ID 
Date 
Author 
Type 
Category 
Subject 
1

Thu May 21 11:51:44 2020 
Koji  General  General  Mariner Elog Test 
The first entry of the Mariner elog post 
2

Thu May 21 12:10:03 2020 
Stephen  General  Resources  Ongoing Mariner Resources 
Ongoing points of updates/content (list to be maintained and added)
Mariner Chat Channel
Mariner Git Repository
Mariner 40m Timeline [20202021] Google Spreadsheet

3

Fri Jun 5 11:13:50 2020 
Raymond  General  Heat Load  Steady state heat load example 
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


4

Thu Mar 4 17:04:52 2021 
Paco  General  Design specs  Silicon TM dichroic coatings for phase I 
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 Silicatantala 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 "insanelooking" solutions). The top picks in Attachment 1 may be a good starting point for a manufacturer. In order of appearance, they are:
 ETM_210218_1632
 ETM_210222_1621
 ETM_210302_1210
 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:
 ITM_210303_1806
 ITM_210204_1547
 ITM_210304_1714

5

Fri Mar 5 11:05:13 2021 
Stephen  General  Design specs  Feasibility 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 asis, 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

6

Wed Mar 17 19:51:42 2021 
Paco  General  Design specs  Silicon TM dichroic coatings for phase I 
Update on ETM
New optima are being found using the same basic code with some modifications, which I summarize below;
 Updated wavelengths to be 2128.2 nm and 1418.8 nm (PSL and AUX resp.)
 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)
 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.
 Included a third wavelength as transOPLV (for the OPLEV laser) which tries to get R ~ 99 % at 632 nm
 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.
 Adapted the MCMC modules (doMC, and cornerPlot) to check the covariance between the transmissivities at 2128 and 1418 for a given design.
 Reintroduced significant weights for TO noise and Brownian noise cost functions (from 1e11 to 1e1) 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.

7

Wed Mar 17 21:24:27 2021 
gautam  General  Design specs  Silicon TM dichroic coatings for phase I 
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?
Quote: 
Attachment 2 shows the stack. Surprisingly not as crazy (or maybe I have internalized the old "crazy" as "normal")


8

Wed Mar 24 17:36:46 2021 
Paco  General  Design specs  Least common multiple stacks and varL cost 
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 mbilayers 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.

9

Wed Mar 24 17:42:50 2021 
Paco  General  Design specs  Silicon TM dichroic coatings for phase I 
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...
Quote: 
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?


10

Fri Apr 2 19:59:53 2021 
Paco  General  Design specs  Differential 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. 
11

Fri Apr 23 10:41:22 2021 
Aidan  General  Design specs  2 um photodiode requirements 
MCT HgCdTe requirements: https://docs.google.com/spreadsheets/d/1lajp17yusbkacHEMSobChKepiqKYesHWIJ6L7fgryY/edit?usp=sharing

12

Tue Apr 27 12:28:43 2021 
Nina Vaidya & Shruti Maliakal  General  Design specs  Arm 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 
13

Fri May 7 09:57:18 2021 
Stephen  General  Equipment  Overall Dimensions for Mariner Suspension Test Chamber Concept 
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?

14

Fri May 7 17:50:31 2021 
Nina Vaidya & Shruti Maliakal  General  Design specs  Arm 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 380.5% = 37.81 (with RoC 56.2) works well.
To summarise the design:
RoC = 56.2 +/ 1%
L = 38 +/ 0.5% 
15

Fri Jun 4 11:09:27 2021 
Paco  General  Design specs  HR coating tolerance analysis 
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? 
16

Tue Jun 22 22:28:09 2021 
Koji  General  Design specs  Test Mass wedge design 
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 invacuum tables. Considering the presence of the cryo baffles, we need to isolate the pickoff 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 invacuum 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 inair 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/ 
17

Wed Jun 30 16:21:53 2021 
Stephen  General  Design specs  
[Stephen, Koji]
WIP  check layout of 60 cm suspension in chamber at 40m, will report here
WIP  also communicate the 
18

Wed Jul 7 16:32:27 2021 
Stephen  General  Equipment  Overall Dimensions for Mariner Suspension Test Chamber Concept 
WIP  Stephen to check on new suspension dimensions and fit into 40m chamber 
19

Tue Jul 27 11:38:25 2021 
Paco  General  Design specs  DOPO single pass PDC efficiency 
Here is a set of curves describing the singlepass downconversion efficiency in the 20 mm long PPKTP crystals for the DOPO. I used the "nondepleted pump approximation" and assumed a planewave (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 linearinpump 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 freespace 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 singlepass 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 (~ 2040 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) 
20

Fri Aug 6 04:34:43 2021 
Koji  General  General  Theoretical Cooling Time Limit 
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 surfacevolume 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. 
21

Tue Aug 17 17:48:57 2021 
Koji  General  Equipment  Crackle 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. 
22

Tue Aug 24 08:15:37 2021 
Jiri Smetana  General  General  Actuation 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 EulerLagrange 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 pointmass 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 rolloff after the resonances, given by
where p is the pole frequency at which we want the rolloff 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 rolloff. I can now provide the ground and noise spectra and propagate them through to work out the fluctuations of the test mass position. 
23

Thu Aug 26 17:40:41 2021 
Stephen  General  Suspension  Selecting MOSstyle frame 
[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 MOSstyle (4 posts, rectangular footprint).
 We looked at a scaledup 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).
MOSstyle it is, moving forward!
Also, Checked In to PDM (see Attachment 2  filename 40mETMsuspension_smallshields.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! 
24

Thu Sep 9 11:25:30 2021 
Paco  General  Design specs  Rerun HR coatings with n,k dispersion 
[Paco]
I've rerun 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 lowtemperature estimates to roomtemperature measured (?) dispersions are able to push the HR transmission up by a few (23) 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. 
25

Thu Sep 9 20:42:34 2021 
Paco  General  Design specs  Rerun HR coatings with n,k dispersion 
[Paco]
Alright, I've done a reoptimization 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. 
26

Wed Sep 15 09:15:21 2021 
Jiri Smetana  General  General  Actuation 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 Smetana  General  General  Actuation Feedback Model and Noise 
Here's the DAC voltage spectrum with its associated RMS.
Also, for clarity, this model is for a lossless pointmass 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.


28

Sun Sep 19 18:52:58 2021 
Paco  General  Design specs  HR 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:
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. 
29

Fri Sep 24 11:02:41 2021 
Koji  General  General  Actuation 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 openloop 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 cutoff frequency from 10Hz to 12Hz to make the damping of the 2nd peak stable.

30

Fri Sep 24 13:12:00 2021 
Radhika  General  Heat Load  Mariner cooldown model status + next steps 
*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 roomtemp 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 temperaturedependent emissivities. It should be straightforward to incorporate the emissivity data once it is available. Currently, the script uses roomtemperature values for the emissivities of various materials.
Future steps:
 Incorporate tabulated emissivity data
 Verify and update inner/outer shield dimensions

31

Mon Sep 27 17:01:53 2021 
rana  General  Heat Load  Mariner cooldown model status + next steps 
How about a diagram so that we can understand what this model includes? 
32

Wed Sep 29 16:15:19 2021 
Radhika  General  Heat Load  Mariner cooldown model status + next steps 
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 roomtemperature 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. 
33

Fri Oct 1 11:52:06 2021 
Paco  General  Design specs  HR 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 ... 
34

Fri Oct 1 12:01:24 2021 
Paco  General  Design specs  TM Barrel coating emissivity 
[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:
 * Air  SiO2 x 800 nm  Ta2O5 x 5 um  Silicon *
 * Air  Ta2O5 x 10 um  Sio2 x 20 nm  Silicon *
 * Air  SiO2 x 100 nm  TiO2 x 1 um  Silicon *
Attachments # 13 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. 
35

Fri Oct 1 13:24:40 2021 
Aidan  General  Design specs  TM Barrel coating emissivity 
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 AIrTa2O5 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 6E6. So whatever is under the Ta2O5 layer should be irrelevant  there is negligible reflection.
Quote: 
[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:
 * Air  SiO2 x 800 nm  Ta2O5 x 5 um  Silicon *
 * Air  Ta2O5 x 10 um  Sio2 x 20 nm  Silicon *
 * Air  SiO2 x 100 nm  TiO2 x 1 um  Silicon *
Attachments # 13 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.


36

Fri Oct 1 14:11:23 2021 
Paco  General  Design specs  TM Barrel coating emissivity 
Agree with this. Quickly running tmm on the same "stacks" gave the Attachment #13. (Ignore the vertical axis units... will post corrected plots) and extend the wavelength range to 100 um. 
37

Tue Oct 5 17:46:14 2021 
Radhika  General  Heat Load  Mariner cooldown model status + next steps 
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 m^{2} 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. 
38

Mon Oct 11 15:22:18 2021 
Yehonathan  General  General  Microcomb alternatives 
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 modelocked lasers.
Indeed, frequency combs generated directly from a modelocked laser are expensive as they require ultrabroadband operation (emitting few fs pulses) to allow for f2f interferometry.
Microcombs are a fancy way of generating combs. They are lowpowerconsuming, chipscale, 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. Lowpower means that the output comb will be weak (on the order of uW of average power). Microscopic/chipscale means that they suffer from thermal fluctuations. High reprate 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 fullsolution frequency combs, we could use much less fancy modelocked 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. Highpower (typically 100mW)
2. Low reprate (typically 100MHz)
3. Relatively cheap
4. "Narrowband" modelocked 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 34:
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 octavespanning 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 1f2f interferometry. These limitations apply only when pumping in the anomalous dispersion regime as traditionally have been done. Pumping in an allnormal (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 meterlong fibers though.

39

Tue Oct 12 12:44:44 2021 
Jiri Smetana  General  General  New Damping Loop Model 
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. 
40

Tue Oct 12 12:49:42 2021 
Jiri Smetana  General  General  Damping Loop (PointMass 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 selfexplanatory. 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 Smetana  General  General  Damping Loop (PointMass 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 selfexplanatory. 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.


42

Fri Oct 15 13:45:55 2021 
Radhika  General  Heat Load  Mariner cooldown model status + next steps 
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 m^{2}, but the relative times should stay roughly consistent with different IS area choices.) 
43

Fri Oct 15 14:31:15 2021 
Radhika  General  Heat Load  Mariner cooldown model status + next steps 
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 m^{2} is negligible. Cooldown time to 123K is ~100 hrs, just over 4 days. I've kept IS area set to 0.22 m^{2} 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. 
44

Tue Oct 26 08:09:08 2021 
Jiri Smetana  General  General  Lagrangian 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 pointmass 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 pointmass 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 pointmass 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 pointmass 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? 
45

Wed Nov 3 02:52:49 2021 
Koji  General  Suspension  Mariner Sus Design 
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 440 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. 
46

Thu Nov 4 00:42:05 2021 
Koji  General  Suspension  Mariner Sus Design 
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. 
47

Fri Nov 5 11:51:50 2021 
Paco  General  Design specs  Estimate of inair absorption near 2.05 um 
[Paco]
I used the HITRAN database to download the set of rovibrational 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 inair 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 inair 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 inair absorption at 2050 nm would amount to ~ 1 ppm. 
48

Tue Nov 16 11:47:54 2021 
Paco  General  Design specs  Estimate of inair 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. 
49

Wed Nov 17 09:27:04 2021 
Jiri Smetana  General  General  Lagrangian 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 inputtooutput 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 Smetana  General  General  Lagrangian 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 nonzero. 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 lengthpitch 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 inputtooutput 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.

