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gwinc/noise/quantum.py
+ 84
− 80
'''Functions to calculate quantum noise
'''
from __future__ import division
from numpy import pi, sqrt, arctan, sin, cos, exp, size, ones, zeros, log10, conj, sum
import numpy as np
from numpy import pi, sqrt, arctan, sin, cos, exp, size, ones, zeros, log10, conj, sum
import logging
from .. import const
@@ -8,13 +11,17 @@ from ..struct import Struct
def shotrad(f, ifo):
"""Quantum noise
"""Quantum noise noise strain spectrum
:f: frequency array in Hz
:ifo: gwinc IFO structure
:returns: strain noise power spectrum at :f:
corresponding author: mevans
modifications for resonant delay lines: Stefan Ballmer
"""
try:
sqzType = ifo.Squeezer.Type
except AttributeError:
@@ -107,7 +114,7 @@ def shotrad(f, ifo):
else:
SQZ_DB = ifo.Squeezer.AmplitudedB # Squeeing in dB
lambda_in = ifo.Squeezer.InjectionLoss # Loss to squeezing before injection [Power]
alpha = ifo.Squeezer.SQZAngle # Freq Indep Squeeze angle
alpha = ifo.Squeezer.SQZAngle # Freq Indep Squeeze angle
ANTISQZ_DB = ifo.Squeezer.get('AntiAmplitudedB', SQZ_DB) # Anti squeezing in db
etaRMS = ifo.Squeezer.get('LOAngleRMS', 0) # quadrature noise
@@ -170,8 +177,8 @@ def shotrad(f, ifo):
# IFO Transfer and Output Filter Cavities
#####################################################
# apply the IFO dependent squeezing matrix to get
# the total noise due to quantum fluctuations coming in from the AS port
# apply the IFO dependent squeezing matrix to get the total noise
# due to quantum fluctuations coming in from the AS port
Msqz = getProdTF(Mifo, Msqz)
# add this to the other noises Mn
@@ -288,32 +295,31 @@ def shotradSignalRecycled(f, ifo):
Mnoise = noise fields produced by losses in the IFO at the AS port
"""
# f # Signal Freq. [Hz]
lambda_ = ifo.Laser.Wavelength # Laser Wavelength [m]
hbar = const.hbar # Plancks Constant [Js]
c = const.c # SOL [m/s]
hbar = const.hbar # Plancks Constant [Js]
c = const.c # SOL [m/s]
omega_0 = 2*pi*c/lambda_ # Laser angular frequency [rads/s]
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
L = ifo.Infrastructure.Length # Length of arm cavities [m]
l = ifo.Optics.SRM.CavityLength # SRC Length [m]
T = ifo.Optics.ITM.Transmittance # ITM Transmittance [Power]
m = ifo.Materials.MirrorMass # Mirror mass [kg]
L = ifo.Infrastructure.Length # Length of arm cavities [m]
l = ifo.Optics.SRM.CavityLength # SRC Length [m]
T = ifo.Optics.ITM.Transmittance # ITM Transmittance [Power]
m = ifo.Materials.MirrorMass # Mirror mass [kg]
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
bsloss = ifo.Optics.BSLoss # BS Loss [Power]
bsloss = ifo.Optics.BSLoss # BS Loss [Power]
mismatch = 1 - ifo.Optics.coupling # Mismatch
mismatch = mismatch + ifo.TCS.SRCloss # Mismatch
# BSloss + mismatch has been incorporated into a SRC Loss
lambda_SR = 1 - (1 - mismatch) * (1 - bsloss) # SR cavity loss [Power]
lambda_SR = 1 - (1 - mismatch) * (1 - bsloss) # SR cavity loss [Power]
tau = sqrt(ifo.Optics.SRM.Transmittance) # SRM Transmittance [amplitude]
rho = sqrt(1 - tau**2) # SRM Reflectivity [amplitude]
tau = sqrt(ifo.Optics.SRM.Transmittance) # SRM Transmittance [amplitude]
rho = sqrt(1 - tau**2) # SRM Reflectivity [amplitude]
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ds = ifo.Optics.SRM.Tunephase # SRC Detunning
phi = ds/2
ds = ifo.Optics.SRM.Tunephase # SRC Detunning
phi = ds/2
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
lambda_arm = 1 - (1 - ifo.Optics.Loss)**2 * (1 - ifo.Optics.ETM.Transmittance)
@@ -352,8 +358,8 @@ def shotradSignalRecycled(f, ifo):
lossArm = sqrt(lambda_arm)
lossSR = sqrt(lambda_SR)
Omega = 2*pi*f # Signal angular frequency [rad/s]
h_SQL = sqrt(8 * hbar / (m * (Omega * L)**2)) # SQL Strain
Omega = 2*pi*f # Signal angular frequency [rad/s]
h_SQL = sqrt(8 * hbar / (m * (Omega * L)**2)) # SQL Strain
K = 16 * P * omega_0 / (m * c**2 * Omega**2)
# arm cavity
@@ -469,45 +475,44 @@ def shotradSignalRecycledBnC(f, ifo):
Mnoise = noise fields produced by losses in the IFO at the AS port
"""
# f % Signal Freq. [Hz]
lambda_ = ifo.Laser.Wavelength # Laser Wavelength [m]
hbar = const.hbar # Plancks Constant [Js]
c = const.c # SOL [m/s]
Omega = 2*pi*f # [BnC, table 1] Signal angular frequency [rads/s]
hbar = const.hbar # Plancks Constant [Js]
c = const.c # SOL [m/s]
Omega = 2*pi*f # [BnC, table 1] Signal angular frequency [rads/s]
omega_0 = 2*pi*c/lambda_ # [BnC, table 1] Laser angular frequency [rads/s]
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
L = ifo.Infrastructure.Length # Length of arm cavities [m]
l = ifo.Optics.SRM.CavityLength # SRC Length [m]
T = ifo.Optics.ITM.Transmittance # ITM Transmittance [Power]
m = ifo.Materials.MirrorMass # Mirror mass [kg]
L = ifo.Infrastructure.Length # Length of arm cavities [m]
l = ifo.Optics.SRM.CavityLength # SRC Length [m]
T = ifo.Optics.ITM.Transmittance # ITM Transmittance [Power]
m = ifo.Materials.MirrorMass # Mirror mass [kg]
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
bsloss = ifo.Optics.BSLoss # BS Loss [Power]
bsloss = ifo.Optics.BSLoss # BS Loss [Power]
mismatch = 1 - ifo.Optics.coupling # Mismatch
mismatch = mismatch + ifo.TCS.SRCloss # Mismatch
# BSloss + mismatch has been incorporated into a SRC Loss
lambda_SR = mismatch + bsloss # SR cavity loss [Power]
tau = sqrt(ifo.Optics.SRM.Transmittance) # SRM Transmittance [amplitude]
rho = sqrt(1 - tau**2 - lambda_SR) # SRM Reflectivity [amplitude]
tau = sqrt(ifo.Optics.SRM.Transmittance) # SRM Transmittance [amplitude]
rho = sqrt(1 - tau**2 - lambda_SR) # SRM Reflectivity [amplitude]
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ds = ifo.Optics.SRM.Tunephase # SRC Detunning
phi = (pi-ds)/2 # [BnC, between 2.14 & 2.15] SR Detuning
ds = ifo.Optics.SRM.Tunephase # SRC Detunning
phi = (pi-ds)/2 # [BnC, between 2.14 & 2.15] SR Detuning
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
lambda_arm = ifo.Optics.Loss*2 # [BnC, after 5.2] Round Trip loss in arm [Power]
gamma_ac = T*c/(4*L) # [KLMTV-PRD2001] Arm cavity half bandwidth [1/s]
epsilon = lambda_arm/(2*gamma_ac*L/c) # [BnC, after 5.2] Loss coefficent for arm cavity
I_0 = ifo.gwinc.pbs # [BnC, Table 1] Power at BS (Power*prfactor) [W]
I_SQL = (m*L**2*gamma_ac**4)/(4*omega_0) # [BnC, 2.14] Power to reach free mass SQL
Kappa = 2*((I_0/I_SQL)*gamma_ac**4)/ \
I_0 = ifo.gwinc.pbs # [BnC, Table 1] Power at BS (Power*prfactor) [W]
I_SQL = (m*L**2*gamma_ac**4)/(4*omega_0) # [BnC, 2.14] Power to reach free mass SQL
Kappa = 2*((I_0/I_SQL)*gamma_ac**4)/ \
(Omega**2*(gamma_ac**2+Omega**2)) # [BnC 2.13] Effective Radiation Pressure Coupling
beta = arctan(Omega/gamma_ac) # [BnC, after 2.11] Phase shift of GW SB in arm
h_SQL = sqrt(8*hbar/(m*(Omega*L)**2)) # [BnC, 2.12] SQL Strain
beta = arctan(Omega/gamma_ac) # [BnC, after 2.11] Phase shift of GW SB in arm
h_SQL = sqrt(8*hbar/(m*(Omega*L)**2)) # [BnC, 2.12] SQL Strain
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
@@ -522,60 +527,60 @@ def shotradSignalRecycledBnC(f, ifo):
cos_2beta = exp_2jbeta.real
invexp_2jbeta = 1/exp_2jbeta
exp_4jbeta = exp_2jbeta**2
C11_L = ( (1+rho**2) * ( cos(2*phi) + Kappa/2 * sin(2*phi) ) -
2*rho*cos_2beta - 1/4*epsilon * ( -2 * (1+exp_2jbeta)**2 * rho + 4 * (1+rho**2) *
cos_beta**2*cos(2*phi) + ( 3+exp_2jbeta ) *
Kappa * (1+rho**2) * sin(2*phi) ) +
lambda_SR * ( exp_2jbeta*rho-1/2 * (1+rho**2) * ( cos(2*phi)+Kappa/2 * sin(2*phi) ) ) )
C11_L = ( (1+rho**2) * ( cos(2*phi) + Kappa/2 * sin(2*phi) ) -
2*rho*cos_2beta - 1/4*epsilon * ( -2 * (1+exp_2jbeta)**2 * rho + 4 * (1+rho**2) *
cos_beta**2*cos(2*phi) + ( 3+exp_2jbeta ) *
Kappa * (1+rho**2) * sin(2*phi) ) +
lambda_SR * ( exp_2jbeta*rho-1/2 * (1+rho**2) * ( cos(2*phi)+Kappa/2 * sin(2*phi) ) ) )
C22_L = C11_L
C22_L = C11_L
C12_L = tau**2 * ( - ( sin(2*phi) + Kappa*sin(phi)**2 )+
1/2*epsilon*sin(phi) * ( (3+exp_2jbeta) * Kappa * sin(phi) + 4*cos_beta**2 * cos(phi)) +
1/2*lambda_SR * ( sin(2*phi)+Kappa*sin(phi)**2) )
C12_L = tau**2 * ( - ( sin(2*phi) + Kappa*sin(phi)**2 )+
1/2*epsilon*sin(phi) * ( (3+exp_2jbeta) * Kappa * sin(phi) + 4*cos_beta**2 * cos(phi)) +
1/2*lambda_SR * ( sin(2*phi)+Kappa*sin(phi)**2) )
C21_L = tau**2 * ( (sin(2*phi)-Kappa*cos(phi)**2 ) +
1/2*epsilon*cos(phi) * ( (3+exp_2jbeta )*Kappa*cos(phi) - 4*cos_beta**2*sin(phi) ) +
1/2*lambda_SR * ( -sin(2*phi) + Kappa*cos(phi)**2) )
C21_L = tau**2 * ( (sin(2*phi)-Kappa*cos(phi)**2 ) +
1/2*epsilon*cos(phi) * ( (3+exp_2jbeta )*Kappa*cos(phi) - 4*cos_beta**2*sin(phi) ) +
1/2*lambda_SR * ( -sin(2*phi) + Kappa*cos(phi)**2) )
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
D1_L = ( - (1+rho*exp_2jbeta ) * sin(phi) +
1/4*epsilon * ( 3+rho+2*rho*exp_4jbeta + exp_2jbeta*(1+5*rho) ) * sin(phi)+
1/2*lambda_SR * exp_2jbeta * rho * sin(phi) )
D1_L = ( - (1+rho*exp_2jbeta ) * sin(phi) +
1/4*epsilon * ( 3+rho+2*rho*exp_4jbeta + exp_2jbeta*(1+5*rho) ) * sin(phi)+
1/2*lambda_SR * exp_2jbeta * rho * sin(phi) )
D2_L = ( - (-1+rho*exp_2jbeta ) * cos(phi) +
1/4*epsilon * ( -3+rho+2*rho*exp_4jbeta + exp_2jbeta * (-1+5*rho) ) * cos(phi)+
1/2*lambda_SR * exp_2jbeta * rho * cos(phi) )
D2_L = ( - (-1+rho*exp_2jbeta ) * cos(phi) +
1/4*epsilon * ( -3+rho+2*rho*exp_4jbeta + exp_2jbeta * (-1+5*rho) ) * cos(phi)+
1/2*lambda_SR * exp_2jbeta * rho * cos(phi) )
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
P11 = 0.5 * sqrt(lambda_SR) * tau * \
( -2*rho*exp_2jbeta+2*cos(2*phi)+Kappa*sin(2*phi) )
P22 = P11
P12 = -sqrt(lambda_SR)*tau*sin(phi)*(2*cos(phi)+Kappa*sin(phi) )
P21 = sqrt(lambda_SR)*tau*cos(phi)*(2*sin(phi)-Kappa*cos(phi) )
P11 = 0.5 * sqrt(lambda_SR) * tau * \
( -2*rho*exp_2jbeta+2*cos(2*phi)+Kappa*sin(2*phi) )
P22 = P11
P12 = -sqrt(lambda_SR)*tau*sin(phi)*(2*cos(phi)+Kappa*sin(phi) )
P21 = sqrt(lambda_SR)*tau*cos(phi)*(2*sin(phi)-Kappa*cos(phi) )
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# this was the PD noise source, but that belongs outside of this function
# I have used the equation for Q11 to properly normalize the other noises
# as well as the input-output relation Mc and the signal matrix Md
Q11 = 1 / \
( invexp_2jbeta+rho**2*exp_2jbeta-rho*(2*cos(2*phi)+Kappa*sin(2*phi)) +
1/2*epsilon*rho * (invexp_2jbeta*cos(2*phi)+exp_2jbeta*
( -2*rho-2*rho*cos_2beta+cos(2*phi)+Kappa*sin(2*phi) ) +
2*cos(2*phi)+3*Kappa*sin(2*phi))-1/2*lambda_SR*rho *
( 2*rho*exp_2jbeta-2*cos(2*phi)-Kappa*sin(2*phi) ) )
Q22 = Q11
Q12 = 0
Q21 = 0
Q11 = 1 / \
( invexp_2jbeta+rho**2*exp_2jbeta-rho*(2*cos(2*phi)+Kappa*sin(2*phi)) +
1/2*epsilon*rho * (invexp_2jbeta*cos(2*phi)+exp_2jbeta*
( -2*rho-2*rho*cos_2beta+cos(2*phi)+Kappa*sin(2*phi) ) +
2*cos(2*phi)+3*Kappa*sin(2*phi))-1/2*lambda_SR*rho *
( 2*rho*exp_2jbeta-2*cos(2*phi)-Kappa*sin(2*phi) ) )
Q22 = Q11
Q12 = 0
Q21 = 0
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
N11 = sqrt(epsilon/2)*tau *(Kappa*(1+rho*exp_2jbeta)*sin(phi)+
2*cos_beta*(invexp_1jbeta*cos(phi)-rho*exp_1jbeta*(cos(phi)+Kappa*sin(phi))))
N22 = -sqrt(2*epsilon)*tau*(-invexp_1jbeta+rho*exp_1jbeta)*cos_beta*cos(phi)
N12 = -sqrt(2*epsilon)*tau*(invexp_1jbeta+rho*exp_1jbeta)*cos_beta*sin(phi);
N21 = sqrt(epsilon/2)*tau*(-Kappa*(1+rho)*cos(phi)+
2*cos_beta*(invexp_1jbeta+rho*exp_1jbeta)*cos_beta*sin(phi))
N11 = sqrt(epsilon/2)*tau *(Kappa*(1+rho*exp_2jbeta)*sin(phi)+
2*cos_beta*(invexp_1jbeta*cos(phi)-rho*exp_1jbeta*(cos(phi)+Kappa*sin(phi))))
N22 = -sqrt(2*epsilon)*tau*(-invexp_1jbeta+rho*exp_1jbeta)*cos_beta*cos(phi)
N12 = -sqrt(2*epsilon)*tau*(invexp_1jbeta+rho*exp_1jbeta)*cos_beta*sin(phi);
N21 = sqrt(epsilon/2)*tau*(-Kappa*(1+rho)*cos(phi)+
2*cos_beta*(invexp_1jbeta+rho*exp_1jbeta)*cos_beta*sin(phi))
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# overall coefficient
@@ -597,10 +602,9 @@ def shotradSignalRecycledBnC(f, ifo):
def make2x2TF(A11, A12, A21, A22):
"""Create transfer matrix with 2x2xnF.
"""
Create transfer matrix with 2x2xnF.
"""
#now using numpy with broadcasting
A11, A12, A21, A22 = np.broadcast_arrays(A11, A12, A21, A22)
M3 = np.array([[A11, A12], [A21, A22]])
return M3.reshape(2, 2, -1)