Abstract

This paper aims to establish and develop a calibration model for two time-of-flight terrestrial laser scanners (TLS): Trimble GX200 and Riegl LMS-Z390i. In particular, the study focuses on measurement errors and systematic instrumental errors to compile an error model for TLS. An iterative and robust least squares procedure is developed to compute internal calibration parameters together with a TLS data set geo-reference in an external reference system. To this end, a calibration field is designed that performs as an experimental platform that tests the different laser scanner methods. The experimental results show the usefulness and potential of this approach, especially when high-precision measurements are requires.

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  1. R. Staiger, “The Geometrical Quality of Terrestrial Laser Scanner (TLS)” presented at FIG Working Week 2005, Cairo, Egypt, 16–21 April. 2005.
  2. W. Boehler, V. M. Bordas, and A. Marbs, “Investigating Laser Scanner Accuracy,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 34(5), 696–701 (2003).
  3. D. Lichti and ., “Calibration and testing of a terrestrial scanner,” Int. Arch. Photogramm. Remote Sens. 33, 485–492 (2000).
  4. T. Schulz, “Calibration of a Terrestrial Laser Scanner for Engineering Geodesy”. Dissertation ETH Zurich Nº 17036. 2007.
  5. G. S. Cheok, S. Leigh, and A. Rukhin, “Calibration Experiments of a Laser Scanner,” National Institute of Standards and Technology U. S. Department of Commerce Gaithersburg, MD 20899, 2002.
  6. Th. Kersten, H. Sternberg, and K. Mechelke, “Investigations into the Accuracy Behaviour of the Terrestrial Laser Scanning System Trimble GS100”,in Optical 3D Measurement Techniques VII Vol. 1, Gruen & Kahmen, eds.(2005), pp. 122–131.
  7. K. Mechelke, T. P. Kersten, and M. Lindstaedt, “Comparative investigations into the accuracy behaviour of the new generation of terrestrial laser scanning systems”, in Optical 3-D Measurement Techniques VIII Vol. I, Gruen & Kahmen, eds. (2007), pp. 319–327.
  8. M. Johansson, “Explorations into the Behaviour of three Different High-Resolution Ground-based Laser Scanners in the Built Environment”, presented at Proceedings of the CIPA WG 6 International Workshop on Scanning for Cultural Heritage Recording, Corfu, Greece, 2003, http://www.isprs.org/commission5/workshop
  9. T. Schulz, and H. Ingensand, “Influencing Variables, Precision and Accuracy of Terrestrial Laser Scanners” presented at INGEO 2004 and FIG Regional Central and Eastern European Conference on Engineering Surveying, Bratislava, Slovakia, 11–13 November. 2004.
  10. T. Schulz and H. Ingensand, “Terrestrial Laser Scanning – Investigations and Applications for High Precision Scanning” presented at FIG Working Week 2004, Athens, Greece, 22–27 May. 2004.
  11. Y. Reshetyuk, “Self-calibration and direct georeferencing in terrestrial laser scanning”. Doctoral thesis in Infrastructure, Geodesy Royal Institute of Technology, Stockholm, Sweden. TRITA-TEC-PHD 09–001. ISBN 978–91–85539–34–5. (2009)
  12. A. Rietdorf, R. Gielsdorf, and L. Grundig, “A Concept for the Calibration of Terrestrial Laser Scanners”, in INGEO 2004 and FIG Regional Central and Eastern Conference on Engineering Surveying, Bratislava, Slovakia. 11–13 November. 2004.
  13. Y. Reshetyuk, “Calibration of terrestrial laser scanners for the purposes of geodetic engineering”, presented at the 3rd IAG/ 12th FIG Symposium, Baden, Germany, 22–24 May. 2006.
  14. D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. 131(4), 135–142 (2005).
    [CrossRef]
  15. D. Lichti, “Error modelling, calibration and analysis of an AM–CW terrestrial laser scanner system,” ISPRS J. Photogramm. Remote Sens. 61(5), 307–324 (2007).
    [CrossRef]
  16. J. Chow, D. Lichti, and B. Teskey, “Self-calibration of the Trimble (Mensi) GS200 Terrestrial Laser Scanner”, in Proceedings of ISPRS Commision V Mid-Term Symposium, “Close range Image Measurement Techniques”, Newcastle upon Tyne, United Kingdom, 22–24 June, 2010.
  17. J. Chow, B. Teskey, and D. Lichti, “Self-calibration and evaluation of the Trimble GX terrestrial laser scanner”, in Proceedings of The 2010 Canadian Geomatics Conference and Symposium of Commission I, ISPRS, Volume XXXVIII, Calgary, Canada, 15–18 June, 2010.
  18. M. Hebert and E. Krotkov, “3D measurements from imaging laser radars: how good are they?” Image Vis. Comput. 10(3), 170–178 (1992).
    [CrossRef]
  19. C. D. Ghilani, and P. R. Wolf, Adjustment Computations: Spatial Data Analysis. 4th edition(John Wiley & Sons, 2006)
  20. M. Balzani, A. Pellegrinelli, N. Perfetti, and F. Uccelli, “A terrestrial laser scanner: accuracy tests” in Proceedings of 18th International Symposium CIPA 2001,(2001),pp. 445 – 453.
  21. S. J. Gordon and D. Lichti, “Terrestrial laser scanners with a narrow field of view: the effect on 3D resection solutions,” Survey Review 37(292), 448–468 (2004).
  22. P. A. Domingo, “Investigación sobre los Métodos de Estimación Robusta aplicados a la resolución de los problemas fundamentales de la Fotogrametría”. Doctoral Thesis. University of Cantabria, Santander, 2000.
  23. A. J. Pope, “The statistics of residuals and the detection of outliers”, NOAA Technical Report NOS 65 NGS 1, National Ocean Service, National Geodetic Survey, US Department of Commerce. Rockville, MD, (1976), p.133.
  24. K. Kraus, Advanced Methods and Applications. Vol.2. Fundamentals and Standard Processes. Vol.1. Institute for Photogrammetry Vienna University of Technology. Ferd. Dummler Verlag. Bonn. (1993)
  25. J. Armesto, B. Riveiro-Rodríguez, D. González-Aguilera, T. Rivas-Brea, “Terrestrial laser scanning intensity data applied to damage detection for historical buildings”, Journal of Archaeological Science 37 (12), 3037-3047 (2010).
  26. J. Chow, A. Ebeling, B. Teskey, “Low Cost Artificial Planar Target Measurement Techniques for Terrestrial Laser Scanning”, presented at FIG Congress 2010, Sydney, Australia, 11–16 April. 2010.

2007

D. Lichti, “Error modelling, calibration and analysis of an AM–CW terrestrial laser scanner system,” ISPRS J. Photogramm. Remote Sens. 61(5), 307–324 (2007).
[CrossRef]

2005

D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. 131(4), 135–142 (2005).
[CrossRef]

2004

S. J. Gordon and D. Lichti, “Terrestrial laser scanners with a narrow field of view: the effect on 3D resection solutions,” Survey Review 37(292), 448–468 (2004).

2003

W. Boehler, V. M. Bordas, and A. Marbs, “Investigating Laser Scanner Accuracy,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 34(5), 696–701 (2003).

2000

D. Lichti and ., “Calibration and testing of a terrestrial scanner,” Int. Arch. Photogramm. Remote Sens. 33, 485–492 (2000).

1992

M. Hebert and E. Krotkov, “3D measurements from imaging laser radars: how good are they?” Image Vis. Comput. 10(3), 170–178 (1992).
[CrossRef]

Boehler, W.

W. Boehler, V. M. Bordas, and A. Marbs, “Investigating Laser Scanner Accuracy,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 34(5), 696–701 (2003).

Bordas, V. M.

W. Boehler, V. M. Bordas, and A. Marbs, “Investigating Laser Scanner Accuracy,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 34(5), 696–701 (2003).

Gordon, S.

D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. 131(4), 135–142 (2005).
[CrossRef]

Gordon, S. J.

S. J. Gordon and D. Lichti, “Terrestrial laser scanners with a narrow field of view: the effect on 3D resection solutions,” Survey Review 37(292), 448–468 (2004).

Hebert, M.

M. Hebert and E. Krotkov, “3D measurements from imaging laser radars: how good are they?” Image Vis. Comput. 10(3), 170–178 (1992).
[CrossRef]

Krotkov, E.

M. Hebert and E. Krotkov, “3D measurements from imaging laser radars: how good are they?” Image Vis. Comput. 10(3), 170–178 (1992).
[CrossRef]

Lichti, D.

D. Lichti, “Error modelling, calibration and analysis of an AM–CW terrestrial laser scanner system,” ISPRS J. Photogramm. Remote Sens. 61(5), 307–324 (2007).
[CrossRef]

D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. 131(4), 135–142 (2005).
[CrossRef]

S. J. Gordon and D. Lichti, “Terrestrial laser scanners with a narrow field of view: the effect on 3D resection solutions,” Survey Review 37(292), 448–468 (2004).

D. Lichti and ., “Calibration and testing of a terrestrial scanner,” Int. Arch. Photogramm. Remote Sens. 33, 485–492 (2000).

Marbs, A.

W. Boehler, V. M. Bordas, and A. Marbs, “Investigating Laser Scanner Accuracy,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 34(5), 696–701 (2003).

Tipdecho, T.

D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. 131(4), 135–142 (2005).
[CrossRef]

Image Vis. Comput.

M. Hebert and E. Krotkov, “3D measurements from imaging laser radars: how good are they?” Image Vis. Comput. 10(3), 170–178 (1992).
[CrossRef]

Int. Arch. Photogramm. Remote Sens.

D. Lichti and ., “Calibration and testing of a terrestrial scanner,” Int. Arch. Photogramm. Remote Sens. 33, 485–492 (2000).

Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.

W. Boehler, V. M. Bordas, and A. Marbs, “Investigating Laser Scanner Accuracy,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 34(5), 696–701 (2003).

ISPRS J. Photogramm. Remote Sens.

D. Lichti, “Error modelling, calibration and analysis of an AM–CW terrestrial laser scanner system,” ISPRS J. Photogramm. Remote Sens. 61(5), 307–324 (2007).
[CrossRef]

J. Surv. Eng.

D. Lichti, S. Gordon, and T. Tipdecho, “Error Models and Propagation in Directly Georeferenced Terrestrial Laser Scanner Networks,” J. Surv. Eng. 131(4), 135–142 (2005).
[CrossRef]

Survey Review

S. J. Gordon and D. Lichti, “Terrestrial laser scanners with a narrow field of view: the effect on 3D resection solutions,” Survey Review 37(292), 448–468 (2004).

Other

P. A. Domingo, “Investigación sobre los Métodos de Estimación Robusta aplicados a la resolución de los problemas fundamentales de la Fotogrametría”. Doctoral Thesis. University of Cantabria, Santander, 2000.

A. J. Pope, “The statistics of residuals and the detection of outliers”, NOAA Technical Report NOS 65 NGS 1, National Ocean Service, National Geodetic Survey, US Department of Commerce. Rockville, MD, (1976), p.133.

K. Kraus, Advanced Methods and Applications. Vol.2. Fundamentals and Standard Processes. Vol.1. Institute for Photogrammetry Vienna University of Technology. Ferd. Dummler Verlag. Bonn. (1993)

J. Armesto, B. Riveiro-Rodríguez, D. González-Aguilera, T. Rivas-Brea, “Terrestrial laser scanning intensity data applied to damage detection for historical buildings”, Journal of Archaeological Science 37 (12), 3037-3047 (2010).

J. Chow, A. Ebeling, B. Teskey, “Low Cost Artificial Planar Target Measurement Techniques for Terrestrial Laser Scanning”, presented at FIG Congress 2010, Sydney, Australia, 11–16 April. 2010.

J. Chow, D. Lichti, and B. Teskey, “Self-calibration of the Trimble (Mensi) GS200 Terrestrial Laser Scanner”, in Proceedings of ISPRS Commision V Mid-Term Symposium, “Close range Image Measurement Techniques”, Newcastle upon Tyne, United Kingdom, 22–24 June, 2010.

J. Chow, B. Teskey, and D. Lichti, “Self-calibration and evaluation of the Trimble GX terrestrial laser scanner”, in Proceedings of The 2010 Canadian Geomatics Conference and Symposium of Commission I, ISPRS, Volume XXXVIII, Calgary, Canada, 15–18 June, 2010.

R. Staiger, “The Geometrical Quality of Terrestrial Laser Scanner (TLS)” presented at FIG Working Week 2005, Cairo, Egypt, 16–21 April. 2005.

T. Schulz, “Calibration of a Terrestrial Laser Scanner for Engineering Geodesy”. Dissertation ETH Zurich Nº 17036. 2007.

G. S. Cheok, S. Leigh, and A. Rukhin, “Calibration Experiments of a Laser Scanner,” National Institute of Standards and Technology U. S. Department of Commerce Gaithersburg, MD 20899, 2002.

Th. Kersten, H. Sternberg, and K. Mechelke, “Investigations into the Accuracy Behaviour of the Terrestrial Laser Scanning System Trimble GS100”,in Optical 3D Measurement Techniques VII Vol. 1, Gruen & Kahmen, eds.(2005), pp. 122–131.

K. Mechelke, T. P. Kersten, and M. Lindstaedt, “Comparative investigations into the accuracy behaviour of the new generation of terrestrial laser scanning systems”, in Optical 3-D Measurement Techniques VIII Vol. I, Gruen & Kahmen, eds. (2007), pp. 319–327.

M. Johansson, “Explorations into the Behaviour of three Different High-Resolution Ground-based Laser Scanners in the Built Environment”, presented at Proceedings of the CIPA WG 6 International Workshop on Scanning for Cultural Heritage Recording, Corfu, Greece, 2003, http://www.isprs.org/commission5/workshop

T. Schulz, and H. Ingensand, “Influencing Variables, Precision and Accuracy of Terrestrial Laser Scanners” presented at INGEO 2004 and FIG Regional Central and Eastern European Conference on Engineering Surveying, Bratislava, Slovakia, 11–13 November. 2004.

T. Schulz and H. Ingensand, “Terrestrial Laser Scanning – Investigations and Applications for High Precision Scanning” presented at FIG Working Week 2004, Athens, Greece, 22–27 May. 2004.

Y. Reshetyuk, “Self-calibration and direct georeferencing in terrestrial laser scanning”. Doctoral thesis in Infrastructure, Geodesy Royal Institute of Technology, Stockholm, Sweden. TRITA-TEC-PHD 09–001. ISBN 978–91–85539–34–5. (2009)

A. Rietdorf, R. Gielsdorf, and L. Grundig, “A Concept for the Calibration of Terrestrial Laser Scanners”, in INGEO 2004 and FIG Regional Central and Eastern Conference on Engineering Surveying, Bratislava, Slovakia. 11–13 November. 2004.

Y. Reshetyuk, “Calibration of terrestrial laser scanners for the purposes of geodetic engineering”, presented at the 3rd IAG/ 12th FIG Symposium, Baden, Germany, 22–24 May. 2006.

C. D. Ghilani, and P. R. Wolf, Adjustment Computations: Spatial Data Analysis. 4th edition(John Wiley & Sons, 2006)

M. Balzani, A. Pellegrinelli, N. Perfetti, and F. Uccelli, “A terrestrial laser scanner: accuracy tests” in Proceedings of 18th International Symposium CIPA 2001,(2001),pp. 445 – 453.

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Figures (8)

Fig. 1
Fig. 1

Scanner axes and axes errors in Trimble GX200. (a) frontal view of the scanner Trimble GX200. The vertical angle θ is fixed by the orientation of the planar oscillating mirror and the horizontal angle φ is determined by the position of the rotation platform that contains the scanner. (b) oscillating planar mirror. An optical lever effect is produced when the planar mirror rotates an angle α, so the reflected ray rotates an angle . This is easy to demonstrate based on the reflection law because the angle between the incident ray I1 and the normal to the mirror is equivalent to the angle between the reflected ray and the normal. R1 is the reflected ray before rotating the mirror, while R2 is the reflected ray after rotating the mirror.

Fig. 2
Fig. 2

Scanner axes and axes errors for the Riegl LMS-390i. (a) lateral view of the Riegl LMS-Z390i laser scanner. The vertical angle θ is fixed by the orientation of the polygonal rotating mirror, and the horizontal angle φ is fixed by the rotation head. (b) rotating polygonal mirror. When the polygon rotates an angle α, the laser beam is reflected, which results in an azimuth angle θ of 2α. Note that this axis presents an eccentricity e in comparison with the Trimble GX200.

Fig. 3
Fig. 3

(a) Layout of the TLS calibration field with the distribution of Trimble (T) and Riegl (R) targets. (b) Detailed distribution of targets in different planes: left front wall, right back wall, right front wall and left back wall.

Fig. 4
Fig. 4

Histograms of the TLS observable errors in distance (a), horizontal angle (b) and vertical angle (c).

Fig. 5
Fig. 5

Error distribution histograms of X, Y, Z coordinate measurements for the Trimble GX200 (a) and Riegl LMS-Z390i (b).

Fig. 6
Fig. 6

Bivariant graphics that illustrate the correlation, (C), between the horizontal angular error and the scanner horizontal angle for Trimble GX200 (a) and RieglLMS-Z390i (b).

Fig. 7
Fig. 7

Bivariant graphics that illustrate the correlation, (C), between the vertical angular error and the horizontal and vertical angles for Trimble GX200 (a) and RieglLMS-Z390i (b).

Fig. 8
Fig. 8

Bivariant graphics, between TLS errors and observations obtained after self-calibration for Trimble GX200 (a), (c) and Riegl LMS-Z390i (b), (d).

Tables (3)

Tables Icon

Table 1 Analysis of TLS observation accuracy before calibration

Tables Icon

Table 2 External and internal parameters obtained from the proposed TLS self-calibration approach

Tables Icon

Table 3 Analysis of the TLS observation accuracies after calibration

Equations (14)

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Δ r = k 0 + m · r
θ c o r r = θ s c a n ( 1 - δ θ ) - θ 0 Δ θ = θ s c a n θ c o r r = θ s c a n δ θ + θ 0 | vertical angles ϕ c o r r = ϕ s c a n ( 1 - δ ϕ ) - ϕ 0 Δ ϕ = ϕ s c a n ϕ c o r r = ϕ s c a n δ ϕ + ϕ 0 | horizontal angles
Δ ϕ c o r r = ( ϕ 0 + c cos θ s c a n + i tan θ s c a n + ϕ s c a n δ ϕ )
Δ θ c o r r = ( θ 0 + θ s c a n δ θ )
[ X Y Z ] = [ Δ X Δ Y Δ Z ] + R ( α 1 , α 2 , α 3 ) [ m ( r s c a n k 0 ) c o s [ ϕ s c a n ( c ) ( i ) ϕ 0 δ ϕ ϕ s c a n ] c o s ( θ s c a n θ 0 δ θ θ s c a n ) m ( r s c a n k 0 ) s i n [ ϕ s c a n ( c ) ( i ) ϕ 0 δ ϕ ϕ s c a n ] c o s ( θ s c a n θ 0 δ θ θ s c a n ) m ( r s c a n k 0 ) s i n ( θ s c a n θ 0 δ θ θ s c a n ) ]
( c ) = c c o s θ s c a n ( i ) = i tan θ s c a n
[ X Y Z ] F 0 = [ Δ X Δ Y Δ Z ] + F 0 α 1 δ α 1 + F 0 α 2 δ α 2 + F 0 α 3 δ α 3 + F 0 m δ m + F 0 k 0 δ k 0 + F 0 c δ c + F 0 i δ i + F 0 θ 0 δ θ 0 + F 0 ( δ θ ) δ ( δ θ ) + F 0 ϕ 0 δ ϕ 0 + F 0 ( δ ϕ ) δ ( δ ϕ )
F 0 = R ( α 1 0 , α 2 0 , α 3 0 ) [ x 0 y 0 z 0 ] = [ r 11 0 r 12 0 r 13 0 r 21 0 r 22 0 r 23 0 r 31 0 r 32 0 r 33 0 ] [ m 0 ( r s c a n k 0 0 ) cos [ ϕ s c a n ( c ) 0 ( i ) 0 ϕ 0 0 δ ϕ 0 ϕ s c a n ] cos ( θ s c a n θ 0 0 δ θ 0 θ s c a n ) m 0 ( r s c a n k 0 0 ) sin [ ϕ s c a n ( c ) 0 ( i ) 0 ϕ 0 0 δ ϕ 0 ϕ s c a n ] cos ( θ s c a n θ 0 0 δ θ 0 θ s c a n ) m 0 ( r s c a n k 0 0 ) sin ( θ s c a n θ 0 0 δ θ 0 θ s c a n ) ]
v T W v = min ; ( v T W v ) x = 0
Σ l l = Σ XYZ + R ( α 1 , α 2 , α 3 ) J Σ inst J T R ( α 1 , α 2 , α 3 ) T
Σ inst = d i a g ( σ r 2 , σ ϕ 2 + σ b e a m 2 , σ θ 2 + σ b e a m 2 )
W ( v i ' ) = e ( | v ' i | 2 )
v P o p e = | v i σ ^ 2 C VV | > P o p e _ t h r e s h o l d
L e v e l i n g Z _ E f f e c t i v e n e s s i = 1 n ( Z L Z T ) 2 n 1 = 0.9 m m ; n = 16

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