Pictures of the razor test apparatus before and after disassembly, to make future reassembly easier.

[Paco]

I've re-run the HR coating designs for both ETM and ITM using interpolated dispersions (presumably at room temperature). The difference is shown in Attachment #1 and Attachment #2.

Basically, all features are still present in both spectral transmission plots, which is consistent with the relatively flat dispersions from 1 to 3 um in Silica and Tantala thin films, but the index corrections of a few percent from low-temperature estimates to room-temperature measured (?) dispersions are able to push the HR transmission up by a few (2-3) times. For instance, the ETM transmission at 2128.2 nm goes up by ~ 3. The new number is still well below what we have requested for phase I so this is in principle not an issue.

A secondary change is the sensitivity (the slope around the specified wavelength) which seems to have increased for the ETM and decreased for the ITM. This was another consideration so I'm running the optimizer to try and minimize this without sacrificing too much in transmission. For this I am using the stack as a first guess in an attempt to run fast optimization. Will post results in a reply to this post.

[Paco]

Alright, I've done a re-optimization targetting a wider T band around 2128 nm. For this I modified the scalar minimization cost to evaluate the curvature term (instead of the slope) around a wide range of 10% (instead of 1%). Furthermore, in prevision of the overall effects of using the updated dispersion, I intentionally optimized for a lower T such that we intentionally overshoot.

The results are in Attachment #1 and Attachment #2.

Since I was focusing on the hot plate code and therefore did not need my weights, I decided to leave them on top of my samples for roughly 2 weeks.

It appears that an increased amount of time under pressure does not result in any noticable differences. A slight increase in surface area (SA) in two places, and a slight decrease in SA in another place, but overall no change. Note that "(initally)" in the picture below refers to http://nodus.ligo.caltech.edu:8081/Mariner/89.

Sat amp seems to be working just fine. There does seem to be a saturation issue with one of the outputs we may need to change a resistor on the board.

In the following test, a single Sat Amp chassis that holds Sat Amp Board S1106078 and S1106077

Verification of Sat Amp

First, as the test of the LED driver circuits in the chassis, 8 of various color LEDs were inserted to the appropriate output pins of the chassis. This resulted in all the LED lit and the LED mon TP was confirmed to have voltage outputs of 5V. (See my previous ELOG)

OSEM tests

Connected OSEMs to the sat amp to test the OSEM LED/PD pairs. With the first test, the PD out gave us 15V. We wondered if this was just the problem of the OSEM or circuit, or just there are too much light for the transimpedance gain of 121K Ohm.

By blocking the OSEM light by a random heat shrink tube found on the table, we saw the number got reduced. This indicates that the OSEM/Satamp outputs are working and there are just too much light.

We decided to reduce the gain: The transimpedance gain R18 was reduced to 16k, which gave us a voltage range from 5V~7V  with some outlier OSEMS at 1V (See the attached table)

There are 24 total OSEMs:

• one apparently not functional
• 20 fell in the range of 5~7V
• 3 fell in the range of  ~1V

(These numbers given after the change of R18 to 16k Ohm)

Note: We originally aimed for 8~9V. However, from a previous study of OSEM at cryogenic temperature, we learned that there was about an about 30% increase in the response.
Therefore, we decided to leave a sufficient margin from 10V considering this expected increase in the response.

[Koji, Stephen]

Kind of a silly post, and not very scientific, but we are sticking to it. During our check in today we discussed Mariner suspension frame design concept, and we chose to proceed with MOS-style (4 posts, rectangular footprint).

 - We looked at a scaled-up SOS (WIP, lots of things broke, just notice the larger side plates and base - see Attachment 1) and we were not super excited by the aspect ratio of the larger side plates - didn't look super stiff - or the mass of the base.

 - We noted that the intermediate mass will need OSEMs, and accommodating those will be easier if there is a larger footprint (as afforded by MOS).

MOS-style it is, moving forward!

Also, Checked In to PDM (see Attachment 2 - filename 40mETMsuspension_small-shields.SLDASM and filepath \llpdmpro\Voyager\mariner 40m cryo upgrade ) the current state of the Mariner suspension concept assembly (using MOS). Other than updating the test mass to the 6" configuration, I didn't do any tidying up, so I'm not perfectly satisfied with the state of the model. This at least puts the assembly in a place where anyone can access and work on it. Progress!

Firstly, last night's heating did not change the contacted surface area greatly, but there is too many factors to speculate as to why that is the case. I leave that for future testing.

I attached the thermocouples by adhering them to the two aluminum plates. I was careful to make sure that the thermocouple was in the dead center of the aluminum plate. The other end of the thermocouples—exposed positive and negative wires—were screwed into the K Type connector so they can be plugged into the thermometer/multimeter. Taking the average between the top and bottom plate will give a more precise estimate of the temperature of the samples.

Have been using the 40m Coatings repo code by Gautam (with some modifications to make dichroic designs under Ta2O5_Voyager), as well as the parameters compiled in the Mariner wiki for Silica-tantala thin films. Here are some of the top picks.

ETM

For ETM, the target transmissivities are 5.0 ppm @ 2128.2 nm and 50.0 ppm @ 1418.8 nm. After different combinations of differential evolution walkers, numbers of layers, thickness bounds, a couple of different optimization strategies, the optimum design has consistently converged with 19 - 26 layer pairs (total of 38 - 52 layers). The picks are based on the sensitivities, E_field at the boundary, and a qualitatively uniform stack (discarded "insane-looking" solutions). The top picks in Attachment 1 may be a good starting point for a manufacturer. In order of appearance, they are:

1. ETM_210218_1632
2. ETM_210222_1621
3. ETM_210302_1210
4. ETM_210302_1454

ITM

For ITM, the target transmissivities are 2000 ppm @ 2128.2 nm and 50.0 ppm @ 1418.8 nm (critically coupled cavity for AUX). The lower trans for 2128.2 nm made this easier faster to converge, although the number of thin film layers was equally centered about ~ 50 layers. Haven't explored as much in the parameter space, but the top picks in Attachment 2 are decent for approaching manufacturer. In order of appearance, they are:

1. ITM_210303_1806
2. ITM_210204_1547
3. ITM_210304_1714

Update on ETM

New optima are being found using the same basic code with some modifications, which I summarize below;

1. Updated wavelengths to be 2128.2 nm and 1418.8 nm (PSL and AUX resp.)
2. The thickness sensitivity cost "sensL" previously defined only for 2128 nm, is now incorporating AUX (1418 nm) in quadrature; so sensL = sqrt(sens(2128) ** 2 + sens(1418)**2)
3. There is now a "starfish" plot displaying the optimized vector cost. Basically, the scores are computed as the inverse of the weighted final scalar costs, meaning the better stats reach farther out in the chart. One of these scalar costs does not actually belong to the optimization (stdevL) and is just a coarse measure of the variance of the thicknesses in the stack relative to the average thickness.
4. Included a third wavelength as transOPLV (for the OPLEV laser) which tries to get R ~ 99 % at 632 nm
   1. Imagine,... a third wavelength! Now the plots for the transmissivity curves go way into the visible region. Just for fun, I'm also showing the value at 1550 nm in case anyone's interested in that.
5. Adapted the MCMC modules (doMC, and cornerPlot) to check the covariance between the transmissivities at 2128 and 1418 for a given design.
6. Reintroduced significant weights for TO noise and Brownian noise cost functions (from 1e-11 to 1e-1) because it apparently forces solutions with lower thickness variance over the stack (not definitive, need to sample more)

Still working to translate all these changes to ITM, but here are samples for some optimum.

• Attachment 1 shows the spectral reflectivity/transmissivity curves with a bunch of labels and the transparent inset showing the starfish plot. Kind of crazy still.
• Attachment 2 shows the stack. Surprisingly not as crazy (or maybe I have internalized the old "crazy" as "normal")
• Attachment 3 shows a very simple corner plot illustrating the covariance between the two main wavelengths transmissions.

I guess you have tried it already - but does enforcing the stacks to be repeating bilayer pairs of the same thickness fail miserably? When doing this for the PR3 optic @1064nm, I found that the performance of a coating in which the layers are repeating bilayers (so only 2 thicknesses + the cap and end are allowed to vary) was not that much worse than the one in which all 38 thicknesses were allowed to vary arbitrarily. Although you are aiming for T=50ppm at the second wavelength (which isn't the harmonic) which is different from the PR3 reqs. This kind of repetitive structure with fewer arbitrary thicknesses may be easier to manufacture (and the optimizer may also converge faster since the dimensionality of the space to be searched is smaller). 

Cool starfish 🌟 . What is the interpretation of the area enclosed by the vertices? Is that the (reciprocal) cost? So the better solution maximizes the area enclosed?

Yeah, the magnitudes are the inverse weighted scalar costs (so they lie on the appropriate relative scale) and indeed larger enclosed areas point to better optima. I would be careful though, because the lines connecting the scalar costs depend on the order of the vector elements (for the plot)... so I guess if I take the cost vector and shuffle the order I would get a different irregular polygon, but maybe the area is preserved regardless of the order in which the scalars are displayed...

Attached is a cartoon partial view into the heat load experienced by the Mariner assembly.

The omnigraffle file with more explicit arrow labelling in the 'layers' tab is available here. The dashed red lines along to top represent vacuum chamber radiation incident on all sides of the OS/IS, not just from the top. Off picture to the right is the BS, left is the beam tube/ETM chamber -- hence the lower absored laser power (solid line) absorbtion (PR power + no HR coating absorption). 

Parameters: 

• Emissivities are listed outside the cartoon.
• Shields consist of polished aluminum outer surfaces and high emissivity inner surfaces. 
• 1 W input power, 50 W power recycling, 30 kW cavity power
• All shields held at 77K 
• IS snout radius is equal to TM radius
• 20 ppm/cm bulk silicon absoprtion, 5 ppm coating absorption

Assumptions

• Steady state condition, where the shields are able to be cooled/held to 77K
• Holes punched into the inner shield for stops, magnets, etc are assumed to shine RT light onto 123K TM
  • This is very conservative, MOS will stablize at some temp and the OS should block ~all vacuum chamber radiation not funneled through inner shield snout

Missing or wrong

• [M] Contribution of MOS conduction and emission on the outer shield heat budget
• [M] Inner shield 
• [W] OS inner surface currently modelled as one surface seeing incident RT light, need to accomodate the view factor of each of the 5 high e sides to the open maw of the OS
• [M] Conduction through shield masses, how efficient is it to link them with straps
• [M] no AR coating absorption 
• [M/W] Cold finger cooling power from room temp shield to 77K cryocooler ('wrong' label because 61W is only the heat load once shields are cooled):
  • Worst case to reach: 1.5m connection between tank flange and shield (from flange at bottom of the tank)
    • Phosphorous deoxidized copper:  5 cm diameter
    • ETP copper:  3.5 cm diameter
  • Best case: 0.5m connection, from flange at level of OS
    • Phos deox Cu: 3 cm diameter
    • ETP Cu: 2 cm diameter
  • ​​​

Yesterday, I did two rounds of slowly heating 4 samples to the maximum hot plate temperature. This was to formally test if my success with a single sample earlier in the week was a fluke. Note that the hot plate takes about 10-15 minutes to reach a stable temperature when it is turned up one notch.

First round:
I bonded 4 samples by putting methanol in the gap between the glass slides and letting it dry to create a gap.
Starting at room temperature, I heated the slides on each setting for roughly 15 minutes, then let them cool down naturally over the course of an hour. 3 broke broke at medium heat, and 1 survived the whole process. I belive these broke because the bonds were weaker and I heated them slightly too quickly. In previous tests, I would manually switch the hot plate on and off, but I wanted to see if the hot plate could heat up slow enough on its own.

Second round:
I bonded 4 samples by scrubbing the slides with methanol, using a compressed air duster to blow off the fibers, rubbing them together with the pressure of my fingers, and repeating this whole procedure until they stuck (it took 2-4 repeats).
Starting at room temperature, I heated the slides on each setting for exactly 20 minutes, then let them cool down naturally over the course of an hour. All of them survived to the maximum temperature (the pictures show them at the start and end of the heating, note the temperature). I credit this to the stronger bonding proceedure and the extra 5 minutes for them to adjust to the temperature. I did not turn the hot plate on or off at any point, I just let it heat up at its own rate.

I cannot tell if the bonds are stronger. The size and shape of the Newtons rings did not change.

Here is a summary of the cryocooler discussion hosted at JPL. 

Dave Glaister of Ball Aerospace presented on their low-vibration cryocooler assemblies (CCAs). A summary of their work can be found in this paper. Ball has their own cryocooler vibration testing setup that they use to assess/characterize their platforms. They did not show frequency-dependent vibration noise with/without their assemblies, but they advertized up to 50x reduction in noise at 50-60 Hz. The paper above does show a spectrum of sorts (unknown units) but it does not display data below 50 Hz. Notably, they have experience in augmenting the Sunpower DS-30 cooler which meets the Mariner cooling requirements (though their CCAs should be cooler-agnostic). 

Notes from their meeting:

- Fanciest Sunpower DS-30 CCA (with all the bells+whistles): $2 million; 12-24 month lead time. Results in few mN of vibration.

- Yukon Soft Ride CCA for Sunpower DS-30 - lowest cost; in the $100,000 range if they use cheaper electronics.

          -vibration attenuation 8x

- They suggested the option of circulating gas instead of a cryocooler for our needs: helium gas lines; keep compressor outside IFO to eliminate almost all vibration.

The Yukon CCA seems to be a reasonable baseline to discuss with them. They can customize to our needs. We should ask them to provide us with vibration measurements of the DS-30 cooler with and without their Yukon CCA down to 1 Hz.

[Paco, Nina, Aidan]

We ran our stack emissivity calculation on different AR stacks to try and make a decision for the TM barrel coatings. This code has yet to be validated by cross checking against tmm as suggested by Chris. The proposed layer structures by Aidan and Nina are:

1. *| Air || SiO2 x 800 nm || Ta2O5 x 5 um || Silicon |*
2. *| Air || Ta2O5 x 10 um || Sio2 x 20 nm || Silicon |*
3. *| Air || SiO2 x 100 nm || TiO2 x 1 um || Silicon |*

Attachments # 1-3 show the emissivity curves for these simple dielectric stacks. Attachment #4 shows the extinction coefficient data used for the three different materials. The next step is to validate these results with tmm, but so far it looks like TiO2 might be a good absorbing film option.

I have to question whether this passes a sanity test. Surely in the case of Stack 2, the 10um thick Ta2O5 will absorb the majority of the incident radiation before it reaches the SiO2 layer beneath. It should at least be similar to just absorption in Ta2O5 with some Fresnel reflection from the AIr-Ta2O5 interface.

For example, at around 18um, K~2, so the amplitude attenuation factor in a 10um thick layer is 160,000x or a gain of 6E-6. So whatever is under the Ta2O5 layer should be irrelevant - there is negligible reflection.

Agree with this. Quickly running tmm on the same "stacks" gave the Attachment #1-3. (Ignore the vertical axis units... will post corrected plots) and extend the wavelength range to 100 um.

Today we looked at possible locations for where we will be setting up Mariner Suspension and Cryo chamber. The first option was the far left table in the CAML lab but it seems that there is going to be an issue with height clearance, so we have come up with another solution which takes a table from Koji's lab which is 3'x4' ft and moving it into CAML lab in the back right of the lab. To move the table we may need to call facilities to help us because we will most likely need to take the table apart to get it out of the lab. The aisle space in Koji's lab is about 43 inches, but the doorway, which is the tightest space, is 35 inches.

After we have set up the table in CAML we are planning on moving the Chamber in DOPO-lab to CAML. We plan to use skyhook with has a load limit of 500lbs/227kg this should be more than enough to move the chamber. We still need to get the wheeled base for skyhook we are in the works in doing so. 

Also, We want to remove the previous setup from the chamber and leave it at DOPO-lab. Stephen is going to figure out how to keep it clean (sort of). Besides these transportation logistics, I am also working on the electronics as an immediate task and the electrical arrangement in the chamber.

to do list
        - Check the table height
        - Check the chamber height (base/cap)
        - Check how much the chamber cap needs to be lifted (so that we can remove it)
        - Is the weight capacity sufficient?

- B246/QIL Skyhook

• Find the base of Skyhook. It should be in the storage room (B246). Stephen contacted Chub for lab access. Done
• Assemble Skyhook with the base and check the stability/safety/capacity/height/etc

- DOPO

• Ask Paco to move the delicate instruments from the table. Done
• Bring Skyhook to DOPO. The chamber seems already vented.
• Find the way to place the cap on the floor safely and cleanly. => Stephen
   
• Open the cap and then remove the crackle interferometer. Wrap it with something and place it somewhere in the room. How? => Stephen
   
• Move the base to a dolly or something. Then put a cap on the base. => It'd be better to ask Caltech Transp for the chamber transportation.
• Do we have to temporarily remove the laser safety curtain?

- OMC Lab

• We probably need to separate the optical table and the base. Ask Caltech Transp to check how the work should be done.
• Do we have to temporarily move anything on the way?
• The table can be rolled out to the corridor and then rolled in to the CAML.

- CAML

• Remove the grey rack and push the desk to the East.
• Place the optical table.
• Place the rack close to the table.

Table moving effort in the OMC lab: See https://nodus.ligo.caltech.edu:8081/OMC_Lab/412

The ETM wedge of 0.5deg will allow us to separate the AR reflections. We will be OK with the ITM wedge of 0.5deg too. 0.36 deg for ITM is also OK, but not for the ETM.

- Attachment 1 shows the deflection of the 2128mn and 1418nm beams by the test mass wedge. Here, the wedge angle of 1deg was assumed as a reference. For the other wedge angle, simply multiply the new number (in deg) to the indicated values for the displacement and angle.

- Attachment 2 shows the simplified layout of the test masses for the calculation of the wedge angle. Here the ITM and ETM are supposed to be placed at the center of the in-vacuum tables. Considering the presence of the cryo baffles, we need to isolate the pick-off beam on the BS table. There we can place a black glass (or similar) beam dump to kill the AR reflection. For the ETM trans, the propagation length will be too short for in-vacuum dumping of the AR reflection. We will need to place a beam baffle on the transmon table.

- I've assumed the cavity parameter of L=38m and RoC(ETM)=57m (This yields the Rayleigh range zR=27m). The waist radii (i.e. beam radii at the ITM) for the 2128nm and 1418nm beams are 4.3mm and 3.5mm, while the beam radii at the ETM are 7.4mm and 6.0mm, respectively,

- Attachment 3: Our requirement is that the AR reflection of the ALS (1418nm) beam can be dumped without clipping the main beam.
If we assume the wedge angle of 0.5deg, the opening of the main and AR beams will be (2.462+4.462)*0.5 = 3.46 deg. Assuming the distance from the ETM to the in-air trans baffle is 45" (=1.14m), the separation of the beams will become 69mm. The attached figure shows how big the separation is compared with the beam sizes. I declare that the separation is quite comfortable. As the main and AR beams are distributed on both sides of the optic (i.e. left and right), I suppose that the beams are not clipped by the optical window of the chamber. But this should be checked.
Note that the 6w size for the 2128nm beam is 44mm. Therefore, the first lens for the beam shrinkage needs to be 3" in dia, and even 3" 45deg BS/mirrors are to be used after some amount of beam shrinkage.

- Attachment 4 (Lower): If we assume the same ITM wedge angle of 0.5deg as the ETM, both the POX/POY and the AR beams will have a separation of ~100mm. This is about the maximum acceptable separation to place the POX/POY optics without taking too much space on the BS chamber.

- Attachment 4 (Upper): Just as a trial, the minimum ITM wedge angle of 0.36deg was checked, this gives us the PO beam ~3" separated from the main beam. This is still comfortable to deal with these multiple beams from the ITM/

The arduino was able to read temperature data and send it to a python program that graphed the data.

Now that I have (relatively) good PWM code, I wanted to do my first real test with actual samples. Since everything went smoothly, I will now work on building the original set up for the project, which included attaching thermocouples to two plates so we could precisely measure the heat between them.

As you can see in the pictures below, I am running an Arduino off of my laptop which controls an AC/DC control replay that turns the AC power to the hot plate on and off.

Note that I am just testing out different techniques, so I have not set up the thermocouples to precisely measure the temperatue.
On Tuesday, I developed a new method of putting water, isopropanol, or methanol on one slide then squishing the other slide on top of it to fill the gap with the afformentioned liquid. The slides are slippery at first, but as they dried, which took about 15 minutes, the bond forms. The bonds were strong enough that I could just barely push the slides appart by applying pressure to the side using my thumbs. I prepared 4 samples this way, 2 with iso and 2 with meth. I took one of each and heated them on Medium for 30 minutes under the brass hunk with the aluminum square on the bottom and copper foil on both sides of the samples. Earlier in the day, I tried heating them without the weight on top, but the heat just broke the bond. I took the remain two and set them aside as controls.
On Thursday, I returned to check the bonds. The heated samples had broken. I intented to check on Wednesday, but I was sick from food poisoning, so I do not know whether the bonds broke immediately after heating or due to sitting for an extra day. For the control samples, one also had a broken bond, but the other had become even stronger.
I noticed that, when the slides are successfully bonded, the shape and appearance of the Newton's rings change, which can be seen in the pictures. I speculate that the circles on the unbroken control are the bonded regions. Ideally, we want to see no Newton's rings.

I intended to test the new thermocouple set up today, but when I plugged them in, both did not read a temperature. It took me a long time to figure out what went wrong: when installing the K Type thermocouple connector, the wires of the thermocouple need to be pushed in as far in as possible, otherwise the circuit would not be completed. It took a lot of trial and error to figure this out. I first created a test "circuit" with wire and a resistor to make sure that the connector itself was not broken. Then I carefully observed how moving the wires in different places affected the reading.

Once I did carefully reassemble the thermocouples, they worked perfectly, as indicated by the non-zero current. I ran tests with my three thermocouples and two devices to see how precise the temperature reading is. The results are below and pictures of the readings can be found in the zip file. I cannot explain why one of the adhered thermocouples is hotter than the other.

Plate #1 and 2 refers to the two different aluminum plates. T1 and T2 refers to the two ports on the Digital Thermometer 343. It cannot read two thermocouples simultaneously (as far as I can tell); it's so one can be used as a baseline/reference value for the other.

I was thinking about how fast we can cool the test mass. No matter how we improve the emissivity of the test mass and the cryostat, there is a theoretical limitation. I wanted to calculate it as a reference to know how good the cooling is in an experiment.

We have a Si test mass of 300K in a blackbody cryostat with a 0K shield. How fast can we cool the test mass?

Then assume the specific heat is linear as

The actual Cp follows a nonlinear function (cf Debye model), but this is not a too bad assumption down to ~100K.

Then the differential equation can be analytically solved:

,

where the characteristic time of t0 is

.

Here T_0 is the initial temperature, cp0 is the slope of the specific heat (Cp(T_0) = c_p0 T_0). epsilon is the emissivity of the test mass, sigma is Stefan Boltzmann constant, A is the radiating surface area, and m is the mass of the test mass.

Up to the characteristic time, the cooling is slow. Then the temperature falls sqrt(t) after that.

As the surface-volume ratio m/A becomes bigger for a larger mass, in general, the cooling of the bigger mass requires more time.

For the QIL 4" mass, Mariner 150mm mass, and the Voyager 450mm mass, t0 is 3.8hr, 5.6hr, and 33.7hr respectively.

• If the emissivity is not 1, just the cooling time is expanded by that factor. (i.e. The emissivity of 0.5 takes x2 more time to cool)
• And if the shields are not cooled fast or have a finite temperature in the end, of course, the cooling will require more time.
• 1.25 t0 and 8 t0 tell us how long it takes to reach 200K and 100K.

This is the fundamental limit for radiation cooling. Thus, we have to use conductive cooling if we want to accelerate the cooling further more than this curve.

Just a general update of what I have been up to deriving Lagrange for double pendulum system and also been looking at code that koji gave to me I've add comment to some of the code also working on my report.

Almost done with coil driver boards 

Sat Amp 

- Changes to sat amp 15.8 k ohm resistors instead of 16k The change has been made on Sat Amp - S1103733 & S1103732 ONLY Channel 4 and 2 have been changed on both boards.

OSEM

- I developed a test bed for our OSEM to measure force 

I will attach images of the setup and some of the results from 3 different OSEMs.

Future Work

- For the current test bed, we are using a clear plastic bin although not ideal it manages to get the job done and works for now there could be a better solution for this,
- Next step for OSEM we want to use 40 m single pendulum to test OSEM and measure the transfer function.

Since the two devices are giving different temperature readings, I would like to find out if this imprecision is linear (e.g. they are always 3°C off, so I just need to add/subtract 3°C after taking the measurements). If not, some sort of calibration is probably required. I decided to figure this out by running the heating tests I did before, but this time with the plates. This also serves as a test to see how the plates heat up.

Or rather, this is what I would have done, had I not realized that the thermometers were going down as the heat was increaing, meaning I had switched the polarity for both thermocouples. It turns out that this mix-up is a common mistake. I thought that I double checked that red was positive for thermocouples, but it is in fact not:
"red is the usual color for positive charges, whereas the red wire in thermocouple cables typically contains the negative signal. This coloration is ANSI standard for thermocouples, but it is not what most people expect."

Update of my current work I have finished one coil driver board and started on the last two that I need here is the progress and Ideally, I'll finish by tomorrow. 

I am trying to design a cantilever setup to find the quality factor of optically bonded silicon. The cantilever will be given an impulse, and the ring down will be measured. In order to determine the Q of the bond, the relative energy contributions from each part of the cantilever must be analyzed. The primary energy contribution should come from the bond.

The below equations come from https://roymech.org/Useful_Tables/Beams/Strain_Energy.html. I believe the relevant ones are the bending and traverse shear energies.

c = distance from neutral axis to outer fibre(m)

E = Young's Modulus (N/m2)

F = Axial Force (N)

G = Modulus of Rigidity (N/m2)(m)

I = Moment of Inertia (m4)(m)

l = length (m)

M = moment (Nm)

V = Traverse Shear force Force (N)

x = distance from along beam (m)

z = distance from neutral (m)

γ = Angular strain = δ/l

δ = deflection (m)

τ = shear stress (N/m2)

τ max = Max shear stress (N/m2)

θ = Deflection (radians)

The young’s modulus (E) of silicon is 130 to 188 GPa from a quick google search. The shear modulus (G) is 50 – 80 GPa. The calculation is easier when using a rectangular beam. In that case, (U traverse) / (U bending) ~ 1.2 * V^2/(50 * bh * M^2) * (bh^3/12 * 188) = (.376 to .16) * (V^2)(h^2)/(M^2) where M depends on the distance from the applied force.

For a circular beam, height is swapped out for diameter, K is 1.11, and I = pi/64 d^4. (U traverse) / (U bending) ~ (.26 to .11) * (V^2)(d^2)/(M^2), which means (U bending) / (U traverse) ~ (3.8 to 9) * (M^2)/((V^2)(d^2)).

However, for a cantilever beam with the bond on the neutral axis, the maximum shear energy would be at the bond. For gentle nodal suspension, the maximum bending energy would be at the top and bottom.

The Arduino / AC PWM interface looks good. I recommend that you maintain the code in GitHub and post a link to the repo whenever you update the code. Use detailed commit messages so that it makes sense.

For the plotting, it would be good if you can use grid lines and markers for the data points. Then we can see the difference between the data and the fits, etc.

And to avoid the hysteresis, etc. you can record the temperature in your Arduino and use feedback to make the heater just go to whatever temperature you specify. So you would have a prescribed T(t) and the PID feedback loop would just make the heater take you there. Can your Arduino read the thermocouple?

For our optical contacting, Jennifer and I are starting out with glass (microscope slides), with the setup in the EE shop next to the drill press (photos from Jennifer to follow).

Some interesting links:

• https://www.laserfocusworld.com/optics/article/16546805/optical-fabrication-optical-contacting-grows-more-robust is a write up on contacting, and the link to Dan Shaddock's paper is also useful (need to sign up to get the acutal TSP writeup)
• Thesis on Silicon Bonding (https://escholarship.org/uc/item/5bm8g42k)
• https://youtu.be/qvBoGoh_-AE