Download M.Evans - LIGO

End to End Simulation of
LIGO detector
Hiro Yamamoto
LIGO Laboratory / California Institute of Technology
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LIGO Laser Interferometer Graviational Wave Observatory
Basics of the Interferometer Detector
Interferometer simulation
Applications of the simulation
LIGO Progress Report : LIGO-G020007 by Alan Weinstein, Caltech
e2e of LIGO - UCLA talk
1
Interferometer for
Gravitational Wave detection
L2
E2
E1
L1
 1-L2
E1- E2L
L1  L2 h~10-23
h
L1-L2~10-19m
L1  L2
e2e of LIGO - UCLA talk
2
The Fabry-Perot Cavity
- the most important dynamics Acav
Ain

F˜
2
Acav
Ain
2
1/ F˜
ITM

TR
xITM
xETM
REF
ETM
L
x  x ITM  x ETM  n  L,   2kx  4 

x /
Acav
imag(Acav )
t ITM
 Ain
1 rITM rETM e i
 Ain
x  

imag(Acav )  x

 

 t ITM

4
˜
F  
 
2
1 rITM rETM  t ITM
x
˜
F (1 i2 
)
˜
 F

Aref  rITM  tITM rETM e i Acav
e2e of LIGO - UCLA talk
x
2
t ITM 2  0.03
t ETM  10e6
F˜  130
2
3
Basic ingredients of LIGO
fL
fL
freq
fL-fRF
EOM
fL
shot noise ~ 1016 /s
Signal to
L/ DOF
L/
DOF
to force
fRF

e2e of LIGO - UCLA talk
Seismic motion ~ 10-6 m 4
Seismic Isolation f-6
Laser
f-2
Thermal noise ~ kT
Astrophysical sources:
Thorne diagrams
LIGO I (2002-2005)
LIGO II (2007- )
Advanced LIGO
seimic
thermal
e2e
of LIGO - UCLA talk
quantum
5
Hanford
Observatory
(H2K and H4K)
LIGO sites
4 km
+ 2 km
Hanford, WA (LHO)
• located on DOE reservation
• treeless, semi-arid high desert
4 km
Livingston
Observatory
(L4K)
• 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!!
e2e of LIGO - UCLA talk
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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
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International network
Simultaneously detect signal (within msec)
LIGO
GEO
Virgo
 detection
TAMA confidence
 locate the sources
 verify light speed
propagation
 decompose the
polarization of
gravitational waves
AIGO
Open up a new
field of astrophysics!
e2e of LIGO - UCLA talk
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Control Room
time
frequency
Spectrogram
e2e of LIGO - UCLA talk
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How does the signal look like
Frequency (Hz), Df = 16 Hz
1.4/1.4 Solar Mass NS/NS Inspiral
signal in AS_Q... (Lormand, Adhikari)
103
102
GPS time (S), DT = 0.062s
e2e of LIGO - UCLA talk
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Sensitivities of
LIGO 3 interferometers
e2e of LIGO - UCLA talk
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Improvements of sensitivities of
Hanford 4k interferometer
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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
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LIGO End to End Simulation
the motivation
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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
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E2E
perspective
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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
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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
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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
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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
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End to End Simulation
coarse view
Laser
Optics system
Mechanical system
x,
Control system
sensor
Feedback force
•Time domain modal model
•Objects : laser, mirror, photo diode, …
•Any planar interferometer
•Fabry-Perot, Mode cleaner,LIGO I,
•Advanced LIGO,…
e2e of LIGO - UCLA talk
actuator
•Transfer function using Digital
filter
•Single Suspended mirror
•Mechanical Simulation Engine
(object-oriented)
22
e2e Graphical Editor
Laser
mirror
mirror
Photo diode
propagator
Photo diode
e2e of LIGO - UCLA talk
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Simulation engine
time loop and independent modules
simulation engine
GUI
construct
and init
loop
data file
time evolution loop
independent modules
Mirror
laser
photo diode
3d mass
matlab, etc
digital filter
derived from
module class
math parser
e2e of LIGO - UCLA talk
M.Evans
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e2e example - 1
Fabry-Perot cavity dynamics
1m/s
ETMz = -10-8 + 10-6 t
Resonant at
Reflected Power
Transmitted Power
X 100
Power = 1 W, TITM=0.03, TETM=100ppm,
Lcavity = 4000m
e2e of LIGO - UCLA talk
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e2e example - 2
Suspended mass with control
Suspension
point
Susp. point
Pendulum
Pendulum
res. at 1Hz
mixer
Force
Force
= filter * mass position
Control on at 10
Mass position
Zmass =
F/m + w2 dz
S2 + a S + w2
e2e of LIGO - UCLA talk
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FUNC primitive module
- command liner in GUI 
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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);
mixer module
gain = -5; lockTime = 10;
out0 = if ( time_now()<lockTime , in0, in0+gain*in1 );
e2e of LIGO - UCLA talk
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e2e physics
Time domain simulation
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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
1
 f
Pendulum motion
x 2
 w 02 xsus 
2 

s  s  w 0 m
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
e2e of LIGO - UCLA talk
+
G
28
e2e physics
Fields and optics
E nm  exp(iw t  ikz  i(n  m  1)(z))um (x)un (y)

Time domain modal model
um (x)  Cm H m ( 2x /w)exp(x 2 (
1
k

i
))
2
w
2R

» field is expanded using Hermite-Gaussian eigen states
» Perturbation around resonant state
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Reflection matrix
»
»
»
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
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
tilt
E 00  E 00   E 01
(w0 ’,-z’)
substrate
(w0 ,z)
z
w0
 exp((x  2z ) 2 /w 2 )
Completely modular
» Arbitrary planar optics configuration
can be constructed by combining
mirrors and propagators
(w0 ’,z’)

coating
waist position
w(z)
(w0 ,-z)
coating
Photo diodes with arbitrary shapes can be attached anywhere
Adiabatic calculation for short cavities for faster simulation
e2e of LIGO - UCLA talk
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e2e physics
Mechanics simulation
(1)
Seismic motion from
measurement
3
» correlations among stacks
» fit and use psd or use time series
(2) Parameterized HYTEC stack
4
2
1
» 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
e2e of LIGO - UCLA talk
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Mechanical noise of one mirror
suspended mirror
(transfer function
or 3d model)
xseismic  xthermal
(power spectral density)
seismic isolation system
(transfer function)
seismic & thermal noises
seismic motion
(power spectral density)
e2e of LIGO - UCLA talk
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Sensing noise
Shot noise for an arbitrary input
Simulation option
Shot noise can be turned
on or off for each photo
diode separately.
Actual number of photons which the
detector senses.
#photons
Average number of photons
  P(t) Dt
n0 (t) 
h
Actual integer number of photons
n(t)  Poisson(n0 (t))
Average number of photons by the input
power of arbitrary time dependence
time
e2e of LIGO - UCLA talk
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First LIGO simulation
Han2k
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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
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Fabry-Perot
ideal vs realistic
ideal
Linear Controllers:
Realistic actuation
modeling plays a
critical role in
control design.
realistic
I
Psus
150mA
V
zFopt
sig_MASS
zVdamp
+z
Popt
z=0
e2e of LIGO - UCLA talk
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Fabry-Perot
Error signal linearization
S
rETM
 SAPDH
2  2
t
tr
sin 
arbitrary unit
arbitrary unit
arbitrary unit
ETM
e2e of LIGO - UCLA talk
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Hanford 2k simulation setup
Field data
6 independent suspended
mirrors with seismic noise
trr
power meter
EtmR
P - total power
photo detector and demodulator
Leng_ArmR
I - inphase demodulated s ignal
Q - quadphase demodulated signal
powers of each frequenc y
corner station :
lower - lower sideband power
upper - upper sideband power
carrier - lower sideband power
ItmR
strong correlation in the low
frequency seismic motion
por
Leng_BS2ItmR
pob
PSL/IOO
Leng_Rec2BS
trt
Leng_BS2ItmT
Rec
BS
ref
asy
Leng_ArmT
pot ItmT
EtmT
Non-linearity of
controller
Psus
Han2k optics setup
zFopt
e2e of LIGO - UCLA talk
sig_MASS
zVdamp
36
+z
Popt
z=0
Automated Control Matrix System
LIGO T000105 Matt Evans
FieldField
signal
signal
Ptrt
Ptrr
Qaym
Iasm
Qpob
IPob
Qref
Iref
DOF gain
errLm
sig_LerrLp
sig_L+
Signal to
errlm
DOF
sig_lerrlp
sig_l+
optical gain
filters
conLm
sig_EtmT
LconLp
L+
l-
conlm
conlp
l+
gainEtmT
sig_EtmR
gainEtmR
DOF to sig_ItmT
Optics
gainItmT
sig_ItmR
gainItmR
Control sys tem
Same c code used
in LIGO servo
and in simulation
e2e of LIGO - UCLA talk
Actuation of mass
Actuation of mass
37
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
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Lock acquisition
real and simulated
e2e of LIGO - UCLA talk
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Second generation LIGO simulation
SimLIGO


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


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Lock instability
Sophisticated lock acquisition
Upgrade trade study
e2e of LIGO - UCLA talk
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SimLIGO
A 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
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SimLIGO
Noise 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
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SimLIGO
System structure
Digital ISC
PSL
IOO
COC
Analog ISC
LOS (mechanics, DSC)
Environment (ground, stack)
Mechanical Interfaces
Optical Interfaces
e2e of LIGO - UCLA talk
Electrical Interfaces
43
SimLIGO
more realistic LIGO simulation
Digital
ISC
Env
LSC
ASC
IOO
COC
PutDigital
Diag
ETM
Optics
ElecOut - analog
Suspension
ETM
LOS
3D suspended
Controller mass w/ OESM
pickoff
telescope
e2e of LIGO - UCLA talk
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SimLIGO
Noise components
10
10
10
10
10
10
10
10
10
SimLIGO Sensitivity (analytic) w/ T AS = 1.25e 3
-11
Total
Seismic
Shot
ADC
DAC
PD
Coil
White
Dewhite
AI
-12
-13
-14
optical lever
-15
-16
-17
-18
-19
10
1
10
2
10
3
10
4
Hz
e2e of LIGO - UCLA talk
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LIGO data vs SimLIGO
rana-1029490757.pdf
Triple Strain Spectra - Thu Aug 15 2002
10
10
10
10
10
10
10
10
10
-13
LHO 4k
LHO 2k
LLO 4k
SimLIGO
-14
-15
-16
-17
-18
-19
-20
-21
10
1
data and simulation
out of date
10
2
10
3
10
4
Frequency (Hz)
e2e of LIGO - UCLA talk
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SimLIGO
sensitivity 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
47
Power flow in the interferometer
Energy loss in substrate
Energy loss by mirror ~ 50ppm
e2e of LIGO - UCLA talk
48Kells
by Bill
Advanced R&D: Optics
Thermal Compensation
Thermoelastic deformation
Thermal lens
100 nm “Bump”
On HR surface
•Extend LIGO I “WFS” to
spatially resolve phase/ OPD errors
•Thermal actuation on core optics
In Input Test Mass
100 nm “lens” for Sapphia
1000 nm “lens” for Silika
10 nm “lens”
In Beam Splitter
e2e of LIGO - UCLA talk
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Dual recycling cavity
simulate 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.
linear approx.
of Ein , z1 , z2
for L2 /c
z1
z3
z2
Ein
L1
e2e of LIGO - UCLA talk
L2
50
Adv. LIGO Mechanics
Quadruple Pendulum structure
e2e of LIGO - UCLA talk
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Adv. LIGO Mechanics
Transfer functions
60cm
e2e of LIGO - UCLA talk
60.1cm
52