Fsi pacman meeting

Frequency Scanning Interferometry (FSI)
measurements
PACMAN internal meeting
28/04/2014
Solomon William Kamugasa

Frequency Scanning Interferometry (FSI) Measurements
1. Background concepts
2. Interferometry: (Displacement & FSI)
3. Sources of error in FSI
4. System components
5. How to determine 3D position using FSI
6. FSI in CLIC
7. Other applications of FSI
8. Ongoing work
PACMAN internal meeting, 28/04/2014
Contents

• Superposition: Resultant displacement produced by a number of waves at a
point is the algebraic sum of displacements of the individual waves.
• Interference: Combination of 2 waves to form composite waves.
Constructive interference
Background
Destructive interference
In phase
Out of phase

Phase: Used to describe a specific location within a cycle of a periodic wave.
Phase =
2𝜋
𝜆
* OPL
Phase ambiguity
when OPL > λ
Phase difference: Describes how far out of sync two waves are.
Phase difference, δ =
2π
λ
* OPD
OPD is Optical Path Difference; OPL is Optical Path Length.
2𝜋
Background
𝜋
0 2𝜋δ 𝜋
0
λ

• Technique based on interference that
measures properties of light waves such
as wave length and optical path length.
Requires:
• Coherent light source.
• Monochromatic light.
• Measures displacement by observing
fringes.
PACMAN internal meeting, 28/04/2014PACMAN internal meeting, 28/04/2014
Interferometry
Coherent light
source
Detector
Beam Splitter
Movable
Reflector
Michelson Interferometer
Fixed
Reflector

• Light of fixed wavelength.
• Precise (fraction of wavelength).
• Cannot measure absolute distance
directly.
• To measure displacements >
𝜆
2
requires
fringe counting.
• Target needs to be physically moved.
• Measurements have to be repeated if
system loses count of cycles.
Displacement Interferometry
Intensity minima
Intensity maxima

• Absolute distance measuring
interferometric technique.
• Measures phase changes in a
measurement and reference
interferometer as frequency is
scanned.
• Δ𝑃ℎ𝑎𝑠𝑒 𝑀 =
2𝜋
𝑐
𝐿 𝑀 ∗ Δ𝑣
• Δ𝑃ℎ𝑎𝑠𝑒 𝑅 =
2𝜋
𝑐
𝐿 𝑅 ∗ Δ𝑣
•
Δ𝑃ℎ𝑎𝑠𝑒 𝑀
Δ𝑃ℎ𝑎𝑠𝑒 𝑅
=
𝐿 𝑀
𝐿 𝑅
(when no drift)
FSI
Tunablelaser
Measurement interferometer
OPD: 𝐿 𝑀
Reference interferometer
OPD:𝐿 𝑅

Advantages
• Measures absolute distance.
• Beams can be interrupted as does not rely on fringe counting.
• Ability to measure several interferometers simultaneously.
Disadvantages
• Tend to be less accurate than displacement interferometry (because it
measurements are made relative to a physical reference).
• Accuracy reduced by drift errors (dominant source of error in FSI).
FSI

Drift: Change of interferometer length during
measurement typically through thermal
expansion or contraction.
In the presence of drift the phase ratio, q is
𝑞 =
Δ𝑃ℎ𝑎𝑠𝑒 𝑅
Δ𝑃ℎ𝑎𝑠𝑒 𝑀
=
2𝜋
𝑐
𝐿 𝑅Δ𝑣+𝑣Δ𝐿 𝑅
2𝜋
𝑐
𝐿 𝑀Δ𝑣+𝑣Δ𝐿 𝑀
𝑞 =
𝐿 𝑅
𝐿 𝑀
1 + Ω𝜀
Where, Ω =
𝑣
Δ𝑣
and 𝜀 =
Δ𝐿 𝑅
𝐿 𝑅
−
Δ𝐿 𝑅
𝐿 𝑀
where:
𝑣 is the average frequency.
Δ𝑣 is the scanned frequency.
Δ𝐿 𝑅 & Δ𝐿 𝑀 are reference &
measurement interferometer
drifts.
Ω is a magnifying factor that
causes much greater error than
the drift itself (typically >100).
𝜀 is the relative drift error.

Drift management
• Limited by control of environmental factors that cause drift.
• Using faster electronics that make measurements quicker.
• Using a stable reference such as Invar (nickel-iron alloy) with low CTE
≈ 1.2 ppm per °C in range of 20-100 °C.
• Reference interferometer drift can be eliminated by replacing physical
length reference.

Corrected by 2 lasers scanning simultaneously
in opposite directions.
• 𝐷1 = 𝐷𝑡𝑟𝑢𝑒 + Ω1 ∗ Δ𝜀1
• 𝐷2 = 𝐷𝑡𝑟𝑢𝑒 + Ω2 ∗ Δ𝜀2
• Δ𝜀 is the drift error & Ω magnification factor
Since beam travel same path, Δ𝜀1=Δ𝜀2
𝐷𝑡𝑟𝑢𝑒 =
𝐷2−𝜌∗𝐷1
1−𝜌
where, 𝜌=
Ω2
Ω1
2 similar lasers scanning in opposite directions
simultaneously 𝜌 ≈ -1.0.
𝐷𝑡𝑟𝑢𝑒≈
𝐷1 + 𝐷2
2.0
Reference interferometer
Tunable laser
Tunable laser
Drift cancellation

• Physical Length =
Optical Path Difference
2η
• Modelled using refractivity, ϱ = ηAir-1
• Refractometer: Directly measures η
• Alternatively by measuring the parameters on which η depends i.e.
temperature, pressure, humidity and CO2.
• Relies on homogeneity of air.
• Use of air tight container (not very practical, severe engineering and
high cost).
Refractive index, 𝜼

• Position of launchers is required in order to
determine that of the fiducials.
• Distance 𝐷𝑖 from launcher to fiducials
determined using FSI.
• Fiducial coordinates previously measured by
CMM.
• Coordinates of fibre launcher determined using
the equation below:
• 𝐷𝑖 = 𝑋 𝐹𝑖 −𝑋 𝐿
2 + 𝑌𝐹𝑖 −𝑌𝐿
2 + 𝑍 𝐹𝑖 −𝑍 𝐿
2
• Where 𝑖 is the fiducial number.
Determining the position of fibre launchers

• Requires at least 3 launchers with known position.
• Unknown coordinates of fiducial (𝑋 𝐹 𝑌𝐹 𝑍 𝐹) determined using the
equation below.
• 𝐷𝑖 = 𝑋 𝐹 −𝑋 𝐿𝑖
2 + 𝑌𝐹 −𝑌𝐿𝑖
2 + 𝑍 𝐹 −𝑍 𝐿𝑖
2
where 𝑖 is the fibre number.
• Networks will be resolved using Least Squares
Adjustments.
Determination of fiducial coordinates

Physical length standard
• Reference needs to be calibrated in order to be traceable.
• Measurements rely on stability of reference.
Alternative
• Wavelength of a He-Ne laser determined by energy levels in the gas
atoms in the laser cavity (little dependence on ambient conditions).
• Atomic transitions lines in an absorption gas cell (weak dependence
on ambient conditions).
• Benefit: Requires a single calibration, valid for the life of the
instrument.
Reference Interferometer

• Each measurement interferometer consists of a quill (two parallel
optical fibres and a beam splitter) and a reflector.
Return fibre
Delivery fibre
Beam Splitter
Retroreflector

Laser
• Narrow line width: Provides good fringe visibility.
• Wide tuning range: Better measurement precision.
• Diode laser most commonly used for FSI.
• Replaced dye lasers.
Main System components

Optical fibres
• Used to deliver light waves from laser to interferometer and to deliver
the return signal from interferometer to photo detector.
• Light propagated through fibres by total internal reflection.
• Single mode fibres (D=8-10μm).
• Sharper light longer distances.
Main system components

Retroreflectors
Incident light is reflected exactly in the direction of origin.
Typically corner cube (3 mutually orthogonal surfaces).
Retroreflectors are made of various materials.
• Aluminium pellets coated with gold to enhance reflectivity
(ATLAS).
• Commercially - Glass prisms (utilise total internal reflection).
• Mirror reflectors are also available.
Main system components

FSI in CLIC
CMM: Most accurate (0.3 μm + 1ppm) for Leitz at CERN.
Loses accuracy beyond measurement volume of 1.2*1.0*0.7m3.
Impossible to use when dimensional control measurements
are required on site.
Existing portable means don’t perform to the required accuracy.
• Faro Romer Arm: Accuracy (5-10 μm at 1σ)
• Leica AT401 Laser Tracker (7-10 μm at 1σ)
• Photogrammetry (12 μm at 1σ)
Therefore need to develop a portable means that is more accurate.
• Microtriangulation (1.3)
• FSI (1.2)

• CMMs show systematic deviations
resulting from aging & elastic
deformations etc.
• FSI will be used to continuously
monitor the CMM to provide
control of systematic deviations.
Monitoring and Control

FSI at ATLAS
Used to remotely monitor shape changes of the SCT.
• Measurement precision of 1μm.
• 3D coordinate reconstruction to 10μm.
• 842 measurement interferometers.
• Radiation-hard low mass components.
• No maintenance over 10 years.
• Fibres 100m long from interferometer to detector/laser.
Other FSI applications
ATLAS Experiment © 2014 CERN

Work in progress
Develop fiducials measureable by FSI, Micro-triangulation & CMM.
Why?
More redundancy and ability to detect faults.
Study the mechanics of fibre ends and targets in order to determine
their systematic offsets/errors and those of the target holders.
Study various configurations of the FSI network in order to select the
best one through simulations.
Extrapolate to a portable solution.
Project 1.2

• Coe P. A (2001) An Investigation of Frequency Scanning Interferometry for the
alignment of the ATLAS semiconductor tracker. Dphil thesis, University of Oxford.
• Dale J. (2009) A Study of Interferometric Distance Measurement Systems on a
Prototype Rapid Tunnel Reference Surveyor and the Effects of Reference Network
Errors at the International Linear Collider. Dphil thesis, University of Oxford.
• Griffet S., Cherif A., Kemppinen J., Mainaud Durand H., Rude V., Sterbini G.
Strategy and validation of fiducialisation for the pre-alignment of CLIC
components, CERN Geneva, Switzerland.
• Griffet S (2010) Fiducialisation and Dimensional Control: Study of existing means
and expected performances. EDMS 1097661.
• Warden M.S (2011) Absolute distance metrology using frequency swept lasers.
DPhil thesis, University of Oxford.
• Absolute Multiline®-Technology A revolution in length metrology. Available on
Indico, Presented by Mainaud Durand H.
References

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