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

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

3. Background
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.
In phase
Constructive interference
Out of phase
Destructive interference
PACMAN internal meeting, 28/04/2014

4. Background
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. λ 𝜋 2𝜋 δ 𝜋 2𝜋
PACMAN internal meeting, 28/04/2014

5. Interferometry Michelson Interferometer
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.
Fixed Reflector
Coherent light source
Beam Splitter
MovableReflector
Detector
PACMAN internal meeting, 28/04/2014
PACMAN internal meeting, 28/04/2014

6. Displacement Interferometry
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.
Intensity minima
Intensity maxima
PACMAN internal meeting, 28/04/2014

7. FSI Absolute distance measuring interferometric technique.
Measures phase changes in a measurement and reference interferometer as frequency is scanned.
Δ 𝑃ℎ𝑎𝑠𝑒 𝑀 = 2𝜋 𝑐 𝐿 𝑀 ∗Δ𝑣
Δ 𝑃ℎ𝑎𝑠𝑒 𝑅 = 2𝜋 𝑐 𝐿 𝑅 ∗Δ𝑣
Δ 𝑃ℎ𝑎𝑠𝑒 𝑀 Δ 𝑃ℎ𝑎𝑠𝑒 𝑅 = 𝐿 𝑀 𝐿 𝑅 (when no drift)
Measurement interferometer OPD: 𝐿 𝑀
Tunable laser
When the laser is tuned, the induced phase shift per unit change in laser frequency is proportional to the interferometer OPD. Hence by measuring the tuning frequency interval and the induced phase shift, the OPD can be determined.
The phase of each GLI is measured indirectly by numerical analysis of the sampled intensity measurements from the photodetector.
Reference interferometer OPD: 𝐿 𝑅
PACMAN internal meeting, 28/04/2014
PACMAN internal meeting, 28/04/2014

8. FSI 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).
PACMAN internal meeting, 28/04/2014

9. In the presence of drift the phase ratio, q is
Drift: Change of interferometer length during measurement typically through thermal expansion or contraction.
In the presence of drift the phase ratio, q is
𝑞= Δ 𝑃ℎ𝑎𝑠𝑒 𝑅 Δ 𝑃ℎ𝑎𝑠𝑒 𝑀 = 2𝜋 𝑐 𝐿 𝑅 Δ𝑣+𝑣Δ 𝐿 𝑅 2𝜋 𝑐 𝐿 𝑀 Δ𝑣+𝑣Δ 𝐿 𝑀
𝑞= 𝐿 𝑅 𝐿 𝑀 1+Ω𝜀
Where, Ω= 𝑣 Δ𝑣 and 𝜀= Δ 𝐿 𝑅 𝐿 𝑅 − Δ 𝐿 𝑅 𝐿 𝑀
where:
𝑣 is the average frequency.
Δ𝑣 is the scanned frequency.
Δ 𝐿 𝑅 & Δ 𝐿 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.
PACMAN internal meeting, 28/04/2014

10. Limited by control of environmental factors that cause drift.
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 °C.
Reference interferometer drift can be eliminated by replacing physical length reference.
FSI phase measurements are made at beat frequencies generated between a fixed-frequency laser & tunable laser. The change of beat frequency over the scan is twice the scan average frequency, and so the magnification of the drift is 0.5
PACMAN internal meeting, 28/04/2014

11. Drift cancellation Corrected by 2 lasers scanning simultaneously
Tunable laser
Corrected by 2 lasers scanning simultaneously
in opposite directions.
𝐷 1 = 𝐷 𝑡𝑟𝑢𝑒 + Ω 1 ∗Δ 𝜀 1
𝐷 2 = 𝐷 𝑡𝑟𝑢𝑒 + Ω 2 ∗Δ 𝜀 2
Δ 𝜀 is the drift error & Ω magnification factor
Since beam travel same path, Δ 𝜀 1 =Δ 𝜀 2
𝐷 𝑡𝑟𝑢𝑒 = 𝐷 2 −𝜌∗ 𝐷 1 1−𝜌 where, 𝜌= Ω 2 Ω 1
2 similar lasers scanning in opposite directions
simultaneously 𝜌 ≈ -1.0.
𝐷 𝑡𝑟𝑢𝑒 ≈ 𝐷 1 + 𝐷
Measurement interferometer
Reference interferometer
Tunable laser
PACMAN internal meeting, 28/04/2014

12. Refractive index, 𝜼 Physical Length= Optical Path Difference 2η
Modelled using refractivity, ϱ= η Air -1
Refractometer: Directly measures η
Alternatively by measuring the parameters on which η depends i.e. temperature, pressure, humidity and CO 2 .
Relies on homogeneity of air.
Use of air tight container (not very practical, severe engineering and high cost).
PACMAN internal meeting, 28/04/2014

13. Determining the position of fibre launchers
Position of launchers is required in order to determine that of the fiducials.
Distance 𝐷 𝑖 from launcher to fiducials determined using FSI.
Fiducial coordinates previously measured by CMM.
Coordinates of fibre launcher determined using the equation below:
𝐷 𝑖 = 𝑋 𝐹𝑖 −𝑋 𝐿 𝑌 𝐹𝑖 −𝑌 𝐿 𝑍 𝐹𝑖 −𝑍 𝐿 2
Where 𝑖 is the fiducial number.
PACMAN internal meeting, 28/04/2014

14. Determination of fiducial coordinates
Requires at least 3 launchers with known position.
Unknown coordinates of fiducial ( 𝑋 𝐹 𝑌 𝐹 𝑍 𝐹 ) determined using the equation below.
𝐷 𝑖 = 𝑋 𝐹 −𝑋 𝐿𝑖 𝑌 𝐹 −𝑌 𝐿𝑖 𝑍 𝐹 −𝑍 𝐿𝑖 2
where 𝑖 is the fibre number.
Networks will be resolved using Least Squares Adjustments.
PACMAN internal meeting, 28/04/2014

15. Reference Interferometer
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.
PACMAN internal meeting, 28/04/2014

16. Measurement interferometer
Each measurement interferometer consists of a quill (two parallel optical fibres and a beam splitter) and a reflector.
Delivery fibre
Return fibre
Retroreflector
Beam Splitter
PACMAN internal meeting, 28/04/2014

17. Main System components
Laser
Narrow line width: Provides good fringe visibility.
Wide tuning range: Better measurement precision.
Diode laser most commonly used for FSI.
Replaced dye lasers.
PACMAN internal meeting, 28/04/2014

18. 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.
PACMAN internal meeting, 28/04/2014

19. 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.
corner cube retro reflectors (3 mutually orthogonal reflective surface).
PACMAN internal meeting, 28/04/2014

20. FSI in CLIC
CMM: Most accurate (0.3 μm + 1ppm) for Leitz at CERN.
Loses accuracy beyond measurement volume of 1.2*1.0*0.7 m 3 .
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)
PACMAN internal meeting, 28/04/2014

21. Monitoring and Control
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.
PACMAN internal meeting, 28/04/2014

22. PACMAN internal meeting, 28/04/2014

23. Other FSI applications
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.
The OPDs of the measured interferometers may vary slightly while the laser is tuning, thus inducing unwanted, additional phase shifts. In addition,
the weakness of the interferometer signals, a consequence of the misalignment tolerant interferometer design, will require much longer measurement times, of the order of a minute, and hence the OPD drift will be much greater.
ATLAS Experiment © 2014 CERN
PACMAN internal meeting, 28/04/2014

24. Project 1.2
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.
PACMAN internal meeting, 28/04/2014

25. References
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
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.
PACMAN internal meeting, 28/04/2014