e2e : overview - ligo e2e/e2e_school/ ¢  e2e school at llo 2 what is e2e : 1 u general

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  • 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

  • E2e school at LLO 2

    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

  • E2e school at LLO 3

    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

  • E2e school at LLO 4

    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

  • E2e school at LLO 5

    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

  • E2e school at LLO 6

    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

  • E2e school at LLO 7

    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

  • E2e school at LLO 8

    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 =

  • E2e school at LLO 9

    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()

  • E2e school at LLO 10

    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

  • E2e school at LLO 11

    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’)

  • E2e school at LLO 12

    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

  • E2e school at LLO 13

    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)

  • E2e school at LLO 14

    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

  • E2e school at LLO 15

    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

  • E2e school at LLO 16

    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

  • E2e school at LLO 17

    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

  • E2e school at LLO 18

    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

  • E2e school at LLO 19

    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

  • E2e school at LLO 20

    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

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