of Application Simulation to LIGO Interferometers
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Who am I?
Matthew Evans, Ph.D. from Caltech on Lock Acquisition
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
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 2
The Fabry-Perot Cavity as an Example System
Optics
Photo-detectors
Electronics
ADC
Mechanics
DAC
Coil-magnet pairs
Matthew Evans, Ph237 April 2002
Mirrors 3
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 5
Electrical Components
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Linear
ADC DAC Analog filters Digital filters
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Non-linear
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 ???
Matthew Evans, Ph237 April 2002
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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
Matthew Evans, Ph237 April 2002
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Example Systems in E2E
Simplified Fabry-Perot LIGO Optics
field source
mirror propagator
compound optical system
Matthew Evans, Ph237 April 2002 9
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 x x
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 10
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 Ph237 Evans, 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.
Power and Demod signals
Laser REF ITM
2
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cav
A
ETM
S demod = -rETM Acav sin( 2kx)
Linear control theory can be used to hold the cavity near resonance.
= 2 / k = 1064nm
Matthew Evans, Ph237 April 2002 12
Error Signal vs. Demodulation Signal
S err = S demod Acav
2
g FP x, for x <<
Mirror Position and Control Force
arbitrary unit
Power and Demod signals arbitrary unit
Matthew Evans, Ph237 April 2002
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LIGO 1 Interferometer
ETMy
Y
h X - Y
REF
RM
ITMy
POB
BS X
Laser
RM
BS ASY
ITMx
ETMx
Matthew Evans, Ph237 April 2002
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Sensing Matrix
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Fabry-Perot cavity
1x1 sensing matrix, M Not always invertible
S demod = g FP Acav x S = M =M S x =
-1
2
S demod g FP Acav
2
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LIGO 1 interferometer
5x4 sensing matrix Invertible in pieces Leads to stepwise lock acquisition
I ref I pob x S = Qasy Qref Q pob
X x Y = RM BS
Matthew Evans, Ph237 April 2002
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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
observable
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Not experimentally observable
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 i...