40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
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ID Date Author Type Category Subject
17   Wed Jun 30 16:21:53 2021 StephenGeneralDesign specs

[Stephen, Koji]

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

WIP - also communicate the

Draft   Thu Oct 27 19:54:20 2022 Jennifer Hritz

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.

Draft   Fri Oct 28 21:39:34 2022
Draft   Mon Oct 31 23:51:15 2022
87   Sat Oct 1 23:00:03 2022 Jennifer HritzGeneralOptical Contacting(RESULTS!) Quick test heat and pressure test

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.

11   Fri Apr 23 10:41:22 2021 AidanGeneralDesign specs2 um photodiode requirements

22   Tue Aug 24 08:15:37 2021 Jiri SmetanaGeneralGeneralActuation Feedback Model

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 xi - the position of the intermediate mass, which is sensed and fed to the actuator servo, and xt - 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

$x_s = G_s(x_i - x_g) + n_s$

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

$\frac{F(s)}{x_s(s)} = G_as$

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

$\frac{F(s)}{x_s(s)} = \frac{G_as}{(s-p)^2}$

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 xg to xt 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.

26   Wed Sep 15 09:15:21 2021 Jiri SmetanaGeneralGeneralActuation Feedback Model and Noise

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.

27   Thu Sep 16 10:02:47 2021 Jiri SmetanaGeneralGeneralActuation Feedback Model and Noise

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.

 Quote: 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.

29   Fri Sep 24 11:02:41 2021 KojiGeneralGeneralActuation Feedback Model and Noise

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.
12   Tue Apr 27 12:28:43 2021 Nina Vaidya & Shruti MaliakalGeneralDesign specsArm Cavity Design 2021

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

14   Fri May 7 17:50:31 2021 Nina Vaidya & Shruti MaliakalGeneralDesign specsArm Cavity Design 2021 update

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%

62   Mon Jul 11 16:24:31 2022 Jennifer HritzGeneralOptical ContactingBaselining the temperature output of the Oster hot plate

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.

71   Wed Jul 27 14:50:20 2022 Jennifer HritzGeneralOptical ContactingBonding without liquids and narrowing down heating issue

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.

88   Sun Oct 2 23:23:07 2022 Jennifer HritzGeneralOptical ContactingCause of improved bond: time or pressure

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.

89   Mon Oct 3 23:32:30 2022 Jennifer HritzGeneralOptical ContactingCause of improved bond: time or pressure (Update)

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).

61   Fri Jul 8 17:09:10 2022 JuanGeneralGeneralCoil Driver and Sat Amp

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.

64   Mon Jul 11 17:39:17 2022 JuanGeneralGeneralCoil driver chassis

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.

21   Tue Aug 17 17:48:57 2021 KojiGeneralEquipmentCrackle SW model

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.

19   Tue Jul 27 11:38:25 2021 PacoGeneralDesign specsDOPO single pass PDC efficiency

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)

40   Tue Oct 12 12:49:42 2021 Jiri SmetanaGeneralGeneralDamping Loop (Point-Mass Pendulums)

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.

41   Thu Oct 14 04:17:36 2021 Jiri SmetanaGeneralGeneralDamping Loop (Point-Mass Pendulums)

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:

 Height [mm] Displacement RMS [nm] DAC Output RMS [V] Q Lower Resonance Q Higher Resonance Driver Resistor {Ohm] 600 560 0.51 5.3 1.5 175 550 580 0.54 5.1 1.4 175 500 610 0.49 5.0 1.4 150 450 630 0.54 5.0 1.4 150
 Quote: 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.

10   Fri Apr 2 19:59:53 2021 PacoGeneralDesign specsDifferential evolution strategies

### 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.

47   Fri Nov 5 11:51:50 2021 PacoGeneralDesign specsEstimate of in-air absorption near 2.05 um

[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.

48   Tue Nov 16 11:47:54 2021 PacoGeneralDesign specsEstimate of in-air absorption near 2.05 um

[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.

5   Fri Mar 5 11:05:13 2021 StephenGeneralDesign specsFeasibility of 6" optic size in CAD

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

65   Wed Jul 13 13:16:33 2022 JuanGeneralGeneralFinished coil driver and sat amp

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

63   Mon Jul 11 17:27:39 2022 Jennifer HritzGeneralOptical ContactingFirst successful bond

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.

56   Mon Jun 27 08:22:22 2022 JuanGeneralGeneralGeneral Update/ Need to do task

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

28   Sun Sep 19 18:52:58 2021 PacoGeneralDesign specsHR coating emissivity

[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:

$1 = \epsilon + R + T$

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.

33   Fri Oct 1 11:52:06 2021 PacoGeneralDesign specsHR coating emissivity

[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 ...

15   Fri Jun 4 11:09:27 2021 PacoGeneralDesign specsHR coating tolerance analysis

The HR coating specifications are:

 2128.2 nm 5.0 ppm $\pm$ 2 ppm 1418.8 nm 50.0 ppm $\pm$ 2 ppm

 2128.2 nm 2000.0 ppm $\pm$ 200 ppm 1418.8 nm 50.0 ppm $\pm$ 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:

$\mathcal{F} = \frac{\pi \sqrt{r_1 r_2}}{1 - r_1 r_2}$

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?

67   Mon Jul 18 18:34:29 2022 PacoGeneralDesign specsHR coating update

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.

68   Fri Jul 22 13:36:55 2022 PacoGeneralDesign specsHR coating update

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.

76   Tue Aug 16 09:58:23 2022 PacoGeneralDesign specsHR coating update

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.

90   Tue Oct 4 22:15:23 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM Test #1

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.

91   Wed Oct 5 23:24:08 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM Test #2

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.

92   Fri Oct 7 00:21:24 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM Test #3

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.

93   Fri Oct 7 21:20:08 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM v2 progress

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.

94   Sat Oct 8 23:22:25 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM v2 test #1

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.

95   Sun Oct 9 21:55:53 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM v2 test #1 & 2

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.

96   Mon Oct 10 15:34:13 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM v2.1,2,3 Test #1 and v2.3 Test #2

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.

97   Tue Oct 11 23:59:07 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM v2.3 Test #1 and 2

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.

98   Wed Oct 12 23:26:48 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM v2.3 Test #3

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.

99   Thu Oct 13 20:56:48 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM v2.4,5 Test #3

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.

101   Sat Oct 15 21:59:13 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM v2.6 Test #1, 2, 3

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.

100   Fri Oct 14 21:36:52 2022 Jennifer HritzGeneralOptical ContactingHot plate PWM v2.6 Test #3

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

49   Wed Nov 17 09:27:04 2021 Jiri SmetanaGeneralGeneralLagrangian Model - Translation & Pitch

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.

50   Wed Dec 15 06:43:43 2021 Jiri SmetanaGeneralGeneralLagrangian Model - Translation & Pitch

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):

 Resonance Type Frequency [Hz] Pendulum 1 0.85 Pendulum 2 2.10 Pitch 1 0.46 Pitch 2 2.37 Roll 1 17.13 Roll 2 46.09

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.

 Quote: 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.

44   Tue Oct 26 08:09:08 2021 Jiri SmetanaGeneralGeneralLagrangian Suspension Model - Extended Body

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?

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