerMini thermal enclosure test

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.

Attachment 1: IMG_5371.JPG
Attachment 2: FullSizeRender.jpg
Attachment 3: IMG_5374.JPG
Attachment 4: IMG_5373.JPG
1986   Thu Jul 23 17:11:18 2015 ArjunMiscPD noiseCMRR of the PDs

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.

1985   Thu Jul 23 16:35:05 2015 ArjunMiscPD noisePD noise update

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.

Attachment 1: Intensity_supp.fig
Attachment 2: Intensity_supp.pdf
1984   Sat Jul 18 22:24:08 2015 ArjunMiscPD noisePD noise update

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.

 Quote: something seems bogus here...the suppression at 1 Hz is much more than the open loop gain. usually this is mathematically impossible...

1983   Fri Jul 17 18:12:36 2015 ranaMiscPD noisePD noise update

something seems bogus here...the suppression at 1 Hz is much more than the open loop gain. usually this is mathematically impossible...

1982   Fri Jul 17 11:51:46 2015 KojiMiscSeismometerQPD calibration

- 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.

1981   Fri Jul 17 11:29:57 2015 AlessandraMiscSeismometerQPD calibration

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.

Attachment 1: Calibrazione_QPD.JPG
1980   Thu Jul 16 18:28:53 2015 ArjunMiscPD noisePD noise update

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.

Attachment 1: Sim_vs_Obs_OLG.fig
Attachment 2: Sim_vs_Obs_OLG.pdf
Attachment 3: Noise_plots.fig
Attachment 4: Noise_plots.pdf
1979   Thu Jul 16 10:21:39 2015 KojiMiscSeismometerOptical lever installation (Re: Rhomboid motion)

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?

1978   Wed Jul 15 23:17:14 2015 AlessandraMiscSeismometerRhomboid motion

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.

Attachment 1: Sensors.JPG
Attachment 2: foto_.JPG
Attachment 3: foto_(1).JPG
1977   Wed Jul 15 22:14:19 2015 ArjunMiscPD noiseIntensity Servo design

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.

1976   Wed Jul 15 16:32:50 2015 MeganMiscSeismometerMore enclosure sides done

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.

Attachment 1: IMG_5184.JPG
Attachment 2: IMG_5183.JPG
1975   Wed Jul 15 15:45:04 2015 ArjunMiscPD noiseIntensity Servo design

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.)

Attachment 1: TF_intensity_servo_remain.png
Attachment 2: filter.pdf
Attachment 3: OLG.pdf
1974   Wed Jul 15 13:40:38 2015 ArjunMiscPD noiseIntensity stabilization servo

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 : $V_o=A_d(V_+-V_-)+\frac{1}{2}A_{cm}(V_++V_-)$, where $A_d$ is the differential gain and $A_{cm}$ is the common mode gain. CMRR is defined as $20\log(\frac{A_d}{A_{cm}})$ in dB.

Consider a generic differential amplifier(like AD620) it has a CMRR of 100dB($10^5$) for a gain of 100. The common mode noise is at $\sim 10^{-5}V/\sqrt{Hz}$ and the noise we wish to detect is at $\sim 10^{-8}V/\sqrt{Hz}$ 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 $10^{-3}$ as CMRR is 100dB. So the final output of the amplifier would be $\sim10^{-3}\times 10^{-5} + 100\times 10^{-8}$ 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.

1973   Wed Jul 15 11:29:11 2015 MeganMiscSeismometerThermal housing walls progress

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.

Attachment 1: IMG_5180.JPG
Attachment 2: IMG_5181.JPG
Attachment 3: IMG_5182.JPG
1972   Tue Jul 14 20:55:50 2015 ArjunMiscPD noiseSome thoughts on the intensity stabilization servo

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.

1971   Tue Jul 14 13:49:56 2015 MeganMiscSeismometerSeismometer thermal housing taking shape

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.

Attachment 1: IMG_5149.JPG
Attachment 2: IMG_5151.JPG
Attachment 3: IMG_5152.JPG
Attachment 4: IMG_5153.JPG
Attachment 5: IMG_5155.JPG
1970   Mon Jul 13 16:47:46 2015 ArjunMiscPD noiseNoise Plots

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.

## noise suppression

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.

Attachment 1: RIN.pdf
Attachment 3: IMG_20150712_154445.jpg
Attachment 4: IMG_20150712_154439.jpg
1969   Sun Jul 12 02:00:15 2015 ArjunMiscPD noisePD noise Update

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 $\frac{\delta P}{P_0}$ 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$(\frac{\delta V}{V_0}\vert_{V_0=1V})$ .  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.

## Analyzing the AOM and the Marconi FG

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:-

1. If the input modulation has no power in it ( or that its amplitude is 0) the power in the out beam is unchanged. That is zero power at modulation port corresponds to no change in the power.
2. If the Input voltage as a -ve value( which I set by using the offset function in the function generator generating the modulated signal) then, the power output of the FG decreases.
3. If the voltage is +ve, the power increases.
4. There are some other constraints one woud have to consider as well. The max power that can go into the AOM( Model:Gooch & Housego R23080-2W) is 2W( which is 33dBm). A power RF ampifier( mini circuits-ZHL-1-2W) is used to amplify the signal from the FG has a gain of 33dB, which I looked up from the data sheet, so the max power of the  FG must be around 0dBm. But just to be safe, today I just explored its features with a input of -2dBm. I have attached a few photos of me toggling the carrier on/off switch and how it modultes the transmitted power, one coud then send a modulation at a fixed frequency of say 1kHz- this would amplitude modulate the power, which is exactly what we want for our excess noise detection scheme. I have attached a image of this as well. But this whole setup of FG+AOM has to be characterised properly- which is what my next task at hand is.

Attachment 1: fig1.pdf
Attachment 2: IMG_20150711_161731.jpg
Attachment 3: IMG_20150711_161741.jpg
Attachment 4: IMG_20150711_161726.jpg
Attachment 5: IMG_20150711_204122.jpg
1968   Fri Jul 10 00:59:49 2015 ArjunMiscPD noisePD-noise update

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.

Attachment 1: cav_inv.fig
Attachment 2: cavity_servo.fil
#---------------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

... 29 more lines ...
Attachment 3: Screenshot_2015-07-10-00-41-15.png
Attachment 4: IMG_20150708_180717.jpg
Attachment 5: Screenshot_2015-07-10-00-51-01.png
Attachment 6: cavity-servo_(2).pdf
1967   Thu Jul 9 14:35:30 2015 AlessandraMiscSeismometerInverted pendolum

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:

$K\simeq {4.1 \frac{N}{m}}$

1966   Thu Jul 9 10:29:49 2015 MeganMiscSeismometerHeater test, more panel work

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.

Attachment 1: IMG_5113.JPG
Attachment 2: IMG_5114.JPG
Attachment 3: IMG_5112.JPG
1965   Thu Jul 9 09:51:49 2015 Alastair, Kate, MeganMiscSeismometerNew upper clamp

Here are the final drawings for the upper clamp.

Attachment 1: Top_Plate2.pdf
Attachment 2: clamping_plate.pdf
Attachment 3: PIn.pdf
Attachment 4: Assem1_-_Sheet1.pdf
1964   Thu Jul 9 00:37:35 2015 Kate, AlessandraElectronicsSeismometerPCB

I have attached some pictures of the PCB required to make digital measurement for the seismometer.

Attachment 1: IMG_1128.JPG
Attachment 2: IMG_1130.JPG
Attachment 3: IMG_1131.JPG
1963   Wed Jul 8 18:32:51 2015 ArjunMiscPD noisePD noise update

The DAQ system in the ATF lab has not been yet setup completely and as mentioned in the previous eLog, we decided to go ahead and build those circuits by hand, as labaorious as they were we were finally able to get a few servo designed, simulated, characterised and running. In this eLog, I describe the servos we built.

# Cavity-Locking Servo

The first servo was the cavity locking servo, as mentioned in a previous post that the SR560 used has very very low output rails(-4V to +4V) and hence can hardly keep the cavity locked in response to the laser drifting for a few minutes. We implemented this as a filter on a solder board, with rails of -15V to +15V but this wasnt enough, to hold the cavity locked for more than 10mins. We needed some very high voltages! So we put to use the piezo driver in the ATF lab.

Our initial servo was a simple one pole active RC filter with a cutoff of ~10Hz and a DC gain of 100. This worked and kept the cavity locked, but it unlocked itself after a 10mins or so. Now, when we implemented the piezo driver, we could keep the cavity locked for much much longer times(~40 mins) but it was only marginally stable and showed some features of instability. This was because the piezo driver itself has a low pass characterstic with a pole of ~8Hz and a gain of 20 and this was making the feedback loop unstable, because now we have ${\frac{1}{f^2}}$ slope after 10Hz and at around unity loop gain frequency ~300Hz the phase margin was very poor ( probably 10's of degrees) this made the loop unstable.

Solution was simple- add a zero and push up the phase margin! This was done with a zero at around 500Hz and an additional flat gain stage was put in with a gain of 30, this was to further increase the UGF and push it beyond ~3-5 Khz. This was first simulated and the built and tested.

The schematic of the setup is given below along with the components values(note: I have simply modeled the piezo driver's response as non-inverting low pass filter,this does not refer to the PZT actuator's response but just the high voltage piezo driver's response)

The following images are comparison of TF simulated on LISO and measured TF for each of the stages and the combined TF as well. But the TF with the piezo could not be taken yet, so just the LISO result is shown. Some comments on them:-

1)

The measured response is almost a perfect match for the simulated LISO response with the gain differing by 0.02dB.  So the flat gain is working as expected with a wide bandwidth of about ~20kHz.

2) The following is the TF with the second boost stage included:-

The TF is as expected. With the zero almost exactly at 500Hz.

3) The full cavity servo simulated TF:-

The features are exactly as predicted, a steep slope from the two poles and a flattening effect by the zero after 500Hz, this combined with a flat gain stage pushes the UGF to almost 7kHz, which is more than sufficient for our purpose and the phase margin has also drastically improved. Also find images of the attached circuit.

# Instensity Control Servo:

The next step was to analyze the and design the intensity servo. For this first the free running laser noise was measured this was around $\sim 10^{-4}$$Vrms/\sqrt{Hz}$, which is very bad. We wanted to reduce this common mode noise to shot noise limit, which would require almost 5 orders of supression. Also we would want to setup a stable offset as if its forced to zer we wont have any power from laser at all. We are in the process of designing this and we should be able achieve this in a few days.

Attachment 1: cavity-servo.pdf
Attachment 2: cav_TF_stage1.pdf
Attachment 3: cav_TF_stage1.pdf
Attachment 4: cav_TF_stage2.pdf
Attachment 5: cav_TF_revised.pdf
Attachment 6: cavity-servo_(1).pdf
1962   Tue Jul 7 11:48:21 2015 Alastair, Kate, MeganMiscSeismometerDrawings for upper clamp

I've attached a few initial drawings for the upper clamp parts, based on using the existing internal collet of the pin vice. Once we're happy on the design I'll tidy up the drawing layouts.PIn.pdfTop_Plate2.pdfclamping_plate.pdf

Attachment 1: PIn.pdf
Attachment 2: Top_Plate2.pdf
Attachment 3: clamping_plate.pdf
1961   Mon Jul 6 19:52:28 2015 Kate, Alastair, MeganMiscSeismometerIdeas for new pin vise clamp

Last week Alastair, Megan, and I had a brainstorming session about how to design a better pin vise clamp. Alastair's suggestion was to take the route of eliminating all of the pin vise parts except for the collet. Our approach so far was to do a lot of machinig on the pin vise handle, but the result is something that's weak, easily breaks, and not very well secured. I'm attaching a picture of the white board with some of our sketches. Alastair's taking the better ideas and making a real drawing that we can review in detail and send to the machine shop. He also suggested we can try using some guitar tuning pegs to take the weight and use the collet only for the purpose of defining the bending point.

Attachment 1: IMG_0834.JPG
1960   Mon Jul 6 17:10:54 2015 MeganMiscSeismometerHoles drilled in aluminum sheeting

Today Ignacio and I drilled the holes in the aluminum side sheeting for the seismometer housing. A 3/8 drill bit (0.375" dia.) was used for the M8 screws (0.31" dia.) in order to leave some room for error.

Attachment 1: One of the side panels held against the frame.

Attachment 2: One of the smaller side panels to be used in the lid part of the housing. These will be attached to the top panel of the housing via hinges, so they did not require any holes along the top or bottom edges.

Attachment 1: IMG_5102.JPG
Attachment 2: IMG_5103.JPG
1959   Mon Jul 6 13:27:48 2015 ranaMiscSeismometerInverted Pendulum links

1. http://dx.doi.org/10.1063/1.1149783
2. http://dx.doi.org/10.1016/j.nima.2007.08.161
3. https://en.wikipedia.org/wiki/Inverted_pendulum
1958   Mon Jul 6 08:15:53 2015 ranaMiscTempCtrltemperature noise plot

Since its hard to find, here is a plot from Frank Siefert from years ago, showing the temperature fluctuations in a metal box compared to ambient and sensor noise.

Attachment 1: tempnoise_final.pdf
1957   Wed Jul 1 17:31:16 2015 ArjunMiscPD noiseUpdates on PD noise setup

In the last few days we were able to get almost all the optics set and aligned. The following few images show the complete setup with all optics aligned and a image showing the laser beam entering the box.

The next thing to do would be to setup the photodiodes and the readout electronics. Since the digital system the lab is not up yet we decided to hardwire the required filters on the LIGO- generic filter board, becasue using SRS560's was making the space too clumsy.

Attachment 3: IMG_20150630_192049.jpg
1956   Tue Jun 30 16:24:06 2015 Megan, KateMiscSeismometerRhomboid is suspended

Today Kate and I suspended the rhomboid and made bumpers for it using some McMaster-Carr frame pieces-

Kate's finger points to the upper pin vise that had not yet been tightened, while the rhomboid's full weight is on the wires.

This is frame after the addition of bumpers. Rubber sheeting was placed along the Al beams, and corners were placed on the beams to protect the other two sides of the rhomboid.

This is the clamp setup above the two upper pin vises. The wires go between the flate plates, which are adjustable. This is where the lengths of the wires can be adjusted (carefully) so the rhomboid hangs straight.

The period of the rhomboid's oscillations was just over 23 seconds, which is about as slow as it should be. The rhomboid did not hang perfectly straight; possible factors are a weight imbalance or an unevenness of the wires due to different pin vise heights. When the left upper pin vise was tightened, the rhomboid did hang closer to straight, suggesting that the height of the pin vises does affect the balance of the rhomboid.

The rhomboid was left suspended when we left this afternoon, to see if the wires and pin vises can hold its weight for a long period of time.

1955   Tue Jun 30 15:43:49 2015 SteveMiscSeismometerpin vises

These may work better. Steel wire will degrade the chuck every time you tie it.

 Quote: We spent the afternoon preparing the rhomboid to be suspended once more. This was done once already with two wires, but we had found the wire lengths were not equal enough to work out. This time we set up a device to carefully adjust the wire lengths. This required cutting new wires and re-clamping them in the pin vises. Unfortunately, one of the upper pin vises broke (see photo). This is one of the two that we had died so that we could screw bolts onto it. It broke at a location such that the mechanism for closing the collet around the wire no longer functions. In a spirit of pushing through to try to get the rhomboid suspended anyway, we mixed up some expoxy and glued the wire into the collet and the collet into the pin vise head. We decided we would adjust the other wire to match this particular wire's length. We prepared the other wire and slowly lowered the rhomboid. Upon letting the 2 wires fully take the weight, the second wire pulled out of its bottom pin vise. The wire didn't break, but the pin vise was simply not clamping it well enough. Upon inspection, it turns out this was the pin vise that had previously been damaged. The collet teeth don't fit together perfectly anymore, and there is indeed a gap between two of them which is most likely the cause of the malfunction. We taped the free end of the wire so it's not a hazard and are leaving the setup as is for now until we get a replacement pin vise.

1954   Mon Jun 29 21:28:46 2015 KojiElectronicsGeneral2ch Photo Sensor circuit

Here the performance measurements for a 2CH reflective photo sensor circuit are presented.

Two sensor heads are driven by Nick's constant current driver. They are connected in series. Therefore the two heads need to be connected at the same time to make them work correctly.

The reflected light is detected by two photo diodes (per head) to cancel angular motion of the mirror. The photocurrent is amplified in the head and sent to the box.

It has a modulation input. One can connect a SYNC output of a signal generator to chop the LED current. The modulation freq of 3~5kHz gives the best result.
In order to use the modulation function, two internal jumpers should be removed to activate AC coupling cirucit.

The final outputs have 500Hz roll-off with 3rd order butterworth.

Attachment 1: Calibration of the photo sensor (CH1 only)

An Al mirror is placed in front of the photo sensor head1 on a sliding stage. When the sensor head is touch the mirror, the diplacement is marked zero. The sensor output depends on the distance of the sensor from the mirror. From the measured profile of the sensor, the near- and far-side calibrations were estimated to 2.6e3 V/m and 0.67e3 V/m, respectively. These numbers depends on the reflecting surface and if the modulation is used or not, as well as the modulation frequency. Therefore the calibration should be done everytime one sets the sensors up.

By disabling the current source, the dark noise level was tested. The PDs have the dark noise level of ~1pA/rtHz floor. This corresponds to the shot noise of 3uA DC current. This measurement has been done at the test points before the final roll off filters.

Attachment 3/4: DC RIN / AC RIN measurements

A head was positioned in front of the mirror with the distance where the response hit the maximum. This corresponds to the measurement of the RIN when there is no modulation. When the modulation is used, we can define a similar quantity to RIN, here we call this AC RIN. I don't see good suppression of the DC fluctuation. It might suggest that the DC amplitude of the LED current is changing this much and the ambient noise is not affecting the performance. So when an ambient noise is not an issue, DC meausrement gives us a better performance. When an ambient noise disturbs the displacement sensing, the modulation function should be used with the cost of noise floor level.

Attachment 5: Displacement noise without modulation

Finally, the displacement equvalent noise level was checked. This measurement has been done by placing Head1 in front of a fixed mirror with the distance about 1.5mm. This corresponds to the DC output of about 5V. The noise level is 0.2~0.5 nm/rtHz above 2Hz and 3/f^3 nm/rtHz below 2Hz. This noise curve actually includes the vibrational noise of the measurement setup.

Attachment 1: PS_Calib.png
Attachment 2: PS_Dark_noise.png
Attachment 3: PS_DC_OUT.png
Attachment 4: PS_AC_OUT.png
Attachment 5: PS_Disp_Noise.png
1953   Mon Jun 29 16:59:47 2015 ArjunMiscPD noisePre-stabilisation of laser

We have managed to pre stabilise the laser using a few SR560's. It is not as stable as the one that would be implemented once the digital system is in place. But it should be good enough for some preliminary data. As described in a previous log we had locked the cavity to track the laser. The PZT actuator in the cavity is driven by a SR560 which has a limited output voltage range from (-4V to +4V) and if due to slow frequency drifts the frequency of the laser drifts beyond the limit to which the PZT can compensate the cavity would unlock itself. Also, currently the intensity noise of laser has not been stabilised, this passes directly through the cavity and will appear at the transmission if its not accounted for. This feedback has been achieved using a AOM. The AOM is driven by a RF function generator and the output power of thr RF function generator can be modulated by this in turn changes the power in the carrier frequency by pushing some power into the first order diffracted beam, thereby stabilising the laser intensity fluctuation by almost 2 orders of magnitude. A brief description of the feed-back loops is given below.

## Frequency Stabilisation

The laser was frequency stabilised for its slow drifts, this could lead to SR650 controlling the cavity not being able to compesnsate for it due to its limited output range. The output of cavity stabilisation was low passed and then fed to the frequency control of the laser. But the gain had to be adjusted appropriately, as otherwise the loop could become unstable. This was done by using a simple resistive divider circuit (potentiometer) to first attenuate the control signal for the cavity stabilisation and then low passed and fed back to counter for the slow frequency drifts of the laser.The cutoff freqeucncy of the secondary feedback loop is also important, so as to ensure that at cross-over frequency nyquist stability condition is satisfied. The cutoff for this was kept at 30mHz.

## Intensity stabilisation

Intensity fluctuations from the laser will appear at the output port of the PMC because of the fact that the cavity is locking itself to laser's frequency. These have to be corrected for in the final setup and this has been achieved using an AOM. A AOM splits power in the beam into a diffracted beam and this splitting of power depends on the power that is injected into the AOM and also the direction in whihc the AOM is oriented. When no power is injected in the AOM the carrier beam passes through unaffected and when some non-zero power is injected a part of power goes into another diffracted beam. The AOM we use has a maximum power input of 2W at 80MHz. For  achieving the required functionality, a RF signal from a RF signal generator is amplified using a high power RF amplifier and this drives the AOM. Now to stabilise the intensity fluctuations going into the PMC we can setup a positive feedback by sensing the power at thePMC's output and using that to modulate the signal generated by RF signal generator thereby modulating the power with which the AOM is driven and finally controlling the way power is split between the two output rays. Hence this way the power entering the PMC has been stabilised. In the actual setup this feedback will be provided by the common mode output of the two photodiodes being tested.The entire pre-stabilisation of laser implemented is shown in the schematic below.

The total stabilisation schematic is shown below-this includes the locking of the cavity, feedback to supress the laser frequency drift and supression of intensity fluctuations.

We were also able to get some more optics fixed, since the table will also be used for another experiment, we divided the beam using a halfwave plate and a polarising beam splitter to control the power going into each of the experiments. A image of the setup assembled is attached below, the read trace is the path of the laser.

Attachment 1: Screenshot_2015-06-29-16-20-55.png
Attachment 6: 20150626_202413.jpg
1952   Mon Jun 29 11:13:21 2015 MeganMiscSeismometerTime constant for heating the seismometer frame

To determine the time constant of the system, a model of the heat flows through the system was made, starting with the basic ΔQ=mcΔT.

$dQ = mc\cdot dT$

$\frac{dQ}{dt}=P=mc\frac{dT}{dt}$

$T(t)=\frac{1}{mc}\int P dt$

Where the value $P$ is the net power flowing through the system, or Pin-Pout. Pin is the power supplied by the heaters, and Pout is the power lost radiatively through the insulation. Pin is a known value, while Pout can be calculated via the K-factor, the thickness of the insulation, the area of a side, and the temperature difference between the two sides. Taking all this into account, the differential equation becomes:

$T_{Al}(t)=\frac{1}{mc}\Big[P_{in}t-\int_{0}^{t}P_{out}dt\Big]$

$T_{Al}(t)=\frac{1}{mc}\Big[P_{in}t-\int_{0}^{t}KA_{side}d_{insul}(T_{Al}(t)-T_{lab})dt\Big]$

This is just a differential equation where the temperatue of the frame (Tal(t)) is related to the integral of itself. The equation can be rearranged such that the temperature is related to the derivative of the temperature (as differential equations typically are).

$T'_{Al}(t)=A-BT_{Al}(t)$

where A and B are defined as follows: A=(1/mc)(Pin-KAsidedinsulTlab), and B=(KAsidedinsul)/(mc). Solving the differential equation via Mathematica yields:

$T_{Al}(t)=\frac{A}{B}+C_1e^{-Bt}$

Therefore the time constant tau is just the reciprocal of B:

$\tau = \frac{1}{B}=\frac{mc}{KA_{side}d_{insul}}$

The units of tau do work out to be time, given that the units of K are taken to be [E]/[A]/[T]/[t]/[d]. Plugging in numbers to get an estimation of the order of magnitude gives:

$\tau=\frac{(10kg)(0.9\frac{J}{g\cdot K})(1000\frac{g}{kg})}{(58.121\frac{J}{K\cdot s\cdot m^2\cdot m})(0.75m^2)(0.0254m)}\approx\boxed{2.25\text{ hours}}$

This value is an estimation so far; within the next couple days I will go measure the frame and get more accurate values. I will also recheck the calculation, because I think that the time constant should have some dependence on the power input to the system.

1951   Fri Jun 26 18:02:17 2015 Kate, Alastair, MeganMiscSeismometerSuspension attempt

We spent the afternoon preparing the rhomboid to be suspended once more. This was done once already with two wires, but we had found the wire lengths were not equal enough to work out. This time we set up a device to carefully adjust the wire lengths. This required cutting new wires and re-clamping them in the pin vises. Unfortunately, one of the upper pin vises broke (see photo). This is one of the two that we had died so that we could screw bolts onto it. It broke at a location such that the mechanism for closing the collet around the wire no longer functions. In a spirit of pushing through to try to get the rhomboid suspended anyway, we mixed up some expoxy and glued the wire into the collet and the collet into the pin vise head. We decided we would adjust the other wire to match this particular wire's length. We prepared the other wire and slowly lowered the rhomboid. Upon letting the 2 wires fully take the weight, the second wire pulled out of its bottom pin vise. The wire didn't break, but the pin vise was simply not clamping it well enough. Upon inspection, it turns out this was the pin vise that had previously been damaged. The collet teeth don't fit together perfectly anymore, and there is indeed a gap between two of them which is most likely the cause of the malfunction. We taped the free end of the wire so it's not a hazard and are leaving the setup as is for now until we get a replacement pin vise.

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1950   Fri Jun 26 17:32:16 2015 KateMiscSeismometerMore on the seismometer frame

Could you elaborate on the plan for how the aluminum fits around the top? We'll need the entire frame, including the top bar, enclosed.

 Quote: Yesterday afternoon I finished building the seismometer frame by adding the cross bar across the top face. Picture below is the frame as of yesterday afternoon (25 June): This morning Ignacio and I went with Steve to the machine shop and cut the aluminum siding panels to the correct size. Sheets were cut for the top and bottom faces as well; the sheet for the top will be modified to fit around the cross bar. Picture below is one of the aluminum sheets next to the frame: The next steps will be measuring where thru holes can be drilled for the M8 attachment screws, and testing the die cuts (to punch holes for electronics wires) on scrap aluminum.

1949   Fri Jun 26 13:41:28 2015 MeganMiscSeismometerMore on the seismometer frame

Yesterday afternoon I finished building the seismometer frame by adding the cross bar across the top face. Picture below is the frame as of yesterday afternoon (25 June):

This morning Ignacio and I went with Steve to the machine shop and cut the aluminum siding panels to the correct size. Sheets were cut for the top and bottom faces as well; the sheet for the top will be modified to fit around the cross bar. Picture below is one of the aluminum sheets next to the frame:

The next steps will be measuring where thru holes can be drilled for the M8 attachment screws, and testing the die cuts (to punch holes for electronics wires) on scrap aluminum.

1948   Fri Jun 26 11:19:24 2015 MeganMiscSeismometerThermal Calculations for Seismometer Housing

Below are calculations to determine the power needed to heat the seismometer, then to keep it at a steady-state temperature.

Heating the Frame and Siding

To bring the frame and the aluminum sides of the seismometer from the assumed room temperature (25oC) up to operating temperature (35oC), the heaters must supply the amount of energy that it takes to bring that mass of aluminum up by 10oC. This amount of energy can be calculated quite simply with the equation:

$Q_{total}=\big(m_{frame}c_{frame}+m_{siding}c_{siding}\big)\Delta T$

where $m$ is the mass of each of the separate components, and $c$ is the specific heat of each of the aluminum alloys used. Assuming that the 10oC temperature difference is what we'll always use for this frame, the value $Q_{total}$ is a constant. Once I measure the mass of the frame and the siding and find the specific heat values for the alloys, it can be calculated. When the interior components of the seismometer are added, their mass and materials must be included in this calculation as well.

How quickly this amount of energy can be delivered into the system is controlled by the heaters. Once the specific energy value is known and a desired heating-up time is decided on, it is a simple calculation to determine how much power the heaters need to supply:

$P_{heaters}=\frac{Q_{total}}{t_{warm-up}}$

My to-do now: measure the mass of the aluminum sheets and frame (or calculate it via given densities/volumes), and calculate the needed energy. Also, a warming time needs to be decided on.

Once the frame and aluminum panels have been brought up to temperature, a certain amount of heating is needed to maintain the 10oC temperature gradient across the foam insulation. McMaster Carr gives the K-factor (thermal conductivity) of the foam as 0.26, no units provided. Because McMaster Carr uses mostly imperial units, and the units of the K-factor are typically imperial, I assumed units of BTU/ft2/oF/hr/in, or energy transferred per sqaure foot, per unit degree difference between the two sides, per hour, per inch thinckness. The area of each foam panel, the temperature difference in oF, and the thickness of the foam are all known, so for the given K-factor a specific energy transfer rate can be calculated:

$0.26\frac{BTU}{ft^2\cdot F^{\circ}\cdot hr\cdot in}(1 in)(18^{\circ}F)(6.875ft^2)=32.175\frac{BTU}{hr}=9.429W$

$0.26\frac{BTU}{ft^2\cdot F^{\circ}\cdot hr\cdot in}(1 in)(18^{\circ}F)(5.252ft^2)=32.175\frac{BTU}{hr}=7.203W$

where the top line is for the vertical sides of the frame, and the bottom line is for the top and bottom faces of the frame. After the heaters (assuming one per face of the frame) have brought the seismometer up to temperature, they must supply at least these amounts of power to keep the temperature gradient in place. This amount is well within the 200W limit of the heaters being used.

1947   Thu Jun 25 18:31:11 2015 ArjunMiscPD noiseResistor noise measurements using the cross correlation method

I have taken a few sets of measurements using the cross correlation method which I have described in log 1942. In this log I briefly describe my circuit and the results I obtained.

## Circuit:

The image below is a snap of my circuit. The circuit is very simple- It has two regulators(7812 and 7912) for +ve and -ve voltage regulation respectively. The instrumentation amplifier used is the standard AD620 with a gain of 100 which corresponds to a gain resistance of $499\Omega$. I soldered two identical sets of amplifiers, the voltage regulator circuit and a then mounted my 0.05% resistor bridge setup onto it using berg connectors. I took extra care of ensuring small details like- proper soldering, using twisted pair of cables and using small wires for all connections.

I then excited the bridge which consists of $1.5k\Omega$ Metal Film Resistors using the lock-in sine output of peak amplitude 5V. The two output time series were directly fed to the DAQ and stored for analysis. The following analysis is on a 2 hour long time series. Since the total accuracy of the method increases with total measurement time(either by ensemble averging or by recording data for extending periods of time). The following plot is of the spectrum obtained at the two amplifier output

As seen above the amplifiers produce almost identical especially at the drive frequency of 1 kHz suggesting that the amplifiers are behaving identically. We then demodulate this signal on MATLAB using the function amdemod with a sine of 1000 Hz.This fuction comes with a lowpass butterworth filter ,making it very convinient for demodulating signals on MATLAB. The resultant spectrum after demodulation for one of the amplifier is shown below.

The output time series was decimated first( so as to get higher resolution at lower frequencies) and then the cross correlated spectrum was calculated, it was curve fit with a straight line. The corresponding results are shown below:

The numbers in the brackets are the 95% confidence bonds on the slope.

## Conclusions:

The above plots still estimate the slope of excess noise spectrum closer to -2 than to -1. Previous estimates are in good agreement with this observation. But, the thing that is bothering me is the reason for this deviation from a $-10dB/decade$ roll off to a $-20dB/decade$ for the amplitude power spectrum which is disagreement with previous studies on this topic. My fear partly is that the error in I am making in the resistor measurements should not carry onto the PD noise setup leading to incorrect results there as well. As stated in a previous log, my suspicion boils down to two places, because, they are only parts I have not played around with. First being a different amplifier, AD620 is the standard instrumentation amplifier and should be the last place to suspect a flaw but it is possible that maybe( however the remote the chance maybe) their could be something wierd in AD620 making it suitable for such noise measurement applications especially when using the heterodyne demodulation technique. It would be interesting to see the results by replacing different amplifiers in place of AD620. Secondly, improper shielding/ external influence. This is more likely I suppose as my shielding attempts were non-exsistent some external source could be causing this deviation. Or another third possible place equally likely could be a flaw in my analysis or my scheme, even though I have done my best to implement the techniques from various sources, as accurately as possible, it is very likely that I may be negligent to some error I am commiting. Any suggestions on the possible sources of error are most welcome.

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1946   Thu Jun 25 15:36:54 2015 ArjunMiscPD noiseUpdates on PD noise setup

Over the past few days we have dismantled the laser gyro setup and started setting up the PD noise measurement setup. We have succesfully mode matched our laser to the cavity and then locked the cavity to our laser by using a 'Homebrew' circuit for implementing the a loose realisation based on the PHD technique.  A brief description is presented on how the mode matching was done and also the circuit which we used to lock the cavity to our laser.

## Mode-Matching the Laser to the Cavity:

We used a combination of 2 lenses and two mirrors to mode match the laser and the cavity. The mirrors were used to steer the beam and get rid of alignment mismatch and the positions of lenses was adjsuted to compensate for curvature mismatch.

1) We first placed the lenses and mirrors at approximately at positions where Zach had them for his gryo setup and used a CCD camera to see the shape of the output mode and that verify that we had locked to correct mode, and tried aligning the beam better using the mirrors to see the best we could do. If the best match we achieved was less than 80%(roughly) then we moved on to aligning the lenses.

2) We iterated the process of finding the maximum transmission by first adjusting the lenses and then adjusting the two mirrors, then finding the maximum mode matching we could achieve. We used a Thor Labs PD to study the output transimission, in conjugation with a CCD camera.

3) One could also study the reflected beam and minimise that to its lowest. After iterating for couple of hours we were finally able to mode match the cavity to the laser with transmission of ~85%.

## Mode-Locking the cavity to laser:

For locking the cavity to the laser we used a 'Homebrewed' locking circut loosely based on the PDH technique, but we have not modulated the laser's phase(this will be our next task- stabilising the laser intensity fluctuations by using a AOM). A dither of 1MHz and amplitude 24dBm was given using a DS345 function generator. This was passed through a power splitter, with half the power going to the RF input of the bias tee and the other half to the LO input of the demodulating mixer after passing it through a 7dB attenuator, this attenuator is necessary as the input power of the mini circuits mixture must have a specific amplitude. The output of the power meter was passed through a DC blocking cicuit as the RF input for the mixer. The IF output of the mixer is then connected to the SRS560-low noise preamplifier. The SRS560 has a programmable input filter which was set to a one pole(roll off of -6dB/octave) low pass filter with a cutoff frequency of 10Hz. This filtered signal was then amplified by a gain of 5000 and this output was the DC input to the Bias Tee. A simple schematic of circuit we used is shown below:

A more detailed schematic is given below with the exact components which  were used:

The image below is a picture of our optical setup and the red line through the image is the laser path.

The following is a image of the output as the amplifer(SRS560) is turned on and the the output of the PMC gets locked. The two traces are the amplifed error signal and the output of the PMC, as seen on a oscillosope:

PS: Also find attached a image of the settings on the DS345 and SRS560.

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1945   Thu Jun 25 15:22:19 2015 KateMiscSeismometerMore thermal enclosure parts purchased

I ordered the remaining foam we'll need to surround the frame, as well as the screws and fasteners we'll use to secure the foam + aluminum panels in place.

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