 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 1

 What is simulation all about?
» The collection and use of operational knowledge in a computationally functional framework.
 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
 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

Optics
Electronics
Coil-magnet pairs
Matthew Evans, Ph237 April 2002
Mechanics
3

 Surfaces
» Reflection
» Transmission
» Distortion
 Media
» Propagation phase
» Propagation delay
» Distortion
 Others
» Field source
» Field modulator (amplitude and phase)
» ...
Matthew Evans, Ph237 April 2002 4

 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

 Linear
» Analog filters
» Digital filters
 Non-linear
» Analog saturation/slew rate effects
» Analog Logic
» Analog-Digital Converters (ADCs)
» Digital-Analog Converters (DACs)
» Digital Algorithms
Matthew Evans, Ph237 April 2002 6

 Linear
» Seismic isolation stacks
» Optic suspension systems
 Non-linear
» Earthquake stops
» ???
Matthew Evans, Ph237 April 2002 7

 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 8

Simplified Fabry-Perot LIGO Optics field source propagator mirror compound optical system
Matthew Evans, Ph237 April 2002 9

 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
 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

 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.)
 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.
 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 11

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
A cav
Laser
REF
ITM ETM
S demod
  r
ETM
A cav
2 sin( 2 kx )
Linear control theory can be used to hold the cavity near resonance.
 
2

/ k

1064 nm
Matthew Evans, Ph237 April 2002 12

S err

S demod
2
A cav
 g
FP x , for x
 
Mirror Position and Control Force
Power and Demod signals
Matthew Evans, Ph237 April 2002 13

Laser
ETM y

Y h
 
X
 
Y
REF
ITM y
POB

RM

BS
RM BS
ITM x
ASY
Matthew Evans, Ph237 April 2002

X
ETM x
14

 Fabry-Perot cavity
» 1x1 sensing matrix, M
» Not always invertible
S demod

 g
FP

M

1

S
A cav
 x
2 x



S
S g
FP

M demod
A cav
2
 LIGO 1 interferometer
» 5x4 sensing matrix
» Invertible in pieces
» Leads to stepwise lock acquisition
S






I
I ref pob
Q asy




Q
Q ref pob








Matthew Evans, Ph237 April 2002

 








Y
X
RM
BS






15

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 16

Matthew Evans, Ph237 April 2002 17





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)
Robustness to Imperfections
» Algorithms developed in the relatively perfect world of simulation must anticipate the imperfections of reality
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 .
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 18




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.
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.
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.
Matthew Evans, Ph237 April 2002 19

 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 20