Transcript Lock Acquisition in Complex Optical Interferometers - Ph237

Application of Simulation to
LIGO Interferometers

Who am I?
» Matthew Evans, Ph.D. from Caltech on Lock Acquisition
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What will I torture you with today?
» Part 1: Interferometer Simulation
– The Fabry-Perot Cavity
– Simulation Ingredients
– Systems in the End-To-End modeling environment (E2E)
» Part 2: Lock Acquisition
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–
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Lock Acquisition Basics
The Sensing Matrix
Stepwise Locking for LIGO 1
Simulation meets Reality
Matthew Evans, Ph237 April 2002
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Part1: Interferometer
Simulation
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What is simulation all about?
» The collection and use of operational knowledge in a computationally
functional framework.
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Why do I care, and why should you?
» Understanding the pieces is, for the most part, easy; understanding what
happens when you put them together can be quite hard.
» Some tough problems that can be addressed are:
– Lock acquisition
– Noise tracking
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What is known about this?
» Frequency-domain simulation can be used to understand linear systems.
» Time-domain simulation is necessary to understand non-linear behavior.
Matthew Evans, Ph237 April 2002
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The Fabry-Perot Cavity as
an Example System
DAC
ADC
Photo-detectors
Electronics
Mechanics
Mirrors
Optics
Coil-magnet pairs
Matthew Evans, Ph237 April 2002
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Optical Components
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Surfaces
» Reflection
» Transmission
» Distortion
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Media
» Propagation phase
» Propagation delay
» Distortion
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Others
» Field source
» Field modulator (amplitude and phase)
» ...
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Linear Components
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Many electrical and mechanical components have a
linear input-to-output response near their operating
point.
These components can be represented by a
frequency-domain transfer function.
A single, universal, transfer function module can be
used for linear components of optical, electrical and
mechanical systems.
Non-linear components must be handled on a caseby-case basis.
Matthew Evans, Ph237 April 2002
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Electrical Components
Linear
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ADC
» Analog filters
» Digital filters
DAC
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Non-linear
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Analog saturation/slew rate effects
Analog Logic
Analog-Digital Converters (ADCs)
Digital-Analog Converters (DACs)
Digital Algorithms
Matthew Evans, Ph237 April 2002
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Mechanical Components
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Linear
» Seismic isolation stacks
» Optic suspension systems
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Non-linear
» Earthquake stops
» ???
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Transducers
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Opto-electrical: photo-detectors
Electro-optical: laser power/phase, phase/amplitude
modulators
Electro-mechanical: coil-magnet pairs
Mechano-electrical: magnetic induction
Mechano-optical: mirrors
Opto-mechanical: radiation pressure
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Example Systems in E2E
Simplified Fabry-Perot
field source
LIGO Optics
mirror
propagator
compound optical system
Matthew Evans, Ph237 April 2002
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Conclusion (of Part 1)
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Simulation helps us to understand complex systems
» Allows physically challenging experiments and measurements
– Direct measurement of field amplitudes (magnitude and phase)
– Adjustment and measurement of absolute positions
» Allows incremental additions/removal of “reality”
– Noise sources
– Asymmetries/Imperfections
» Quick and inexpensive research and development environment
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E2E used to develop lock acquisition algorithm for
LIGO 1 interferometers
Simulation capable of detailed noise tracking
currently under construction in E2E
Matthew Evans, Ph237 April 2002
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Part 2: Lock Acquisition
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What is Lock Acquisition?
» The process by which an uncontrolled interferometer is brought to its
operating point. (Relative mirror motions are reduced by more than 6
orders of magnitude.)
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Why do I care, and why should you?
» If you can’t lock your interferometer, you can’t use it as a gravitational wave
detector.
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What is known about this?
» For simple configurations (no coupled cavities), it is easy.
» For complex systems, it can be much more difficult. (Read my thesis.)
Matthew Evans, Ph237 April 2002
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The Fabry-Perot Cavity
The simplest optical resonator, a Fabry-Perot cavity, consists of only two mirrors
and is sufficient to demonstrate many of the principals of lock acquisition.
x
Power and Demod signals
Acav
Laser
REF
ITM
ETM
S demod  rETM Acav sin( 2kx)
2
Linear control theory can be used
to hold the cavity near resonance.
  2 / k  1064nm
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Error Signal vs.
Demodulation Signal
S demod
Acav
2
Mirror Position and Control Force
 g FP x, for x  
Power and Demod signals
arbitrary unit
arbitrary unit
S err 
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LIGO 1 Interferometer
ETMy
Y
h   X  Y
ITMy
REF
 RM
Laser
RM
POB
 BS
X
BS
ITMx
ETMx
ASY
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Sensing Matrix
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Fabry-Perot cavity
» 1x1 sensing matrix, M
» Not always invertible
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x  S  M
S demod  g FP Acav
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1
M S x
2
S demod
g FP Acav
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LIGO 1 interferometer
» 5x4 sensing matrix
» Invertible in pieces
» Leads to stepwise lock acquisition
 I ref 


I
 pob 
 
S  Qasy 


Qref 


Q pob 
Matthew Evans, Ph237 April 2002
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 X 
  Y 


 RM 



 BS 
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Stepwise Locking for LIGO 1
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.
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Lock Acquisition
Real and Simulated
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Evolution of the Lock
Acquisition Code at Hanford
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From Simulation to the Real World
» Developed in the E2E simulation
» Written for direct portability (the code written for the simulation is used,
without modification, to control the interferometer)
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Robustness to Imperfections
» Algorithms developed in the relatively perfect world of simulation must
anticipate the imperfections of reality
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Measurement Bootstrapping
» The lock acquisition algorithm requires information about the interferometer
» This information must be measurable in states which can be attained
without the desired information.
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Alternate Configuration Locking
» Originally, the lock acquisition algorithm was designed with only the final
operating configuration in mind.
» It is now capable of locking other states (single arm, interferometer without
power recycling, etc.)
Matthew Evans, Ph237 April 2002
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Making the Interferometer
“Lockable”
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Measuring and Inverting the Sensing Matrix
» Additional detectors and ADC channels were required to measure the
elements of the sensing matrix.
» Software development was necessary to integrate the lock acquisition
algorithm into the existing control software.
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Maintaining Signal Integrity
» The power in the interferometer varies by more than 2 orders of magnitude
over the course of lock acquisition.
» Noise and saturation problems not present in the operating state appear
during lock acquisition.
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Alignment
» Wave-front-sensing is not available during lock acquisition.
» Large impulsive drive forces are applied, inevitably exciting angular motion.
» Optical lever feedback, not in the original detector design, was used to
achieve robust alignment control.
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Conclusion
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The LIGO1 interferometers have all been locked
using this acquisition scheme.
Lock acquisition is best thought about in the
interferometer design phase.
Future work: developing a lock acquisition scheme
for an advanced LIGO dual recycled interferometer.
Matthew Evans, Ph237 April 2002
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