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ID Date Authorup Type Category Subject
  3252   Tue Jul 20 17:38:16 2010 GopalConfigurationOptic StacksStack Type Clarifications

Some clarification is warranted regarding the different shapes of stacks. Corrections are appreciated:

1) The single-leg stack that I just completed should function as a working model for the IO, OO, and MC1/3. Rana commented, however, that the current dimensions are slightly off for MC1/3 (which makes sense since I could only find drawings for the IOC). If anyone knows the whereabouts of similar drawings for MC1/3, I'd much appreciate it.

2) A triple-leg stack can model the BS, ITMX, and ITMY chambers. I don't have exact dimensions for these, but I can make decent approximations from to-scale stack drawings. I'll probably work on a model for this style next, since at least I have some information regarding this version.

3) The MC2 chamber has its own stack model, about which I haven't found any drawings in the binders. I can't start on MC2C at all until I find such drawings.

  3255   Wed Jul 21 11:57:59 2010 GopalUpdateWIKI-40M Update7.14.10-7.21.10 Weekly Update

Summary of this week's activities:

7/14: Analytical calculation of Viton spring constant; updated Viton values in models; experimental confirmation of COMSOL eigenfrequencies (single stack layer)

7/15: Extensions to 2-, 3-, and 4-layer stack legs. Eigenfrequency characterizations performed for each level. Meshing issues with 4-layer stack prevented completion.

7/19: Debugged the 4-layer stack. Turned out to be a boundary condition issue because of non-sequential work-plane definitions. Successful characterization of single-leg eigenfrequencies.

7/20: Prototype three-legged stack completed, but dimensions are incorrect. Read Sievers paper for details of triple-legged stack. Sorted through many stack design binders in efforts to distinguish IOC/OOC, BSC/ITMX/ITMY, MC1/MC3, and MC2 dimensions.

7/21: Researched frequency domain analysis testing in COMSOL. Attempting to first find transfer function of a single-layer stack --> currently running into some run-time errors that will need some more debugging in the afternoon.

  3261   Wed Jul 21 17:41:17 2010 GopalConfigurationOptic StacksPictures of Stacks

Now that venting is complete, this is a request for anyone who opens any chamber:

1) Please notify me immediately so I can take pictures of the stacks in that chamber.

2) If I'm not around, please take a few pictures for me. I'm most interested in the shape, number of layers, size, and damper arrangements of each stack.

This is most important for the MC1/MC3 chamber, MC2 chamber, and BS/ITMX/ITMY chambers.

Thanks!

  3276   Fri Jul 23 14:26:01 2010 GopalUpdateOptic StacksSimple Frequency Response Measurements in COMSOL

Over the past couple days, I discovered a simple, direct method for calculating frequency responses with a combination of COMSOL and any plotter such as Excel or MatLab. The simple case of rectangular prism of steel was analyzed using this method; details will be posted shortly on the COMSOL Wiki page. The frequency response matched theoretical reasoning: the bar acts as a simple mechanical low-pass filter, rapidly attenuating driving frequencies at the base beyond the first eigenmode.

It therefore shouldn't be too difficult to extend this analysis to the MC1/MC3 stack. The many eigenfrequencies will produce a more complicated transfer function, and so more data points will be taken.

The major shortcoming of this method involves dealing with the imaginary components of the eigenfrequencies. As of now, I haven't found a way of measuring the phase lag between the drive and the response. I also haven't found a way of changing the damping constants and therefore playing with phase components.

 

  3291   Mon Jul 26 11:15:23 2010 GopalHowToCOMSOL TipsPictures from Transfer Function Tutorial on the Wiki

The attached pictures give a brief overview of my transfer function measurement procedure in COMSOL. For more details, please see the Wiki.

Screen_shot_2010-07-23_at_2.57.14_PM.png

Screen_shot_2010-07-23_at_2.57.38_PM.png

Screen_shot_2010-07-23_at_2.57.45_PM.png

Screen_shot_2010-07-23_at_2.58.05_PM.png

Screen_shot_2010-07-23_at_2.58.18_PM.png

Screen_shot_2010-07-23_at_2.59.02_PM.png

Screen_shot_2010-07-23_at_3.00.37_PM.png

  3298   Tue Jul 27 12:02:31 2010 GopalUpdateOptic StacksPreliminary Transfer Function Measurements on MC1/MC3

I have successfully completed a preliminary transfer function measurement test on the MC1/MC3 stack in COMSOL. Using the measurement scheme described on the Wiki, I initialized a 1 N/m^2 sinusoidal perturbation on the bottom of the stack and measured the maximum displacement of the top layer. This preliminary test just calculated the responses to 1-,2-,3-,4-, and 5-Hz drives along the x-axis (pictures attached).

Currently, I am rerunning the same test but from 1-10 Hz with 0.1-Hz steps. When both x- and y-axis responses have been plotted, I can move on to repeating this entire process on the MC2 stack.

Attachment 1: MC1_MC3_FDA_1.png
MC1_MC3_FDA_1.png
Attachment 2: MC1_MC3_FDA_2.png
MC1_MC3_FDA_2.png
Attachment 3: MC1_MC3_FDA_3.png
MC1_MC3_FDA_3.png
Attachment 4: MC1_MC3_FDA_4.png
MC1_MC3_FDA_4.png
Attachment 5: MC1_MC3_FDA_5.png
MC1_MC3_FDA_5.png
  3301   Tue Jul 27 18:42:57 2010 GopalUpdateOptic StacksBode Magnitude Plot and Concerns

I completed the frequency domain analysis mentioned previously in the x-direction. Although I ran it from 1-10 Hz, with 0.1-Hz increments, COMSOL was unable to complete the task past 7 Hz because the relative error was beyond the relative tolerance. To solve this issue, I'd have to rerun the simulation with a finer mesh, an unfavorable option because of the already-extensive run times. The Bode magnitude plot from this simulation is attached:

Bode_Mag_MC1_MC3.png

 

This simulation raises some questions about the feasibility of this method:

 

1) Do we have the computing power necessary?

 

I already moved my work from my personal Mac Pro to Kallo (4 GB --> 12 GB RAM difference). Now, instead of crashing the program constantly, I typically wait a half hour for a standard run of the model. Preferably, I could move my work to Megatron or some other workhorse-computer... but I also know that many of the big boys are already being strained as is.

 

2) Is it possible to take measurements through Matlab?

 

This way, I could write a script to instruct COMSOL and just run a few tests at a time overnight. Also, I wouldn't have to sit and record measurements manually as I've done here. The benefits of such an improvement warrant further attention. I'll work on this option next.

 

3) Up until what frequency do we need to model?

 

As I've shown, normal meshing yields data up to 7 Hz. Is this enough? Do we need more data? Certainly not less, I'm quite sure. We need to keep in mind that as frequency range increases, run times increase exponentially.

 

4) How do we incorporate gravity into the equation?

 

Gravity will produce a bit of extra force in the non-restoring direction for off-axis deviations, slightly decreasing the expected frequency. Whether or not this is an important effect is questionable, since the deviations are typically on the order of a micron, which is orders of magnitude smaller than the initial displacement I'm using on the base. I've decided to ignore this complication for now.

 

 

  3306   Wed Jul 28 12:16:03 2010 GopalUpdateSEIBode Magnitude Plot and Concerns

Quote:

1) Gravity has to be included because the inverted pendulum effect changes the resonant frequencies. The deflection from gravity is tiny but the change in the dynamics is not. The results are not accurate without it. The z-direction probably is unaffected by gravity, but the tilt modes really feel it.

2) You should try a better meshing. Right now COMSOL is calculating a lot of strain/stress in the steel plates. For our purposes, we can imagine that the steel is infinitely stiff. There are options in COMSOL to change the meshing density in the different materials - as we can see from your previous plots, all the action is in the rubber.

3) I don't think the mesh density directly limits the upper measurement frequency. When you redo the swept-sine using the matlab scripting, use a logarithmic frequency grid like we usually do for the Bode plots. The measurement axis should go from 0.1 - 30 Hz and have ~100 points.

In any case, the whole thing looks promising: we've got real solid models and we're on the merge of being able to duplicate numerically the Dugolini-Vass-Weinstein measurements.

I made some progress on a couple issues:

1) I figured out how to create log-transfer function plots directly in COMSOL, which eliminates the hassle of toggling between programs.

2) Instead of plotting maximum displacement, which could lead to inconsistencies, I've started using point displacement, standardizing to the center of the top surface.

3) I discovered that the displacement can be measured as a field vector, so the minor couplings between each translational direction (due to the asymmetry in the original designs) can be easily ignored. 

Bode_Disp_MC1_MC3_y.png

  3307   Wed Jul 28 12:31:00 2010 GopalUpdateWIKI-40M Update7.21.10-7.28.10 Weekly Update

Summary of this week's activities:

7/21: Frequency Domain Analysis of rectangular bar; discussed with Koji how to convert complex eigenfrequencies into phase factors.

7/23: Created Wiki page about FDA; Journal Club

7/26: Recreated Stack_1234.mph due to boundary value issues; FDA for 1,2,3,4,5 Hz

7/27: Discovered MC2 logbooks for later design; ran the complete x-translational FDA for Stack_1234.mph

7/28: Finished y-translational FDA (posted previously); "Tapered Cantilever" COMSOL tutorial for gravity-load analysis.

  3322   Thu Jul 29 17:11:16 2010 GopalUpdateCOMSOL TipsIncluding Gravity in COMSOL

[Gopal, Jan]

For the past couple of days, Jan and I have been discussing a major issue in COMSOL involving modeling both oscillatory and non-oscillatory forces simultaneously while using FDA. It turns out that he and I had run into the same problem at different times and with different projects. After discussing with an expert, Jan had decided in the past that this simple task was impossible via direct means.

The issue could still be resolved if there was a way for us to work on the Weak Form of the differential equations describing the system:

  • Usually, one must define weight as a body load in the negative-z direction. However, this problematically instantiates a new force in COMSOL, which is automatically driven over the range of frequencies during FDA.
  • Instead, we could define gravity as an anti-restoring force, since we assume that the base of the stack is fixed.
  • In other words, Fg = (ρ*g/L)*x + (ρ*g/L)*y for a point mass which is constrained on the bottom (for small angles).
  • Working in Weak Form then, we'd never have to define an explicit gravity load-- this could just be an extra couple of terms in the differential equation which are related entirely to the x- and y-vectors (well-defined for each mesh point). This would fool COMSOL into never tacking on the oscillatory term during FDA. 

According to current documentation however, Weak Form analysis is not yet possible in COMSOL 4.0. Jan suggested moving my work over to ANSYS or waiting for the 4.0 upgrade, but there's probably not enough time left in my SURF for either of these options. I suggested attempting a backwards-compatibility test to COMSOL 3.5; Jan and I will be exploring this option some time next week. 

  3324   Thu Jul 29 20:43:32 2010 GopalSummaryOptic StacksModeling Tips and Tilts

I have discovered a method of completely characterizing the 6x6 response of all six types (x-,y-, and z- translational/rotational) of oscillatory disturbances at the base of the stack.

  • "Tipping" drives are trivial, and simply require a face load in the appropriate direction.
  • "Tilting" drives could use a torque, but I am instead implementing multiple edge loads in opposing directions to create the appropriate net curl. This curl will be kept constant across the three axes for sake of comparing the resulting transfer functions.
  • "Tipping" responses are once again trivial, and merely require the displacement vector of the top center coordinate to be recorded.
  • "Tilting" responses require the normal vector to be recorded and manipulated to produce the angular coordinates (assuming right-handed coordinate system):
    • θx = tan-1(x/z)
    • θy = tan-1(y/z)
    • θz = tan-1(y/x)

The first three concepts have been confirmed through simulations to produce correct transfer functions. The last test seems to be producing some problems, in that the vector normal to the equilibrium position (an obvious and useless piece of information) is sometimes given instead of the vector normal to the position of maximum displacement. This means that, as of now, I have the capability of measure the half of the complete 6x6 matrix of transfer functions in the coming weeks. The first three of eighteen transfer functions are attached below and will be included in my progress report.

XTrans_XDisp.pngYTrans_XDisp.pngZTrans_XDisp.png

  3339   Sat Jul 31 04:03:11 2010 GopalSummaryOptic StacksComplete Displacement Translational Transfer Function Matrix

Over the past 36 hours, I've run full-fledged FDAs on KALLO.

The transfer functions for translational drives and responses are neatly described by the attached transfer function "matrix."

Progress_Report_2.png

Next steps:

1) Extend the 3x3 analysis to include tilts and rotations in a 6x6 analysis.

2) Figure out how to do the same types of tests for phase instead of displacement.

  3363   Wed Aug 4 20:58:22 2010 GopalUpdateWIKI-40M Update7.28.10 - 8.4.10 Weekly Update

Summary of this week's activities:

7/28:    Finished Y-Translational 4-Stack Analysis

"Tapered Cantilever" COMSOL tutorial

Tried (and failed) isolating gravity from oscillation

7/29:    Developed tilt/rotation load combinations for torsional inputs and showed these to work in the model

Tried using Normal Vector mode on top plate to obtain output tilts; worked for the rectangular bar, but not for the full stack

Talked to Jan about a 1st-order alternative to gravity - requires Weak Form (only found in COMSOL 3.5 right now)

Began Z-Translational 4-Stack Analysis -- Ran Overnight

7/30:    Progress Report 1st Draft

Completed Z-Translational 4-Stack Analysis

8/1:      Progress Report 2nd Draft

8/2:      Progress Report 3rd Draft

Submitted Progress Report

8/3:      Finalized Eigenfrequency Analysis for MC1/MC3 Stack

24 Physical Eigenmodes plotted and recorded, as expected

Should be good enough for the final report --> focus on transfer function analysis for the remainder of the SURF

8/4:      Prescribed Displacement Tests on Simple Rectangular Block --> shown to better produce displacement-displacement transfer functions

X-to-X Transfer Function seems much better when plotted

Should now be able to do the Displacement portion of Transfer Function Analysis on MC1/MC3 for Translational Modes

(I apologize that this update is a little late)

  3376   Fri Aug 6 15:50:29 2010 GopalUpdateOptic Stacks(Much Better Looking) Displacement-Displacment Transfer Functions

I reran the FDA in COMSOL on the MC1/MC3 Stack and produced the following Displacement-Displacement Transfer Functions:

X-Translational Drive has a blue background

Y-Translational Drive has a red background

Z-Translational Drive has a green background

Obtaining the Displacement-to-Phase part of the Transfer Function still produces difficulties -- I'm still working on the COMSOL-Matlab interface to perhaps better facilitate this.

RA: I have deleted those plots because they weren't transfer functions. Transfer functions must always be the ratio of something to something. For example: if I had a nickel for every bad plot I see, I would be a millionaire. In that example, the transfer function would have the units of nickels/plots. For the stacks, it should be meters/meter.

 

Attachment 1: MC1_MC3_XTrans.png
MC1_MC3_XTrans.png
Attachment 2: MC1_MC3_YTrans.png
MC1_MC3_YTrans.png
Attachment 3: MC1_MC3_ZTrans.png
MC1_MC3_ZTrans.png
  3380   Fri Aug 6 19:46:59 2010 GopalUpdateOptic Stacks(Much Better Looking) Displacement-Displacment Transfer Functions

Quote:

I reran the FDA in COMSOL on the MC1/MC3 Stack and produced the following Displacement-Displacement Transfer Functions:

X-Translational Drive has a blue background

Y-Translational Drive has a red background

Z-Translational Drive has a green background

Obtaining the Displacement-to-Phase part of the Transfer Function still produces difficulties -- I'm still working on the COMSOL-Matlab interface to perhaps better facilitate this.

RA: I have deleted those plots because they weren't transfer functions. Transfer functions must always be the ratio of something to something. For example: if I had a nickel for every bad plot I see, I would be a millionaire. In that example, the transfer function would have the units of nickels/plots. For the stacks, it should be meters/meter.

 

My apologies for the mislabeled axes on my previous plots. They have been corrected to a ratio (in./in.), as Rana so kindly suggested in his helpful, not-at-all-condescending response.

I have chosen to stay in the English system because all of the original stack drawings are in inches as well.

  3418   Fri Aug 13 01:53:12 2010 GopalUpdateOptic StacksGravity Implementation Confirmed

Time Domain Analysis on a Driven, Damped Simple Pendulum has produced a method for implementing gravity.

COMSOL made this simple task a cryptic one: the following methods had previously failed:

  • Previous Frequency Domain testing lead to unwanted oscillations of all loads.
  • Prescribed accelerations at first seemed to create a constant gravity, but instead incorrectly constrained net acceleration to the inputted amount

Methodology:

1) An (approximately) impulse displacement was applied in the horizontal direction. The pendulum bob's displacement was observed for varying pendulum lengths.

2) The drive and response displacements vs. time were FFT'd to produce transfer functions.

3) The fundamental frequencies were inverted, squared, and plotted against frequency.

4) Since the graph is linear with an R^2 of over 0.99, it is reasonable to assume that gravity is properly acting as a restoration force.

Pendulum_Length.png

Attachment 1: Pendulum_Length.png
Pendulum_Length.png
Attachment 2: Pendulum_Length.png
Pendulum_Length.png
  3142   Wed Jun 30 11:35:06 2010 Gopal UpdateGeneral6.23.10 - 6.30.10 Weekly Update

Summary of this Week's Activities:

6/23: LIGO Safety Tour; Simulink Controls Tutorial

6/24: Simulink Diagram for Feedback Loop; Constructed Pendulum Transfer Function; Discussion with Dr. Weinstein

6/25: Prepare for pump-down of vacuum chamber; crane broken due to locking failure; worked through COMSOL tutorials

6/28: Ran through Python Tutorials; Began learning about Terminal

6/29: Wrote Progress Report 1 First Draft

6/30: Began editing Progress Report 1

  3193   Mon Jul 12 11:20:56 2010 Gopal HowToCOMSOL TipsIntrusions (Negative Extrusions)

For the sake of future users, I have decided to periodically add tips and tricks in using COMSOL that I have figured out, most probably after hours of circuitous efforts. They will always be listed under the new COMSOL Tips category.

Today's topic: Intrusions

COMSOL has a very user-friendly interface for taking objects from 2D to 3D using the "extrusion" feature. But suppose one wants to design an object which contains screw holes or some other indentation. I've found that creating "punctures" in COMSOL is either impossible or very complicated.

Instead, COMSOL encourages users to always "add" to the object. In other words, one must form the lowest level first, then build layers sequentially on top using new work plane and boolean difference operators. This will probably be a bit clearer with an example:

1) First, create the planar projection in a work plane:

Screen_shot_2010-07-12_at_10.51.22_AM.png

2) Extrude the first layer only in the regular fashion:

Screen_shot_2010-07-12_at_10.51.28_AM.png

 3) Add a new work plane which is offset in the z-direction to the deepest point of the intrusion.

Screen_shot_2010-07-12_at_10.52.08_AM.png

 4) Now, create the shape of the intrusion in this new work plane.

Screen_shot_2010-07-12_at_10.53.53_AM.png

5) Use the Boolean "Difference" to let COMSOL know that, on this plane, the object has a hole.

 Screen_shot_2010-07-12_at_10.54.36_AM.png

 6) Extrude once more from the second work plane to complete the intrusion.

Screen_shot_2010-07-12_at_10.55.36_AM.png

  3219   Wed Jul 14 13:03:04 2010 Gopal UpdateWIKI-40M Update7.8.10 - 7.14.10 Weekly Update

Summary of this Week's Activities:

Wed. 7/7: COMSOL Busbar tutorials; began stack design; began base; Viton rubber research

Thurs. 7/8: Completed Viton rubber research; updated materials; finished designing the base layer

Fri. 7/9: Research model coupling papers; extensive eLog entry about base design and troubleshooting

Sun. 7/11: Played around with Busbar to find first eigenfrequency; continued crashing COMSOL

Mon. 7/12: Intrusions in COMSOL eLog tutorial entry; research eigenfrequency analysis; successfully got first eigenmode of rectangular bar

Tues. 7/13: Updated Poisson ratio of Viton and subsequently succeeded in running eigenfrequency tests on base stack layer. Systematic Perturbation Tests were documented in the most recent elog entry. Discussed results with Rana and decided this didn't make sense. Analytical study required.

Wed. 7/14: Went over to machine shop to experimentally extrapolate spring constant of Viton. Calculations to be done in the afternoon.

  3397   Wed Aug 11 11:51:45 2010 Gopal UpdateWIKI-40M Update8.5.10 - 8.11.10 Weekly Update

Summary of this Week's Activities:

Thursday, August 5:

X-Displacement Transfer Function Measurement

JPL Tour

Friday, August 6:

Y-Displacement Transfer Function Measurement

Z-Displacement Transfer Function Measurement

Monday, August 9:

Worked on COMSOL/MatLab Interface --> problems may be due to older version

Discussed with Koji options for calling our COMSOL sales representative

Jan and I decided that there is in fact something wrong with the installations on both my Mac and Kallo

Reinstalled on both machines, but the problem was not solved

Jan said we'd go see Larry tomorrow

Tuesday, August 10:

Attempted to figure out Time-Dependent Modal Analysis --> don't think it's what we need

Began reading the LiveLink for MatLab documentation --> even the directions in this produced issues

Discovered "Prescribed acceleration" option for gravity:

A test with it on the simplest stack eliminated the unwanted oscillation, which I guess is a partial success...

Trying the same thing with Koji on a simple pendulum, however, didn't produce the expected increase in resonant frequency

(Jan was unable to see Larry today, but we're meeting on Wednesday instead).

Wednesday, August 11 (morning):

Some background research on multiple-layer stack theory

Began working on presentations

 

 

 

  2193   Fri Nov 6 12:56:30 2009 HaixingUpdateSUSMagnet has been levitated

  In this experiment, we used a feedback control to create a stable trap for a NdFeB permanent magnet. The block diagram is the following:

block_diagram.PNG

 

 

The displacement of the magnet is sensed by the Hall-effect sensor, whose output voltage is proportional to the magnetic flux produced

by the permanent magnet. It has a flat response within the frequencies we are interested in. It is driven by a 5 V power supplier and its

output has a DC voltagle of 2.5 V. We subtracted the DC voltage and used the resulting signal as the error signal. This was

simply achieved by using two channels "A" and "B". The output is "A-B" with a gain equal to one. We then put the error

signal into another  SR560 as a low-pass filter with a gain of 100 above 30 Hz. We used the "DC" coupling modes in both

preamplifers. The output is then used to drive a coil. The coil has a dimension of 1.5 inch in diameter and 2 inch in length.

The inductance of the coil is around 0.5 H and the resistance is 4.7 Om. Therefore, it has a corner frequency aournd 10/2pi Hz.

The coil has a iron core inside to enhance the DC force to the permanent magnet. The low-frequency 1/f response of the magnet is produced

by the eddy current damping of the aluminum plane that is below the magnet. This 1/f response is essential for a stable configuration. In the

next stage, we will remove the aluminum plane, and instead we will use a filter to create similar transfer function. At high-frequencies, it behaves as 

a free-mass and has a 1/f^2 response. Finally, the magnet is stably levitated.

 

Attachment 1: DSC_0964.JPG
DSC_0964.JPG
  2202   Fri Nov 6 23:02:44 2009 HaixingUpdateGeneralSR785 Spectrum Analyzer

I am using SR785 Spectrum Analyzer now and also tomorrow. 
I will put it back on Sunday. If anyone needs it during the weekend,
please just take it and I can reset it by myself later. Thanks.

  2203   Sat Nov 7 23:50:45 2009 HaixingUpdateGeneralOpen-loop transfer function of the magnetic levitation system

I measured the open-loop transfer function of the magnetic levitation system.

The schematic block diagram for this measurement is the following:

transfer_function_meas_bd.PNG

I injected a signal at a level of 20mV between two preamplifiers, and the corresponding open-loop

transfer function is given by B/A.  I took a picture of the resulting measurement, because

I encountered some difficulties to save the data to the computer via the wireless network.

The bode plots for the transfer function shown on the screen is the following:

Transfer_function_meas.jpg

 

I am puzzled with the zero near 10 Hz. I think it should come from the mechanical response function, because there is no zero in the transfer functions

of the preamplifer and the coil itself. I am not sure at the moment.

The corresponding configuration of the levitated magnet is

magnetic_levitation.jpg

  2245   Wed Nov 11 21:30:20 2009 HaixingUpdateGeneralmagnetic levitation modelling files uploaded to svn

I have created a directory under the svn. The link is https://nodus.ligo.caltech.edu:30889/svn/trunk/docs/haixing

In the directory, there are three folders are related to the magnetic levitation.

 

The experimental data is in the "experiment_data".

 

The comsol numerical modelling files are in "mag_levi_comsol_modelling" which contains "1x1 magnets",

"4x4 magnets" and "16x16 magnets" sub-folders where detailed modelling results are included.The mathematica

notebooks in those folders are used to produce the plots I posted on the wiki page.

 

The "mag_levi_feedback" contains the Simulink modelling of the feedback loop. To generate the plot for the

open-loop transfer function. One needs to ruc the "mag_lev.m" file.

 

 

 

  2307   Fri Nov 20 11:32:48 2009 HaixingUpdateSUSMagnetic levitation

I added an integrator to increase the gain at low frequencies (below 5 Hz). In addition, I increased

the band of the differentiator. The schematics for both integrator and differentiator are the following:

IntDiff.PNG

The magnetic is stably levitated.

S8007340.jpg

I turned off the light to get rid of 60Hz noise on the photodiode. I tried to measured the

open-loop transfer function of this setup, but somehow the SR560 is always saturate

when I injected the signal from SR785, which produces some weird results at

low-frequencies.

 

In addition, I found out that when the light is turned on, the levitation

can be stable even when I inverted the sign of the control loop. The control signal

on the osciloscope is the following:

S8007333.jpg

 

This oscillator is around 120 Hz, which should be  the harmonics of 60 Hz from light pollution.

I am not sure exactly why it is stable when the control-loop sign is flipped. This could

be similar to the Pauli trap in the iron trap, because the coil not only provides a force

but also provides the rigidity. The sign of such rigidity depends on the sign of the control

current. If such oscillating rigidity changes at a frequency much higher than the response

frequency of the magnet, it will stablize  the system simply by significantly increasing

the inertial of the magnet.More investigations are essential to completely understand it.

 

For information about Pauli trap, one can look at the wikipedia:

http://en.wikipedia.org/wiki/Quadrupole_ion_trap

 

 

 

  2494   Sun Jan 10 13:32:09 2010 HaixingUpdateSUStransfer function measurement of the quadrant maglev circuit

I have assembled the circuit and the control box for the quadrant magnetic levitation yesterday. The final setup is shown

in the figure below:

Quad_maglev_ctrl_box_in.JPGQuad_maglev_ctrl_box_front.JPG

 

Due to my carelessness, I I connected the wrong ends of the power supply. I damaged 4 op-amp and one voltage 

regulator during this assembly. This stupid mistake spent me several hours to fix, and I got a bitter lesson;-(

 

Afterwards, I replaced those op-amps and reconnected the power supply . Kiwamu helped me and we measured

the transfer function of this circuit.  The transfer function agrees with  the specification in the schematics which

has a integrator below 1 Hz and a differentiator from 5 to 20 Hz. The bode plot for the measured transfer function

is the following:

quad_mag_tf_amp.png

 quad_mag_tf_phs.png

Today I tested the photodetector parts and found that there is a mysterious oscillation. Whenever I connect the

photodector input A of the circuit (as indicated in the figure below),

PD.PNG

the output of the op-amp has a 500k Hz oscillation shown up in the oscilloscope.This happens even A is disconnected from

the photodetector and connected to an open end wire. I don't know how to eliminate it, and its amplitude is so large (peak to

peak is around 2.5 V) which completely dominates the photodetector output. Does anybody has some ideas? Thanks.

 

Quad_mag_lev_osc.JPG

  2497   Sun Jan 10 16:50:34 2010 HaixingUpdateSUStransfer function measurement of the quadrant maglev circuit

Quote:

1. Why do all of the BNCs have no GND connection? Each should have the individual cables to the ground. Each signal line and the corresponding ground line should be twisted together.

2. This looks the (usual) oscillation of the V-I conversion stage but I can't tell anything as I don't have the circuit diagram of the whole circuit.

3. In a certain case, putting some capacitance at the feedback may help. Read P.11 of the data sheet of LT1125. Try to put some capacitors from 20pF to some larger one whether it changes the situation or not. I suppose the bandwidth of your sensor can be ~1kHz. So putting a capacitance less than 10nF still has no effect to the servo.

 1. They are all connected to the box which has a single connection to the board ground. If I connect each of them to the ground, there would be many small loops

of ground. Of course, I should have replaced all the connectors such that the they are disconnected to the box as point out by Robert.

2. The oscillation disappears after I add 5 nF capacitor in parallel to the existing resistor. Thank you very much for pointing this out.

  2510   Tue Jan 12 13:24:50 2010 HaixingUpdateSUSQuadrant Magnetic Levitation

I have tried to make the quadrant magnetic levitation work but unfortunately I did not succeed. During the experiment, I have made

the following changes to the circuit and setup:

 

(1) I added small resistors (6K) in parallel to R11, R23, R35 and R47 (indicated in the following schematics)  to increase

the control bandwidth from 20 Hz  to 80 Hz.

 

 

schmematic.png

 

(2) I changed RLED1, RLED2, RLED3, RLED4 from 2.2K to 1.5K  in the LED driver such that the current of the

LED increases and in turn the displacement sensitivity increases.

 

(3) I changed R51 and R51 (in the differencing block for PD1 and PD2) from 5K to 1 K. Correspondingly,

I increased R52 and R54 from 5K to 50K. This changes increase the gain in the differential control by a

factor of 50, which compensates the gain loss after increasing the control bandwidth.

 

 (4) The trim pots in the coil drive block have the following values: 100K for pot1 and pot4, 1K fro pot 2 and pot3.

To increase the gain, I replaced R17, R30, R31, R41 by 102 Om resistors (we run out of 100 Om chip resistors.)

 

(5) I wrapped the OSEM flags by plastic tubes to block the light from the LED more efficiently. This also removed

the changes of the photocurrent in the photodetector when the levitated plate moves horizontally.

 

Possible issues that cause the setup not working at the moment:

 

(1) The feedback gain could be probably still not enough. During the experiment, I can't feel any force changes when the

flags crossing the zero point. The error signals and control signal has the right sign.

 

(2) The levitated weight may be not enough and the working point is below the extremum of the DC attracting force.

This could give rise to a large negative spring which requires unreasonable feedback gain to compensate.

 

(3) The DC attracting force between the magnets are differing each other too much (mismatch) and can't

be compensated by the coil driving force.

 

(4) The control bandwidth may be still not  large enough. Initially my design was 100 Hz, but I forgot to divide

the angular frequency by 2pi and the resulting circuit has a bandwidth of 20 Hz. Later I increase it up to 80 Hz

by changing the resistors as mentioned before.

 

(5) The polarization of the coil could have a wrong sign. I have checked with Gauss meter, but still the absence

of zero-point crossing force change makes me worry about this.

 

For continuation of this work, I will finish writing my document and summarize all the results and outline what

needs to be done in the future. If everything goes well, I will be back in June and can spend more time on this

experiment. I can also work with the summer students together on this project.

  15224   Tue Feb 25 19:58:06 2020 HangUpdateIOOMC2 coil balancing

[Yehonathan, Hang]

We did some quick DC balancing of the MC2 coil drivers to reduce the l2a coupling. We updated the gains in the C1:SUS-MC2_UL/UR/LR/LLCOIL to be 1, -0.99, 0.937,-0.933, respectively. The previous values were 1, -1, 1, -1.

The procedures are the following:

Lock IMC.

Drive UL+LR and change the gain of LR to zero pitch.

Drive UR+LL and change the gain of LL to zero pitch.

Lastly, drive all 4 coils and change UR & LR together to zero yaw. 

We used C1:SUS-MC2_LOCKIN1_OSC to create the excitations at 33 Hz w/ 30,000 cts. The angular error signals were derived from IMC WFSs.

While this time we did things by hand, in the future it should be automated as the procedure is sufficiently straightforward. 

  15265   Wed Mar 11 16:46:25 2020 HangUpdateIOOMC2 coil balancing

My old scheme was flawed as I used pitch as the readback. The pitch signal could not distinguish the cross-coupling due to coil imbalance and that due to the natural suspension L2P. A new scheme based on yaw alone has been developed and will be integrated into ifo_test. For now we revert the C1:SUS-MC2_UL/UR/LR/LLCOIL gains back to 1, -1, 1, -1. 

Quote:

[Yehonathan, Hang]

We did some quick DC balancing of the MC2 coil drivers to reduce the l2a coupling. We updated the gains in the C1:SUS-MC2_UL/UR/LR/LLCOIL to be 1, -0.99, 0.937,-0.933, respectively. The previous values were 1, -1, 1, -1.

The procedures are the following:

Lock IMC.

Drive UL+LR and change the gain of LR to zero pitch.

Drive UR+LL and change the gain of LL to zero pitch.

Lastly, drive all 4 coils and change UR & LR together to zero yaw. 

We used C1:SUS-MC2_LOCKIN1_OSC to create the excitations at 33 Hz w/ 30,000 cts. The angular error signals were derived from IMC WFSs.

While this time we did things by hand, in the future it should be automated as the procedure is sufficiently straightforward. 

  15322   Fri May 8 14:27:25 2020 HangUpdateBHDNew SRC gouy phase

[Jon, Hang]

After updating the 40 m finesse file to incorporate the new SRC length (and the removal of SR2), we find that the current SRM radius curvature is fine. Thus a replacement of SRM is NOT required

Basically, the new one-way SRC gouy phase is 11.1 deg according to Finesse, which is very close to the previous value of 10.8 deg. Thus the transmode spacing should be essentially the same. 

In the first attached plot is the mode content calculated with Finesse. Here we have first offset DARM by 1m deg and misaligned the SRM by 10 urad. From the top to bottom we show the amplitude of the carrier fields, f1, and f2 sidebands, respectively. The red vertical line is the nominal operating point (thanks Koji for pointing out that we do signal recycling instead of extraction now). No direct co-resonance for the low-order TEM modes. (Note that the HOMs appeared to also have peaks at \phi_srm = 0. This is just because the 00 mode is resonant and thus the seed for the HOMs is greater. )

We can also consider a clean case without mode interactions in the second plot. Indeed we don't see co-resonances of high order modes. 

Attachment 1: mode_spec_finesse.pdf
mode_spec_finesse.pdf
Attachment 2: mode_spec_ideal.pdf
mode_spec_ideal.pdf
  15336   Mon May 18 18:00:16 2020 HangUpdateBHDBHD mode-matching study

[Jon, Tega, Hang]

We proposed a few BHD mode-matching telescope designs and then preformed a few monte-carlo experiments to see how the imperfections would change the story. We assumed a 2 mm (1-sigma) error on the location of the components and 1% (1-sigma) fractional error on the RoC of the curved mirrors. The angle of incidence has not yet been taken into account (no astigmatism at the moment but will be included in the follow-up study.)

For the LO path things are mostly fine. We can use LO1 and LO2 as the actuators (Sec. 2.2 of the note), and when errors are taken into account more than 90% of times we can still achieve 98% mode matching. The gouy phase separation between LO1 and LO2 > 34 deg for 90% of the time, which corresponds to a condition number of the sensing matrix of ~ 3. 

The situation is more tricky for the AS path. While the telescopes are usually robust against 2 or 3 mm of positional error, the 1% RoC does affect the performance quite significantly. In the note we choose two best-performing ones but still only 50% of the time they can maintain a power-overlap of > 99%. In fact, the 1% RoC error assumed should be quite optimistic... Not sure if we could achieve this in reality. 

One potential way out is to ignore the MM for the first round of BHD. Here anyway we only need to test the ISC schemes. Then in the second round when we have the whole BHD board suspended, we can then use AS1 and the BHD board as the actuators. This might be able to make things more forgiving if we don't need to shrink the AS beam very fast so that it could be separated from AS4 in gouy phase.

Attachment 1: MM.pdf
MM.pdf MM.pdf MM.pdf MM.pdf MM.pdf MM.pdf MM.pdf MM.pdf
  15339   Wed May 20 18:45:22 2020 HangUpdateBHDBHD mode-matching study--corner plot & adjustment requirement

As Rana suggested, we present the scattering plot of the AS path mode matching for various variables. The plot is for the AS path, Plan 2 (whose params we summarize at the end of this entry).

In the corner plot, we color-coded each realization according to the mode matching. We use (purple, olive, grey) for (MM>0.99, 0.98<MM<=0.99, MM<=0.98), respectively. From the plot, we can see that it is most sensitive to the RoC of AS1. The plot also shows that we can compensate for some of the MM errors if we adjust the distance between AS1-AS3 (note that AS2 is a flat mirror). The telescope is quite robust to other errors.

The compensation requirement is further shown in the second plot. To correct for the 1% RoC error of AS1, we typically need to adjust AS1-AS3 distance by ~ 1 cm (if we want to go back to MM=1; the window for >0.99 MM spans also about 1 cm). This should be doable because the nominal distance between AS1-AS3 is 115 cm. 

The story for plan1 is similar and thus not shown here. 

==============================================================

AS path plan2 nominal params:

label     z (m)     type             parameters  
-----     -----     ----             ----------  
SRMAR          0    flat mirror      none:     
AS1       0.7192    curved mirror    ROC: 2.5000 
AS2       1.2597    flat mirror      none:     
AS3       1.8658    curved mirror    ROC: -0.5000
AS4       2.5822    curved mirror    ROC: 0.6000  
OMCBS1    3.3271    flat mirror      none:   
Attachment 1: AS_MM_scat2.pdf
AS_MM_scat2.pdf
Attachment 2: AS_MM_adj2.pdf
AS_MM_adj2.pdf
  15357   Tue May 26 19:19:30 2020 HangUpdateBHDBHD MM-- effects of astigmatism

Please see the attached doc. 

I think the conclusion is that if the AS1 RoC error is not significantly more than 1%, then with some adjustment of the AS1-AS3 distance (~ 1 cm), we could find a solution that simultaneously makes the AS path mode-matching better than 99% for the t- and s-planes. 

The requirement of the LO path is less strict and the current plan using LO1-LO2 actuation should work. 

Attachment 1: MM.pdf
MM.pdf MM.pdf MM.pdf MM.pdf MM.pdf MM.pdf MM.pdf MM.pdf
  15363   Tue Jun 2 14:05:24 2020 HangUpdateBHDMM telescope actuation range requirments

We computed the required actuation range for the telescope design in elog:15357. The result is summarized in the table below. Here we assume we misalign an IFO mirror by 1 urad, and then compute how many urad do we need to move the (AS1, AS4) or (LO1, LO2) mirrors to simultaneously correct for the two gouy phases. 

Actuation requirement in urad per urad misalignment
[urad/urad] ITMX ITMY ETMX ETMY BS PRM PR2 PR3 SR3 SRM
AS1 1.9 2.1 -5.0 -5.5 0.5 0.5 -0.3 0.2 0.1 0.6
AS4 2.9 2.0 -8.8 -5.5 -5.9 -0.7 1.3 -0.7 -0.5 0.7
LO1 -4.0 -3.9 11.0 10.4 1.9 -0.4 -0.2 0.1 0.0 -1.1
LO2 -5.0 -3.7 15.1 10.4 8.7 0.8 1.9 1.1 0.7 -1.3

The most demanding ifo mirrors are the ETMs and the BS, for every 1 urad misalignment the telescope needs to move 10-15 urad to correct for that. However, it is unlikely for those mirrors to move more 100 nrad for a locked ifo with ASC engaged. Thus a few urad actuation should be sufficient. For the recycling mirrors, every 1 urad misalignment also requires ~ 1 urad actuation. 

As a result, if we could afford 10 urad actuation range for each telescope suspension, then the gouy phase separations we have should be fine. 

================================================================

Edits:

We looked at the oplev spectra from gps 1274418500 for 512 sec. This should be a period when the ifo was locked in the PRFPMI state according to elog:15348. We just focused on the yaw data for now. Please see the attached plots. The solid traces are for the ASD, and the dotted ones are the cumulative rms. The total rms for each mirror is also shown in the legend. 

I am now confused... The ITMs looked somewhat reasonable in that at least the < 1 Hz motion was suppressed. The total rms is ~ 0.1 urad, which was what I would expect naively (~ x100 times worse than aLIGO). 

There seems to be no low-freq suppression on the ETMs though... Is there no arm ASC at the moment???

Attachment 1: TM_OL_spec_1274418500_512.pdf
TM_OL_spec_1274418500_512.pdf
Attachment 2: CORNER_OL_spec_1274418500_512.pdf
CORNER_OL_spec_1274418500_512.pdf
  15380   Mon Jun 8 11:50:02 2020 HangUpdateBHDAstigmatism and scattering plots

We consider the astigmatism effects of the stock options. The conclusions are:

1. For the AS path, the stock should work fine for the phase-one of BHD, if we could tolerate a few percent MM loss. The window for length adjustment to achieve >99% MM for both s and t is only 1 mm for 1% RoC error (compared to ~ 1 cm in the customized case). 

2. The LO path seemed tricky. As LO3 & LO4 are both significantly curved (RoC<=0.5 m), the non-zero angle of incidence makes the astigmatism quite sever. For the t-plane the nominal MM can be 0.98, yet for the s-plane, the nominal MM is only 0.72. We could move things around to achieve a MM ~ 0.85, which is probably fine for the phase-one implementation but not long term. 

Details:

Attachments 1-3 are for the AS path; 4-6 are for the LO path. 

1 & 4. Marginalized MM distribution for the AS/LO paths. Here we assumed 5 mm positional error and 1% fractional RoC error. Due to the astigmatism, the nominal s-plane MM is only 0.72 for the LO path. 

2 & 5. Scattering plots for the AS/LO paths. We color coded the points as the following: pink: MM>0.99; olive: 0.98<MM<=0.99; grey: MM<=0.98. For the AS path, MM is mostly sensitive to the AS1 RoC and can be adjusted by changing AS1-AS3 distance. For the LO path, the LO3 RoC and LO3-LO4 distance are most critical for the MM. 

3 & 6. Assuming +- 1% AS1 (LO3) fractional RoC error, how much can we compensate for it using AS1-AS3 (LO3-LO4) distance. For the AS path, there exists a ~ 1 mm window where the MM for s and t can simultaneously > 99%. For the LO path, the best we can do is to make s and t both ~ 85%. 

Quote:

Summary

For the initial phase of BHD testing, we recently discussed whether the mode-matching telescopes could be built with 100% stock optics. This would allow the optical system to be assembled more quickly and cheaply at a stage when having ultra-low loss and scattering is less important. I've looked into this possibility and conclude that, yes, we do have a good stock optics option. It in fact achieves comprable performance to our optimized custom-curvature design [ELOG 15357]. I think it is certainly sufficient for the initial phase of BHD testing.

Vendor

It turns out our usual suppliers (e.g., CVI, Edmunds) do not have enough stock options to meet our requirements. This is for two reasons:

  • For sufficient LO1-LO2 (AS1-AS4) Gouy phase separation, we require a very particular ROC range for LO1 (AS1) of 5-6 m (2-3 m).
  • We also require a 2" diameter for the suspended optics, which is a larger size than most vendors stock for curved reflectors (for example, CVI has no stock 2" options).

However I found that Lambda Research Optics carries 1" and 2" super-polished mirror blanks in an impressive variety of stock curvatures. Even more, they're polished to comprable tolerances as I had specificied for the custom low-scatter optics [DCC E2000296]: irregularity < λ/10 PV, 10-5 scratch-dig, ROC tolerance ±0.5%. They can be coated in-house for 1064 nm to our specifications.

From modeling Lambda's stock curvature options, I find it still possible to achieve mode-matching of 99.9% for the AS beam and 98.6% for the LO beam, if the optics are allowed to move ±1" from their current positions. The sensitivity to the optic positions is slightly increased compared to the custom-curvature design (but by < 1.5x). I have not run the stock designs through Hang's full MC corner-plot analysis which also perturbs the ROCs [ELOG 15339]. However for the early BHD testing, the sensitivity is secondary to the goal of having a quick, cheap implementation.

Stock-Part Telescope Designs

The following tables show the best telescope designs using stock curvature options. It assumes the optics are free to move ±1" from their current positions. For comparison, the values from the custom-curvature design are also given in parentheses.

AS Path

The AS relay path is shown in Attachment 1:

  • AS1-AS4 Gouy phase separation: 71°
  • Mode-matching to OMC: 99.9%
Optic ROC (m) Distance from SRM AR (m)
AS1 2.00  (2.80) 0.727  (0.719)
AS2 Flat   (Flat) 1.260  (1.260)
AS3 0.20  (-2.00) 1.864  (1.866)
AS4 0.75  (0.60) 2.578  (2.582)

LO Path

The LO relay path is shown in Attachment 2:

  • LO1-LO2 Gouy phase separation: 67°
  • Mode-matching to OMC: 98.6%
Optic ROC (m) Distance from PR2 AR (m)
LO1 5.00  (6.00) 0.423  (0.403)
LO2 1000 (1000) 2.984  (2.984)
LO3 0.50  (0.75) 4.546  (4.596)
LO4 0.15  (-0.45) 4.912  (4.888)

Ordering Information

I've created a new tab in the BHD procurement spreadsheet ("Stock MM Optics Option") listing the part numbers for the above telescope designs, as well as their fabrication tolerances. The total cost is $2.8k + the cost of the coatings (I'm awaiting a quote from Lambda for the coatings). The good news is that all the curved substrates will receive the same HR/AR coatings, so I believe they can all be done in a single coating run.

 

Attachment 1: AS_MM_hist_stock.pdf
AS_MM_hist_stock.pdf
Attachment 2: AS_MM_t_scat_stock.pdf
AS_MM_t_scat_stock.pdf
Attachment 3: AS_MM_adj_stock.pdf
AS_MM_adj_stock.pdf
Attachment 4: LO_MM_hist_stock.pdf
LO_MM_hist_stock.pdf
Attachment 5: LO_MM_s_scat_stock.pdf
LO_MM_s_scat_stock.pdf
Attachment 6: LO_MM_adj_stock.pdf
LO_MM_adj_stock.pdf
  15503   Tue Jul 28 13:55:11 2020 HangUpdateBHDExploring bilinear SRCL->DARM coupling

We explore bilinear SRCL to DARM noise coupling mechanisms, and show two cases that by doing BHD readout the noise performance can be improved. In the first case, the bilinear piece is due to residual DHARD motion (see also LHO:45823), and it matters mostly for the low-frequency (<100 Hz) part, and in the second piece the bilinear piece is due to residual SRCL fluctuation and it matters mostly for the a few x 100 Hz part. Details are below:

=================================================

General Model:

We can write the SRCL to DARM transfer function as (Evan Hall's thesis, eq. 2.29)

Z_s2d(f) = C_lf(f) * F^2 * x_D + C_hf(f) * F * dphi_S * x_D    ---- (1)

where

C_lf ~ 1/f^2 and C_hf ~ f are constants at each frequency unless there are major upgrades to the IFO,

F is the finesse of the arm cavity which depends on the alignment, spot position on the TMs, etc., 

dphi_S is the SRCL detuning (wrt the nominal 90 deg value), 

x_D is the DC DARM offset. 

The linear part of this can be removed with feedforward subtractions and it is the bilinear piece that matters, which reads

dZ_s2d = C_lf * <F>^2 * dx_D + C_hf * <F> * <dphi_S> * dx_D

             + 2C_lf * <F> * <x_D>  * dF + C_hf * <dphi_S> * <x_D> * dF

             + C_hf  * <F> * <x_D> * d(dphi_S).     ---- (2)

The first term in (2) is due to residual DARM motion dx_D. This term does not depends on the DC value of DARM offset <x_D> and thus does not depend on doing BHD or DC readout. On the other hand, the typical residual DARM motion is 1 fm << 1 pm of DARM offset. Since the current feedforward reduction factor is about 10 (see both Den Martynov's thesis and Evan Hall's thesis), clearly we are not limited by the residual DARM motion. 

The second term is due to the change in the arm finesse, which can be affected by, e.g., the alignment fluctuation (both increasing the loss due to scattering into 01/10 modes and affecting the spot positon and hence changing the losses), and is likely to be the reason why we see the effect being modulated by DHARD. 

The last term in (2) is due to the residual SRCL fluctuation and is important for the ~ a few x 100 Hz band.

=================================================

DHARD effects. 

As argued above, the DHARD affects the SRCL -> DARM coupling as it changes the finesse in the arm cavity (through scattering into 01/10 modes; in finesse we cannot directly simulate the effects due to spot hitting a rougher location). 

Since in the second term of eq. (2) the LF part depends on the DARM DC offset <x_D>, this effect can be improved by going from DC readout to BHD. 

To simulate it in finesse, at a fixed DARM DC offset, we compute the SRCL->DARM transfer functions at different DHARD offsets, and then numerically compute the derivative \partial Z_s2d / \partial \theta_{DH}. Then multiplying this derivative with the rms value of DHARD fluctuation \theta_{DH} we then know the expected bilinear coupling piece. 

The result is shown in the first attached plot. Here we have assumed a flat SRCL noise of 5e-16 m/rtHz for simplicity (see PRD 93, 112004, 2016). We do not account for the loop effects which further reduces the high frequency components for now. The residual DHARD RMS is assumed to be 1 nrad. 

In the first plot, from top to bottom we show the SRCL noise projection at different DARM DC offsets of (0.1, 1, 10) pm. Since the DHARD alignment only affects the arm finesse starting at quadratic order, it thus matters what DC offset in DHARD we assume. In each pannel, the blue trace is for no DC offset in DHARD and the orange one for a 5 nrad DC offset. As a reference, the A+ sensitivity is shown in grey trace in each plot as a reference. 

We can see if there is a large DC offset in DHARD (a few nrad) and we still do DC readout with a few pm of DARM offset, then the bilinear piece of SRCL can still contaminate the sensitivity in the 10-100 Hz band (bottom panel; orange trace). On the other hand, if we do BHD, then the SRCL noise should be down by ~ x100  even compared to with the top panel. 

(A 5 nrad of DC offset in DHARD coupled with 1 nrad RMS would cause about 0.5% RIN in the arms. This is somewhat greater than the typically measured RIN which is more like <~ 0.2%. See the second plot). 

=================================================

SRCL effect. 

Similarly we can consider the SRCL->DARM coupling due to residual SRCL rms. The approach is very similar to what we did above for DHARD. I.e., we compute Z_s2d at fixed DARM offset and for different SRCL offsets, then we numerically evaluate \partial Z_s2d / \partial dphi_S. A residual SRCL rms of 0.1 nm is then used to generate the projection shown in the third figure. 

Unlike the DHARD effect, the bilinear SRCL piece does not depend on the DC SRCL detuning (for the 50-500 Hz part). It does still depends on the DARM DC offset and therefore could be improved by BHD.

Since we do not include the LP of the SRCL loop in this plot, the HF noise at 1 kHz is artifical as it can be easily filtered out. However, the LP will not be very strong around 100-300 Hz for a SRCL UGF ~ 30 Hz, and thus doing BHD could still have some small improvements for this effect. 

Attachment 1: SRCL_bilin_DHARD.pdf
SRCL_bilin_DHARD.pdf
Attachment 2: ARM_RIN.pdf
ARM_RIN.pdf
Attachment 3: SRCL_bilin_SRCL.pdf
SRCL_bilin_SRCL.pdf
  16373   Mon Oct 4 15:50:31 2021 HangUpdateCalibrationFisher matrix estimation on XARM parameters

[Anchal, Hang]

What: Anchal and I measured the XARM OLTF last Thursday.

Goal: 1. measure the 2 zeros and 2 poles in the analog whitening filter, and potentially constrain the cavity pole and an overall gain. 

          2. Compare the parameter distribution obtained from measurements and that estimated analytically from the Fisher matrix calculation.

          3. Obtain the optimized excitation spectrum for future measurements.   

How: we inject at C1:SUS-ETMX_LSC_EXC so that each digital count should be directly proportional to the force applied to the suspension. We read out the signal at C1:SUS-ETMX_LSC_OUT_DQ. We use an approximately white excitation in the 50-300 Hz band, and intentionally choose the coherence to be only slightly above 0.9 so that we can get some statistical error to be compared with the Fisher matrix's prediction. For each measurement, we use a bandwidth of 0.25 Hz and 10 averages (no overlapping between adjacent segments). 

The 2 zeros and 2 poles in the analog whitening filter and an overall gain are treated as free parameters to be fitted, while the rest are taken from the model by Anchal and Paco (elog:16363). The optical response of the arm cavity seems missing in that model, and thus we additionally include a real pole (for the cavity pole) in the model we fit. Thus in total, our model has 6 free parameters, 2 zeros, 3 poles, and 1 overall gain. 

The analysis codes are pushed to the 40m/sysID repo. 

===========================================================

Results:

Fig. 1 shows one measurement. The gray trace is the data and the olive one is the maximum likelihood estimation. The uncertainty for each frequency bin is shown in the shaded region. Note that the SNR is related to the coherence as 

        SNR^2 = [coherence / (1-coherence)] * (# of average), 

and for a complex TF written as G = A * exp[1j*Phi], one can show the uncertainty is given by 

        \Delta A / A = 1/SNR,  \Delta \Phi = 1/SNR [rad]. 

Fig. 2. The gray contours show the 1- and 2-sigma levels of the model parameters using the Fisher matrix calculation. We repeated the measurement shown in Fig. 1 three times, and the best-fit parameters for each measurement are indicated in the red-crosses. Although we only did a small number of experiments, the amount of scattering is consistent with the Fisher matrix's prediction, giving us some confidence in our analytical calculation. 

One thing to note though is that in order to fit the measured data, we would need an additional pole at around 1,500 Hz. This seems a bit low for the cavity pole frequency. For aLIGO w/ 4km arms, the single-arm pole is about 40-50 Hz. The arm is 100 times shorter here and I would naively expect the cavity pole to be at 3k-4k Hz if the test masses are similar. 

Fig. 3. We then follow the algorithm outlined in Pintelon & Schoukens, sec. 5.4.2.2, to calculate how we should change the excitation spectrum. Note that here we are fixing the rms of the force applied to the suspension constant. 

Fig. 4 then shows how the expected error changes as we optimize the excitation. It seems in this case a white-ish excitation is already decent (as the TF itself is quite flat in the range of interest), and we only get some mild improvement as we iterate the excitation spectra (note we use the color gray, olive, and purple for the results after the 0th, 1st, and 2nd iteration; same color-coding as in Fig. 3).   

 

 

 

Attachment 1: tf_meas.pdf
tf_meas.pdf
Attachment 2: fisher_est_vs_data.pdf
fisher_est_vs_data.pdf
Attachment 3: Pxx_evol.pdf
Pxx_evol.pdf
Attachment 4: fisher_evol.pdf
fisher_evol.pdf
  16384   Wed Oct 6 15:04:36 2021 HangUpdateSUSPRM L2P TF measurement & Fisher matrix analysis

[Paco, Hang]

Yesterday afternoon Paco and I measured the PRM L2P transfer function. We drove C1:SUS-PRM_LSC_EXC with a white noise in the 0-10 Hz band (effectively a white, longitudinal force applied to the suspension) and read out the pitch response in C1:SUS-PRM_OL_PIT_OUT. The local damping was left on during the measurement. Each FFT segment in our measurement is 32 sec and we used 8 non-overlapping segments for each measurement. The empirically determined results are also compared with the Fisher matrix estimation (similar to elog:16373).

Results:

Fig. 1 shows one example of the measured L2P transfer function. The gray traces are measurement data and shaded region the corresponding uncertainty. The olive trace is the best fit model. 

Note that for a single-stage suspension, the ideal L2P TF should have two zeros at DC and two pairs of complex poles for the length and pitch resonances, respectively. We found the two resonances at around 1 Hz from the fitting as expected. However, the zeros were not at DC as the ideal, theoretical model suggested. Instead, we found a pair of right-half plane zeros in order to explain the measurement results. If we cast such a pair of right-half plane zeros into (f, Q) pair, it means a negative value of Q. This means the system does not have the minimum phase delay and suggests some dirty cross-coupling exists, which might not be surprising. 

Fig. 2 compares the distribution of the fitting results for 4 different measurements (4 red crosses) and the analytical error estimation obtained using the Fisher matrix (the gray contours; the inner one is the 1-sigma region and the outer one the 3-sigma region). The Fisher matrix appears to underestimate the scattering from this experiment, yet it does capture the correlation between different parameters (the frequencies and quality factors of the two resonances).

One caveat though is that the fitting routine is not especially robust. We used the vectfit routine w/ human intervening to get some initial guesses of the model. We then used a standard scipy least-sq routine to find the maximal likelihood estimator of the restricted model (with fixed number of zeros and poles; here 2 complex zeros and 4 complex poles). The initial guess for the scipy routine was obtained from the vectfit model.  

Fig. 3 shows how we may shape our excitation PSD to maximize the Fisher information while keeping the RMS force applied to the PRM suspension fixed. In this case the result is very intuitive. We simply concentrate our drive around the resonance at ~ 1 Hz, focusing on locations where we initially have good SNR. So at least code is not suggesting something crazy... 

Fig. 4 then shows how the new uncertainty (3-sigma contours) should change as we optimize our excitation. Basically one iteration (from gray to olive) is sufficient here. 

We will find a time very recently to repeat the measurement with the optimized injection spectrum.

Attachment 1: prm_l2p_tf_meas.pdf
prm_l2p_tf_meas.pdf
Attachment 2: prm_l2p_fisher_vs_data.pdf
prm_l2p_fisher_vs_data.pdf
Attachment 3: prm_l2p_Pxx_evol.pdf
prm_l2p_Pxx_evol.pdf
Attachment 4: prm_l2p_fisher_evol.pdf
prm_l2p_fisher_evol.pdf
  16388   Fri Oct 8 17:33:13 2021 HangUpdateSUSMore PRM L2P measurements

[Raj, Hang]

We did some more measurements on the PRM L2P TF. 

We tried to compare the parameter estimation uncertainties of white vs. optimal excitation. We drove C1:SUS-PRM_LSC_EXC with "Normal" excitation and digital gain of 700.

For the white noise exciation, we simply put a butter("LowPass",4,10) filter to select out the <10 Hz band.

For the optimal exciation, we use butter("BandPass",6,0.3,1.6) gain(3) notch(1,20,8) to approximate the spectral shape reported in elog:16384. We tried to use awg.ArbitraryLoop yet this function seems to have some bugs and didn't run correctly; an issue has been submitted to the gitlab repo with more details. We also noticed that in elog:16384, the pitch motion should be read out from C1:SUS-PRM_OL_PIT_IN1 instead of the OUT channel, as there are some extra filters between IN1 and OUT. Consequently, the exact optimal exciation should be revisited, yet we think the main result should not be altered significantly.

While a more detail analysis will be done later offline, we post in the attached plot a comparison between the white (blue) vs optimal (red) excitation. Note in this case, we kept the total force applied to the PRM the same (as the RMS level matches).

Under this simple case, the optimal excitation appears reasonable in two folds.

First, the optimization tries to concentrate the power around the resonance. We would naturally expect that near the resonance, we would get more Fisher information, as the phase changes the fastest there (i.e., large derivatives in the TF).

Second, while we move the power in the >2 Hz band to the 0.3-2 Hz band, from the coherence plot we see that we don't lose any information in the > 2 Hz region. Indeed, even with the original white excitation, the coherence is low and the > 2 Hz region would not be informative. Therefore, it seems reasonable to give up this band so that we can gain more information from locations where we have meaningful coherence.

Attachment 1: Screenshot_2021-10-08_17-30-52.png
Screenshot_2021-10-08_17-30-52.png
  16390   Mon Oct 11 13:59:47 2021 HangUpdateSUSMore PRM L2P measurements

We report here the analysis results for the measurements done in elog:16388

Figs. 1 & 2 are respectively measurements of the white noise excitation and the optimized excitation. The shaded region corresponds to the 1-sigma uncertainty at each frequency bin. By eyes, one can already see that the constraints on the phase in the 0.6-1 Hz band are much tighter in the optimized case than in the white noise case. 

We found the transfer function was best described by two real poles + one pair of complex poles (i.e., resonance) + one pair of complex zeros in the right-half plane (non-minimum phase delay). The measurement in fact suggested a right-hand pole somewhere between 0.05-0.1 Hz which cannot be right. For now, I just manually flipped the sign of this lowest frequency pole to the left-hand side. However, this introduced some systematic deviation in the phase in the 0.3-0.5 Hz band where our coherence was still good. Therefore, a caveat is that our model with 7 free parameters (4 poles + 2 zeros + 1 gain as one would expect for an ideal signal-stage L2P TF) might not sufficiently capture the entire physics. 

In Fig. 3 we showed the comparison of the two sets of measurements together with the predictions based on the Fisher matrix. Here the color gray is for the white-noise excitation and olive is for the optimized excitation. The solid and dotted contours are respectively the 1-sigma and 3-sigma regions from the Fisher calculation, and crosses are maximum likelihood estimations of each measurement (though the scipy optimizer might not find the true maximum).

Note that the mean values don't match in the two sets of measurements, suggesting potential bias or other systematics exists in the current measurement. Moreover, there could be multiple local maxima in the likelihood in this high-D parameter space (not surprising). For example, one could reduce the resonant Q but enhance the overall gain to keep the shoulder of a resonance having the same amplitude. However, this correlation is not explicit in the Fisher matrix (first-order derivatives of the TF, i.e., local gradients) as it does not show up in the error ellipse. 

In Fig. 4 we show the further optimized excitation for the next round of measurements. Here the cyan and olive traces are obtained assuming different values of the "true" physical parameter, yet the overall shapes of the two are quite similar, and are close to the optimized excitation spectrum we already used in elog:16388

 

Attachment 1: prm_l2p_tf_meas_white.pdf
prm_l2p_tf_meas_white.pdf
Attachment 2: prm_l2p_tf_meas_opt.pdf
prm_l2p_tf_meas_opt.pdf
Attachment 3: prm_l2p_fisher_vs_data_white_vs_opt.pdf
prm_l2p_fisher_vs_data_white_vs_opt.pdf
Attachment 4: prm_l2p_Pxx_evol_v2.pdf
prm_l2p_Pxx_evol_v2.pdf
  16399   Wed Oct 13 15:36:38 2021 HangUpdateCalibrationXARM OLTF

We did a few quick XARM oltf measurements. We excited C1:LSC-ETMX_EXC with a broadband white noise upto 4 kHz. The timestamps for the measurements are: 1318199043 (start) - 1318199427 (end).

We will process the measurement to compute the cavity pole and analog filter poles & zeros later.

Attachment 1: Screenshot_2021-10-13_15-32-16.png
Screenshot_2021-10-13_15-32-16.png
  16467   Tue Nov 16 11:37:26 2021 HangHowToSUSFitting suspension model--large systematic errors

One goal of our sysID study is to improve the aLIGO L2A feedforward. Our algorithm currently improves only the statistical uncertainty and assumes the systematic errors are negligible. However, I am currently baffled by how to fit a (nearly) realistic suspension model...

My test study uses the damped aLIGO QUAD suspension model. From the Matlab model I extract the L2 drive in [N] to L3 pitch in [rad] transfer function (given by a SS model with the A matrix having a shape of 103x103). I then tried to use VectFIT to fit the noiseless TF. After removing nearby z-p pairs (defined by less than 0.2 times the lowest pole frequency) and high-frequency zeros, I got a model with 6 complex pole pairs and 4 complex zero pairs (21 free parameters in total). I also tried to fit the TF (again, noiseless) with an MCMC algorithm assuming the underlying model has the same number of parameters as the VectFIT results. 

Please see the first attached plots for a comparison between the fitted models and the true one. In the second plot, we show the fractional residual

    | TF_true - TF_fit | / | TF_true |,

and the inverse of this number gives the saturating SNR at each frequency. I.e., when the statistical SNR is more than the saturating value, we are then limited by systematic errors in the fitting. And so far, disappointingly I can only get an SNR of 10ish for the main resonances...

I wonder if people know better ways to reduce this fitting systematic... Help is greatly appreciated!

Attachment 1: L2L_L3P_fit.pdf
L2L_L3P_fit.pdf
Attachment 2: L2L_L3P_residual.pdf
L2L_L3P_residual.pdf
  16486   Mon Nov 29 15:24:53 2021 HangHowToGeneralFisher matrix vs length of each FFT segment

We have been discussing how does the parameter estimation depends on the length per FFT segment. In other words, after we collected a series of data, would it be better for us to divide it into many segments so that we have many averages, or should we use long FFT segments so that we have more frequency bins?

My conclusions are that:

1). We need to make sure that the segment length is long enough with T_seg > min[ Q_i / f_i ], where f_i is the resonant frequency of the i'th resonant peak and the Q_i its quality factor. 

2). Once 1) is satisfied, the result depends weakly on the FFT length. There might be a weak hint preferring a longer segment length (i.e., want more freq bins than more averages) though. 

=================================================================

To reach the conclusion, I performed the following numerical experiment.

I considered a simple pendulum with resonant frequency f_1 = 0.993 Hz and Q_1 = 6.23. The value of f_1 is chosen such that it is not too special to fall into a single freq bin. Additionally, I set an overall gain of k=20. I generated T_tot = 512 s of data in the time domain and then did the standard frequency domain TF estimation. I.e., I computed the CSD between excitation and response (with noise) over the PSD of the excitation. The spectra of excitation and noise in the readout channel are shown in the first plot. 

In the second plot, I showed the 1-sigma errors from the Fisher matrix calculation of the three parameters in this problem, as well as the determinant of the error matrix \Sigma = inv(Fisher matrix). All quantities are plotted as functions of the duration per FFT segment T_seg. The red dotted line is [Q_1/f_1], i.e., the time required to resolve the resonant peak. As one would expect, if T_seg <~ (Q_1/f_1), we cannot resolve the dynamics of the system and therefore we get nonsense PE results. However, once T_seg > (Q_1/f_1), the PE results seem to be just fluctuating (as f_1 does not fall exactly into a single bin). Maybe there is a small hint that longer T_seg is better. Potentially, this might be due to that we lose less information due to windowing? To be investigated further... 

I also showed the Fisher estimation vs. MCMC results in the last two plots. Here each dot is an MCMC posterior. The red crosses are the true values, and the purple contours are the results of the Fisher calculations (3-sigma contours). The MCMC results showed similar trends as the Fisher predictions and the results for T_seg = (32, 64, 128) s all have similar amounts of scattering << the scattering of the T_seg=8 s results. Though somehow it showed a biased result. In the third plot, I manually corrected the mean so that we could just compare the scattering. The fourth plot showed the original posterior distribution. 

 

Attachment 1: setup.pdf
setup.pdf
Attachment 2: Fisher_vs_Tperseg.pdf
Fisher_vs_Tperseg.pdf
Attachment 3: fisher_vs_mcmc_offset_removed.png
fisher_vs_mcmc_offset_removed.png
Attachment 4: fisher_vs_mcmc.png
fisher_vs_mcmc.png
  17011   Mon Jul 18 15:17:51 2022 HangUpdateCalibrationError propagation to astrophysical parameters from detector calibration uncertainty

1. In the error propogation equation, it should be \Delta \Theta = -H^{-1} M \Delta \Lambda, instead of the fractional error. 

2. For the astro parameters, in general you would need t_c for the time of coalescence and \phi_c for the phase. See, e.g., https://ui.adsabs.harvard.edu/abs/1994PhRvD..49.2658C/abstract.

3. Fig. 1 looks very nice to me, yet I don't understand Fig. 3... Why would phase or amplitude uncertainties at 30 Hz affect the tidal deformability? The tide should be visible only > 500 Hz. 

4. For BBH, we don't measure individual spin well but only their mass-weighted sum, \chi_eff = (m_1*a_1 + m_2*a_2)/(m_1 + m_2). If you treat S1z and S2z as free parameters, your matrix is likely degenerate. Might want to double-check. Also, for a BBH, you don't need to extend the signal much higher than \omega ~ 0.4/M_tot ~ 10^4 Hz * (Ms/M_tot). So if the total mass is ~ 100 Ms, then the highest frequency should be ~ 100 Hz. Above this number there is no signal. 

 

  17029   Sun Jul 24 08:56:01 2022 HangUpdateCalibrationError propagation to astrophysical parameters from detector calibration uncertainty

Sorry I forgot to put tc & phic in the example. 

I modified astroFisherLib.py to include these parameters. Please note that their meaning is that we don't know when the signal happens and at which phase it merges.

It does not mean the time & phase from a reference frequency to the merger. This part is not free to vary because it is fixed by the intrinsic parameters.  

It might be good to have a quick scan through the Cutler & Flanagan 94 paper to better understand their physical meanings.

 

  10083   Fri Jun 20 18:33:53 2014 HarryUpdateGeneralRazorblade Beam Analysis Setup

 Eric Q and I set up the optical configuration for razorblade beam analysis on SP table for future use.

It has been aligned, and will be in use on Monday.

The beam will be characterized for future characterization of optical fibers.

  10098   Wed Jun 25 09:16:52 2014 HarryUpdateGeneralRazorblade Measurements

Purpose

To use a razorblade to measure beam waist at multiple points along the optical axis, so as to later extrapolate the modal profile of the entire beam. This information will then be used to effectively couple AUX laser light to fibers for use in the frequency offset locking apparatus.

Data Acquisition

1) Step the micrometer-controlled razorblade across the beam at a given value of Z, along optical axis, in the plane orthogonal to it (arbitrarily called X).

2) At each value of X, record the corresponding output of a photodiode, (Thorlabs PD A55) here given in mV.

3) Repeat process at multiple points along Z

Analysis

Data from each iteration in the X were fitted to the error function shown below.

V(x) = A*(erf((x-m)/s)+c)

In the Y, they were fitted to:

V(x) = -A*(erf((x-m)/s)+c)

'A' corresponds to an amplitude, 'm' to a mean, 's' to a σ, and 'c' to an offset.

(Only because in Y measurements, the blade progressed toward eclipsing the beam, as opposed to in the X where it progressively revealed the beam.

These fits can be solved for x = (erf-1((V/A)-c)*s)+m1  which can be calculated at the points (Vmax/e2) and (Vmax*(1-1/e2)). The difference between these points will yield beam waist, w(z).

Conclusion

Calculations yielded waists of: X1=66.43um, X2=67.73um, X3=49.45um, Y1=61.20um, Y2=58.70, Y3=58.89

These data seem suspect, and shall be subjected to further analysis.

 

Attachment 1: 40m.zip
  10100   Wed Jun 25 09:30:44 2014 HarryUpdateGeneralWeekly Update

See attached weekly update

Attachment 1: Weekly_Update—June_25_thru_July_1.pdf
Weekly_Update—June_25_thru_July_1.pdf
  10103   Wed Jun 25 17:49:36 2014 HarryUpdateGeneralRazorblade Analysis Pt. 2

Reconfigured razorblade analysis setup on the PD table as per instructions. Used it to collect data to calculate beam waist with, analyses to follow.

See attached schematic for optical setup.

Attachment 1: RazorbladeSetup.pdf
RazorbladeSetup.pdf
ELOG V3.1.3-