The first entry of the Mariner elog post

Ongoing points of updates/content (list to be maintained and added)
Mariner Chat Channel
Mariner Git Repository
Mariner 40m Timeline [2020-2021] Google Spreadsheet
 

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
  • ​​​

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

6" vs 4" optic size comparison using CAD - worth hopping into the 3D geometry using the link below, but also posting a couple of images below.

1) We can adjust all parameters relating to the suspension frame except the beam height. Is there enough clearance under the optic for the internal shield?

--> Using the representation of the MOS structure as-is, there is about 1" of clearance between the bottom panel of the first/internal shield under the 6" case, compared with 2" of clearance in the 4" case. This is not very scary, and suggests that we could use a 6" optic size.

2) Any other concerns at this point?

--> Not really, there are degrees of freedom to absorb other issues that arise from the simple 4" --> 6" parameter shift

EASM posted at https://caltech.app.box.com/folder/132918404089

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?

Update on ETM/ITM coating design;

- Following what seemed like a good, intuitive suggestion from Anchal, I implemented a parameter called Ncopies, which takes a stack of m-bilayers and copies it a few times. The idea here was to have stacks where m is the least common multiple of the wavelength fractional relation e.g. m(2/3) = 6 so as to regain some of the coherent scattering in a stack. Unfortunately, this didn't work as planned for m=6, 3, and 2.

- While the target transmissivities are reached with comparably fewer layers using this method, the sensitivity and the surface E field are affected and become suboptimal. The good thing is we can do the old way just by setting Ncopies = 0 in the optimization parameters yaml file.

- An example of such a coating is in Attachment 1.

- I decided to just add the 'varL' scalar cost to the optimizer. Now we minimize for the variance in the coating stack thicknesses. As a target I started with 40% but will play with this now.

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...

Differential evolution strategies 'benchmarking' for thin film optimization

Since I have been running the ETM/ITM coatings optimization many times, I decided to "benchmark" (really just visualize) the optimizer trajectories under different strategies offered by the scipy.optimize implementation of differential evolution. This was done by adding a callback function to keep track the convergence=val at every iteration. From the scipy.optimize.differential_evolution docs, this "val represents the fractional value of the population convergence".

Attachment 1 shows a modest collection of ~16 convergence trajectories for ETM and ITM as a function of the iteration number (limited by maxiter=2000) with the same targets, weights, number of walkers (=25), and other optimization parameters. The vertical axis plots the inverse val (so tending to small numbers represent convergence).

tl;dr: Put simply, the strategies using "binary" crossover schemes work better (i.e. faster) than "exponential" ones. Will keep choosing "best1bin" for this problem.

MCT HgCdTe requirements: https://docs.google.com/spreadsheets/d/1lajp17yusbkacHEMSobChKepiqKYesHWIJ6L7fgr-yY/edit?usp=sharing

Rana’s code: R_c = 57.3

-->New code with optimization: sweeping through a range of R_c, using a cost function that puts value on peak height, distance of the peaks from the zero order, and mode number. This cost function can be edited further to adapt to more aims (Slides attached).  Currently (code attached) gives --> R_c = 58.4 with very slightly different peaks and  energy distribution in the modes

1) Range of R_c is 57 to 60, for some reason lower values of R_c in the range are giving error --> debug this 

2) Find how sensitive the model is for 1% change in R_c value

3) Make sure the side bands are not resonating

Koji, Stephen

Putting together Koji's design work with Stephen's CAD, we consider the size of a test chamber for the Mariner suspension.

Koji's design uses a 6" x 6" Si optic, with an overall height of about 21.5".

Stephen's offsets suggest a true shield footprint of 14" x 14" with an overall height of 24".

With generous clearances on all sides, a test chamber with a rectangular footprint internally of about 38" x 32" with an internal height of 34" would be suitable. This scale seems similar to the Thomas Vacuum Chamber in Downs, and suggests feasibility. It will be interesting to kick off conversations with a fabricator to get a sense for this.

This exercise generated a few questions worth considering; feel welcome to add to this list!

• do we need to have the suspended snout(s)?
• are we studying an ITM or ETM (or both)?
• relays or other optical components on the baseplate?
• angles of optical levers?
• off center mounting?
• two doors for front/back access?

Here are the final slides with all the results on the Arm Cavity Design, please review. 

For RoC of 56.2 +/- 1% things are working well. Tolerance of 0.5% will be better however, 1% is still working; as long as we do not want any peaks ~50kHz away.

For length, 38+0.5% = 38.19 (with RoC 56.2) not ideal, peak is close (48.8kHz) but maybe ok? @Rana thoughts? and 38-0.5% = 37.81 (with RoC 56.2) works well.

To summarise the design:

RoC = 56.2 +/- 1%

L = 38 +/- 0.5%

The HR coating specifications are:

ETM Transmission specs

2128.2 nm	5.0 ppm 2 ppm
1418.8 nm	50.0 ppm 2 ppm

ITM Transmission specs

2128.2 nm	2000.0 ppm 200 ppm
1418.8 nm	50.0 ppm 2 ppm

Analysis

• Main constraint: Relative arm finesses @ 2128.2 nm should not differ by > 1%.
• Secondary constraint: Relative arm finesses @ 1418.8 nm may differ, but the ETM and ITM pair should ensure critically coupled cavity to benefit ALS calibration PD shot noise.

Just took the finesse of a single arm:

and propagated transmissivities as uncorrelated variables to estimate the maximum relative finesse. Different tolerance combinations give the same finesse tolerance, so multiple solutions are possible. I simply chose to distribute the relative tolerance in T for the test masses homogeneously to simultaneously maximize the individual tolerances and minimize the joint tolerance.

A code snippet with the numerical analysis may be found here.

Tue Jun 8 11:52:44 2021 Update

The arm cavity finesse at 2128 nm will be mostly limited by the T = 2000 ppm of the ITM, so the finesse changes mostly due to this specification. Assuming that the vendor will be able to do the two ETM optics in one run (x and y), we really don't care so much about the mean value achieved in this run as much as the relative one. Therefore, the 200 ppm tolerance (10% level) is allowed at the absolute level, but a 20 ppm tolerance (1% level) is still preferred at the relative level; is this achievable?. Furthermore, for the AUX wavelength, we mostly care about achieving critical coupling but there is no requirement between the arms. Here a 20 ppm tolerance at the absolute level should be ok, but a 2 ppm tolerance between runs is highly desirable (although it seems crazier); is this achievable?

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/

[Stephen, Koji]

WIP - check layout of 60 cm suspension in chamber at 40m, will report here

WIP - also communicate the

WIP - Stephen to check on new suspension dimensions and fit into 40m chamber

Here is a set of curves describing the single-pass downconversion efficiency in the 20 mm long PPKTP crystals for the DOPO. I used the "non-depleted pump approximation" and assumed a plane-wave (although the intensity matches the peak intensity from a gaussian beam). Note that these assumptions will in general tend to overestimate the conversion efficiency.

The parameters use an effective nonlinear coefficient "d_eff" of 4.5 pm/V, and assume we have reached the perfect (quasi) phase matching condition where delta_k = 0 (e.g. we are at the correct crystal operating temperature). The wavelengths are 1064.1 nm for the pump, and 2128.2 nm for degenerate signal and idler. The conversion efficiency here is for the signal photon (which is indistinguishable from the idler, so am I off by a factor of 2?)...

Attachment 1 shows the single pass conversion efficiency "eta" as a function of the pump power. This is done for a set of 5 minimum waists, but the current DOPO waist is ~ 35 um, right in the middle of the explored range. What we see from this overestimates is an almost linear-in-pump power increase of order a few %. I have included vertical lines denoting the damage threshold points, assuming 500 kW / cm ^2 for 1064.1 nm (similar to our free-space EOMs). As the waist increases, the conversion efficiency tends to increase more slowly with power, but enables a higher damage threshold, as expected.

At any rate, the single-pass downconversion efficiency is (over)estimated to be < 5 % for our current DOPO waist right before the damage threshold of ~ 10 Watts, so I don't think we will be able to use the amplified pump (~ 20-40 W) unless we modify the cavity design to allow for larger waist modes.

The important figure (after today's group meeting) would be a single pass downconversion efficiency of ~ 0.5 % / Watt of pump power at our current waist of 35 um (i.e. the slope of the curves below)

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.

As a kickoff of the mariner sus cryostat design, I made a tentative crackle chamber model in SW.

Stephen pointed out that the mass for each part is ~100kg and will likely be ~150kg with the flanges. We believe this is with in the capacity of the yellow Skyhook crane as long as we can find its wheeled base.

I'm posting a summary of the work I've done on the Lagrangian analysis of the Mariner suspension design and a state space model of the actuator control loop. The whole feedback mechanism can be understood with reference to the block diagram in attachment 1.

The dynamics of the suspension are contained within the Plant block. To obtain these, I derived the system Lagrangian, solved the Euler-Lagrange equations for each generalised coordinate and solved the set of simultaneous equations to get the transfer functions from each input parameter to each generalised coordinate. From these, I can obtain the transfer functions from each input to each observable output. In this case, I inserted horizontal ground motion at the pivot point (top of suspension) and a generic horizontal force applied to at the intermediate mass. These two drives become the two inputs to the Plant block. The two observables are x_i - the position of the intermediate mass, which is sensed and fed to the actuator servo, and x_t - the test mass position that we are most interested in. I obtained the transfer functions from each input to each output using a symbolic solver in Python and then constructed a MIMO state space representation of these transfer functions in MATLAB. For this initial investigation, I've modelled the suspension in the Lagrangian as a lossless point-mass double pendulum with two degrees of freedom - the angle to the horizontal of the first mass and the angle to the horizontal of the second mass. The transfer functions are very similar to the more advanced treatment with elastic restoring forces and moments of inertia and the system can always be expanded in a later analysis.

For the sensor block I assumed a very simple model given by

where G_s is the conversion factor from the physical distance in metres to the electronic signal (in, for example, volts or ADC counts) and n_s is the added sensor noise. A more general sensor model can easily be added at a later date to account for, say, a diminishing sensor response over different frequency ranges.

The actuator block converts the measured displacement of the intermediate mass into an actuation force, with some added actuator noise. The servo transfer function can be tuned to whatever filter we find works best but for now I've made two quite basic suggestions: a simple servo that actuates on the velocity of the intermediate mass, given by

and an 'improved' servo, which includes a roll-off after the resonances, given by

where p is the pole frequency at which we want the roll-off to occur. Attachment 2 shows the two servo transfer functions for comparison.

The state space models can then be connected to close the loop and create a single state space model for the transfer functions of the ground and each noise source to the horizontal test mass displacement. Attachment 3 contains the transfer functions from x_g to x_t and shows the effect of closing the loop with the two servo choices compared to the transfer function through just the Plant alone. We can see that the closed loop system does damp away the resonances as we want for both servo choices. The basic servo, howerver, loses us a factor of 1/f^2 in suppression at high frequencies, as it approximates the effect of viscous damping. The improved servo gives us the damping but also recovers the original suppression at high frequencies due to the roll-off. I can now provide the ground and noise spectra and propagate them through to work out the fluctuations of the test mass position.

[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!

[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.

I've implemented a more extensive feedback model that uses proper conversions between metres, volts, counts etc. and includes all the (inverse) (de)whitening filters, driver, servo and noise injections in the correct places. I then closed the loop to obtain the transfer function from horizontal ground motion and each noise source to test mass displacement. I tuned the servo gain to reduce the Q of both resonances to ~20.

Our idea was then to compensate servo gain with the output resistance of the coil driver to raise the RMS of the DAC output signal in order to raise SNR and thus suppress DAC noise coupling. I found that raising the output resistor by a factor of 10 above the nominal suggestion 2.4 kOhm gave me a DAC output RMS of 0.3 V, so in line with our safety factor of 10 requirements. This also coincidentally made all the noise sources intersect at approximately the same frequency when these noises begin to dominate over the seismic noise. All these initial tests are subject to change, particularly depending on the design of the servo transfer function. I'm attaching the relevant plots as well as the MATLAB script I used and the two files required for the script to run.

Here's the DAC voltage spectrum with its associated RMS.

Also, for clarity, this model is for a lossless point-mass double pendulum system with equal masses and equal lengths of 20 cm.

[Paco, Nina]

We have been working on an estimate of the wavelength dependent emissivity for the mariner test mass HR coatings. Here is a brief summary.

We first tried extending the thin film optimization code to include extinction coefficient (so using the complex index of refraction rather than the real part only). We used cubic interpolations of the silica and tantala thin film dispersions found here for wavelengths in the 1 to 100 um range. This allowed us to recompute the field amplitude reflectivity and transmissivity over a broader range. Then, we used the imaginary part of the index of refraction and the thin film thicknesses to estimate the absorbed fraction of power from the interface. The power loss for a given layer is exponential in the product of the thickness and the extinction coefficient (see eq 2.6.16 here) . Then, the total absorption is the product of all the individual layer losses times the transmitted field at the interface. This is true when energy conservation distributes power among absorption (=emission), reflection, and transmission:

The resulting emissivity estimate using this reasoning is plotted as an example in Attachment #1 for the ETM design from April. Two things to note from this; (1) the emissivity is vanishignly small around 1419 and 2128 nm, as most of the power is reflected which kind of makes sense, and (2) the emissivity doesn't quite follow the major absorption features in the thin film interpolated data at lower wavelengths (see Attachment #2), which is dominated by Tantala... which is not naively expected?

Maybe not the best proxy for emissivity? Code used to generate this estimates is hosted here.

We had a meeting with the code open in ZOOM. Here are some points we discussed:

• The code requires another file ground.m. It is attached here.
   
• The phase of the bode plots were not wrapped. This can be fixed by applying the "PhaseWrapping" options as
  opts=bodeoptions('cstprefs');
opts.PhaseWrapping = 'on';
bode(A,opts)
   
• We evaluated the open-loop transfer function of the system. For this purpose, we added the monitor point ('F') at the actuator and cut the loop there like:
  sys = connect(P, S, W, ADC, Winv, A2, DWinv, Dinv, DAC, DW, D, R, C, {'xg' 'nADC', 'nDAC', 'nd', 'nth'}, 'xt', {'F','VDAC'});
OLTF=getLoopTransfer(sys(1),'F');
figure(2)
clf
bode(OLTF,opts);
   
• We played with the loopgain (Ga2). When Ga2 is a positive number, the loop was stable. We had to shift the low pass cut-off frequency from 10Hz to 12Hz to make the damping of the 2nd peak stable.

*Note: the current modeling script can be found at: CryoEngineering/MarinerCooldownEstimation.ipynb

Nina pointed me to the current mariner cooldown estimation script (path above) and we have since met a few times to discuss upgrades/changes. Nina's hand calculations were mostly consistent with the existing model, so minimal changes were necessary. The material properties and geometric parameters of the TM and snout were updated to the values recently verified by Nina. To summarize, the model considers the following heat sources onto the testmass (P_in):

- laser absorption by ITM bulk (function of incident laser power, PR gain, and bulk absorption)

- laser absorption by ITM HR coating (function of incident laser power and HR coating absorption)

- radiative heating from room-temp tube snout (function of snout radius and length, and TM radius)

The heat transfer out of the testmass (P_out) is simply the sum of the radiative heat emitted by the HR and AR faces and the barrel. Note that the script currently assumes an inner shield T of 77K, and the inner/outer shield geometric parameters need to be obtained/verified.

Nina and Paco have been working towards obtaining tabulated emissivity data as a function of temperature and wavelength. In the meantime, I created the framework to import this tabulated data, use cubic spline interpolation, and return temperature-dependent emissivities. It should be straightforward to incorporate the emissivity data once it is available. Currently, the script uses room-temperature values for the emissivities of various materials. 

Future steps:

- Incorporate tabulated emissivity data

- Verify and update inner/outer shield dimensions

How about a diagram so that we can understand what this model includes?

Attachment 1 is a geometric diagram that reflects the current state of the ITM cooldown model, introduced in [30]. The inner shield is assumed to be held at 77K for simplicity, and 2 heat sources are considered: laser heating, and radiative heating from the room-temperature snout opening. The view factor F_ij between the snout opening and test mass (modeled as 2 coaxial parallel discs separated by length L - equation found in Cengel Heat Transfer) is calculated to be 0.022. The parameters used in the model are noted in the figure.

Attachment 2 is a simplified diagram that includes the heating/cooling links to the test mass. At 123K, the radiative cooling power from the inner shield (at 77K) is 161 mW. The radiative heating from the snout opening is 35 mW, and the laser heating (constant) is 101.5 mW. Due to the tiny view factor betwen the snout opening and the test mass, most of the heat emitted by the opening does not get absorbed. 

The magnitudes of heating and cooling power can be seen in Attachment 3. Lastly, Attachment 4 plots the final cooldown curve given this model. 

My next step is to add the outer shield and fix its temperature, and then determine the optimal size/location of the inner shield to maximize cooling of the test mass. This is question was posed by Koji in order to inform inner shield/outer shield geometric specs. Then, I will add a cold finger and cryo cooler (conductive cooling). Diagrams will be updated/posted accordingly.

[Paco, Nina, Aidan]

Updated the stack emissivity code to use the Kitamura paper fused silica dispersion which has a prominent 20 um absorption peak which wasn't there before... (data was up to 15 um, and extrapolated smoothly beyond). The updated HR stack emissivities are in Attachments #1 - #2. A weird feature I don't quite understand is the discontinous jump at ~ 59 um ... 

[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.

Building on [32], I added a copper cold finger to conductively cool the inner shield, instead of holding the inner shield fixed at 77K. The cold finger draws cooling power from a cyro cooler or "cold bath" held at 60K, for simplicity. I added an outer shield and set its temperature to 100K. The outer shield supplies some radiative heating to the inner shield, but blocks out 295K heating, which is what we want. The expanded diagram can be seen in Attachment 1. 

I wanted to find the optimal choice of inner shield area (A_IS) to maximize the radiative cooling to the test mass. I chose 5 values for A_IS (from A_TM to A_OS) and plotted the test mass cooldown for each in Attachment 2. The radiative coupling between the inner shield and test mass is maximized when the ratio of the areas, A_TM/A_IS, is minimized. Therefore, the larger A_IS, the colder the test mass can be cooled. Even though choosing A_IS close to A_OS increases the coupling between the 2 shields, the resulting heating from the outer shield is negligible compared to the enhancement in cooling.

I chose A_IS = 0.22 m² to model the inner shield and test mass cooldown in Attachment 3. The test mass reaches 123 K at ~ 125 hours, or a little over 5 days. I have pushed the updated script which can be found under mariner40/CryoEngineering/MarinerCooldownEstimation.ipynb.

Following our discussion at the Friday JC meeting, I gathered several resources and made a small simulation to show how frequency combs might be generated on platforms other than microcombs or mode-locked lasers.

Indeed, frequency combs generated directly from a mode-locked laser are expensive as they require ultra-broadband operation (emitting few fs pulses) to allow for f-2f interferometry.

Microcombs are a fancy way of generating combs. They are low-power-consuming, chip-scale, have a high repetition rate, and are highly compatible with Silicon technology. While these are huge advantages for industry, they might be disadvantageous for our purpose. Low-power means that the output comb will be weak (on the order of uW of average power). Microscopic/chip-scale means that they suffer from thermal fluctuations. High rep-rate means we will have to worry about tuning our lasers/comb to get beat notes with frequencies smaller than 1GHz.

Alternatively, and this is what companies like Menlo are selling as full-solution frequency combs, we could use much less fancy mode-locked lasers emitting 50fs - 1ps pulses and broaden their spectrum in a highly nonlinear waveguide, either on a chip or a fiber, either in a cavity or linear topologies. This has all the advantages:

1. High-power (typically 100mW)

2. Low rep-rate (typically 100MHz)

3. Relatively cheap

4. "Narrowband" mode-locked lasers are diverse and can come as a fiber laser which offers high stability.

As a proof of concept, I used this generalized Schrodinger equation solver python package to simulate 1d light propagation in a nonlinear waveguide. I simulated pulses coming out of this "pocket" laser (specs in attachment 1) using 50mW average power out of the available 180mW propagating in a 20cm long piece of this highly nonlinear fiber (specs in attachment 2).

The results are shown in attachments 3-4:

Attachment 3 shows the spectrum of the pulse as a function of propagation distance.

Attachment 4 shows the spectrum and the temporal shape of the pulse at the input and output of the fiber.

It can be seen that the spectrum is octave-spanning and reaches 2um at moderate powers.

One important thing to consider in choosing the parameters of the laser and fiber is the coherence of the generated supercontinuum. According to this paper and others, >100fs pulses and/or too much power (100mW average is roughly the limit for 50fs pulses) result in incoherent spectra which is useless in laser locking or 1f-2f interferometry. These limitations apply only when pumping in the anomalous dispersion regime as traditionally have been done. Pumping in an all-normal (but low) dispersion (like in this fiber) can generate coherent spectra even for 1ps pulses according to this paper and others. So even cheaper lasers can be used. ps pulses will require few meter-long fibers though.

I've ironed out the issues with my MATLAB model so that it now shows correct phase behaviour. The problem seems to arise from infinite Q poles where there is an ambiguity in choosing a shift of +/- 180 deg in phase. I've changed my state space model to include finite but very high Q poles to aid with the phase behaviour. The model has been uploaded to the GitLab project under mariner40 -> mariner_sus -> models -> lagrangian.

Now that I have correct phase and amplitude behaviour for my MIMO state space model of the suspension and the system is being correctly evaluated as stable, I'm uploading the useful plots from my analysis. File names should be fairly self-explanatory. The noise plots are for a total height of 550 mm, or wire lengths of 100 mm per stage. I've also attached a model showing the ground motion for different lengths of the suspension.

Here are the DAC and residual displacement spectra for different suspension heights ranging from 450 mm to 600 mm. I aimed to get the Q of the lower resonance close to 5 and the DAC output RMS close to 0.5 V but as this was just tweaking values by hand I didn't get to exactly these values so I'm adding the actual values for reference. The parameters are as follows:

I used the same model in [37] to consider how test mass length affects the cooldown. Attachment 1 plots the curves for TM length=100mm and 150mm. The coupling between the test mass and inner shield is proportional to the area of the test mass, and therefore increases with increasing length. Choosing l=100mm (compared to 150mm) thus reduces the radiative cooling of the test mass. The cooldown time to 123K is ~125 hrs or over 5 days for TM length=150mm (unchanged from [37]), but choosing TM length=100m increases this time to ~170 hrs or ~7 days. (Note that these times/curves are derived from choosing an arbitrary inner shield area of 0.22 m², but the relative times should stay roughly consistent with different IS area choices.)

I reran the cooldown model, setting the emissivity of the inner surface of the inner shield to 0.7 (coating), and the emissivity of the outer surface to 0.03 (polished Al). Previously, the value for both surfaces was set to 0.3 (rough aluminum). 

Attachment 1: TM cooldown, varying area of the inner shield. Now, the marginal improvement in cooldown once the IS area reaches 0.22 m² is negligible. Cooldown time to 123K is ~100 hrs, just over 4 days. I've kept IS area set to 0.22 m² moving forward.

Attachment 2: TM/IS cooldown, considering 2 lengths for the test mass. Choosing l=100m instead of 150mm increases cooldown time from ~100 hrs to ~145 hrs, or 6 days.

I've been testing out the extended body lagrangian models and I'm trying to understand the ground motion and force coupling to the test mass displacement. I've compared the two point-mass model to the extended model and, as expected, I get very similar results for the ground coupling. Attachment 1 shows the comparison and asside from more agressive damping of the point-mass model making a small difference at high frequency, the two models look the same. If I look at the force coupling, I get a significantly different result (see attachment 2). I think this makes sense because in the point-mass model I am driving purely horizontal displacement as there is no moment of inertia. However, for the extended body I drive the horizontal position of the centre of mass, which then results in an induced rotation as the change propagates through the dynamics of the system. To obtain a consistent result with the point-mass model, I would need to apply a force through the CoM as well as a counteracting torque to maintain a purely horizontal displacement of the mass. What I am wondering now is, what's the correct/more convenient way to consider the system? Do I want my lagrangian model to (a) couple in pure forces through the CoM and torques around the CoM and then find the correct actuation matrix for driving each degree of freedom in isolation or (b) incorporate the actuation matrix into the lagrangian model so that the inputs to the plant model are a pure drive of the test mass position or tilt?

All parameters are temporary:

Test mass size: D150mm x L140mm
Intermediate mass size W152.4mm x D152.4mm x H101.6mm
TM Magnets: 70mm from the center

Height from the bottom of the base plate
- Test mass: 5.0" (127mm) ==> 0.5" margin for the thermal insulation etc (for optical height of 5.5")
- Suspension Top: 488.95mm
- Top suspension block bottom: 17.75" (450.85mm)
- Intermediate Mass: 287.0mm (Upper pendulum length 163.85mm / Lower pendulum length 160mm)

OSEMs
- IM OSEMs: Top x2 (V/P)<-This is a mistake (Nov 3 fixed), Face x3 (L/Y/P), Side x 1 (S)
- TM OSEMs: Face x4
- OSEM insertion can be adjusted with 4-40 screws

To Do:
- EQ Stops / Cradle (Nov 3 50% done)
- Space Consideration: Is it too tight?
- Top Clamp: We are supposed to have just two wires (Nov 3 50% done)
- Lower / Middle / Upper Clamps & Consider installation procedure
- Fine alignment adjustment
- Pendulum resonant frequencies & tuning of the parameters
- Utility holes: other sensors / RTDs / Cabling / etc

- Top clamp options: rigid mount vs blade springs
- Top plate utility holes
- IM EQ stops

Discussion with Rana

- Hoe do we decide the clear aperture size for the TM faces?
- OSEM cable stays
- Thread holes for baffles

- Light Machinery can do Si machining
- Thermal conductivity/expansion
- The bottom base should be SUS... maybe others Al except for the clamps

- Suspension eigenmodes separation and temperature dependence

# Deleted the images because they are obsolete.

Some more progress:

- Shaved the height of the top clamp blocks. We can extend the suspension height a bit more, but this has not been done.

- The IM OSEM arrangement was fixed.

- Some EQ stops were implemented. Not complete yet.

[Paco]

I used the HITRAN database to download the set of ro-vibrational absorption lines of CO2 (carbon dioxide) near 2.05 um. The lines are plotted for reference vs wavenumber in inverse cm in Attachment #1.

Then, in Attachment #2, I estimate the broadened spectrum around 2.05 um and compare it against one produced by an online tool using the 2004 HITRAN catalog.

For the broadened spectrum, I assumed 1 atm pressure, 296 K temperature (standard conditions) and a nominal CO2 density of 1.96 kg/m^3 under this conditions. Then, the line profile was Lorentzian with a HWHM width determined by self and air broadening coefficients also from HITRAN. The difference between 2050 nm and 2040 nm absorption is approximately 2 orders of magnitude; so 2040 nm would be better suited to avoid in-air absorption. Nevertheless, the estimate implies an absorption coefficient at 2050 nm of ~ 20 ppm / m, with a nearby absorption line peaking at ~ 100 ppm / m. 

For the PMC, (length = 50 cm), the roundtrip loss contribution by in-air absorption at 2050 nm would amount to ~ 40 ppm. BUT, this is nevery going to happen unless we pump out everything and pump in 1 atm of pure CO2. So ignore this part.

Tue Nov 9 08:23:56 2021 UPDATE

Taking a partial pressure of 0.05 % (~ 500 ppm concentration in air), the broadening and total absorption decrease linearly with respect to the estimate above. Attachment #3 shows the new estimate.

For the PMC, (length = 50 cm), the roundtrip loss contribution by in-air absorption at 2050 nm would amount to ~ 1 ppm.

[Paco]

There was an error in the last plot of the previous log. This was correctly pointed out by rana's pointing out that the broadening from air should be independent of the CO2 concentration, so nominally both curves should coincide with each other. Nevertheless, this doesn't affect the earlier conclusions -->

The PMC loss by background, pressure broadened absorption lines at 2049.9 nm by CO2 is < 1 ppm.

The results posted here are reflected in the latest notebook commit here.

I've been having a look at the transfer functions for the translation and pitch of both masses. I'm attaching the plot of all input-to-output transfer functions of interest so far. Here I've identified the pitch resonances of the two masses (one each) as well as the two pendulum modes. I need to now investigate if they occur in the correct places. I have confirmed the DC response by directly solving the statics problem on paper.

I've checked the validity of my state space model in a couple of ways so that we have confidence in the results that it gives. I've checked the DC gain of the transfer functions where it is non-zero. I did this by solving the static balance of forces problem in the extended body model by hand to get the DC CoM position as well as the pitch angle of both masses. In the previous ELOG entry I didn't quite do this for all transfer functions so here I completed the check. My values agree with the model's values to within 10% at the worst end and to within 0.1% at the best end. I performed a second check to see if the frequencies occur in the correct places by considering the case of very low coupling between the different resonant modes. It's difficult to check this in the case where the modes are strongly coupled (for example length-pitch is strong or the two pitch modes are close together) but if I sufficiently separate them, I get very good agreement between my analytic approximation and the state space model.

The model can easily be converted from one that gives motion in X and RY into one that gives motion in Y and RX. Running the model for both directions gives the following list of resonances (note pendulum modes in X and Y direction are identical):

Given that I think the model seems to give sensible values, I've pushed the updated model to the GitLab repository. It is now possible to quickly change the parameters of the suspension and very quickly see the corresponding shift in the resonances. To change the parameters, open the plain text file called 'params' and change the values to the new ones. Afterwards, run the file 'ss_extended.py', which will solve the state space model, save the resulting ABCD matrices to a folder and print out the values of the resonances to terminal.

Does this work? Is this insane?

cool

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

I've managed to cut and crimp wires for the power board for coil driver. I will begin adding components to the coil driver board.

- Add Components to Coil Driver board 

 - Replace some Sat Amp Componetns

- Still working on moving optical table to CAML

- Unsure if cryochamber has been cleaned and moved

I've completed one coil driver board. 
Hopefully next week I can finish the other 2 boards and make the modifications to the sat amp baords. 
 

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. 

Almost done with coil driver boards 

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

All three coil driver boards are complete and have been tested. Modification for all 4 sat amp have been completed. Ideally, I would like to finish all the chassis on Monday I have one just about done. 
 

This was performed last Friday (7/8).

I secured a thermocouple perpendicular against the hotplate and recorded the maximum temperature the hotplate reached at Low, Medium, and High. It took about 5 minutes to reach a stable temperature, where stable means that the temperature stayed within +/- 0.5°C for a minute. The hotplate maintains a certain temperature by turning itself on and off, so the temperature would drop slightly (at most, a few °C) while the hotplate was off. The maximums were:
Low: 51°C
Medium: 185°C
High: 263°C
At the max temperature, I moved the perpendicular thermocouple around to roughly find the variation in tempearture at different locations on the hotplate. Facing the nob, the top right quadrant is about 10-20°C cooler than the other quadrants, which are within 5°C of eachother. Excluding the cooler quandrant, the center and the outer edge are within 5°C of eachother. The temperature increases as one approaches half the radius, with it being about 20-40°C greater than the center and outer edge. The highest recorded temparture was 289°C at half the radius in the bottom left quandrant. This was only meant to be a rough test to see how even the heating is.

Note that the slides have "GLOBE" printed on one side. I always bond the opposite using the opposite side without the text.

On Monday (7/11), I began experimenting with bonding, starting with "air-bonding," which is trying to make dry, gently cleaned slides stick. I achieved my first succesful optical contact with what I call "acidental water-assisted direct bonding" or "water-bonding," where I accidentally clasped two wet slides together while washing my dirty finger prints off them. After the accidental discovery, I repeated it by running water over the slides while there were clasped together and achieved the same result. After a few hours, I attempted partially sliding apart the second water-bonded sample. I could slowly push them apart by pressing my thumbs against the long edge, but it took quite a bit of force. I decided to let 4 samples sit overnight: 1 air-bonded, 1 air-bonded with the brass hunk on top of it, and 2 water-bonded. Neither time nor pressure improved the air-bonded samples as they still slid apart very easily. The first water-bonded sample slid apart easier, but one part remained stubornly attached until I began shaking it violently. The second water-bonded sample was much harder to slide apart than the last time I tested it. With all the force of my fingers, I could barely make it budge.

Finished all 3 Coil Drover chassis and power lines still need to install the rear cables will do that after I finish Sat Amp chassis tomorrow. 

I have finished all coil driver and sat amp chassis they all seem to be functioning properly.
 

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've been running the HR coating optimization for mariner TMs. Relative to the specifications found here we now are aiming for

• ITM HR coating of 2000 ppm @ 2050.15 nm, and 1000 ppm @ 1550 nm
• ETM HR coating of 25 ppm @ 2050.15 nm, and 1000 ppm @ 1550 nm.

Both the PSL and AUX cavity finesses range the few couple of thousands, and the goal is not to optimize the coating stack for noise, but more importantly for the transmission values and tolerances. This way we ensure the average finesse and differential finesse requirements are met. Anyways, Attachment #1-2 shows the transmission plots for the optimized coating stacks (so far). Attachments #3-4 show the dielectric stacks. The code still lives in this repository.

I'm on the process of assessing the tolerance of this design stacks against perturbations in the layer thicknesses; to be posted in a follow-up elog.

Here are some corner plots to analyze the sensitivity of the designs in the previous elog to a 1% gaussian distributed perturbation using MCMC.

Attachment #1 shows the ETM corner plot 

Attachment #2 shows the ITM corner plot.

I let the indices of both high and low index materials vary, as well as the physical thicknesses and project their covariances to the transmission for PSL and AUX wavelengths.

The result shows that for our designs it is better to undershoot in the optimization stage rather than meet the exact number. Nevertheless, 1% level perturbations in the optical thickness of the stack result in 30% deviations in our target transmission specifications. It would be nice to have a better constraint on how much each parameter is actually varying by, e.g. I don't believe we can't fix the index of refraction to better than 1%., but exactly what its value is I don't know, and what are the layer deposition tolerances? These numbers will make our perturbation analysis more precise.

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.

we have 23 OSEMS they look all full built and I will try and test them this week and or next week.

I have found that, after cleaning the glass with methanol (or even sometimes with just a dry lense-cleaning cloth), I can get glass slides to bond by rappidly rubbing them together until something sticks. This was inspired by watching "Wizard of Vaz" perform bonds on YoutTube. While cleaning, I now use enough strength to make the glass squeak, as advised by him.

Upon heating, I encountered the same issue as when I bonded them by putting a liquid (water, methanol, etc.) in the gap, which leads me to now believe that the broken bond is not due to the expansion of a liquid. Further, even at the low temperature of 60°C, placing the liquid-less sample on the hotplate breaks the bond in seconds, which I caught on video. In the attached video*, you can see that, before the heat, the bond is strong enough that I cannot push it appart with my fingers, but after the heat, it slides easily. Note that, outside of taking the video, I always lay the entire slide on the center of the metal so the sample is evenly heated.

*This is my first time attaching a video. If it didn't attach properly, I'll add it on to a later log. I also want to record myself performing the rubbing bonding technique.

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.

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.

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.

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.

A couple of coating stacks with better tolerance (transmission +- 10%). Attachments #1-2 show the spectral reflectivities for ETM/ITM respectively, while Attachments #3-4 show the corner plots. I think the tolerances are inflated by the fact that all the stack indices and thicknesses are varying, while in reality these two effects are degenerate because what matters is the optical thickness. I will try to reflect this in the MCMC code next. Finally, attachments # 5-6 are the hdf5 files with the optimization results.

We succeeded in setting up an apparatus for quantifiying the razor blade test. After mounting the glass slides such that the razor edge rested against the gap, we slowly turned the knob to push the blade into the gap. We started with the knob at 0.111, and at 0.757, the bond between the glass slides failed. As we approached 0.757, the interference pattern in the glass shifted, foreshadowing the break.

(Edit by Koji. This 0.757 is 0.0757 I suppose...? And the unit is in inch)

Instead of varying individual layer thicknesses using the MC sampler, I made sure both the thickness and index of refractions are varied as a global systematic error to estimate the design sensitivity. The results for ITM/ETM respectively, with 1e5 samples this time, are in Attachments 1-2 below.

Here I describe the current radiative cooldown model for a Mariner test mass, using parameters from the most recent CAD model. A diagram of all conductive and radiative links can be seen in Attachment 1. Below are some distilled key points:

All parameters have been taken from CAD, with the exception of:

Attachment 2 contains the cooldown curves for the system components. With the above assumptions, the test mass takes ~59hrs to reach 123K, and the final steady-state temperature is 96K. (*This was edited - found a bug in previous iteration of code that underestimated the TM cooldown time constant and incorrectly concluded ~36hrs to reach 123K. The figures have been updated accordingly.)

Attachment 3-6 are power budgets for major components: TM, IS, Cage, OS (can produce for UM if there's interest). For each, the top plot shows the total heating and cooling power delivered to the component, and the bottom plot separates the heating into individual heat loads. I'll discuss these below:

The next post will describe optimization of the snout length/radius for cooldown.

Here is a more detailed analysis of varying the length and radius of the snout.

Attachment 1 plots the heat load (W) from the snout opening as a function of temperature, for different combinations of snout length and radius. The model using the CAD snout parameters (length=0.67m end-to-end; radius=5.08cm) results in ~0.3W of heat load at steady state. The plot shows that the largest marginal reduction in heat load is achieved by doubling the length of the snout (green curve), which cuts the heat load by over a factor of 2/3. This validates the choice in snout length used in the previous ELOG entry analysis. The bottom line is that the end-to-end snout length should be on the order of 1 meter, if physically possible.

The next marginal improvement comes from reducing the radius of the snout. Attachment 1 considers reducing the radius by a half in addition to doubling the length (red curve). A snout radius of an inch is quite small and might not be feasible within system constraints, but it would reduce the snout heat load to only 25mW at steady state (along with length doubling). 

The cooldown model resulting from optimizing parameters of the snout (length=1.33m, radius=2.54cm) is shown in Attachment 2. The test mass reaches 123K in ~57hrs - only 2 hours faster than the case where only the snout length is doubled (see previous ELOG entry) - and the test mass reaches steady state at 92K - only 6K colder than in the previous case. This could discourage efforts to reduce the radius of the snout at all, since increasing the length provides the most marginal gains. 

The attached plot (upper) compares the heat load delivered to the test mass from various snout lengths (end to end), as a function of test mass temperature. (At steady state, our point of interest is 123K.) Note that these curves use the original CAD snout radius of 5.08cm (2").

The greatest marginal reduction in heat load comes from increasing the end-to-end snout length to 1m, as concluded in the prevous ELOG. This drops the heat load from just under 0.5W (from snout length 0.5m) to 0.15W. Further increase in snout length to 1.5m drops the heat load to well under 0.1W. After this point, we get diminishing marginal benefit for increase in snout length. 

The effect on the TM cooldown curve can be seen in the lower plot. A snout length of 1m drops the steady-state TM temperature to under 100K. Then, like above, increasing the length to 1.5m makes the next non-negligible impact. 

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

While finalizing my work plan for the quarter, I decided to look at the Thor Lab slides. This was instructive because they highlighted the troubles I will have with working with silicone. They are fragile and their small, thin sizes makes cleaning and manipulating them (without contamination) much more difficult compared to the glass sides from before.

I tried cleaning and bonding them the same way as the larger slides. Rubbing them together did not work like with the larger sides, but that may also be a function of being more careful, as not to break them. Once I cleaned them, it only took a tap from my finger to get the center to bond, but the bonded surface area still did not spread out like it did in the YouTube videos (http://youtu.be/se3K_MWR488?t=80). By pressing down around the bonded area, I could expand it slighty. Note that I did crack one slide in the process of doing this, as shown in the pictures.

Because the slides are so thin, I think they will benefit greatly from being left under a heavy object, although it may be difficult to put the weight on the slides without them breaking.

Continuining with my casual exploration of the Thor Lab slides, I heated them from off --> low --> med --> high, with 10 minutes on each setting. The only pressure I applied was 3 larger glass slides, and that was only to flatten out the copper that the smaller, bonded slides sat on top of (so the contact with the heating plate was even).

The heat made the bonded area smaller, but it did not break. As the slides cooled, the bond area increased slightly but not back to the original size. Next I will try this with slower heating and additional pressure.

Given that these glass slides are much thinner than the ones I worked with prior, I suspected they would be more receptive to pressure. I decided to replicate the tests I performed with the larger slides: I prepared 8 samples, 4 by smushing the slides together with methanol in the middle and another 4 by cleaning the slides with methanol before pressing them together with my fingers. I put 2 of each type under the cylindrical weight, and 2 of each type under the rectangular weight with the addition of heating. The heating consisted of switching the temperature from off --> low --> med --> high with 15 minutes on each setting.

I will check the results in the morning. I need to wait until the rectangular weight is completely cooled, otherwise I cannot remove it from the hot plate in manner that does not risk cracking the glass.

The first sample picture shows the pressed slides on the top and the smushed slides on the bottom. For the second picture, this is reveresed. Correction: the order is the same for both samples.

These are the results from the previous log.

At long last, there was an improvement with pressure and heat! Pressure without heat and pressure with heat both showed a small improvement. Although the improvement was not major, it does show that pursuing this method of adding weight and heat are viable. Since this was a test, I put less weight on and heated it fast than intended, but now I feel confident to add more weight and slower/greater amounts of heat.
 

Before jumping to conclusions based on my previous results, I wanted to check that it was indeed heat and pressure, not time, that led to the bonds improving.

I prepared 4 samples, all with my standard pressing technique (which still leaves room for improvement). 2 samples will simply be left to sit undisturbed, and the other 2 will be left under both (rectangular and cylindrical) weights. I will check these in roughly 24 hours, just like the last test.

The 2 slides on the right are the ones under the weights.

I was unable to check the samples because I could not get access to Bridge, so they will be checked tomorrow and the results will be added as an edit to this log.
Given that I was unable to do work in the lab, I instead began a second attempt at writing code for the Arduino to use PWM to control the hot plate temperature.

As expected, the suface area of the bond only increased for the samples under the weights. I did notice something worrying: one of the non-weighted samples actually had its surface area decrease. It is unclear if this is a one-time thing or if all of the bonds deteriorate with time. Unrelated, but I also noticed that the bonded areas always have small dots that refuse to bond. It's unclear if that is due to imperfections or contamination (I suspect the latter).
I left all 4 samples under both weights out of curiosity to see if the bonded surface area would increase further (or possibly decrese further).

I wrote a program to control the heating rate of the hot plate using Pulse Width Modulation (PWM), and it was a great success!

For roughly 6 minutes, the hot plate was power cycled with a rate of 100 ms on followed by 900 ms off. Based on my calculations, this should correspond to a 0.08°C/sec temperature increase. In other terms, we expect a 24°C increase in the span of 5 minutes. For comparision, without PWM, the hot plate heats up roughly 100°C in that same timespan. I recorded the temperature by filming a thermometer and transcribing that video into a text file, which could be analyzed and graphed. I only transcribed the first 5 minutes of the 17 minute video (I also filmed part of the cool down) because 5 minutes was enough to show clear results.

At t=0, the hot plate was 21.4°C, and at t=300, the hot plate was 49.7°C. That is a 28.3°C increase in the span of 5 minutes, only 4.3°C higher than the predicted value. The rate, 0.094°C/sec, is only slightly faster than the desired 0.08°C/sec. Further, as shown in the graph, the temperature increase was almost perfectly linear, which is ideal. Overall, using an Arduino to PWM the hot plate is looking very promising.

I repeated the first test, but let the hot plate run longer. It revealed that the linearity for the lower temperatures completely falls apart at the higher temperatures. I think it should be fairly straightforward to modify the code to accommodate this.

The previous test was cycled with 0.3s on follwed by 0.7s off*. This test was 0.7s on followed by 0.3s off. I intended to let it run longer, but I accidetly knocked the thermocouple over while trying to move the cable father from the hot plate so the plastic would not risk melting.

Like before, we see that it starts out relatively linear. I noticed the heating light kind of fluttering around 200°C which appeared in the data as a small decrease around 450s on the graph. I do not know the source of this issue, but I fear it may be the hot plate overriding my cycling with its own built-in cycle; something left for future testing. This is the last data I will gather using v1 of my Arduino code, as am I now working on implementing what I have learned in a smarter v2 of the code. I included v1 of the code, and the txt files for the first three tests.

*I think. Could have been 0.1 on, 0.9 off. Note to self: double check this.

I had a little set back regarding the non-linear portion of the heating. After about 150°C, if the heating rate is kept constant, the heating graph transitions from linear to logarithmic. I was able to show graphically that, yes, it is indeed logarithmic, but I could not think of an algorithmic way to translate this logarithmic curve into the increase in heating rate to maintain a linear heating rate. I do have some ideas which I will test tomorrow.

I had some trouble with the code not working as intended (partially because it has been I while since I coded in C++). However, I was able to run two tests with the new code, although I ran out of time to type up the data for the 2nd. Graphing the 1st test's data, it appears that my improved code is an improvement, but the heating is still slowing down as it approaches 200°C. I need to re-run this test, but with v1 of the code, for better comparison.

The hot plate was supposed to increase 180°C in 10 minutes (so that I would reach 200°C), but due to an inscrutable bug, it did not exit the while loop, so it continued past 10 minutes.

For the following two graphs, I ram four tests: two using the the v1 of the PWM code and two using v2 of the PWM code. The graphs show the heating rate I was aiming for and the actual results. It turns out, my v2 does not work better than my v1. Before 150°C (which is where I believed that (assuming the rate is kept constantly) the heating rate shifted from linear to logarithmic), v1 is an overshoot and v2 is slightly less of an overshoot. The goal of v2 was to increase the rate after 150°C to compensate for this drop off, but it does not appear to have worked.

While I would still like to refine my code, I think it will be good enough to try using it to actually heat the samples.

Before trying the PWM on actual samples, I wanted to make one final attempt at improving my code (labled as v2.1). This change appears to have 1) broken the code regulating the basic heat cycling process 2) caused the hot plate to heat up far, far too quick. Since the thermometer strangely turned off halfway through, I only have two pictures as evidence that this test existed: a screenshot of the Arduino program telling me that the max cycle rate had been reached (which should have not happened) and a frame from the video filming the thermometer showing the peak temperature (which is 100°C high than expected). Somehow the hot plate reached over 300°C, which I thought was impossible because the hot plate's built-in heat cycle should have kicked in around 260°C. Unrelated, but I am performing this test in my dorm room because I was quarentined due to COVID exposure, and I like using my personal fan and the house's freezer to cool down the hot plate quicker.

I made some adjustments (labled as v2.2), and I had the same failure as v2.1, except I managed to capture it on camera.

Finally, with v2.3, I managed to fix all the issues. I ran out time today to transcribe the temperatures for graphing, but this itteration of the code managed to reach 200°C in 10 and 7 minutes for test #1 and #2, respectively. I also managed to fix the problem of the hot plate not turning off after the desired heating time. The real test will be trying a slower heating time, like 20 minutes, but I am glad I postponed using actual samples because this fix has given me code that appears to work exactly as I hoped.

Here are the graphed results from yesterday's tests, both by themselves and overlayed with the previous tests. I am satisfied with my code; it has given me the (roughly) linear heat increase that I desired. The only last thing I would like to test is heating over a signficantly slower time. 

I tried increasing the temperature by 180°C over 20 minutes. As suspected, it did not quite reach the target temperature because the temperature started to drop off around 100°C instead of 150°C, as the program expected. This should be an easy adjustment, since it is just a matter of increasing the duration of the cycle at an earlier time.

My two corrections ended up being huge overshoots. The drop off time (100°C) is correct, but the default rate increase that worked in the other cases is not working at all here.

The goal of "v2.X test #3" is to heat the hot plate to 200°C over the course of 20 minutes, and with v2.6, I have effectively succeeded. There will likely be more issues once I try, for example, to heat the hot plate to 300°C over the course of 60 minutes, but for now, I want to stick with lower temps and shorter times while I work out the kinks. Now that I understand the difficulties of PWMing a hot plate, adapting the code to combat future issues should be straightforward.

To summarize my code, I control the heating rate by cycling the hot plate's power on and off for some % of 1000ms. In other words, the hot plate is on 300ms then off 700ms then on 300ms etc., where the relation between target heating rate and hot plate on time is based on previously gathered data. This produces a nice, linear(ish) temperature increase up until a certain temperature, at which point it plateaus. In the previous versions, the way I compensated for this was by increasing the on time by 5ms for every cycle after 150°C. This did not work for slower heating rates, so the newer versions changed this by making the 5ms and 150°C varry depending on the target heating rate. The exact value is a linear extrapoliation from previous data. This is imperfect, but I do not think perfection will ever be possible with the current equipent, and I think I have reached something good enough that now I can finally apply it to my optically contacted samples.

Since I have finished this "stage" of work, for completeness, I am including all of the code, data*, and graphs involved so far.
*the .txt data files are in the cycle_vX_graphs folders; these folders also have the Jupyter notebooks I used for graphing the data

I realized that, after changing so much from v2.3 to 6, I should check that my first two tests produce correct results with the latest version. This was good because all three tests turned out to be innaccurate, as they were all short roughly 10°C. However, they were very precise. For all three, the final temperature was 193.15±1.5°C.

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.

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.

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.

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.

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."

I performed the same tests I have been doing prior (+180°C in 10 minutes) but now with the (correctly wired) thermocouples attached to the metal plates. The top plate is thermocouple #1 attached to the Fluke and the bottom plate is thermocouple #2 attached to the TPI (the lime green one).

The base heating rate for the new set up will require some tweaking to the code because the plates heat up much slower, but as I have mentioned previously, I do not think this will require a lot of extra work since I now know the tips and tricks to PWMing the hot plate. The only difficulty might come from the increase in hysteresis (i.e. the plates continue to increase in the temperature long after it turns off). For future tests, I need to remember to continue recording the temperature after program finishes its 10 min cycle.

On the positive, I think this test shows that taking the average of the two thermocouples to find the temperature in the center (where the optically contacted samples are) is a worthwhile endevor, considering how much the top plate lags behind the bottom plate in terms of heating speed.

With v3.0, I took a couple steps backwards by getting rid of the feature that increases the heating rate so I can isolate the base heating rate for the two plates. In my experience, the best way to figure out how to modify the program is to try a bunch of different target temperatures and heating times and look for correlations. I started with (attempting) to increase the plates by 280°C in 10 minutes.

For a future release, I am thinking of radically (relatively speaking) changing the function parameters: the user only inputs the target heating rate and how long the plates should be heated at this rate. This is to address the hysteresis in this new set-up, which I will elaborate on if I make the change.

I decided test how fast the plates would heat up if the heat was just on constantly on for 5 minutes. In general, these tests are raising a lot of questions in regards to controlling the temperature given the hysteresis in the system. It is also apparent that the bottom plate heats up signficantly faster than the top one, which means I need to heat the samples much longer than, say 10 minutes, if I want to avoid unevenly heating both parts of the optically contacted piece.

I also have to be conscientious that I am already half way through the quarter and ideally should be devoting time to bond strength testing rather than continuing to fiddle with the hot plate.

To combat the bottom plate heating up much faster than the top plate, I decided to try increasing the cycle period from 1000ms (1s) to 10000ms (10s). In other words, taking the test I today ran as an example, the hot plate will now be on for 1000ms then off for 9000ms then repeat. Hopefully this should give more time for the heat to transfer to the top plate, but even in this short test, it still appears to be a problem.

Due to the slower heating times, this will be a bit more challenging to test as each test could take hours to complete, but this is more in line with the final intended use anyways. Perhaps my cycle of 1000ms on is too much (e.g. I should do 100ms on then 9900ms off, although I think that might be so slow that it will never heat up; this also raising the question as to how I will deal with mantaining this slow heat up at the higher temperatures).

[I'm behind on data processing, but I'm creating an entry on the day I actually run the tests]

[I'm (once again) behind on data processing, but I'm creating an entry on the day I actually run the tests]

Somehow I never thought of this before, but instead of increasing the "on" time of the hot plate to account for the heating drop-off, I should keep that constant and instead decrease the "off" time. That feels more logical given that I am trying to keep the temperature of the two plates as close as possible.

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?

The bond quality measurements can be split into two categories: destructive and nondestructive. For destructive, we have measuring tensile and shear strength, and for nondestructive, we have gap distrance and mechanical quality. I am also currently searching for more ways to measure the strenght, but I am having a hard time finding any others.

Tensile strength 
Proposed method: based off of the traditional razor test, a blade will be systematically inserted into the gap. For a prototype, I used optical bread board components to hold the razor while a knob was slowly turned to push the razor forward. The knob had markings on it, which could be used to estimate the amount of force applied to the gap. The prototype was made for the larger glass slides, so it is too big and forceful for the silicon and smaller, more fragile glass slides. However, the principles of the protoype had potential to be adapated to be gentler.

Shear strength
Proposed method: a cord will be adhered to the outer sides of the sample such that one side will be hung to the ceiling while the other will have weight hanging from it. Weight us added to the latter cord until the bond breaks. This could pontentially be a little dangerous as it could shatter when the bond finally breaks, so a protective barrier of some sort will have to be set up.

Alternative: affix one outer surface to the table so that it cannot move. Attach the other surface to something that can spun/twisted. The more twists it takes to break the bond corresponds to the shear strenght.

Gap distance
Proposed method: use ellipsometry to find how big the gap is between the two bonded surfaces. I think this would be great to combine with one of the destructive methods since, if you could relate the nm thickness of the gap to, say, the tensile strength, then you could estimate the tensile strength of future bonds without having to destroy them. I read a lot about ellipsometry over winter break, and I know what components are needed for it.

Mechanical quality
Proposed method: this would be based around the paper which measured the ring down of an optically contacted tuning fork. My focus would be on varying the parameters to find the most precise and accurate dimensions of the fork. Although it sounds interesting, I am not sure how practical it would be to pursue as it requires a lot of modeling and building. However, given the application of these measurements (specifically, for Voyager, (if my understanding is correct) the use of optical contacting will resolve the issue of messy noise caused by unpredictable thermal vibration of adhesives), knowing the mechanical quality of the bond seems valuble.

I am getting started on building the arduino circuit as well as setting up my computer so I can communicate between jupyter notebook and the arduino. I will need a USB adapter for my computer before I can make much more progress.

I was able to get a USB adapter for my computer so I could test my code. The Arduino can read the temperature of the room and output the values with a tenth of a second time delay. Jupyter Notebook recognizes the Arduino and can receive temperature data from it.

1) Paco cleared the path in the DOPO lab. We'll need a flat dolly or wooden bars (covered with a mylar sheet) to place the lid on it while we will remove the suspension. The suspension will be placed next to the wall and wrapped with mylar sheets.

We'll need:
(from the 40m) a dooly, mylar sheets, spare slings
(from Downs) heavy-duty inline scale
(from OMC lab) some tapes

2) The crane base is in CAML right now.

3) The yellow crane is in QIL right now. We'll dismount the top part and mount it on the base.

----

Steps

- Remove the lid. Place it on a clean safe platform.
- Remove the suspension, wrap it, and place it next the wall.
- Put the lid on.
- The chamber will be moved to CAML on Thu morning.

[JC, Stephen, Paco, Gabriele, Aidan, Radhika, Koji]

We have successfully extracted the crackle suspension from the chamber at the DOPO lab. We ended up using the engine hoist brought from the cryo lab instead of the yellow Skyhook as Skyhook's arm was too short.

Attachment 1 shows how the hoist is inserted to the table and how the lid was lifted. The lid was placed on a cardboard box wrapped with a Mylar sheet. It could be slid on the floor.

Attachment 2 shows how the suspension was lifted and placed on a similar Mylar-wrapped cardboard box. Upon the removal of the suspension, the cables were disconnected from the suspension. A few OSEM wires needed to be cut so that the suspension to be free.

Attachment 3 We are ready for the chamber transportation.

See the attachments.

[JC, Koji]

Caltech transport came in this morning. They first went to the OMC lab and moved the 3ft x 4ft table out. They lifted the heavy objects only with human power.

Then the suspension chamber was moved with a hydraulic lifter. (Attachment 1)
The chamber bottom was sled on the table. We asked them to leave the chamber lid on the mylar + cardboard sheet (Attachment 2) so that we can carefully close the lid with a crane (Attachment 3).

JC and I continued to work on the chamber closure, but it wasn't so straightforward.

The nominally planned location of the table (seen in Attachment 3) has a low ceiling and was not a great place to open/close the lid. It is high enough just to close the lid but we can't do anything else.

We worked on the crane operation close to the lab entrance (Attachment 4). We found that the chamber needed to be offset from the center of the table because the legs of the hoist turned out to be too wide to get in between the table legs. This low ceiling had ~3" gap to the crane when the lid was closed (Attachment 5). Meaning, we can't put anything in the chamber if the lid gets stuck with the low ceiling.

Anyway, the chamber was closed and the table was rolled to the end of the lab (for storage) (Attachment 6).

BTW, the rolling of the table further destroyed the floor (Attachment 7)

So, how high the ceiling should be, so that we can put a tall suspension in the chamber? We probably need to use the northeast part of the lab where the ceiling is much higher. But the crane itself can be another limitation. It needs careful consideration.

I made a quick investigation of the crane configuration for the suspension test chamber.

Conclusions:

• The table and the suspension test chamber need to be placed in the northwest corner of CAML where the ceiling height is 105"
• The engine hoist needs to be connected to the chamber with a shackle or something similar to avoid the interference of the chamber lid and the tilted crane jib.
  This shackle needs to raise the hanging point by ~3".

CAML has three types of ceilings.
1) Low ceiling area (west side) the clearance height 75.5"
2) Mid ceiling area (most of the lab area) 85.5". This is limited by the height of the FL light cover.
3) High ceiling area (northeast corner) 105". This is limited by the height of the FL light cover there.

Attachment P1
Nominal closed state: The chamber top height is about 68". Even in the low ceiling area, there is 7.5" space and the crane can remove the lid when the chamber is empty.

Attachment P2
Open chamber with suspension (direct connection): If the lid and the hook are directly connected, the corner of the chamber is going to be very close to the jib arm when the chamber is fully opened with ~1" clearance. This is not a safe condition, considering that the chamber can oscillate due to the lateral motion associated with raising the jib arm.

Attachment P3
Open chamber with suspension (connection via a 3" shackle): When the lid and the hook are connected via a 3" shackle, we'll observe a safe amount of clearance between the chamber and the jib arm. And the crane height is still 96" which is lower than the ceiling height of the high ceiling area of the lab.

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

Upper limits on the mechanical loss of silicate bonds in a silicon tuning fork oscillator​ and
Temperature Dependence of Losses in Mechanical Resonator Fabricated via the Direct Bonding of Silicon Strips
 https://www.sciencedirect.com/science/article/pii/S0375960117302359
https://link.springer.com/article/10.1134/S1063782620010200 (I don't have access, but I was given a PDF of this paper over the summer)

WIP
 

Previously, we had one Arduino taking the two thermocouple readings and another, separate one controlling the PWM of the hot plate. I have since combined them together, which is better because now only one computer and one set of Arduino code is needed to do all of the work. This also gives us the potential to, in the future, use re-time temperature feedback to control the heating rate.

Everything was a success. The PWM of the hot plate works the same as it did when I was using the other Arduino, and adding the PWM Arduino code to the thermocouple Arduino code has not broken the handshake with the Python code. I plan to play around with the code for bit, and try to see if I can get some real-time temperature feedback working.

I also added fork spade U-type connectors (stud size 10, WIRE18-22 AWG, McMAST 69145L433) to the wires going to the thermocouple, to make them easier to plug into the thermocouple-reading Arduino component (MAX6675). I used a hammer and a little solder to make sure the connectors stay on. To securely attach the connectors to the component, you need to unscrew, insert, and re-screw, which gives a nice, tight connection. Red should be positive and green should be negative, but I need to double check.

Here we lay out the Mariner cryocooler requirements and discuss the most recent cooldown model, which includes a cryocooler that cools down the inner shield and a separate LN2 dewar that cools the outer shield.

The chosen cryocooler must supply at least 2x the cooling power to the TM than the heat loads on the TM, at 123 K. Implicit in this requirement is that in the absense of temperature control, the cooling power must be enough to cool the TM to well below 123 K.

Attachment 1 is the latest Mariner ITM cooldown model. This updated model is pushed to mariner40/CryoEngineering/MarinerCooldownEstimation.ipynb. Before running the notebook you can toggle between IS cooling sources: LN2, DS30, CH-104, or in the future any crycoolers we are considering. All attachments are generated using the cooling curve of the DS30. 

Since the OS is no longer a heat load on the cryocooler, the IS gets cooled more efficiently and reaches within 5 K of the coldhead. The heat loads on the TM (snout, apertures, laser heating) make its temperature plateau just under 100 K. It reaches 123K in ~50 hours.

Attachment 2 is a power budget for the TM. We see that at 123K, the heat loads sum to ~0.4 W. The cooling power at this temperature is around 1 W. The DS30 satisfies our cryocooler cooling requirement; however vibration requirements / vacuum interface compatibility still need to be determined.

Lastly, Attachment 3 is an updated block diagram of the heat transfer couplings considered by the model. (The model also considers radiative links between the inner shield and cage, and inner shield and upper mass; these are omitted from the diagram for simplicity.)

Summarizing the current Mariner ITM cooldown model assumptions:

- Inner shield and outer shield have snouts of equal length (1 m end-to-end)

- Laser off during cooldown

- Inner shield cooled by DS30; outer shield cooled by LN2 tank

- ITM barrel emissivity = 0.9

Takeaways:

A simplified block diagram can be found in Attachment 4. 

I simulated the Mariner cooldown with an additional LN2 tank connected to the main cold strap shared by the cryocooler. LN2 can aid in the initial cooldown from room temperature, and once the inner shield is sufficienly cold the cryocooler can take full control. (The LN2 should not be on the whole time - once the inner shield crosses 77K the LN2 would be contributing heat.) In the model I chose the inner shield temperature of 90K to signal when to turn off the LN2 (any lower and the IS temperature starts to flatten out as it approaches 77K).

The closer the LN2 tank sits towards the chamber/IS (and away from the cold head), the better. This is because the cold head of the cryocooler drops rapidly to ~60K, and the LN2 joint would contribute to heating the cold head. Plus, the cooling of the IS is more efficient if the LN2 source is closer. The model assumes the LN2 tank sits halfway between the coldhead of the cryocooler and the inner shield.

The last assumpion made is that the LN2 tank volume is large enough such that the tip in contact with LN2 remains at 77K. 

In Attachment 1, the dashed traces show the cooldown of the cold head, inner shield, and test mass without the additional LN2 cooling. The solid traces include LN2 cooling and use the assumptions above in green. We see that the inner shield is cooled significantly faster with LN2 (on par with the cold head until 150K). As a result, the heat load the inner shield puts on the cold head is reduced, and that reduction more than compensates for the additional heating on the cold head from the LN2 at 77K. Thus the cold head cools much faster in the first 10 hours. The kinks in the cold head/inner shield traces are presumably from the system re-equilibriating after the LN2 source is shut off - it's not clear why the cryocooler doesn't immediately continue the downward trend.

The effect on the test mass is more subtle, but we see the test mass cools to 123K ~2 hours faster (in 28 h). I was then curious if we could get the same gains by simply moving the cryocooler/cold head halfway closer to the inner shield. This simulation is in Attachment 2 - it takes ~1 h longer for the test mass to reach 123K, since we don't get the added cooling power from the LN2.

While there's merit to the additon of LN2, maybe an improvement of a few hours isn't enough to justify the increase in complexity.

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.

Here is the model including an additional LN2 tank aiding in inner shield cooldown, applied to Voyager [Attachment 1]. The same assumptions have been made as in the previous ELOG. The LN2 is switched off once the inner shield reaches 90K.

Using LN2 in such a way cools down the test mass to 123K 5 hours faster. This is a ~6% improvement from the original 85 hours of cooldown [Attachment 2]. Note that the fundamental radiative cooling limit for a Voyager-like test mass is ~68 hours.

I am trying to use fminsearch to find the best cantilever dimensions to maximize the bond/cantilever energy ratio. Fminsearch takes in a function and a set of intial parameters. The function that is passed in should be a function of the parameters, but my getEnergy function does not work unless the COMSOL model is passed in as an argument. I tried to make a helper function, but I run into the same problem.

After running getRatio (attempted helper function):

>> getRatio
The COMSOL model is now accessible using the variable 'model'
Unrecognized function or variable 'model'.

Error in getRatio (line 3)
ratio = getEnergy(model, L, h, d)
 
>> 

The code works now. If the function is specified by a file, there should be an @ symbol front of it when it is passed into fminsearch.

Restricting the search to nothing less than the initial parameters (L = 2 cm, h = 0.3 mm, d = 0.55 mm), fminsearch outputs L = 2.0088 cm, h = 0.3000 mm, d = 0.5776 mm.

With the search restricted to L >= 1 cm, h >= 0.1 mm, and d >= 0.5 mm, fminsearch outpus L = 1.0313 cm, h = 0.1000 mm, and d = 0.5033 mm.

I am trying to get a plot of the fminsearch data, but I was not sure how to extract the data. But fminsearch has built in plots that I think capture the data pretty well.

Here is the code to generate a random list of parameters and evaluate the energy ratio of each. 

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.