Introduction to Micro-Triangulation

Introduction to Micro-Triangulation

Vasileios VLACHAKIS

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PACMAN meeting, CERN - Geneva, 26 May 2014

PACMAN meeting, CERN – Geneva, 26 May 2014


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Outline

• Principle of triangulation

• Historical triangulations• Precision at the level of microns

• QDaedalus System

• Hardware - Instrumentation

• Software - Algorithms

• Past results at CERN

• Future developments



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Principle of triangulationMeasurements / Observations:•Distances (in order to fix the scale)•Directions (w.r.t. the horizontal plane)•Angles (as differences of directions)

– Horizontal– Vertical or Zenith

Calculations / Estimations:•Distances (Unknown/Unmeasured) •Angles (Unknown/Unmeasured)

+ Coordinates w.r.t a reference system/frameATLAS Network measurements (LS1 - Feb 2014)

Hz

V

Zenith



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Principle of triangulation

As the Triangulation Network expands…•Incompatibility between Observations and Calculations!•Variation between repeated Observations!



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Incompatibility between Theory and Observations:Closure residuals•a + b + c ≠ 180° or 200g or π [degrees] [grads/gons] [rads]

•c + d + e + f ≠ 360° or 400g or 2π

Variation between repetitive Observations:•Environment → better control•Instrumentation → more precise + accurate•Observer → better to avoid him!

Problem in Theoretical Model? OR / AND in Observations?

a

bcd e

f



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Problem:As the Triangulation Network expands…

…the errors propagate + accumulate!


Solution:Measurements:

•Sufficient

•Repeated

•Redundant

Adjustment of observations:

•Least Squares Adjustment

•BLUE (Best Linear Unbiased Estimation)



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Evolution of angle measuring instruments

DioptraHeron of Alexandria (10-70 CE)



TheodoliteJesse Ramsden (1735-1800)•Dimensions: 540x720x550 mm•Weight: 28kg •Accuracy: 20’’ - 60’’

Total StationLeica Geosystems (1996)•Dimensions: 220x350x180 mm•Weight: 7.5kg •Accuracy: 0.5’’

http://www.samosin.gr/exhibition/exhibits_uk.html

http://www.makingthemodernworld.org.uk/icons_of_invention/science/1750-1820/IC.014/



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Measuring the Meter!



Before the French Revolution, about 250,000 units of length and

weight exist in France

http://pahar.in/survey-of-india-report-maps/http://www.noa.gr/museum/english/organo_32_en.html

“Repeating circle” of Jean-Charles de Borda (1733 -1799 )

• Pierre François André Méchain (1744-1804)

and Jean Baptiste Joseph Delambre (1749-

1822) measured the meridian arc Dunkerque-

Paris-Barcelona

• This effort took place during the period from

1792 to 1799

• “The meter" was defined as 1/10,000,000 of

the distance North Pole - Equator.

• The metric system was to be "pour tous pour

toujours"

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Measuring Earth's highest mountain



Great Trigonometric Survey (19th century)

•Colonel William Lambton established

the mission in 1802

•George Everest took leadership in 1823

•Andrew Scott Waugh replaced Everest as

Surveyor-General in 1843

Mount Everest was calculated (1852, published 1856) to be exactly 29000 ft / 8839.2 m high

Current high 29029 ft / 8848 m

Error of 9.5 cm in a baseline of 11.6 km (≈ 8ppm)

http://pahar.in/survey-of-india-report-maps/



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Principle of triangulation:

Measurements / Observations:•Distances (in order to fix the scale)•Directions (w.r.t. the horizontal plane)•Angles (as differences of directions)

Calculations / Estimations:•Distances (Unknown/Unmeasured) •Angles (Unknown/Unmeasured)

+Coordinates w.r.t a reference frame

Micro-triangulationPrecision in level of micrometers:

•Total Station precision ≈ 0.00015g or 1.5 cc•Precision of 2.4μm/m•Precision at 4 m < 10 μm

dφ ≈ 1.5 cc

ds = R d∙ φ

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QDaedalus

Measurement System:•Developed at ETH Zürich (Geodesy and Geodynamics Lab)•Performs contactless, automatic, high precision measurements•Originally developed for rapid and easy determination of astronomical φ, λ, Α•Successor of ICARUS•Low-cost, non-destructive upgrade for automated theodolites (or total stations)•Composed of both, hardware and software developments



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The basic idea

How it works?•The operator’s eye is replaced by a CCD camera•Non-destructive way•Easily and rapidly mount•A software reads out the image and the angles •Angle measurements obtained faster and more precise

What could be the precision?•Optical system resolution ≈ 4 arcsec/pixel•Object extraction ≈ 1/10 pixel or better•The achievable precision ≈ 0.4 arcsec (1.2 cc)•Total Station precision ≈ 0.5 arcsec (1.5 cc)



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Components - Hardware

The complete system is composed by:•A Total Station / theodolite

– TDA5005 by Leica Geosystems (1.5 cc)

•A CCD camera– Guppy F-080C by Allied Vision Technologies (4.65 µm, 30 fps)

•A steering device for the focus mechanism– P110 064 by Portescap

•Interface box (CCD Triggering synchronization of multiple system)•A laptop with the software QDaedalus



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• QDaedalus is developed in C++ on the open source development platform Qt• Qt allows fast creation of cross-platform programs with a graphical user interface• The image processing algorithms are based on the open-source library OpenCV• The management of the data is based on the database engine SQLite

Algorithms - Software

Optical target recognition (OTR) and measurement:1.Center of mass

2.Template least-squares matching

3.Circle matching

4.Ellipse matching

Computer vision processing operations:•Image acquisition•Pre-processing (resampling, de-noising,…)•Feature extraction (lines, circles, regions,…)•Segmentation•High-level processing (compute center, size,...)



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Main features

Feature w.r.t. space/time resolution:•Density of points•Precision and Accuracy•Physical materialization of points•Sampling rate of measurements

Other important features have to be considered:•Automation degree•Palpate / touchless•Measurement range•Transportability•Easy handling•Price



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CLIC module application

Automatic Micro-triangulation:1.Import of approximate positions of station and targets

2.Definition of camera, focus, image processing parameters

3.Start of measurements, fully automatic process



Source: Sébastien Guillaume

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Measurement of May 2012

Targets:•9 fixed and illuminated spheres of Ø8 mm Comparison:•CMM with a precision of 6 μm MPE•After 3D Helmert transformationResults:•1.5 cc, horizontal direction•1.5 cc, zenithal angles



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Future developments

Hardware•Instrumental precision is sufficient•Wireless transmission of data and image triggering capabilities•Size reduction would be welcome (easier mechanical adaptation of the camera to the telescope)•Higher acquisition (frame) rates, up to 50 Hz

Software•Synchronous steering of several total stations •Detection algorithm for an oscillating stretched wire and new fiducials

Targets•Develop and evaluate different types of fiducials, compatible with FSI•Method of marking points on the stretched wire



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References

•Bürki, B., Guillaume, S., Sorber, P., Oesch, H.-P. (2010). DAEDALUS: A versatile usable digital clip-on measuring

system for Total Stations. International Conference on Indoor Positioning and Indoor Navigation (IPIN), Zürich, IEEE.

•Griffet, S. (2010). Evaluation des performances du prototype de Micro-Triangulation. Survey report EDMS

Document No 1106507, Genève, CERN.

•Guillaume, S., Bürki, B., Griffet, S., Mainaud-Durand, H. (2012). QDaedalus : Augmentation of Total Stations by CCD

Sensor for Automated Contactless High-Precision Metrology. FIG Working week 2012 Proceedings.

•Schmid, M., Wanner, M., Manyoky, M. (2010). Suitability of the Daedalus System for Micro-triangulation. Geodetic

Project Course, Geomatics Engineering and Planning.

•Waniorek, S. (2011). Automatic Micro-triangulation. Survey report EDMS Document No 1152343, Genève, CERN.





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Summary

• Triangulation is a very old technique

• Useful to obtain geometrical information

• In short distances it is able to be precise at micrometer level

• Changing the eye-piece with CCD we avoid the observer

• Non-destructive upgrade of common Total Stations

• Full exploitation of angle measurement precision at short distances (1-4 m)

• The precision can be well predicted and it is completely depended on the

configuration of the Micro-triangulation network

• Developments needed in software, targets and hardware

Thank you!

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Introduction to Micro-Triangulation

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