e2e of LIGO - UCLA talk 1 End to End Simulation of LIGO detector LIGO - Laser Interferometer Graviational Wave Observatory Basics of the Interferometer Detector Interferometer simulation Applications of the simulation Hiro Yamamoto LIGO Laboratory / California Institute of Technology LIGO Progress Report : LIGO-G020007 by Alan Weinstein, Caltech
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E2e of LIGO - UCLA talk1 End to End Simulation of LIGO detector LIGO - Laser Interferometer Graviational Wave Observatory Basics of the Interferometer.
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Basics of the Interferometer Detector Interferometer simulation Applications of the simulation
Hiro YamamotoLIGO Laboratory / California Institute of Technology
LIGO Progress Report : LIGO-G020007 by Alan Weinstein, Caltech
e2e of LIGO - UCLA talk 2
Interferometer forGravitational Wave detection
L1
L2
€
h =L1 − L2
L1 + L2
h~10-23
L1-L2~10-19m
E1E2
E1- E2∝ L1-L2
€
∝
e2e of LIGO - UCLA talk 3
The Fabry-Perot Cavity- the most important dynamics -
TR
REF
ETMITMxITM xETM
Acav
L
€
x=xITM +xETM =nλ−L,
€
φ=2kx=4πxλ
€
Acav = Ain
tITM
1− rITM rETM e iφ
≈ Ain˜ F (1+ i2π ⋅
x
λ ˜ F )
€
Aref = rITM − tITM rETM e iφ Acav€
x << λ
€
Acav
2
Ain
2
€
imag(Acav )
€
Ain
€
˜ F =tITM
1− rITM rETM
⎛
⎝ ⎜
⎞
⎠ ⎟
2
≈4
tITM2
€
˜ F
€
1/ ˜ F
€
x /λ
€
tITM2 = 0.03
tETM2 =10e−6
˜ F =130
€
imag(Acav )∝ x
e2e of LIGO - UCLA talk 4
Basic ingredients of LIGO
Laser EOM
PD
fL fL
fL-fRF
fL
fRF
freq
Signal to DOF
DOFto force
Seismic motion ~ 10-6 m
Thermal noise ~ kT
shot noise ~ 1016 /s
Seism
ic Isolation f-6
f-2
€
L /θ
€
L /θ
e2e of LIGO - UCLA talk 5
Astrophysical sources: Thorne diagrams
LIGO I (2002-2005)
LIGO II (2007- )
Advanced LIGO
seimic thermal quantum
e2e of LIGO - UCLA talk 6
LIGO sitesHanford Observatory
(H2K and H4K)
LivingstonObservatory(L4K)
Hanford, WA (LHO)
• located on DOE reservation
• treeless, semi-arid high desert
• 25 km from Richland, WA
• Two IFOs: H2K and H4K
Livingston, LA (LLO)
• located in forested, rural area
• commercial logging, wet climate
• 50km from Baton Rouge, LA
• One L4K IFO
Both sites are relatively seismically quiet, low
human noise - NOT!!
4 km + 2 km
4 km
e2e of LIGO - UCLA talk 7
Logging at Livingston
Less than 3 km a few 100 meters away… Dragging big logs …Remedial measures at LIGO are in progress;this will not be a problem in the future.
e2e of LIGO - UCLA talk 8
International network
LIGO
Simultaneously detect signal (within msec)
detection confidence
locate the sources
verify light speed propagation
decompose the polarization of gravitational waves Open up a new field of astrophysics!
GEO VirgoTAMA
AIGO
e2e of LIGO - UCLA talk 13
Control Room
Spectrogram
time
frequency
e2e of LIGO - UCLA talk 14
How does the signal look like
1.4/1.4 Solar Mass NS/NS Inspiral signal in AS_Q... (Lormand, Adhikari)
GPS time (S), T = 0.062s
Fre
qu
en
cy
(H
z), f
= 1
6 H
z
103
102
e2e of LIGO - UCLA talk 15
Sensitivities ofLIGO 3 interferometers
e2e of LIGO - UCLA talk 16
Improvements of sensitivities ofHanford 4k interferometer
e2e of LIGO - UCLA talk 17
Different cultures in HEP and GW- my very personal view
High Energy Physics Gravitational Wave Detection group
people know of simulation very few people know of simulation
simulation and hardware developments go side-by-side, stimulating each other
simulation is used only when there is no other way, and a model is developed only for that problem. fortran, matlab, mathematica, LabView, etc
simulation is used to understand the integrated system
overall performance is maintained by noise budgets assigned to each subsystem
hardware people intend to use simulation to understand problems
hardware people try to address problems by dealing with hardware
use of simulation for data analysis is a well known procedure
simulation for data analysis is non existent
e2e of LIGO - UCLA talk 18
LIGO End to End Simulation the motivation
Assist detector design, commissioning, and data analysis To understand a complex system
» back of the envelope is not large enough» complex hardware : pre-stabilized laser, input optics, core optics, seismic
isolation system on moving ground, suspension, sensors and actuators» feedback loops : length and alignment controls, feedback to laser» non-linearity : cavity dynamics to actuators» field : non-Gaussian field propagation through non perfect mirrors and
General purpose GW interferometer simulation framework» Generic tool like matlab or mathematica» Time domain simulation written in C++» Optics, mechanics, servo, ...
– time domain modal model, single suspended 3D mass.– analog and digital controller - ADC, DAC, digital filter, etc
End to End simulation environment» Simulation engine - modeler, modeler_freq» Description files defining what to simulate - Simple pendulum, …, full
LIGO (constituent files are called “box files” or simply “boxes”)» Graphical Editor to create description files - alfi
LIGO I simulation packages» Han2k : used for the lock acquisition design» SimLIGO : to assist LIGO I commissioning
e2e of LIGO - UCLA talk 21
GW Interferometer simulation- difficulties -
Simulate chronologically dependent time series» parallelization is difficult
Control systems connect various subsystems very tightly» optimal choice of system time step is hard
Mirror motions may need quad precision» micro seismic peak ~ 10-6 m» relative mirror motion of interest for LIGO I ~ 10-20 m» relative mirror motion of interest for LIGO II < 10-21 m
•Fabry-Perot, Mode cleaner,LIGO I, •Advanced LIGO,…
sensor actuator
•Transfer function using Digital filter•Single Suspended mirror•Mechanical Simulation Engine (object-oriented)
Control system
e2e of LIGO - UCLA talk 23
e2e Graphical Editor
Laser
Photo diode
mirrormirror
propagatorPhoto diode
e2e of LIGO - UCLA talk 24
Mirror
digital filter3d mass
laser
Simulation engine time loop and independent modules
GUI data file
matlab, etcsimulation engine
independent modules
photo diode
time evolution loop
math parser
derived frommodule class
constructand init
loop
M.Evans
e2e of LIGO - UCLA talk 25
e2e example - 1Fabry-Perot cavity dynamics
ETMz = -10-8 + 10-6 t
Resonant at
Power = 1 W, TITM=0.03, TETM=100ppm,Lcavity = 4000m
Reflected Power
Transmitted PowerX 100
1 / s
e2e of LIGO - UCLA talk 26
e2e example - 2Suspended mass with control
Force
Mass position
Suspensionpoint
Susp. point
Force= filter * mass position
Pendulum
Pendulumres. at 1Hz
Control on at 10
mixer
F/m + 2 dz
S2 + a S + 2Zmass =
e2e of LIGO - UCLA talk 27
FUNC primitive module- command liner in GUI -
GUI is not always the best tool FUNC is an expression parser, based on c-like syntax all basic c functions, bessel, hermite special functions : time_now(), white_noise,
(1) Seismic motion from measurement» correlations among stacks» fit and use psd or use time series
(2) Parameterized HYTEC stack» Ed Daw
(3) Simple single suspended mirror» M.Rakmanov, V.Sannibale» 4/5 sensors and actuators» couple between LSC and ASC
(4) Thermal noise added in an ad hoc way» using Sam Finn’s model
1
2 3
4
e2e of LIGO - UCLA talk 31
Mechanical noise of one mirrorseismic & thermal noises
seismic motion(power spectral density)
seis
mic
isol
atio
n sy
stem
(tra
nsfe
r fu
ncti
on)suspended mirror
(transfer function or 3d model)
€
xseismic+δxthermal(power spectral density)
e2e of LIGO - UCLA talk 32
Average number of photons
Actual integer number of photons
Simulation option
Sensing noiseShot noise for an arbitrary input
€
n0(t)=η ⋅P(t)⋅Δth⋅ν
€
n(t)=Poisson(n0(t))
Shot noise can be turned on or off for each photo diode separately.
Average number of photons by the input power of arbitrary time dependence
Actual number of photons which thedetector senses.
time
#pho
tons
e2e of LIGO - UCLA talk 33
First LIGO simulationHan2k
Matt Evans Thesis Purpose
» design and develop the LHO 2k IFO locking servo» simulate the major characteristics of length degree of freedom
under 20 Hz.
Simulation includes» Scalar field approximation» 1 DOF, everywhere» saturation of actuators» Simplified seismic motion and correlation» Analog LSC, no ASC» no frequency noise, no shot noise, no sensor/actuator/electronic
noise
e2e of LIGO - UCLA talk 34
Fabry-Perotideal vs realistic
idea
lre
alis
tic
Linear Controllers:Realistic actuationmodeling plays acritical role incontrol design.
Calculated from a time series of data» Major ingredients of the real LIGO included» Interferometer, Mechanics, Sensor-actuator, Servo electronics» Known noises» Signal to sensitivity conversion
Demonstration of the capability to simulate the major behavior of LIGO» Reliable tool for fine tuning a complex device» Almost any assumptions can be easily tested - at least qualitatively» Trade study» Subsystem design» …
e2e of LIGO - UCLA talk 48
Power flow in the interferometerEnergy loss in substrate
Energy loss by mirror ~ 50ppm
by Bill Kells
e2e of LIGO - UCLA talk 49
Advanced R&D: OpticsThermal Compensation
Thermal lens
Thermoelastic deformation
100 nm “Bump”On HR surface
10 nm “lens”In Beam Splitter
In Input Test Mass100 nm “lens” for Sapphia1000 nm “lens” for Silika
•Extend LIGO I “WFS” to spatially resolve phase/ OPD errors•Thermal actuation on core optics
e2e of LIGO - UCLA talk 50
Dual recycling cavitysimulate FAST
Can be simulated today, but slow… simulation time step = cavity length / speed of light Module based on an approximate calculation of fields in a short cavity
runs 500 (~L2 / L1 ) faster than simulation using primitive mirrors. M.Rakmanov (UF) worked on a dual recycling cavity formulation and
did its validation using matlab and e2e primitive optics. Not completed.