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End to End Simulation of LIGO detector. Hiro Yamamoto LIGO Laboratory / California Institute of Technology. LIGO - Laser Interferometer Graviational Wave Observatory Basics of the Interferometer Detector Interferometer simulation Applications of the simulation. - PowerPoint PPT Presentation
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e2e of LIGO - UCLA talk 1
End to End Simulation ofLIGO detector
LIGO - Laser Interferometer Graviational Wave Observatory
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
lenses» noise : mechanical, thermal, sensor, field-induced, laser, etc : amplitude
and frequency : creation, coupling and propagation» wide dynamic range : 10-6 ~ 10-20 m
As easy as back of the envelope
e2e of LIGO - UCLA talk 19
E2E perspective
e2e development started after LIGO 1 design completed (1997 ~ )
LIGO 1 lock acquisition was redesigned successfully using e2e by M.Evans (2000 ~ 2001)
Major on going efforts for LIGO I (2001 ~ )» Realistic noise of the locked state interferometer» Effect of the thermal lensing on the lock acquisition
Efforts for Advanced LIGO (2000 ~ )» Development of optics and mechanics modules» Trying to expand users who can contribute
– A.Weinstein (CIT), J.Betzwieser (MIT), M.Rakmanov (UF), M.Malec (GEO)
e2e of LIGO - UCLA talk 20
End to End Simulation overview
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
e2e of LIGO - UCLA talk 22
End to End Simulationcoarse view
Optics system Mechanical systemLaser
x,
Feedback force
•Time domain modal model•Objects : laser, mirror, photo diode, …•Any planar interferometer
•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,
digital_filter(poles, zeros), fp_guoypahse(L,R1,R2), … predefined constants : PI, LIGHT_SPEED, … inline functions : leng(x,y) = sqrt(x*x+y*y); L = leng(2,3);
gain = -5; lockTime = 10;
out0 = if ( time_now()<lockTime , in0, in0+gain*in1 );
mixer module
e2e of LIGO - UCLA talk 28
e2e physicsTime domain simulation
Analog process is simulated by a discretized process with a very small time step (10-7~ 10-3 s)
Linear system response is handled using digital filter» e2e DF = PF’s pziir.m (bilinear trans (s->z) + SOS) + CDS filter.c
» Transfer function -> digital filter
» Pendulum motion
» Analog electronics
Easy to include non linear effect» Saturation, e.g.
A loop should have a delay» Need to put explicit delay when needed
» Need to choose small enough time step
x=1
s2 +γs+ω02
fm
+ω02xsus
⎛ ⎝
⎞ ⎠
xsus(t)f(t)x
+
G
e2e of LIGO - UCLA talk 29
e2e physics Fields and optics
Time domain modal model» field is expanded using Hermite-Gaussian eigen states» Perturbation around resonant state
Reflection matrix» tilt» »
Completely modular» Arbitrary planar optics configuration
can be constructed by combining mirrors and propagators
Photo diodes with arbitrary shapes can be attached anywhere Adiabatic calculation for short cavities for faster simulation
w0
z
(w0,z)
(w0,-z)waist position
w(z)
coating
coating
substrate(w0’,-z’)
(w0’,z’)
€
Enm = exp(iωt − ikz + i(n + m +1)η (z))um (x)un (y)
um (x) = CmHm ( 2x /w)exp(−x 2(1
w2+ i
k
2R))
€
E00 → E00 + θ E01
∝ exp(−(x − 2zθ)2 /w2)
€
θ
e2e of LIGO - UCLA talk 30
e2e physicsMechanics simulation
(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.
+z
z=0
Psus
Popt
zVdamp
sig_MASSzFopt
V
I150mA
e2e of LIGO - UCLA talk 35
Fabry-PerotError signal linearization
€
S=SPDHAtr
2 =−rETMtETM2 sinφ
arbi
trar
y un
it
arbi
trar
y un
itar
bitr
ary
unit
e2e of LIGO - UCLA talk 36
Hanford 2k simulation setup
Han2k optics setup
EtmR
ItmR
EtmTItmTBSRec
trr
trtpob
potasyref
Leng_ArmR
Leng_ArmT
Leng_Rec2BS
Leng_BS2ItmR
Leng_BS2ItmT
por
lower - lower sideband powerupper - upper sideband powercarrier - lower sideband power
I - inphase demodulated signalQ - quadphase demodulated signal
photo detector and demodulator
powers of each frequency
Field data
P - total power
power meter
PSL/IOO
6 independent suspended mirrors with seismic noise
corner station :strong correlation in the low frequency seismic motion
+z
z=0
Psus
Popt
zVdamp
sig_MASSzFopt
Non-linearity of controller
e2e of LIGO - UCLA talk 37
Automated Control Matrix SystemLIGO T000105 Matt Evans
Control system
Signal toDOF
DOF toOptics
PtrtPtrr
QaymIasm
QpobIPobQrefIref
sig_EtmT
sig_EtmR
sig_ItmT
sig_ItmR
filters
L-
L+
l-
l+
errLm
errLp
errlm
errlp
sig_L-
sig_L+
sig_l-
sig_l+
DOF gainconLm
conLp
conlm
conlp
gainEtmT
gainEtmR
gainItmT
gainItmR
optical gainField signal
Actuation of mass
Same c code usedin LIGO servo
and in simulation
Field signal
Actuation of mass
e2e of LIGO - UCLA talk 38
Multi step locking
State 1 : Nothing is controlled. This is the starting point for lock acquisition.
State 2 : The power recycling cavity is held on a carrier anti-resonance. In this state the sidebands resonate in the recycling cavity.
State 3 : One of the ETMs is controlled and the carrier resonates in the controlled arm.
State 4 : The remaining ETM is controlled and the carrier resonates in both arms and the recycling cavity.
State 5 : The power in the IFO has stabilized at its operating level. This is the ending point for lock acquisition.
e2e of LIGO - UCLA talk 39
Lock acquisitionreal and simulated
obse
rvab
le
Not
exp
erim
enta
lly
obs
erva
ble
e2e of LIGO - UCLA talk 40
Second generation LIGO simulationSimLIGO
Assist noise hunting, noise reduction and lock stability study in the commissioning phase
Performance of as-built LIGO» effect of the difference of two arms, etc
Noise study» Non-linearity
– cavity dynamics, electronic saturations, digitization, etc
» Bilinear coupling
Lock instability Sophisticated lock acquisition Upgrade trade study
e2e of LIGO - UCLA talk 41
SimLIGOA Detailed Model of LIGO IFO
Modal beam representation» alignment, mode matching, thermal lensing
3D mechanics» Correlation of seismic motions in corner station
» 6x6 stack transfer function
» 3D optics with 4/5 local sensor/actuator pairs
Complete analog and digital electronics chains with noise» Common mode feedback
» Wave Front Sensors
» “Noise characterization of the LHO 4km IFO LSC/DSC electronics” by PF and RA, 12-19 March 2002 included
e2e of LIGO - UCLA talk 42
SimLIGONoise sources
All major noise sources» seismic, thermal, sensing, laser frequency and intensity, electronics,
mechanical IFO
» optical asymmetries (R, T, L, ROC)» non-horizontal geometry (wedge angles, earth's curvature)» phase maps» scattered light
Mechanics» wire resonances, test mass internal modes
Sensor» photo-detector, whitening filters, anti-aliasing
Digital system» ADC, digital TF, DAC
Actuation» anti-imaging, dewhitening, coil drivers
e2e of LIGO - UCLA talk 43
SimLIGOSystem structure
Digital ISC
PSL
LOS (mechanics, DSC)
IOO COC Analog ISC
Environment (ground, stack)
Mechanical Interfaces Optical Interfaces Electrical Interfaces
e2e of LIGO - UCLA talk 44
SimLIGOmore realistic LIGO simulation
DigitalISC
COC
IOO
Suspension
OpticsElecOut - analog
LSC
ASC
Diag
PutDigital
Controller
LOS
ETM
ETM
pickofftelescope
Env
3D suspendedmass w/ OESM
e2e of LIGO - UCLA talk 45
SimLIGONoise components
101
102
103
104
10-19
10-18
10-17
10-16
10-15
10-14
10-13
10-12
10-11
Hz
SimLIGO Sensitivity (analytic) w/ TAS
= 1.25e3
TotalSeismicShotADCDACPDCoilWhiteDewhiteAI
optical lever
e2e of LIGO - UCLA talk 46
LIGO data vs SimLIGO
101
102
103
104
10-21
10-20
10-19
10-18
10-17
10-16
10-15
10-14
10-13
LHO 4kLHO 2kLLO 4kSimLIGO
Triple Strain Spectra - Thu Aug 15 2002St
rain
(h/
rtH
z)rana-1029490757.pdf
Frequency (Hz)data and simulationout of date
e2e of LIGO - UCLA talk 47
SimLIGOsensitivity curve
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.
L1 L2
z1 z2z3
Ein
linear approx.of Ein , z1 , z2
for L2 /c
e2e of LIGO - UCLA talk 51
Adv. LIGO MechanicsQuadruple Pendulum structure
e2e of LIGO - UCLA talk 52
Adv. LIGO Mechanics Transfer functions
60cm 60.1cm