E2e school at LLO 1Mar. 18, 2002

E2E : Overview

1. e2e Overview : Hiro Yamamoto ß What is e2e ß Software organization ß Simple example

2. Physics tools in e2e : Biplab Bhawal 3. LIGO I simulation : Matt Evans

Hiro Yamamoto LIGO Laboratory / California Institute of Technology

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What is e2e : 1

u General purpose GW interferometer simulation package » Original version designed and developed by M.Evans » Generic tool like matlab or mathematica » Easy to simulate a wide range of configuration without modifying

and revalidating codes u Simulation program

» Time domain simulation written in C++ » Optics, mechanics, servo ... » Easy to add new phenomena by concentrating on physics, not on

programming

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What is e2e : 2 e2e vs matlab

1+2 = 3 Melody b R.Beausoleil

Laser+2 mirrors = FP LIGO1 model by M.Evans

General purpose calculator

Quick prototyping of wide variety of problems

Easy construction of LIGO like opto-mechanical system

Language

simulinkAlfiGUI

execute m-files in matlabExecute box files in modeler, (compound module)

User programs

math functions, strings, graphics, etc

Primitive modules : Mirror, michelson cavity, 3d mass, digital_filter, etc

Built-in function

matlabe2e

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Simulation setup

Setup a configuration using Graphical Interface

or Text Editor

Configuration files describing what to

simulate

Time domain simulation

Simulated time series of data

Auxiliary inputs

•Flexibility •Ease of use

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Box files Simulation setup

Add_Submodules { field_gen Laser; mirror2 ITM; mirror2 ETM; propagator I2E; propagator E2I; data_in Power; ... } Settings Laser { max_mode_order = 2 distance_waist_X = distz compute_mismatch_curvature = yes; ... } Settings I2E { length = CavLength } Settings E2I { length = CavLength } Settings Power {init = 1; type = vector_real} ... Add_Connections { Power 0 -> Laser power; Laser 0 -> ITM Bin; ITM Aout -> I2E 0; I2E 0 -> ETM Ain ETM Aout -> E2I 0; E2I 0 -> ITM Ain ETM Bout -> TransPower 0; TransPower 0 -> this Tran0 ... }

Content of box file

Laser

Photo diode

mirrormirror

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Mirror primitive

Input field to coated side

output field from coated side

Input field to substrate side

output field from substrate side

Mass position and orientation struct clamp{ double x, y, z; double thetax,… int statusBits; }

struct field { double amps[n]; int mode; int polarization; double waistPos; }

Bout= t Ain + r eikz Bin

Aout= t Bin - r e-ikz Ain

A B Static parameters : Reflectivity, transmittance, surface curvature, etc

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Fabry-Perot cavity dynamics

ETMz = -10-8 + 10-6 t

Resonant at

Power = 1 W, TITM=0.03, TETM=100ppm, Lcavity = 4000m

Reflected Power

Transmitted Power X 100

1 m / s

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Suspended mass with control

Force

Mass position

Suspension point

Susp

Force = filter * mass position

Mass position

Pendulum Pendulum res. at 1Hz

Control on at 10 mixer

F/m + w2 dz S2 + a S + w2

Zmass =

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FUNC primitive module - command liner in GUI -

u GUI is not always the best tool u FUNC is an expression parser, based on c-like syntax u all basic c functions, bessel, hermite u special functions : time_now(), white_noise,

digital_filter(poles, zeros), fp_guoypahse(L,R1,R2), … u predefined constants : PI, LIGHT_SPEED, … u inline functions : leng(x,y) = sqrt(x*x+y*y); L = leng(2,3);

gain = -5; lockTime = 10; out0 = if ( time_now()

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Time domain simulation u Analog process is simulated by a discritized process

with a very small time step (10-7~ 10-3 s) u 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

u Easy to include non linear effect » Saturation, e.g.

u A loop should have a delay » Need to put explicit delay when needed » Need to choose small enough time step

x = 1 s 2 +gs +w0

2 f m

+ w0 2 xsus

Ê Ë

ˆ ¯

+

G

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Fields and optics

u Time domain modal model » field is expanded using Hermite-Gaussian eigen states

u Completely modular » Build planar optics configuration by combining mirrors and

propagators » Photo diodes with arbitrary shapes can be attached anywhere

w0

z (w0,z)

(w0,-z)waist position

w(z)

coating coating

substrate (w0’,-z’)

(w0’,z’)

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Mechanics simulation (1) Seismic motion from

measurement » Need improvemention including

correlations among stacks (2) Parameterized HYTEC stack

» Ed Daw (3) Simple single suspended mirror

» Malik » 4 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

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Mechanical noise of one mirror seismic & thermal noises

seismic motion (power spectral density)

se is

m ic

is ol

at io

n sy

st em

(t ra

ns fe

r fu

nc tio

n)

suspended mirror (transfer function

or 3d model)

†

xseismic +dxthermal (power spectral density)

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Average number of photons

Actual integer number of photons

Simulation option

Sensing noise Shot noise for an arbitrary input

†

n0(t) = h ⋅ P(t ) ⋅ Dt

h ⋅n

†

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 the detector senses.

time

#p ho

to ns

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LIGO Simulation model I

Optics system Mechanical systemLaser

x,f

Feedback force

Primitive optics : any planar, slow FP, MC, PRM, LIGO,advanced LIGO,…

Summation cavity : fast, case-by-case FP, MC, PRM

* Digital filter * Single Suspended * MSE(later)

sensor

actuator

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LIGO simulation model II

EtmR

ItmR

EtmTItmTBS Rec

trr

trt pob

pot

asyref

por

PSL/IOO

corner station strong correlation in the low frequency seismic motion

detectors with shot noise

6 suspended mirrors with seismic and thermal noise

+z

z=0

Psus

Popt

zVdamp sig_MASS

zFopt

actuator with saturation

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Simulated sensitivity curve baseline fundamental noise by realistic simulation

•Interferometer •Mechanics •Sensor-actuator •Servo electronics •Signal extraction •Noises

•Mechanical •Sensor •Laser •Mode Cleaner •Electronics

Simulation can include

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E2E simulation package Components

alfi modeler

modeler_freq

e2ecalc

detmap

e2emacro

simulation helperGUI

e2eDB.mcr *.par

*.dat

*.dhr

*.in *.set

*.prm *.xbm *.cc

(mirror2) (mirror2.prm)

*.box

*.mapmatlab

emacs

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Time domain simulation engine

Module base class

Initialize() Action()

Laser Mirror

Photo diode

Based on the description file, module objects are created and placed in the order of execution

Laser

Mirror1

Mirror2

Photodiode

Laser.action()

Mirror1.action()

Mirror2.action()

Photodiode.action()

output

Knows how to be put in a time loop

Derived class code adds a specific new physics

Class structure Event queue Time loop

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Simulation engine framework time and frequency domain

modeler

t1 x1 y1

t2 x2 y2

t3 x3 y3

...

analyze

LIGO.dat time

xval

yval

LIGO.dhrtime loop

LIGO.box modeler_freq (a.la. spectrum analyzer)

t1 x1 y1

t2 x2 y2analyze

LIGO _dump.dat (optional)time loop

f=f1,f2,...

f1 Xamp1 Xphi1 Yamp1 Yphi1

f2 Xamp2 Xphi2 Yamp2 Yphi2

f3 Xamp3 Xphi3 Yamp3 Yphi3

...

LIGO.dat

time

yval

xval

LIGO.dhr

force to arrange the columns this order

seed=100

param1=3.14

a connected to b

macro definitions

...

LIGO.set

FFT