S1600439, not annealed, as received from Mark Optics

Design of optical lever electronics

Design

Koji, Rich, and I recently came up with a new QPD design which is better for general lab use than the aLIGO ones (which have a high-noise preamp copied from iLIGO).

https://dcc.ligo.org/LIGO-D1500467

This page has the mechanical drawing only, but perhaps Rich can tell us if he's ready to make the first version for you or not. I think you can get by with the old design, but this new one should be lower noise for low light levels.

131

Wed Sep 28 10:26:58 2016

rana

General

references on ideal glasses

Some easy to read reviews on thin films and ideal glass for people getting started in this Q measuring game.

M. D. Ediger, in PNAS (2014), pp. 11232–11233.
A. J. Leggett and D. C. Vural, arXiv cond-mat.dis-nn, arXiv:1310.3387 (2013).
L. Berthier and M. D. Ediger, arXiv cond-mat.mtrl-sci, 40 (2015). Phys. Today.
G. Parisi and F. Sciortino, Nature Materials 12, 94 (2013).
S. Singh, M. D. Ediger, and J. J. de Pablo, Nature Materials 12, 139 (2013).

244

Sat Dec 17 06:29:15 2016

rana

Timing issue: is it a DAC issue?

Configuration

I find sometimes that the probe configuration can give these distorted signals. For the Tektronix probes, its best to use a 500 MHz probe instead of the BNC clip leads. The probe also should be compensated by attaching to the gold fingers square wave generator on the scope front and adjusting the capacitor in the probe with a little screwdriver until the square wave becomes perfect.

Wed Jul 11 23:01:01 2012

janosch

Optics

Characterization

starting the multi-color scatter experiment

Steve Maloney, a visiting highschool teacher, and I have started to set up a new scattering experiment in the Richter lab. The idea is to take images of large-angle scattered light using different lasers. We have one 633nm laser, and 532nm and 405nm laser pointers. The goal is to uniformly illuminate the same disk of about 1cm diameter on a silver-coated mirror with all three colors. We use a silver-coated mirror to make sure that the light is reflected from the same layer so that all colors are scattered from the same abberations.

The image shows one of the laser pointers and the HeNe laser. The first step is to widen the beam with a f=5cm broadband, AR coated lens (Newport PAC15AR.15). The diverging beam is then aligned through an iris to give it the right size on the mirror. In this way, illumination is almost uniform on the mirror surface.

The mirror is mounted over the rotation axis of a unipolar stepper motor. For the moment we only took images from fixed direction (initially with a commercial digital camera, later with a monochromatic Sony XT-ST50 CCD camera. The problem with the commercial camera was that you cannot completely control what the camera is doing. Also it would have been very difficult to calibrate the image once you start comparing scattering with different colors. A f=7.5cm lens is used to image the illuminated disk on the CCD chip to make maximal use of its resolution. The CCD signal is read out on a Windows machine with an EasyCap video capture device connected to a USB port. Standard software can then be used to take images or record videos. For some reason the capture device reduces the image size to 640x480 pixels (a little less than the size of the CCD chip).

Eventually the camera and lens will be mounted on a metal arm whose orientation is controlled by the stepper motor. The stepper motor was part of the Silicon Motor Reference Design (Silicon Laboratories). It comes with all kinds of cables and a motor control board. Software is provided to upload compiled C code to the board, but for our purposes it is easiest to use primitive communication methods between the PC and the board. We are working with HyperTerminal that used to be part of Windows installations, but now it has to be downloaded from the web. This program can send simple commands through TCP/IP and COM ports. These commands allow us to position the motor and define its rotation speed. Since our PC does not have a serial port, we purchased a Belkin USB Serial Adapter. You will have to search the web to find suitable drivers for Windows 7 x64. Luckily, Magic Control Technology has similar products and the driver for their U232-P9 USB/serial adapter also works for the Belkin product.

So our goal for the remaining weeks is to take many images from various angles and to set up the experiment in a way that we can VNC into our lab PC and control everything from the Red Door Cafe.

Fri Jul 13 10:34:35 2012

We were confused a bit about how the camera image changes when you move the arm that holds the camera and lens around the mirror. It seems that scattering centers move in ways that cannot be explained by a misaligned rotation axis. So we wanted to make sure that the mirror surface is actually imaged as we intended to. We generated a white grid with 0.7cm spacing and black background on a monitor. The image that we saw is exactly how we expected it to be. So the image mystery has other reasons.

Fri Jul 13 20:53:35 2012

The following two pictures were taken from the same angle with green (left) and red (right) incident laser at an angle of 15deg from the incident beam (reflected to about -5deg). Some scattering centers are collocated. The green laser power is about 5 times as high as the red laser power, but this factor does not seem to calibrate the image well (the green image becomes too dark dividing all pixel values by 5). So there seems to be a significant difference in the divergence of the two lasers. We will have to use a photodiode to get the calibration factor. These images were taken after cleaning the mirror. Before cleaning, there was way too much scattering and the images were mostly saturated.

Tue Jul 17 18:32:11 2012

We have the new 405nm laser pointer. The image to the left shows the scattered light from the red laser, the image to the right scattered light from the purple laser. Both images were taken 30deg with respect to the normal of the mirror surface. Also, we got a new gallon of Methanol. After cleaning the mirror multiple times, the scattered light became significantly weaker. So the purple images look very different from red and green. It could be that the lens that we use to image the mirror surface is the problem since it is specified for the wavelength range 1000nm-1550nm. Could it also be the CCD camera? Anyway, to be sure I will order another broadband lens.

Wed Jul 18 18:43:34 2012

Here a little purple video. It starts with scattering angle around 15deg and stops at about 80deg.
There are some clear point defects visible especially at small angles.
I will not start to think about some other interesting details of this video before I got the new lens.

Ed: The AVI did not run on Mac. I posted it on youtube. Koji

Fri Jul 20 18:35:42 2012

janosch

Optics

Characterization

purple improvements and first uncalibrated BSDF curves

Today we improved alignment of the lens-camera arm. We discovered earlier that this alignment affects the amount of "snowfall" on the scattering images. Looking at the latest 405nm video (see attachment), one can still see snowfall, but it is considerably weaker now and the true scatter image is clearly visible. We took a set of scatter images at certain scattering angles and produced BSDF curves. The shape of these curves has partially to do with the snowfall contribution, but one also has to keep in mind that the mirror quality is much worse than what has been used in the Fullerton measurement. We still need to calibrate these curves. The calibration factor is different for the two images so that you cannot even compare them at the moment except for their shape.

Today we also got the new broadband lens for the camera arm. First measurements show that image quality is better. Playing a bit around with distances between object mirror, lens and image plane, we also found that image quality becomes better when the lens and camera get closer to the mirror (which is only an issue for the 405nm measurement since 633nm and 532nm look very good anyway). So we are thinking to change the camera arm setup to make it much shorter.

Tue Jul 24 10:59:59 2012

janosch

Optics

Characterization

sum of purple and red

We played around with Matlab today. The first step was to convert light wavelengths into RGB colors. In this way we can combine images taken at different colors. The picture shows the purple and red images (stored in gray scale) in heat colormap. Then the sum of these two images is calculated in their natural RGB colors.

Fri Oct 12 16:23:20 2012

Nothing has happened since Steve, the visiting highschool teacher, has left. Meanwhile, some parts of the multi-color BRDF setup were delivered. I assembled everything today and realigned the lasers. Everything is ready now for a three-color BRDF measurement (the previous Richter record was 2 colors). I will claim back my video capture device as soon as possible from my neighbors and then take new images.

173

Thu Nov 10 14:13:34 2016

gabriele

MATLAB code to control Thorlabs stages

Configuration

To be used to automate the laser polishing.

Thu Jul 14 15:30:48 2016

ericq

S1600713 S1600714 S1600715 S1600716

Configuration

Cymac RTS configuration

We played around a bit with the cymac, in efforts to make things better.

We disabled some more fancy-sounding options in the machine's BIOS
I created safe.snap files for the x3iop and x3tst models
- x3iop's was created by booting the model while mashing the EPICS command to set the burt restore bit, and then saving the EPICS database to file via the SDF screen
- x3tst's was created by copying an existing .snap file
I gave the controls user ownership of /frames via sudo chown controls:controls /frames
I then created the following folders (which the daqd log was complaining about not finding_
- /frames/full
- /frames/trend/minute
- /frames/trend/minute_raw
- /frames/trend/second
I also created the folder /opt/rtcds/tst/x3/target/fb, since that is listed in the daqd config as the nds job dir. (However nds does not seem to be running. Is it needed? I couldn't compile it in the rtbuild directory)

As I see it, the main problems that persist are:

daqd crashes over and over again every few seconds
- The logs seem to be complaining about EPICS server problems. Is the related to whatever situation made the epics-env script neccessary?
The IOP seems to be taking too much time: 8-9 usec
- This is especially problematic as Gabriele actually wants to run the IOP at an even faster rate than the current 64k, which isn't possible with the current timing

702

Fri May 24 15:08:19 2019

alena

General

Measurements

2019-05-24

15:00 in chamber
- S1600713 in CR1
- S1600714 in CR2
- S1600715in CR3
- S1600716 in CR4
15:08 roughing pump on
15:22 turbo pump on

Low pressure gauge glitching again. Tried restarting the gauge a few times - no result. Vented the chamber.

15:50 restarted the rouging pump, then the tubbo - no result. Aborted the measurement

689

Mon May 13 18:37:47 2019

Mon May 13 18:37:37 2019

Entered CRIME lab to borrow 4x hair nets and face masks. Can you please advise on what I should order for clean lab equipment? There are more options on techmart than I anticipated. We're in the process of increasing the cleanliness of the SiQ experiment.

696

Mon May 20 10:35:45 2019

Aaron,

There is a buy list of approved clean room supplies posted here https://dcc.ligo.org/LIGO-E1300399. This list is used by designated people to keep clean rooms supplies stock at each site including LIGO labs in Downs, 40m and the CRIME lab. Not sure what lab you are working in and what regulations you have there. Typically we study the list of the approved supplies, figure out what budget can be used for supplies for a particular experiment. Depending on what your project is, you may be able to just take what you need from the existing LIGO stock (I believe there is one for Downs and one for Bridge and 40m) or work with Liz, Bob or Chub on ordering it for your via approved channels.

Quote:

Mon May 13 18:37:37 2019

401

Wed Aug 9 17:07:57 2017

2017-08-09

From the data I have gathered from a variety of MATLAB sweeps, I think that the optimal geometry I can produce has the parameters in the attached image. Neither the original or optimized drawing is to scale. The gap between the arms of the electrodes should be 1.25 mm, the arm width 0.55 mm, the arm length 16 mm, and the offset of the arms 3.5 mm.
It is also optimal to place the ESD as close to the sample disk as can reasonably be achieved, at around 0.5 mm away. Since the force on the disk scales exponentially with the distance from the ESD, decreasing that gap is the most substantial way to impact the excitation. Decreasing the gap from 1 mm to .5 mm increases the excitation of the modes by approximately a factor of 8.
From my simulations, the shift in geometry alone still has a useful impact on the excitation. Modes 1 and 3 are the only two modes that are less excited by the new geometry, mode 1 is 10% weaker and mode 5 is 5% weaker. Modes 5 and 6 are nearly unaffected by the shift, mode 5 is 2% stronger and mode 6 is 5% stronger. Modes 7, 18 and 19 are outliers, 7 is excited by a factor of 7, 18 by a factor of 4 and 19 by a factor of 17. The rest of the modes are improved by between a factor of 1.5 and 3. For mode numbers, shapes, and frequencies a plot is included.

420

Fri Aug 18 15:10:23 2017

2017-08-18

We created a prototype of PCB for the ESD design. Unfortunately the orientation of the two combs was flipped, so it will require some creative mounting to get right. The final design had a 6 mm offset between the two combs, .5 mm traces and 1 mm gaps between them The vertical traces are 12 mm long and there is a 3.75 mm gap between the end of the vertical traces and the opposite horizontal one. The ESD will arrive on Tuesday to be installed Wednesday and we will see how the new design works out.

421

Wed Aug 23 14:11:13 2017

Zach, Gabriele

Measurements

Installing ESD Prototype

2017-08-23

Installed ESD Prototype design by taping it to the older design, we then lowered the mount until it was as close as we could reasonably get it. The new PCB lines up when the top of the new PCB is lined up with the last electrode on the old one. The new PCB was slightly too narrow, the mounting holes are very close to the edge of the PCB, this can easily be corrected in later models.
Installed sample S1600541 into the single sample apparatus
Roughing pump on at 12:32
Turbo pump on at 2:28pm

Link to image1.JPG Link to image2.JPG

351

Thu Jun 22 13:16:37 2017

Beginning with COMSOL

2017-06-21

4:30 pm- Installed COMSOL, began modeling current ESD by creating parameters and the first arm of the comb

352

Thu Jun 22 15:37:20 2017

2017-06-22

Created the geometry of the ESD by creating blocks and joining them with Unions. I then created a block to serve as the domain and added air to that region
This plot is a combination of a Surface plot of the potential and a Streamline plot of the electric field
I created another model of the ESD with more accurate measurements to the real thing and added the silica disc to the model

353

Fri Jun 23 12:02:12 2017

2017-06-23

I created plots of the E field and potential from my rough model of the ESD. This model has 1mm electrode arm widths and spacings, the length of each arm is 16 mm, and the resulting total size is 38mm x 20 mm x 0.1 mm. One comb has ten arms while the other has nine to match the actual ESD currently in use in the lab.
I set the ten arm comb to a potential of 100 V and the other to ground. I then used physics controlled mesh with an extremely fine element size to computer the simulations. With mesh sizes larger than extra fine, there was clearly non-physical error in the electric field and potential graphs that appeared as inexplicable field lines, spikes, and coarseness in the plots.
To create readable plots of the potential I created a Cut Plane in the center of the ESD perpendicular to both the arms and the plane of the device. The plots are attached with a milimeter length scale. I created a filled contour plot of the potential that is very clean, I tried a couple of different options for the electric field because it is harder to represent well. I created a contour plot for the norm of the electric field as well as superimposing a streamline plot of the field lines over that. Everything behaves generally as expected though I do suspect the spikes in electric field at the edges of each electrode are due to the fact that they are sharp corners and not smooth edges.

356

Tue Jun 27 14:17:47 2017

Further plots and improving models

2017-06-27

I built a new model of the ESD to determine whether or not the spikes in the electric field at the corners was affecting the results enough that it had to be accounted for in further models. To create the model, I created a 2D profile of the arm used in my original model and filleted the corners at a radius of .05 mm, since the electrode model is .1 mm thick, this made completely rounded edges. In creating this model I caught an earlier mistake in the original one, I only set one half of the surface of the electrodes to have a potential or to ground, the "bottom" was left with no charge. I fixed this mistake and then compared the two models at a potential of 1000 V. For speed of computation I ran both models with a finer mesh size and then calculated the electric field at approximately the middle of the ESD, 1mm above the fourth electrode arm. For the rounded electrodes the field had a value of 84024 V/m and for the rectangular electrodes the field had a value of 80728 V/m, which is less than a 4% difference in field magnitude. Furthermore, the field shapes appear nearly indistinguishable; I am confident from this test that I can proceed modelling the arms of the ESD as rectangles.

359

Thu Jun 29 16:40:41 2017

Accurate model and force profile

2017-06-29

I created a much more accurate model of the current ESD setup from the technical drawings. My resulting ESD has dimensions of 21.3x24.3x.1mm with 1 mm spacings and 17.5 mm long electrode arms. The sample has a diameter of 75 mm and thickness of 1mm, the ESD is 1mm below the sample in the current model. I still have to compare the technical drawings to confirm that is the actual distance in the current lab setup.
I was able to calculate the force profile on the disk from the ESD. COMSOL struggled to resolve the data with a small mesh size over the whole domain, so I created a region of extremely fine mesh around the ESD and the disk and then made the rest of the mesh size normal sized. Over the domain near the ESD my mesh size ranges from 2.5*10^-3 to .25 mm and over the rest of the domain it's automatically setup at the normal size.
The force on a single dipole is given as $F = (P \cdot \nabla)E$ , since fused silica is isotropic it's polarization is proportional to E so $F = \chi_e \epsilon_0 \nabla (E^2)$ . The electric suscepitibility of fused silica is 1.09, I plotted the profile of the force perpendicular to the plane of the disk and exported data files of the full vector quantity of the force for use with Matlab.

360

Fri Jun 30 11:02:18 2017

2017-06-30

I adjusted the plot parameters slightly so that it only showed the actual force profile on the sample in the direction perpendicular to the sample surface. Additionally I compared the two methods of computing the force, as $\vec{F} = -(\vec{P}\cdot \nabla)\vec{E}$ and as $\vec{F} =- \chi_e \epsilon_0 \nabla \vec{E}^2$ . The profile of the force in both instances appear equal, but they differ in magnitude by exactly a factor of 2, I plotted the force computed with the explicit polarization doubled and the force magnitudes matched exactly. I'm still not entirely sure where this factor of two could be coming from.

361

Fri Jun 30 16:27:56 2017

Double Checking Model

2017-06-30

In order to confirm the accuracy of my model I checked some easily computable quantities between what real values and what COMSOL produced. My expected electric field magnitude between the electrodes is 10⁶ V/m and COMSOL reads out 1.015*10⁶which is less than a 2% error. When I went to compute the electric field gradient however, I discovered that I had been calculating my derivatives wrong, I was calculating full derivatives when I needed partial derivatives. Due to some subtleties of the numerics involving curl calculations are the order of the variables, in order to calculate a partial I belive that I have to map the results of the electric field to Lagrange elements.

363

Wed Jul 5 12:01:51 2017

Force plots-Correct plots, force issue

2017-07-05

I sorted out my mathematical lapse in logic and computed the correct force profiles in the perpendicular direction in both disks. The issue is that now the force profiles don't match up. The fact that there is a measured force distribution for the E^2 case outside the disk is only an artifact of the numerics because it is being calculated only from the electric field data which is defined outside the sample. It can be easily removed for final plots once the force distributions are matched by either redefining the cut plane or putting a data filter specifically on the E^2 plot. The jumps in the E^2 plot suggest that the meshing is still too large, I will try to fix this first, hopefully it will help resolve the difference.

364

Wed Jul 5 16:40:51 2017

Force disparity-improvement

2017-07-05

In order to improve my data I shrunk the region of the finer meshing slightly and made the mesh even smaller and then recalculated the force profiles. This time I tried sampling regions inside the disc rather than immediately at the surface. The attached graphs were sampled at the center of the disc. These two techniques vastly improved the data, now the profiles appear the same, but the magnitudes differ by a factor of 2 again. Previously this was due to an error in my calculation of the force, now I do not believe this to be the case. I will leave my work here for the purposes of my first report, it is an interesting result. I also restricted my data set to the finely meshed box which resolved the earlier data display issue.

365

Thu Jul 6 12:08:35 2017

Checking physical parameters

2017-07-06

I compared the electric field and the polarization to make sure that those calculations made sense. Since $P = \epsilon_0 \chi_e E$ due to the linear dielectric, I plotted the electric field and the polarization divided by the proportionality constant and they match exactly.
This confirms both the constant value and the polarization distribution but gets me no closer to resolving the factor of two

366

Thu Jul 6 12:48:54 2017

Resolving the factor of two

2017-07-06

I resolved the factor of two from Griffiths' discussion of dipoles in non-uniform electric fields. The force on a dipole in a non-uniform field is $\textbf{F}=\textbf{F}_+ + \textbf{F}_-=q(\Delta \textbf{E})$ where $\Delta \textbf{E}$ is the difference in the field between the plus end and the minus end. Component wise, $\Delta E_x = (\nabla E_x) \cdot \textbf{d}$ where d is a unit vector. This holds for y and z, the whole thing can also be written as $\Delta \textbf{E} = (\textbf{d} \cdot \nabla) \textbf{E}$ . Since p=qd, we can write $\textbf{F} = (\textbf{p} \cdot \nabla) \textbf{E}$ .

Jackson derives it differently by deriving the electrostatic energy of a dielectric from the energy of a collection of charges in free space. He then derives the change in energy of a dielectric placed in a fixed source electric field to derive that the energy density w is given by $w = -\frac{1}{2} \textbf{P} \cdot \textbf{E}_0$ . This explicity explains the factor of two and is an interesting alternative explanation.

367

Wed Jul 12 15:08:59 2017

Model of actuator and sample

2017-07-12

I am attaching the first fully functioning model of the actuator and sample. I cleared both meshes and solutions to make the file a reasonable size, but they can quickly be built/solved again.

368

Fri Jul 14 16:43:24 2017

Force profile matlab script

2017-07-14

I have completed a rough, but functioning script that calculates the modal force profiles. The force values are still coming out incorrect (on the order of 10^14) but the script can take in my model as a .m file and return an array with a force value per mode. I am attaching both the .m file and the matlab script
I have done very little work with the numerical integration itself, based on the 2D numerical integration code I received I just appended a z component and left it at that so when I return from Livingston I will fix that component

371

Thu Jul 20 11:37:01 2017

2017-07-20

I believe my MATLAB script successfully calculates the force distribution into each of the modes specified by the parameters. My previous error was caused by my neglecting the proportionality factor of $\frac{1}{2}\chi_e\epsilon_0$ . Now the force order of magnitude is on the order of 10³. I am currently unclear how to think about the units of the mode shapes from the disk_frequencies script, but I will pick it apart more carefully and try to figure that out. Then it will be a matter of converting units so that it matches with the N/m^3 from the COMSOL script and then comparing with real lab results. It seems to me that the error in force distribution should be inversely proportional to the number of modes calculated, in which case it would be useful to determine an appropriate number of modes to calculate.

375

Mon Jul 24 09:13:45 2017

2017-07-24

I wrote a MATLAB script that is capable of sweeping parameters, the code is attached. The next step is to create nested loops so that I can sweep multiple parameters in a single run. I also should add a function in the script to eliminate the modes that cannot be measured by the experimental setup.
My first sweep was for the gap between electrodes and swept from 1 to 2 mm. In the plot the gap grows from steps 1 to 6 and the only obvious effect in the plot is a decrease in force from the highest mode. Intuitively it makes sense that a wider gap would decrease the force because the electric field is diminished by spreading out the electrodes.
I would like to add a parameter for the overlap of the electrodes, but this would require substantial redesigning of the COMSOL model due to the multilevel dependency on parameters.

378

Tue Jul 25 13:38:30 2017

Parametric Sweep of ESD gap

2017-07-25

I completed a short sweep of the gap between the drive and the sample, between .5 and 1 mm in .1 mm increments. It appears that a 1 mm distance is the ideal distance by approximately a factor of two. I will next sweep larger distances and see how the force profile behaves at greater distances.

379

Wed Jul 26 09:27:40 2017

Sweeping the space between ESD and sample

2017-07-26

I ran a sweep of the gap between the ESD and the sample, first from .5 mm to 1 mm. That sweep suggested that there is a significant jump in force across almost all of the modes at 1 mm. To confirm this I double checked the geometry and it appears that COMSOL is building everything as expected when changing the spacing parameter. Then I ran a finer sweep in .02 mm increments for the spacing between .9 and 1.1 mm. Once again it appears there is a large jump as the gap approaches 1 mm, but the behavior does not seem to be symmetric about that point, the force appears to diminish linearly as the gap increases beyond 1 mm. I will run a sweep of the ESD arm spacing along with the vertical gap to confirm that the jump occurs when the gap between the ESD and the sample is equivalent to the spacings between the ESD arms.

381

Wed Jul 26 21:22:50 2017

Parametric Sweep Results

2017-07-26

I resolved the major bugs in the parametric sweep scripts and ran low resolution sweeps of the gap between the ESD and sample (Gap Sweep) and the spacing between the ESD arms (ESD Arm Gap Sweep).
The arm gap sweep largely behaved in a reasonable way with a maximum excitation at a 1.25 mm gap. However modes 14, 19, and 25 did not follow the general trends and had sharp drops and increases compared to the other modes.
The sample gap sweep had less intuitive behavior, all of the modes followed the same general double peak trend that drops to zero when the gap is 1.5 mm. I cannot explain exactly why it is behaving that way, I will run a higher resolution sweep and examine the geometry in greater detail.

382

Thu Jul 27 13:37:31 2017

Corrected sample gap sweep

2017-07-27

I resolved a couple more data processing bugs and calculated a sweep of the ESD-Sample gap from a distance of .5 mm to 1.5 mm. The resulting data behaves far more like I would expect from a force generated by an electric field, it seems to drop off like distance squared. This is a very strong correlation with a good intuitive explanation, and would suggest that it is prudent to place the ESD as close to the sample as possible.
I also computed a higher resolution sweep of the gap between the arms of the ESD. It did not resolve the strange behavior at all, so I will investigate coupling into the mode pairs as a possible source.

383

Thu Jul 27 16:56:03 2017

2017-07-27

I ran a low resolution sweep of the offset in the arms of the ESD, the space between the end of the arm and base of the opposite combs. The trends are much more subtle and are not coherent across as many of the modes. The lower frequency modes decrease slightly, while the force in the higher frequency modes increase more drastically. This is an interesting parameter, I will definitely run another sweep once I have written code that accounts for the mode pairs. Assuming the apparent trends are physically accurate, this could be a useful parameter because a greater offset gives a greater relative increase to the higher order modes while still leaving a substantial force on the lower order modes that are excited more easily anyway.

386

Tue Aug 1 16:10:42 2017

2017-08-01

I completed an improved sweep of the gap between the ESD arms. I resolved some code issues, since it was passing the maximum value not the most extreme, smaller magnitude positive values were being included rather than the strongest force calculation.
There are still three modes that show unique behavior relative to the others: 14, 19, and 25. Mode 14 is the (2,2), mode 19 is the (2,3) and mode 25 is (3,2).
Plots of the mode shapes are included for reference. The black rectangle represents the region covered by the ESD.

388

Wed Aug 2 13:47:47 2017

2017-08-02

I ran a sweep of the width of the ESD arms. There appears to be a linear relationship across the modes except for mode 25. Mode 25 exhibits a very similar behavior as in the arm gap sweep. I realized that the abrupt change in direction (also noticeable in mode 14) is likely caused by the fact that the force profile is calculated as absolute value, there might be an exponential relationship that gets converted into that shape by the absolute value function.

389

Wed Aug 2 15:40:00 2017

I am posting a diagram of the geometric parameters that I swept. The only one not included is the vertical space between the ESD and sample that sweeps perpendicularly out of the image

394

Mon Aug 7 13:19:48 2017

2017-08-07

I included the modal mass factors in the code and renormalized my data. The normalization has a noticeable impact, but does not change the general trends of the data
In fact the impact is not even significant enough to warrant a change in the ideal parameters I picked for the rectangular ESD in my interim report

398

Tue Aug 8 16:20:24 2017

2017-08-08

I rotated the ESD and calculated it's modal projections by rotating the data array that MATLAB extracts from COMSOL. I confirmed that this was properly done by plotting the profile and then computed and plotted both the rotated and normal projections.
The rotated ESD actually increases the force in some of the modes but decreases the forces in others. It markedly improved the force in 7 of the modes: 3, 6, 12, 18, 19, 22, and 26 while being quite weaker in about 4 of the modes: 9, 13, 14, and 15. This suggests that it may actually be useful to rotate the ESD as it excites some of the higher order modes a noticeable amount more. I am including plots of both modal profiles as well as a chart with mode numbers, shapes, and frequencies.

399

Wed Aug 9 12:10:47 2017