Download Lock Acquisition in Complex Optical Interferometers

Application of Simulation to LIGO Interferometers
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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 Fabry­Perot Cavity
– Simulation Ingredients
– Systems in the End­To­End modeling environment (E2E)
» Part 2: Lock Acquisition
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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?
» Frequency­domain simulation can be used to understand linear systems.
» Time­domain simulation is necessary to understand non­linear behavior.
Matthew Evans, Ph237 April 2002
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The Fabry­Perot 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)
» ...
Matthew Evans, Ph237 April 2002
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Linear Components
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Many electrical and mechanical components have a linear input­to­output response near their operating point.
These components can be represented by a frequency­domain transfer function.
A single, universal, transfer function module can be used for linear components of optical, electrical and mechanical systems.
Non­linear components must be handled on a case­
by­case 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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Non­linear
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»
»
»
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Analog saturation/slew rate effects
Analog Logic
Analog­Digital Converters (ADCs)
Digital­Analog 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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Non­linear
» Earthquake stops
» ???
Matthew Evans, Ph237 April 2002
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Transducers
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Opto­electrical: photo­detectors
Electro­optical: laser power/phase, phase/amplitude modulators
Electro­mechanical: coil­magnet pairs
Mechano­electrical: magnetic induction
Mechano­optical: mirrors
Opto­mechanical: radiation pressure
Matthew Evans, Ph237 April 2002
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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 Fabry­Perot 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
Laser
Acav
REF
ITM
ETM
2
S demod = −rETM Acav sin( 2kx)
Linear control theory can be used
to hold the cavity near resonance.
λ = 2π / k = 1064nm
Matthew Evans, Ph237 April 2002
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Error Signal vs. Demodulation Signal
S demod
Acav
2
Mirror Position and Control Force
≈ g FP x, for x << λ
Power and Demod signals
arbitrary unit
arbitrary unit
S err =
Matthew Evans, Ph237 April 2002
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LIGO 1 Interferometer
ETMy
∆Y
h ∝ ∆ X − ∆Y
ITMy
REF
∆ RM
Laser
RM
POB
∆ BS
∆X
BS
ITMx
ETMx
ASY
Matthew Evans, Ph237 April 2002
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Sensing Matrix
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2
Fabry­Perot cavity
» 1x1 sensing matrix, M
» Not always invertible
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
x → S = M∆
S demod = g FP Acav
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⇒ ∆ = M −1S → x =
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
S demod
g FP Acav
2
∆ 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.
Matthew Evans, Ph237 April 2002
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Lock Acquisition
Matthew Evans, Ph237 April 2002
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Not experimentally
observable
observable
Real and Simulated
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
» Wave­front­sensing 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.
Matthew Evans, Ph237 April 2002
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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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