E2e of LIGO - UCLA talk1 End to End Simulation of LIGO detector LIGO - Laser Interferometer Graviational Wave Observatory Basics of the Interferometer

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


Interferometer forGravitational Wave detection

L1

L2

€

h =L1 − L2

L1 + L2

h~10-23

L1-L2~10-19m

E1E2

E1- E2∝ L1-L2

€

∝


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


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


Astrophysical sources: Thorne diagrams

LIGO I (2002-2005)

LIGO II (2007- )

Advanced LIGO

seimic thermal quantum


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


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.


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


Control Room

Spectrogram

time

frequency


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


Sensitivities ofLIGO 3 interferometers


Improvements of sensitivities ofHanford 4k interferometer


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


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 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)


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


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


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 Graphical Editor

Laser

Photo diode

mirrormirror

propagatorPhoto diode


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 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 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 =


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 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 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 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


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)


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


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


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


Fabry-PerotError signal linearization

€

S=SPDHAtr

2 =−rETMtETM2 sinφ

arbi

trar

y un

it

arbi

trar

y un

itar

bitr

ary

unit


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


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


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.


Lock acquisitionreal and simulated

obse

rvab

le

Not

exp

erim

enta

lly

obs

erva

ble


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


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


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


SimLIGOSystem structure

Digital ISC

PSL

LOS (mechanics, DSC)

IOO COC Analog ISC

Environment (ground, stack)

Mechanical Interfaces Optical Interfaces Electrical Interfaces


SimLIGOmore realistic LIGO simulation

DigitalISC

COC

IOO

Suspension

OpticsElecOut - analog

LSC

ASC

Diag

PutDigital

Controller

LOS

ETM

ETM

pickofftelescope

Env

3D suspendedmass w/ OESM


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


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


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» …


Power flow in the interferometerEnergy loss in substrate

Energy loss by mirror ~ 50ppm

by Bill Kells


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


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


Adv. LIGO MechanicsQuadruple Pendulum structure


Adv. LIGO Mechanics Transfer functions

60cm 60.1cm

Documents

E2e of LIGO - UCLA talk1 End to End Simulation of LIGO detector LIGO - Laser Interferometer Graviational Wave Observatory Basics of the Interferometer