Tutorial
Measuring at Picometer Accuracy
Dennis Weise
International Conference on Space Optics
6. Oct. 2010
Outline
• Introduction
• Interferometry Basics
• Noise Sources in the Measurement Chain
• Specific Challenges for Inter-S/C Metrology
6. Oct. 2010
International Conference on Space Optics 2010
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Outline
• Introduction
• Interferometry Basics
• Noise Sources in the Measurement Chain
• Specific Challenges for Inter-S/C Metrology
6. Oct. 2010
International Conference on Space Optics 2010
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Quantum Metrology in Space
Space-Time Anisotropy
Research
© ESA
LISA Pathfinder
International Conference on Space Optics 2010
Search for Anomalous
Gravitation using Atomic
Sensors
© TESAT
Laser Communication
Formation Flying
Terrestrial Planet Finder
Cosmic Vision
SIM PlanetQuest
Matter Wave eXplorer of
Gravity
Cosmic Vision
© NASA
Fundamental Physics
NG2
Geodesy
Large Structures
International X-Ray
Observatory
© NASA
Gravitational Waves
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Laser Interferometer Space Antenna
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A “Picometer” is really not very much…
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What does Picometer “Accuracy” Mean?
• Terminology
 “Accuracy”: deviation of the measured value from the actual value
 “Precision”:
deviation between the results of repeated measurements (“reproducibility”)
 Here, we look at detection of translation at picometer precision!
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Tutorial
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Measuring at Picometer Accuracy
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Dennis Weise
International Conference on Space Optics
6. Oct. 2010
Timescales
• The “precision” to report generally depends on the applicable measurement time
 “Measurement Band”: sampling time – vs. – uninterrupted duration of measurement
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Time Domain Analysis
Allan Standard Deviation
• IEEE and NIST recommend to use the Allan Variance for specification of stability in the
time domain
 David W. Allan et al., 1966
 Mostly used in the context of clocks to characterize frequency fluctuations
fractional stability over integration time 
“two-sample variance”
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Frequency Domain Analysis
(Root) Power Spectral Density
• More common in the context of interferometry is an analysis in the frequency domain
 “Root Power Density Spectrum”
 The direct Fourier transform would yield an energy spectrum
(Parseval’s Theorem)
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Fundamental Limits
Translation of Macroscopic Objects
• The lateral extension of the “measurement beam” averages to some extent over microscopic
surface features
• The applicability of the term “translation” for bulk objects is fundamentally limited by the presence
of “thermal noise”
 Conversion of random (Brownian) motion into length fluctuations by mechanical loss
 According to the “fluctuation dissipation theorem” (Callen & Greene, 1952)
(typ. magnitude at room
temperature for Zerodur)
L:
A:
Length of (cylindrical) spacer
Cross Section of (cylindrical) spacer
Material
Mechanical Quality Q
Mechanical Loss  = 1/Q
Young’s Modulus E [GPa]
Zerodur
3.1  103
3.2  10-4
90.1
ULE
6.1 
1.6 
67.6
Fused Silica
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104
106
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10-5
10-6
71.7
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Outline
• Introduction
• Interferometry Basics
• Noise Sources in the Measurement Chain
• Specific Challenges for Inter-S/C Metrology
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International Conference on Space Optics 2010
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Optical Metrology – Interferometry
Gaussian Beams
• Propagation of laser beams is generally described by decomposition into “HermiteGaussian Modes”. These fit particularly well with actual eigenmodes of
 Laser resonators with spherical mirrors
 Singlemode fibers
Polarization
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Spatial Power Distribution
Propagation Phase
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Optical Metrology – Interferometry
Superposition
• At the output of an interferometric beam splitter, a photodetector delivers a signal
proportional to the light intensity of the superposed waves
 Finite bandwidth
 Energy conservation
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Optical Metrology – Interferometry
Superposition
• At the output of an interferometric beam splitter, a photodetector delivers a signal
proportional to the light intensity of the superposed waves
 Finite bandwidth
 Energy conservation
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Optical Metrology – Interferometry
Homodyne Interferometers
• Homodyne interferometers utilize a single (narrow linewidth) laser frequency
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Optical Metrology – Interferometry
Homodyne Interferometers
• Homodyne interferometers utilize a single (narrow linewidth) laser frequency
 Various beam routing possibilities, depending on the application
Multiple-Beam Interference
Optical Resonator (Cavity)
Fabry-Perot
Michelson
Mach-Zehnder
Sagnac
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Optical Metrology – Interferometry
Homodyne Interferometers
• Homodyne interferometers detect translation by observing variations in the light
intensity on the photodetector
 “Dark fringe” detection @ DC
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Optical Metrology – Interferometry
Heterodyne Interferometers
• Detection @ DC suffers from various environmental noise sources
 Typically @ acoustic frequencies: DC – approx. 100 kHz
 Heterodyne detection
of the beat signal
phase above this
frequency band
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Optical Metrology – Interferometry
Heterodyne Interferometers
• The initial phase of the utilized laser beams – and therefore  – is arbitrary and in
general unstable
 Phase comparison between Measurement Interferometer and Reference Interferometer
A successful comparison relies
on pathlength stability in the
Reference Interferometer!
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Optical Metrology – Interferometry
Phase Measurement
• The photodetection process converts photon flux into photo current
 Responsivity /Quantum Efficiency of photodiode substrate
 Heterodyne Efficiency / Contrast
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Optical Metrology – Interferometry
Phase Measurement
• The detection of the beat signal phase is typically performed by “mixing it down to DC”
 Both analog and digital processing is common
 The “Phasemeter” clock defines the timebase
 “Quadrature” detection removes the amplitude ambiguity
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Optical Metrology – Interferometry
A typical Interferometric System
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Outline
• Introduction
• Interferometry Basics
• Noise Sources in the Measurement Chain
• Specific Challenges for Inter-S/C Metrology
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Noise Sources
Laser Frequency Noise
• If the individual optical pathlengths are not equal, variations of the laser frequency
cause a variation of the measured phase
 Pathlength “matching”
‒ The laser phase noise of each laser shall reach all fiducial points of the measurement at the same time
‒ Symmetric setups
 Frequency-stable lasers
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Noise Sources
Choice of Laser System
• The choice of laser system is driven by requirement for maximum “free-running”
frequency stability
 The choice laser wavelength  is a secondary criterion, and strongly restricted by available
laser sources
e.g. Innolight Mephisto
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Noise Sources
Choice of Laser System
FBH/Astrium DBR Diode Laser
Innolight NPRO
Koheras DFB Fiber Laser
TESAT LTP RLU
 In general it is necessary to improve the stability of the free-running laser by active
frequency stabilization
 In particular for metrology between 2 or more satellites/spacecraft!
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Noise Sources
Frequency Stabilization
• Most common for “medium-term” stabilization of the laser frequency is Pound-Drever-Hall
locking to an Optical Resonator (Cavity)
 R. V. Pound (1946)
Best result achieved to date
 R. W. P. Drever, J. L. Hall (1983)
• Alternatives include
 Hänsch-Couillaud stabilization (1980)
‒ Comparatively low complexity
‒ Relies on polarization dispersion in the cavity
 Unequal Armlength Interferometer (!)
6. Oct. 2010
J. Alnis et al., “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally
compensated ultralow-expansion glass Fabry-Pérot cavities”, Physical Review A 77, 2008.
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Noise Sources
Frequency Stabilization
• For observation over very long timescales (days, weeks, months), stabilization to an
absolute reference could be more suitable
 Systematic drifts of cavities due to temperature, material relaxation, etc.
 Our future time will be “optical” (I2, Sr, Hg, Al, …)
Astrium GmbH Iodine Clock (2007)
Iodine Standard
ULE Cavity
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Noise Sources
Frequency Combs
• The frequency transfer between frequency references and the application wavelength
can be accomplished by optical “Frequency Combs”
 Precise “rulers” at optical frequencies
 Available since  2000 (Hänsch, Hall, et al.)
 Mode-locked lasers with “carrier-envelope phase control” (fs pulse duration)
Frequency Comb at HU Berlin (Prof. A. Peters)
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Noise Sources
Differential Pathlength Noise
• Only non-common-mode pathlength variations result in
measurement noise
 Provide dimensional stability of the Interferometer Core
 Minimize impact of temperature fluctuations
‒ Low CTE spacer material
Structural Material
CTE [10-6/K]
Titanium
8.8
SiC 100
2.2
Invar36
1.8
CFRP (isotropic)
0.2
ULE
0.03
Zerodur (Class 0)
0.02
‒ Ultrastable optics integration
‒ Exploit symmetry for common-mode suppression
‒ Provide passive thermal shielding of the interferometer core
“Energy Separator Cubes”
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Noise Sources
Differential Pathlength Noise
• Astrium is investigating the limits of CTE tuning of CFRP by Laser Dilatometry
 The ability to tune the CTE of CFRP – also to negative values – allows the development of
larger structures with low “System CTE” (e.g. for telescopes)
 Partner: XPerion Friedrichshafen
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Noise Sources
Differential Pathlength Noise
• Quasi-static process control with sinusoidal excitation by radiative heat transfer
 Cycle times >> thermalization timescales
 Low pass transfer function for maximum suppression of environmental thermal noise
‒ Minimal conduction & convection
 Laser frequency noise can be monitored by comparison to a cavity-stabilized laser
Sample Length:
 11 cm
Temperature Variation:  1 K
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Expansion:
 20 nm
 CTE:
1.8 x 10-7/K
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Noise Sources
Integration Technology
• Hydroxide Catalysis Bonding
 Creation of siloxane chains between (polished)
surfaces of materials containing silica
‒ Si, Zerodur, Fused Silica, ULE, granite, SiC, …
‒ Alkaline bonding solution (NaOH, KOH, Na2SiO3)
 Perfected by the University of Glasgow (H. Ward)
‒ Bond thickness approx. 20 – 100 nm
‒ Absolute beam placement accuracy < 10 µm
 Fully qualified for space application
‒ Utilized to integrate the OBI of LISA Pathfinder
‒ Baseline integration technology for LISA Optical Bench
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Noise Sources
Integration Technology
S. Ressel et al., Applied Optics 49(22), p. 4296
• Adhesive Bonding
 Developed by Astrium GmbH as alternative
integration technology for Optical Systems
‒ Tunable curing times and less critical process offer
potential simplifications for some applications
‒ Space-qualified epoxy (Hysol)
‒ Bond thickness approx. 1.4 µm
 Qualified with respect to environmental loads and
dimensional stability
‒ Thermal cycling
 8x cycling between -20°C and 50°C @ 2K/min
‒ Shock and vibration testing according to ECSS
 Sine vibration: max. 75g @ 61Hz
 Random vibration: 23.5g rms
‒ Within our measurement accuracy, hydroxide and
adhesive bonded mirrors show identical pathlength
and pointing stability
 10 pm/Hz @ 10 mHz
 10 nrad/Hz @ 10 mHz
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Noise Sources
Measurement Chain
• More general, noise in the “Measurement Chain” may be separated into the
following main contributions
 Pathlength Noise:
variations in the optical field “piston” on the detector
 Photodetection Noise:
noise in the “Analog Chain”
 Phase Measurement Noise: noise in the “Phase Measurement”
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Noise Sources
Photodetection Noise
• Ghost Beams/Stray Light
 Causes pathlength measurement noise, if its phase on the detector varies
‒ Ghost beams often are as stable as the reference beams
‒ Stray light is often not mode-matched well (low heterodyne efficiency)
 “Balanced Detection” suppresses “in-phase” noise on a dual-ended receiver
‒ Detect at both output ports of the beam splitter
‒ Determine both amplitude and phase of the beat signals
‒ Normalize the beat vectors to equal length before correction
Individual Phases
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Balanced Detection
Normalized Correction
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Noise Sources
Photodetection Noise
• Ghost Beams/Stray Light – Example for normalized stray light correction
“Optical Bench Development for LISA”
ESA Contract No. 22331/09/NL/HB
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Noise Sources
Photodetection Noise
• Shot Noise
 The photon flux is subject to Poisson statistics
 “Additive noise” is directly mapped to phase variations
 for synchronous phase detection
 relative to the signal amplitude
5 nW correspond to approx. 1 pm/Hz @ 1064 nm
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Noise Sources
Photodetection Noise
• Amplitude Variations
 May also be described by an “additive noise” model
• Best practice: minimize by active stabilization
 Laser Intensity Noise (RIN) 
 Polarization Fluctuations

Power Stabilization
Polarization cleanup before Photodetectors
A RIN of 10-5/Hz corresponds
to approx. 1 pm/Hz
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Noise Sources
Phase Measurement Noise
• The phase measurement of the analog beat signal adds 2 main noise contributions
 A/D Quantization Noise
‒ Discretization by finite bit depth
 A/D Timing Jitter
‒ Non-synchronous sampling of the individual channels
‒ Impact of jitter is relative to sampling frequency!
 Further digital processing is free of uncertainties!
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Astrium Interferometer Performance
Phase Measurement Noise
FPGA Phasemeter
(10 kHz)
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Astrium Interferometer Performance
Photodetection & Phase Measurement Noise
FPGA Phasemeter
(10 kHz)
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Astrium Interferometer Performance
End-to-End Performance – Aluminum Board
FPGA Phasemeter
(10 kHz)
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Astrium Interferometer Performance
End-to-End Performance – First Results of Bonded Setup
FPGA Phasemeter
(10 kHz)
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Astrium Interferometer Performance
End-to-End Performance – First Results of Bonded Setup
FPGA Phasemeter
(10 kHz)
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Astrium Interferometer
Setup
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LISA Optical Bench
Current Design Status
cf. Talk on Friday, 11:20
“Optical Bench Development for LISA”
Lightweighted
Zerodur Baseplate
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Outline
• Introduction
• Interferometry Basics
• Noise Sources in the Measurement Chain
• Specific Challenges for Inter-S/C Metrology
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Inter S/C Interferometry
• The physical separation of spacecraft linked by optical metrology over a comparatively
large distance involves specific challenges
 Optical link budget
 S/C pointing and line-of-sight dynamics
 Time keeping over the constellation
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Inter S/C Interferometry
Link Budget
• The receiving aperture is in general much smaller than the far field beam width
 Transmission of a Gaussian Beam  Reception of a “top hat plane wave”
 Dedicated and separated beam conditioning in TX and RX paths
 Shot noise is important!
 TX ghosts/stray light are important in monostatic systems
LISA Off-Axis Telescope
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Inter S/C Interferometry
Pointing Dynamics
• One of the most dominant noise sources on inter-s/c links is coupling of pointing
variations into the longitudinal signal
 Geometrical interpretation: “Phase Center Offset” from the desired fiducial point
 Results from a combination of alignment errors & optical (wavefront) errors
 Appropriate imaging optics in TX as well as RX paths!
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Inter S/C Interferometry
Pointing Dynamics
• “Differential Wavefront Sensing” (DWS)
 Very accurate acquisition of wavefront tilt (i.e. beam pointing) relative to the LO
 Spatially resolved phase measurement by use of Quadrant Photodetectors
 Tilt:
Piston:
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Quadrant Difference
Quadrant Sum
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Inter S/C Interferometry
Pointing Dynamics
• The “weak link” in the AOCS are thus usually the actuators (i.e. thrusters)
 µN Propulsion
‒ Field Emission Electric Propulsion (FEEP)
‒ RF Ion Thruster (RIT)
‒ High Efficiency Multistage Plasma Thruster (HEMPT)
 (In-orbit) calibration of the coupling coefficient
 Post-correction of the data on the basis of the
ultra-precise DWS pointing information
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Inter S/C Interferometry
Pointing Dynamics
• Example: DWS Correction
 Pointing instabilities occur not only between s/c!
“Optical Bench Development for LISA”
ESA Contract No. 22331/09/NL/HB
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Inter S/C Interferometry
Pointing Dynamics
cf. Talk on Friday, 12:00
“Picometer Stable Scan Mechanism for Gravitational Wave Detection in Space”
• Extreme demands on any beam manipulation mechanisms in the measurement path
 Pathlength stability 
 Pointing stability
pm
 nrad
• Typical solution
 Piezo-based actuation principle
 Monolithic hinges
 Thermally compensated, isostatic support
Point-Ahead Angle Mechanism
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In-Field Pointing Mechanism
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Inter S/C Interferometry
Line-of-Sight Dynamics
• The maximum beat frequency to be accommodated equals (at least) the Doppler shift
 Line-of-Sight motion of the respective s/c
• Constant Doppler shift “just” generates a constant frequency offset
 Varying Doppler shifts require a “tracking” Phasemeter
 Optical frequency plan to avoid zero-crossings
Astrium 8 Channel, RF DPLL Phasemeter
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Summary
• In order to achieve Picometer measurement precision, each individual noise contribution in your
Measurement Chain must be below a millionth of a cycle
 Employ heterodyne interferometry
‒ 1 – 10 MHz beat frequencies
 Ensure dimensional stability
‒
‒
‒
‒
Low CTE baseplate
Ultrastable, quasi-monolithic optics integration
Athermal, isostatic mounting of mechanisms
Passive & massive thermal shielding
 Active stabilization is better than post-correction
‒ Laser frequency stabilization
‒ Power stabilization
‒ Polarization cleanup
 Apply post-correction where stabilization reaches its limits
‒ Balanced Detection
‒ DWS detection of beam pointing fluctuations
 Optimize your Phase Measurement Chain
‒ Carefully select the laser powers on the detectors
‒ Care about the modematching of your beams
‒ Use the best ADCs with low timing jitter and high bit resolution
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Acknowledgments
•
Astrium

•
DLR

•
Joep Pijnenburg, Harm Hogenhuis, Ben Braam, …
ESA

6. Oct. 2010
Karsten Danzmann, Gerhard Heinzel, Michael Tröbs, …
TNO Science & Industry

•
Harry Ward, David Robertson, Ewan Fitzsimons, Christian Killow,
Alasdair Taylor, Michael Perreur-Lloyd
Albert-Einstein Institute

•
Achim Peters
University of Glasgow

•
Claus Braxmaier
HU Berlin

•
“Untersuchungen zur Systemleistung alternativer Nutzlastkonzepte für LISA”
(DLR Contract No. 50OQ0701)
HTWG Konstanz

•
Hans Reiner Schulte, Martin Gohlke, Ulrich Johann, …
Luigi D’Arcio
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