Length Sensing and Control for an
Advanced Gravitational Wave Detector
Robert Ward
PhD Candidacy
Caltech, 17 Jan 2006
Jan 17th 2006
Ward Candicacy
1
introduction
lock acquisition
modeling
DC readout
Jan 17th 2006
Ward Candicacy
2
A New Window on the Universe
• Once Gravitational Waves are
detected, a new field of Gravitational
Wave Astronomy will open up.
– GW stochastic background can tell us
about cosmology (Big Bang, Inflation)
– Cosmic Strings
– Compact binary inspirals
– GRBs
– Supernova collapse
– Black Hole ringdowns
• GW Astronomy will allow us to listen
to what we cannot see.
Jan 17th 2006
Ward Candicacy
3
The Michelson Interferometer
as a Gravitational Wave Detector
Gravitational Waves act on
freely falling masses:
mirrors
laser
Beam
splitter
Dark port
photodiode
Antenna pattern
Suspend the
masses
Jan 17th 2006
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4
Upgrading the Michelson
Gravitational Waves are tiny:
they interact very weakly
with matter. Need more
than a simple michelson
to have a chance of
detection.
LASER
OOM
1 km arms
10W NdYAG
h = 10^-21
1 photon
Jan 17th 2006
GWD
Ward Candicacy
5
Upgrading the Michelson
• Fabry-Perot Arm
Cavities (Like having
longer arms)
2
Ga 
1  rf
GWD
Jan 17th 2006
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6
Upgrading the Michelson
•
Fabry-Perot Arm Cavities (Like having
longer arms)
2
Ga 
1  rf
• Power Recycling (Like
having a bigger LASER->lower
shot noise)
1
Gr 
1  rr rarm
GWD
Jan 17th 2006
Ward Candicacy
7
Upgrading the Michelson
•
Fabry-Perot Arm Cavities (Like
having longer arms)
2
Ga 
1  rf
•
Power Recycling (Like having a
bigger LASER)
1
Gr 
1  rr rarm
• Signal Recycling (Reshape
G  g( f )
the SIGNAL)
Jan 17th 2006
Ward Candicacy
GWD
8
Why Signal Recycle?
Why RSE?
•
•
•
Problem 1: If the current Initial LIGO optical
configuration (power-recycled Michelson with
Fabry-Perot arms) is retained in AdLIGO, the
increased laser power (needed for better
sensitivity in the high-frequency shot-noiselimited regime) will put intolerable
thermal load on the transmissive
(absorptive, lossy) optics in the power recycling
cavity (BS, ITM substrates).
Solution 1: increase the finesse (optical gain) of
the F-P arms, decrease the gain in the PRC.
Problem 2: Increasing the finesse of the
arms causes the cavity pole frequency
to decrease, leading to reduced
Laser
bandwidth for GW signal.
Solution 2: resonant sideband
subtraction!
Jan 17th 2006
FP cavity
•
PRM
Ward Candicacy
Power
FP cavity
BS
GW signal
SEM
9
The Reason for AdLIGO:
Initial and Advanced LIGO
•
Factor 10 better amplitude
sensitivity
– (Reach)3 = rate
•
•
Factor 4 lower frequency
bound
NS Binaries: for three
interferometers,
– Initial LIGO: ~20 Mpc
– Adv LIGO: ~300 Mpc
•
BH Binaries:
– Initial LIGO: 10 Mo,
100 Mpc
– Adv LIGO : 50 Mo, z=2
•
Stochastic background:
– Initial LIGO: ~3e-6
– Adv LIGO ~3e-9
Jan 17th 2006
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10
Improvement of reach with
Advanced LIGO
Improve amplitude
sensitivity by a factor
of 10x, and…
 Number of sources
goes up 1000x!
Virgo cluster
LIGO I
Jan 17th 2006
Ward Candicacy
AdLIGO
11
AdLIGO noise curve
Fight the Fundamental
Noise Sources:
1) Seismic
2) Thermal
3) Quantum
Quantum noise
Seismic noise
Suspension thermal noise
Silica Brownian thermal noise
Coating Brownian noise (1/f)
Gravity Gradients
Total noise
-21
10
Bench
Active Seismic Isolation
External Seismic PreIsolation
Quadruple pendulum
suspensions
40 kg, fused silica Test
Masses
125W Laser
Strain [1/  Hz]
-22
10
-23
10
-24
10
1
2
10
Jan 17th 2006
3
10
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10
Frequency [Hz]
12
Caltech 40 meter prototype interferometer
Objectives
• Develop a lock acquisition procedure for suspended-mass detuned RSE
interferometer with power recycling, preferably one that will be applicable to
Advanced LIGO
PRM
 Characterize and optimize optical
configuration (for robust control
and sensitivity)
Bright
port
 Characterize noise mechanisms
 Develop DC readout scheme
 Test QND techniques
 Extrapolate to AdLIGO via
simulation
 Prototyping will yield crucial information
about how to build and run AdLIGO
Jan 17th 2006
BS
SRM
Dark
port
X arm
Y arm
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13
Bench: 40m Sensitivity
-17
10
40 Meter Strain Sensitivity
-18
h(f) [1/ Hz1/2]
10
m ic
Seis
Not very likely that
we’ll actually detect
any gravitational
waves here, but
hopefully we’ll learn
some things about
operating
interferometers,
especially about the
quantum noise.
-19
10
Total noise
-20
10
 quantum
si
en
sp
Su
Tes t M
-21
10
on
Residual Gas
as s In
ter nal
Therm
al
m
er
Th
Bench
al
-22
10
1
10
2
3
10
10
4
10
f [Hz]
Jan 17th 2006
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14
40m DARM Optical Plant
UGF
The 40m operates in a
detuned RSE
190
Mag (dB)
configuration, which
gives rise to two
peaks in the DARM
transfer function:
210
170
150
130
180
1) Optical Resonance
2) Optical Spring
Phase (deg)
90
0
-90
-180
0
10
1
10
2
3
10
10
4
10
5
10
Frequency (Hz)
Jan 17th 2006
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15
Detune Cartoon
•IFO Differential Arm mode is
detuned from resonance at
operating point
IFO DARM/CARM
500
200
 0
slope related to
spring constant
100
SRC
LSB
-10000
USB
-5000
0
5000
10000
frequency offset from carrier [Hz]
•Responses of GW USB and GW LSB are
different due to the detuning of the signal
recycling cavity.
Jan 17th 2006
DARM
•IFO Common Arm mode is
detuned from resonance at
intial locking point
fsig
50
 0
 0
FWHM
Carrier frequency
Sideband amplitude [a.u.]
1000
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 0
 0
PRC
CARM
16
Signal Extraction Scheme
Carrier
-f2
-f1
• Single demodulation
• Arm information
f1
f2
PRM
• Double demodulation
• Central part information
•
•
•
Arm cavity signals are extracted from beat between carrier and f1 or f2.
Central part (Michelson, PRC, SRC) signals are extracted from beat between f1
and f2, not including arm cavity information.
Only +f2 sideband resonates in combined PRC+SRC
Jan 17th 2006
Ward Candicacy
17
5 DOF for length control
Signal Extraction Matrix (in-lock, DC)
40m
ETMy
Phase Modulation
f1=33MHz
f2=166MHz
Ly=38.55m
Finesse=1235
Port
Dem.
Freq.
L
L
l
l
ls
SP
f1
1
0
-0.001
0
0
AP
f2
0
1
0
0.001
0
SP
f1  f2
-0.002
-0.001
1
-0.032
-0.100
AP
f1  f2
-0.001
0.002
0.750
1
0.070
PO
f1  f2
0.004
0.003
0.460
-0.023
1
ITMy
PRM
Laser
ly
lx
lsy
BS
ETMx
Lx =38.55m
Finesse=1235
lsx
SRM
PO
SP
ITMx
Common of arms
: L=( Lx Ly) / 2
Differential of arms
: L= Lx Ly
Power recycling cavity : l=( lx ly) / 2
=2.257m
Michelson
: l= lx ly = 0.451m
Signal recycling cavity : ls=( lsx lsy) / 2
=2.15m
AP
Jan 17th 2006
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18
Lock Acquisition
Jan 17th 2006
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19
What does it mean to be locked?
•
GW IFOs are actively-nulled instruments with narrow linear operating
ranges.
– Locked: All degrees of freedom are within linear operating range,
held there by an active control system
-3
4
x 10
40M single arm cavity:
= 1200 → less than 0.1%
of available space offers
good control signals
2
0
less than 1 nm
1 ms at 1µm/s
-2
-4
0
45
90
135
180
Pound-Drever-Hall error signal for a single cavity
Jan 17th 2006
Ward Candicacy
20
Lock Acquisition
• Gravitational Wave Interferometers do not come ‘ready to use’
– Natural state is totally uncontrolled (with nonlinear, heavily coupled signals)
• Lock Acquisition is the process by which an IFO is brought from an
uncontrolled state to the controlled operating point.
– Should be considered during the DESIGN phase of an IFO
• Money = commissioning + runtime
– Can have a very large impact on duty cycle
• duty cycle = events
Jan 17th 2006
Ward Candicacy
21
From a Bunch of Swinging Mirrors
to a Gravitational Wave Detector
• AdLIGO will be much harder to lock than LIGO-1
– 4 DOFs to 5 DOFs + SRM scramble
– factor 10000 smaller actuation potential
– all signals come with offsets
• Prototyping can address:
– Bootstrapping problem
– LIGO I set itself a difficult problem by deciding to lock ONLY at
the operating point.
• It’s better to cheat (offsets, misalignments, etc).
– GOAL: A robust, reliable, and easily diagnosable LA procedure.
• Less time spent locking = more time for science!
Jan 17th 2006
Ward Candicacy
22
40m Lock Acquisition part I:
Off-resonant lock scheme for a single cavity
Transmitted light is used
as
Resonant Lock
1
 offset
Transmitte d power
Off-resonant
Lock point
10x higher finesse than
LIGO
Jan 17th 2006
Ward Candicacy
23
40m Lock acquisition procedure (v 1.0)
Start with
no DOFs
controlled,
all optics aligned.
ITMy
166MHz
ITMx
13m MC
BS
33MHz
PRM
SP33
PO DDM
SRM
SP166
SP DDM
AP166
AP DDM
Jan 17th 2006
Ward Candicacy
24
40m Lock acquisition procedure (v 1.0)
1/sqrt(TrY)
DRMI + 2arms
with offset
Average wait : 3 minute
(at night, with tickler)
ITMy
166MHz
ITMx
13m MC
33MHz
BS
1/sqrt(TrX)
PRM
T =7%
SP33 SP166
I
SP DDM
Q
SRM
T =7%
PO DDM
AP166
AP DDM
Jan 17th 2006
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25
40m Lock acquisition procedure (v 1.0)
Short DOFs -> DDM
DARM -> RF signal
CARM -> DC signal
1/sqrt(TrX)+ 1/sqrt( TrY)
CARM -> Digital CM_MCL
servo
+
ITMy
166MHz
-1
DARM
+
ITMx
13m MC
33MHz
CARM
BS
PRM
SP33 SP166
SP DDM
PO DDM
SRM
To DARM
AP166
AP DDM
Jan 17th 2006
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AP166 / sqrt(TrX+TrY)
26
40m Lock acquisition procedure (v 1.0)
Reduce CARM offset:
1. Go to higher ARM power
2. Switch on AC-coupled analog
CM_AO servo, using REFL DC as
error signal.
3. Switch to RF error signal (POX) at
half-max power.
4. Reduce offset/increase gain of
CM_AO.
-1
DARM
ITMy
166MHz
ITMx
13m MC
BS
SP166
33MHz
PRM
PO DDM
SRM
SP33
SP DDM
REFL
To DARM
AP166
AP DDM
Jan 17th 2006
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AP166 / (TrX+TrY)
27
DARM TFs as CARM offset is reduced
Jan 17th 2006
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28
Other Lock Acquisition Schemes
Alternative Locking Schemes are on the way!
• Deterministic Locking:
– Locking occurs in stages, with each stage having robust control
– Each stage can (and should) lock on the first ‘fringe’, or be robust to
fringes.
– Transitions between stages are smooth and robust.
• Advantages:
– Easier to diagnose problems
– Should require less actuation potential
• If we can lock a single arm cavity, we can lock the IFO.
40M:
7 mN
1.3 kg test mass
AdLIGO
f/m = 5
Jan 17th 2006
20 µN
40 kg test mass
f/m =5e-4
Ward Candicacy
29
Digital length control system
D/A
mixer
Jan 17th 2006
Ward Candicacy
Output to suspensions
A/D
Feedback filters
AP166
Demodulated signal from PD
D/A
30
Compensating the resonances
Compensation Filters for the two resonances
associated with the signal cavity:
UGFs ~ 250Hz
Optical
DARM
CARM
Jan 17th 2006
Opto-mechanical
4kHz >> UGF
no compensation
AdLIGO: 180 Hz ~ UGF
40Hz < UGF
no compensation
AdLIGO: 70Hz?
1kHz -> 100Hz ~ UGF
dynamic compensation
0->100Hz ~ UGF
Not yet coherently
compensated
Ward Candicacy
31
Dynamic compensation filter
for CARM servo
Open loop TF of CARM
Optical gain of CARM
• Optical gain (normalized
by transmitted arm
power) shows moving
peaks due to reducing
CARM offset.
• We have a dynamic
compensative filter
having nearly the same
shape as optical gain
except upside down.
Designed using
FINESSE.
• Open loop transfer
function has no phase
delay in all CARM
offset.
Jan 17th 2006
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32
CARM optical springs
CARM optical springs at different CARM offsets
140
Arm power = 6
Arm power = 8
Arm power = 10
•Solid lines are from TCST
•Stars are 40m data
•Max Arm Power is ~80
•Also saw CARM anti-springs,
but don’t have that data
130
CARM optical response (dB)
120
110
100
90
80
2
3
10
10
f (Hz)
Jan 17th 2006
Ward Candicacy
33
Mode healing/injuring at Dark Port
Negative spring constant with
optical spring
Positive spring constant
with no optical spring
Carrier power at DP is 10x
smaller
• Repeatable
• The same alignment quality
Jan 17th 2006
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34
Modeling
Jan 17th 2006
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35
What’s modeling all about?
• With 5 DOFs and detuned cavities, Advanced LIGO will have a very
complicated optical configuration, with a rich frequency response.
We need good modeling tools, and we need to use them in order to
understand AdLIGO, before it is built.
• We already rely heavily on modeling at the 40m because the
configuration is so complicated.
• Building a prototype, and then using modeling to extrapolate, is a
good way to understand AdLIGO in advance!
Jan 17th 2006
Ward Candicacy
36
Optickle: Frequency Domain
IFO Simulation
• Optickle is a new frequency domain IFO modeling tool:
– Written in Matlab
• Matlab allows easy integration to other modeling efforts (a frequency-domain
e2e, like LinLIGO)
• Easily Extensible
• Uses Matlab classes for generality
– Uses the methods outlined in T. Corbitt et al: “Mathematical
framework for simulation of quantum fields in complex
interferometers using the two-photon formalism” (LIGO-P030071-00R)
to calculate the IFO opto-mechanical frequency response.
– Designed for concrete units (Watts, meters, Hz)
Jan 17th 2006
Ward Candicacy
37
Optickle example: detuned FP cavity
• Response of front mirror to
back mirror ‘excitation’
• 1 nm detune
• finesse ~ 1200
0
Mag (dB)
-50
-100
-150
-200
180
1
100
10000
100000
100000000
135
Phase (deg)
90
45
0
-45
-90
-135
-180
0
10
Jan 17th 2006
1
10
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2
10
Frequency (Hz)
3
4
10
10
38
Optickle Example: AdLIGO
•
Normalized row of DC readout signal matrix
40
CARM
PRC
SRC
MICH
20
0
-20
dB mag
•
Easy to create a frequency
dependent coupling matrix,
useful for, e.g., estimating
the contribution of loop
noise to DARM.
This plot is Open Loop.
Closed loop coming soon!
-40
-60
-80
-100
-120
-2
10
Jan 17th 2006
0
10
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2
10
f (Hz)
4
10
6
10
39
Optickle v. the 40m
DARM Response
DARM Response
80
80
70
70
60
50
dB (a.u.)
dB (a.u.)
60
50
40
40
30
20
10
30
0
40m Data
Optickle
20
10
1
10
2
3
10
10
40m Data
Optickle
-10
4
10
-20
1
10
2
3
10
4
10
10
f (Hz)
f (Hz)
Optickle
Modeling
Jan 17th 2006
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40
DC Readout
Jan 17th 2006
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41
Quantum Noise: Heterodyne vs Homodyne
-20
Quantum noise curves
plotting using formulas
in:
10
A. Buonanno, Y. Chen, N.
Mavalvala, “Quantum noise in
laser-interferometer
gravitational-wave detectors
with a heterodyne readout
scheme” PHYSICAL REVIEW
D 67,122005 2003
10
-21
GREEN = RF
RED = HOMODYNE
-22
h
10
-23
10
-24
10
-25
10
1
2
10
3
10
10
f (Hz)
Jan 17th 2006
Ward Candicacy
42
What is DC Readout and
how does it relate to Homodyne Detection?
DC Readout is Homodyne detection, using light circulating in the
interferometer as a local oscillator.
Advantage: LO light has been filtered by the <1Hz coupled cavity pole
Disadvantage: limited ability to control homodyne phase
OMC
Jan 17th 2006
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43
Technical noise sensitivity
Noise Source
Laser frequency noise
Laser amplitude noise
Laser pointing noise
Oscillator phase noise
Jan 17th 2006
RF readout
DC readout
~10x more sensitive
Less sensitive
since carrier is
filtered
Sensitivity identical for frequencies below
~100 Hz; both driven by technical radiation
pressure
10-100x more
sensitive above
100Hz
Carrier is filtered
Sensitivity essentially the same
-140 dBc/rtHz at
100 Hz
Ward Candicacy
NA
44
RF vs DC
o Phase modulate the input light
o RF sidebands act as local
oscillator for GW signal, after
passing through (unstable)
recycling cavity(ies)
o GW signal is an audio
frequency sideband of RF
photocurrent
o Mix GW signal down to nearDC
o Acquire GW signal at DC with
ADC
Jan 17th 2006
 Eliminate the RF sidebands at
Dark Port with an Output Mode
Cleaner
 Eliminate junk light at the Dark
Port with Output Mode Cleaner
 Carrier light acts as a local
oscillator
 GW signal is an audio
frequency photocurrent
 Acquire GW signal at DC with
ADC
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45
Making the DC local oscillator
•
Two components
– Carrier field due to loss differences (not
LIGO I GW
parallel to
DC offset
controllable? TCS?)
•
•
fringe
– Carrier field due to dark fringe offset
offset
(controllable)
– An output mode cleaner should take care of
the rest. (RF sidebands, junk light)
Loss mismatch component
– Average arm round trip loss: 200 ppm
– Difference between arms: 50 ppm
– Output power due to mismatch: 20 µW
Detection angle, β
– Tuned by adjusting fringe offset
β
Loss mismatch
• Can tune from 0-80 deg with 0-10pm of DARM offset
• 1 mW LO
– Angle of GW is frequency dependent in
detuned RSE
Jan 17th 2006
Ward Candicacy
Detuned RSE:
GW signal gets fdependent phase
shift in SRC
Some linear
component
No
slope
46
Laser Intensity Noise
•
•
calculated using
rsenoise
10 pm DARM offset
for DC
1e-13m residual L-
RF: noise sidebands of
RF sidebands beat
against residual length
offset
DC: dark port power
proportional to input
power
Radiation pressure effects not
included
Jan 17th 2006
-5
10
Ampl. noise equiv shot noise 1/rtHz
•
RF
-6
DC
10
-7
10
-8
10
-9
10
0
10
1
10
2
10
3
10
4
10
f (Hz)
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47
Laser Frequency Noise
•
•
calculated using
rsenoise
10 pm DARM offset
for DC
1e-13m residual LRF: frequency noise
sidebands of RF
sidebands beat against
static carrier contrast
defect
DC: Arm cavity pole
imbalance couples
carrier frequency noise
to dark port
-1
10
Freq. noise equiv shot noise Hz/rtHz
•
-2
10
RF
-3
10
DC
-4
10
-5
10
-6
10
-7
10
-8
10
-9
Radiation pressure effects not
included
Jan 17th 2006
10
0
10
1
10
2
10
3
10
4
10
f (Hz)
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48
OMC Properties
The Output Mode Cleaner
filters the light coming out of
the dark port, cleaning away
the junk and transmitting the
GW-signal containing TEM00
mode of the carrier
Transmission of HOM versus g-factor, Max Mode Number = 3
2
10
Transmission %
10
11
12
23
1
10 3 0
31
32
43
22
23
31
01
12
33
30
22
11
32
23
31
0
10
-1
10
-2
Maxmimum Unwanted Transmission
Transmission of higher order TEMs
Transmission of RF
Transmission of TEM00
10
-3
10
Jan 17th 2006
02
20
32
0
0.1
0.2
0.3
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0.4
0.5
g-factor
0.6
0.7
0.8
0.9
1
49
OMC design in SolidWorks
•
•
•
•
•
•
Small number of pieces
HV compatible
– some glue near the PZT mirror
Mirrors mounted mechanically, on
silver washers (no glue)
ALGOR FEA: lowest mech
resonance at ~770 Hz
Construct out of well-damped
material, to minimize effect of
resonances: Copper
All high-quality (REO super-polished
and coated) mirrors available from
LIGO lab spares (the 4th HR mirror, 0o
incidence, came from Newport)
Mike Smith
Jan 17th 2006
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50
The Vacuum Compatible DC Photodiode
Ben Abbott
DC Readout
Jan 17th 2006
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51
Summary & Future Directions
Things I may spend significant
time on
Things I’ve already spent
significant time on, and will
spend more on
• Lock Acquisition
• Modeling
• DC Readout
Jan 17th 2006
•
•
•
•
Ward Candicacy
Revamping the LSC Scheme
QND Techniques
SPI
Data Analysis
52