Abstract

Three-dimensional (3D) surface topographic analysis, measurement, and assessment techniques have raised great interest not only among researchers but also among industrial users. Many industrial processes and applications are directly influenced by the small-scale roughness of surface finishes. This paper describes the development and implementation of a noncontact, three-dimensional, microtopography measuring system. The instrument is formed by combining a modified light-sectioning microscope subsystem with a computer subsystem. In particular, optical system characteristics of the light-sectioning microscope are investigated, and a textured steel sheet is measured to demonstrate good practical outcomes. Details of measuring processes and image processing algorithms are provided, such as procedures for measurement, image edge extraction, and 3D topography reconstruction. After the 3D topography of the measured surface has been reconstructed, the topography field description parameters are calculated. A standard roughness block was used for calibration of the surface microtopography measuring system. Results obtained showed the measurement method output has good agreement with the actual asperity (unevenness or roughness) of the surface. The computer subsystem is used to process and control asperity measurements and image generation, and for image acquisition and presentation.

© 2012 Optical Society of America

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    [CrossRef]

2011

X. Luo, Y. Wang, C. Peifeng, and L. Zhou, “Investigation of CO2 laser beam modulation by rotating polygon,” Opt. Lasers Eng. 49, 132–136 (2011).
[CrossRef]

2010

O. B. Abouelatta, “3D surface roughness measurement using a light sectioning vision system,” Lect. Notes Comput. Sci. Eng. 2183(1), 698–703 (2010).

2007

A. Bogner, P. H. Jouneau, G. Thollet, D. Basset, and C. Gauthies, “A history of scanning electron microscopy,” Micron 38, 390–401 (2007).
[CrossRef]

X. Jiang, P. J. Scott, D. J. Whitehouse, and L. Blunt, “Paradigm shifts in surface metrology. Part II. the current shift,” Proc. R. Soc. A 463, 2071–2099 (2007).
[CrossRef]

2005

F. Pernkopf, “3D surface acquisition and reconstruction for inspection of raw steel products,” Comput. Ind. 56, 876–885 (2005).
[CrossRef]

A. Gruen and D. Akca, “Least squares 3D surface and curve matching,” J. Photogramm. Remote Sens. 59, 151–174(2005).
[CrossRef]

R. J. Hocken, N. Chakraborty, and C. Brown, “Optical metrology of surfaces,” CIRP Ann. 54, 169–183 (2005).
[CrossRef]

2003

W. Wang and P. L. Wong, “The dynamic measurement of surface topography using a light-section technique,” TriboTest 9, 305–316 (2003).
[CrossRef]

2002

2001

P. J. Scott, “An algorithm to extract critical points from lattice height data,” Int. J. Mach. Tools Manuf. 41, 1889–1897 (2001).
[CrossRef]

M. Vermeulen and J. Scheers, “Micro-hydrodynamic effects in EBT textured steel sheet,” Int. J. Mach. Tools Manuf. 41, 1941–1951 (2001).
[CrossRef]

2000

H. L. Mitchell and P. L. Houtekamer, “An adaptive ensemble Kalman filter,” Mon. Weather Rev. 128, 416–433 (2000).
[CrossRef]

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

1998

M. Kiran, B. Ramamoorthy, and V. Radhakrishnan, “Evaluation of surface roughness by vision system,” Int. J. Mach. Tools Manuf. 38, 685–690 (1998).
[CrossRef]

M. Pfestorf, U. Engel, and M. Geiger, “3D-surface parameters and their application on deterministic textured metal sheets,” Int. J. Mach. Tools Manuf. 38, 607–614 (1998).
[CrossRef]

1997

D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
[CrossRef]

1996

M. F. M. Costa, “Surface inspection by an optical triangulation method,” Opt. Eng. 35, 2743 (1996).
[CrossRef]

1992

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992).
[CrossRef]

1991

D. Y. Yim and S. W. Kim, “Optimum sampling interval for Ra roughness measurement,” Proc. Inst. Mech. Eng. 205, 139–142 (1991).

M. R. Stytz and G. Frieder, “Three-dimensional medical imaging: algorithms and computer systems,” ACM Comput. Surv. 23, 421–499 (1991).
[CrossRef]

1990

D. Rugar and P. K. Hansma, “Atomic force microscopy,” Phys. Today 43, 23–30 (1990).
[CrossRef]

1988

J. Loomis, A. Lightman, A. Poe, and R. Caldwell, “Automated dimensional analysis using a light-sectioning microscope,” Proc. SPIE 1036, 88–99 (1988).

1985

1983

G. Binnig and H. Rohrer, “Scanning tunneling microscope,” Surf. Sci. 126, 236–244 (1983).
[CrossRef]

1981

1979

S. Uchida, H. Sato, and M. Ohori, “Two-dimensional measurement of surface roughness by the light sectioning method,” CIRP Ann. 28, 419–423 (1979).

Abouelatta, O. B.

O. B. Abouelatta, “3D surface roughness measurement using a light sectioning vision system,” Lect. Notes Comput. Sci. Eng. 2183(1), 698–703 (2010).

Akca, D.

A. Gruen and D. Akca, “Least squares 3D surface and curve matching,” J. Photogramm. Remote Sens. 59, 151–174(2005).
[CrossRef]

Basset, D.

A. Bogner, P. H. Jouneau, G. Thollet, D. Basset, and C. Gauthies, “A history of scanning electron microscopy,” Micron 38, 390–401 (2007).
[CrossRef]

Bennett, J. M.

Bhushan, B.

Binnig, G.

G. Binnig and H. Rohrer, “Scanning tunneling microscope,” Surf. Sci. 126, 236–244 (1983).
[CrossRef]

Blunt, L.

X. Jiang, P. J. Scott, D. J. Whitehouse, and L. Blunt, “Paradigm shifts in surface metrology. Part II. the current shift,” Proc. R. Soc. A 463, 2071–2099 (2007).
[CrossRef]

L. Blunt and X. Jiang, “Advanced techniques for assessment surface topography: development of a basis for the 3D surface texture standards,” in SURFSTAND, 1st ed. (Kogan Page Science, 2003), pp. 17–40.

K. J. Stout and L. Blunt, Three-Dimensional Surface Topography2nd ed., (Penton, 2000).

Bogner, A.

A. Bogner, P. H. Jouneau, G. Thollet, D. Basset, and C. Gauthies, “A history of scanning electron microscopy,” Micron 38, 390–401 (2007).
[CrossRef]

Brown, C.

R. J. Hocken, N. Chakraborty, and C. Brown, “Optical metrology of surfaces,” CIRP Ann. 54, 169–183 (2005).
[CrossRef]

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Caldwell, R.

J. Loomis, A. Lightman, A. Poe, and R. Caldwell, “Automated dimensional analysis using a light-sectioning microscope,” Proc. SPIE 1036, 88–99 (1988).

Chakraborty, N.

R. J. Hocken, N. Chakraborty, and C. Brown, “Optical metrology of surfaces,” CIRP Ann. 54, 169–183 (2005).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Costa, M. F. M.

M. F. M. Costa, “Surface inspection by an optical triangulation method,” Opt. Eng. 35, 2743 (1996).
[CrossRef]

Dancy, J. H.

de Groot, P.

de Lega, X. C.

Engel, U.

M. Pfestorf, U. Engel, and M. Geiger, “3D-surface parameters and their application on deterministic textured metal sheets,” Int. J. Mach. Tools Manuf. 38, 607–614 (1998).
[CrossRef]

Frieder, G.

M. R. Stytz and G. Frieder, “Three-dimensional medical imaging: algorithms and computer systems,” ACM Comput. Surv. 23, 421–499 (1991).
[CrossRef]

Gauthies, C.

A. Bogner, P. H. Jouneau, G. Thollet, D. Basset, and C. Gauthies, “A history of scanning electron microscopy,” Micron 38, 390–401 (2007).
[CrossRef]

Geiger, M.

M. Pfestorf, U. Engel, and M. Geiger, “3D-surface parameters and their application on deterministic textured metal sheets,” Int. J. Mach. Tools Manuf. 38, 607–614 (1998).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing(Addison-Wesley, 1992).

Gruen, A.

A. Gruen and D. Akca, “Least squares 3D surface and curve matching,” J. Photogramm. Remote Sens. 59, 151–174(2005).
[CrossRef]

Hansma, P. K.

D. Rugar and P. K. Hansma, “Atomic force microscopy,” Phys. Today 43, 23–30 (1990).
[CrossRef]

Hocken, R. J.

R. J. Hocken, N. Chakraborty, and C. Brown, “Optical metrology of surfaces,” CIRP Ann. 54, 169–183 (2005).
[CrossRef]

Houtekamer, P. L.

H. L. Mitchell and P. L. Houtekamer, “An adaptive ensemble Kalman filter,” Mon. Weather Rev. 128, 416–433 (2000).
[CrossRef]

Jiang, X.

X. Jiang, P. J. Scott, D. J. Whitehouse, and L. Blunt, “Paradigm shifts in surface metrology. Part II. the current shift,” Proc. R. Soc. A 463, 2071–2099 (2007).
[CrossRef]

L. Blunt and X. Jiang, “Advanced techniques for assessment surface topography: development of a basis for the 3D surface texture standards,” in SURFSTAND, 1st ed. (Kogan Page Science, 2003), pp. 17–40.

Jouneau, P. H.

A. Bogner, P. H. Jouneau, G. Thollet, D. Basset, and C. Gauthies, “A history of scanning electron microscopy,” Micron 38, 390–401 (2007).
[CrossRef]

Kim, S. W.

D. Y. Yim and S. W. Kim, “Optimum sampling interval for Ra roughness measurement,” Proc. Inst. Mech. Eng. 205, 139–142 (1991).

Kiran, M.

M. Kiran, B. Ramamoorthy, and V. Radhakrishnan, “Evaluation of surface roughness by vision system,” Int. J. Mach. Tools Manuf. 38, 685–690 (1998).
[CrossRef]

Koliopoulos, C. L.

Kramer, J.

Lightman, A.

J. Loomis, A. Lightman, A. Poe, and R. Caldwell, “Automated dimensional analysis using a light-sectioning microscope,” Proc. SPIE 1036, 88–99 (1988).

Loomis, J.

J. Loomis, A. Lightman, A. Poe, and R. Caldwell, “Automated dimensional analysis using a light-sectioning microscope,” Proc. SPIE 1036, 88–99 (1988).

Luo, X.

X. Luo, Y. Wang, C. Peifeng, and L. Zhou, “Investigation of CO2 laser beam modulation by rotating polygon,” Opt. Lasers Eng. 49, 132–136 (2011).
[CrossRef]

Mitchell, H. L.

H. L. Mitchell and P. L. Houtekamer, “An adaptive ensemble Kalman filter,” Mon. Weather Rev. 128, 416–433 (2000).
[CrossRef]

Ohori, M.

S. Uchida, H. Sato, and M. Ohori, “Two-dimensional measurement of surface roughness by the light sectioning method,” CIRP Ann. 28, 419–423 (1979).

Peifeng, C.

X. Luo, Y. Wang, C. Peifeng, and L. Zhou, “Investigation of CO2 laser beam modulation by rotating polygon,” Opt. Lasers Eng. 49, 132–136 (2011).
[CrossRef]

Pernkopf, F.

F. Pernkopf, “3D surface acquisition and reconstruction for inspection of raw steel products,” Comput. Ind. 56, 876–885 (2005).
[CrossRef]

Pfestorf, M.

M. Pfestorf, U. Engel, and M. Geiger, “3D-surface parameters and their application on deterministic textured metal sheets,” Int. J. Mach. Tools Manuf. 38, 607–614 (1998).
[CrossRef]

Poe, A.

J. Loomis, A. Lightman, A. Poe, and R. Caldwell, “Automated dimensional analysis using a light-sectioning microscope,” Proc. SPIE 1036, 88–99 (1988).

Radhakrishnan, V.

M. Kiran, B. Ramamoorthy, and V. Radhakrishnan, “Evaluation of surface roughness by vision system,” Int. J. Mach. Tools Manuf. 38, 685–690 (1998).
[CrossRef]

Ramamoorthy, B.

M. Kiran, B. Ramamoorthy, and V. Radhakrishnan, “Evaluation of surface roughness by vision system,” Int. J. Mach. Tools Manuf. 38, 685–690 (1998).
[CrossRef]

Rohrer, H.

G. Binnig and H. Rohrer, “Scanning tunneling microscope,” Surf. Sci. 126, 236–244 (1983).
[CrossRef]

Rugar, D.

D. Rugar and P. K. Hansma, “Atomic force microscopy,” Phys. Today 43, 23–30 (1990).
[CrossRef]

Sato, H.

S. Uchida, H. Sato, and M. Ohori, “Two-dimensional measurement of surface roughness by the light sectioning method,” CIRP Ann. 28, 419–423 (1979).

Scheers, J.

M. Vermeulen and J. Scheers, “Micro-hydrodynamic effects in EBT textured steel sheet,” Int. J. Mach. Tools Manuf. 41, 1941–1951 (2001).
[CrossRef]

Schmaltz, G.

G. Schmaltz, Technische Oberflächenkunde (Springer-Verlag, 1936), p. 73.

Scott, P. J.

X. Jiang, P. J. Scott, D. J. Whitehouse, and L. Blunt, “Paradigm shifts in surface metrology. Part II. the current shift,” Proc. R. Soc. A 463, 2071–2099 (2007).
[CrossRef]

P. J. Scott, “An algorithm to extract critical points from lattice height data,” Int. J. Mach. Tools Manuf. 41, 1889–1897 (2001).
[CrossRef]

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Stout, K. J.

K. J. Stout and L. Blunt, Three-Dimensional Surface Topography2nd ed., (Penton, 2000).

Stytz, M. R.

M. R. Stytz and G. Frieder, “Three-dimensional medical imaging: algorithms and computer systems,” ACM Comput. Surv. 23, 421–499 (1991).
[CrossRef]

Thollet, G.

A. Bogner, P. H. Jouneau, G. Thollet, D. Basset, and C. Gauthies, “A history of scanning electron microscopy,” Micron 38, 390–401 (2007).
[CrossRef]

Tizhoosh, H. R.

H. R. Tizhoosh, “Fast fuzzy edge detection,” in Proceedings of Fuzzy Information Processing Society (2002), pp. 239–242.

Turzhitsky, M.

Uchida, S.

S. Uchida, H. Sato, and M. Ohori, “Two-dimensional measurement of surface roughness by the light sectioning method,” CIRP Ann. 28, 419–423 (1979).

Vermeulen, M.

M. Vermeulen and J. Scheers, “Micro-hydrodynamic effects in EBT textured steel sheet,” Int. J. Mach. Tools Manuf. 41, 1941–1951 (2001).
[CrossRef]

Wang, W.

W. Wang and P. L. Wong, “The dynamic measurement of surface topography using a light-section technique,” TriboTest 9, 305–316 (2003).
[CrossRef]

Wang, Y.

X. Luo, Y. Wang, C. Peifeng, and L. Zhou, “Investigation of CO2 laser beam modulation by rotating polygon,” Opt. Lasers Eng. 49, 132–136 (2011).
[CrossRef]

Weber, H.

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992).
[CrossRef]

Whitehouse, D. J.

X. Jiang, P. J. Scott, D. J. Whitehouse, and L. Blunt, “Paradigm shifts in surface metrology. Part II. the current shift,” Proc. R. Soc. A 463, 2071–2099 (2007).
[CrossRef]

D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
[CrossRef]

Wong, P. L.

W. Wang and P. L. Wong, “The dynamic measurement of surface topography using a light-section technique,” TriboTest 9, 305–316 (2003).
[CrossRef]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing(Addison-Wesley, 1992).

Wyant, J. C.

Yim, D. Y.

D. Y. Yim and S. W. Kim, “Optimum sampling interval for Ra roughness measurement,” Proc. Inst. Mech. Eng. 205, 139–142 (1991).

Zhou, L.

X. Luo, Y. Wang, C. Peifeng, and L. Zhou, “Investigation of CO2 laser beam modulation by rotating polygon,” Opt. Lasers Eng. 49, 132–136 (2011).
[CrossRef]

ACM Comput. Surv.

M. R. Stytz and G. Frieder, “Three-dimensional medical imaging: algorithms and computer systems,” ACM Comput. Surv. 23, 421–499 (1991).
[CrossRef]

Appl. Opt.

CIRP Ann.

R. J. Hocken, N. Chakraborty, and C. Brown, “Optical metrology of surfaces,” CIRP Ann. 54, 169–183 (2005).
[CrossRef]

S. Uchida, H. Sato, and M. Ohori, “Two-dimensional measurement of surface roughness by the light sectioning method,” CIRP Ann. 28, 419–423 (1979).

Comput. Ind.

F. Pernkopf, “3D surface acquisition and reconstruction for inspection of raw steel products,” Comput. Ind. 56, 876–885 (2005).
[CrossRef]

Int. J. Mach. Tools Manuf.

P. J. Scott, “An algorithm to extract critical points from lattice height data,” Int. J. Mach. Tools Manuf. 41, 1889–1897 (2001).
[CrossRef]

M. Pfestorf, U. Engel, and M. Geiger, “3D-surface parameters and their application on deterministic textured metal sheets,” Int. J. Mach. Tools Manuf. 38, 607–614 (1998).
[CrossRef]

M. Vermeulen and J. Scheers, “Micro-hydrodynamic effects in EBT textured steel sheet,” Int. J. Mach. Tools Manuf. 41, 1941–1951 (2001).
[CrossRef]

M. Kiran, B. Ramamoorthy, and V. Radhakrishnan, “Evaluation of surface roughness by vision system,” Int. J. Mach. Tools Manuf. 38, 685–690 (1998).
[CrossRef]

J. Photogramm. Remote Sens.

A. Gruen and D. Akca, “Least squares 3D surface and curve matching,” J. Photogramm. Remote Sens. 59, 151–174(2005).
[CrossRef]

Lect. Notes Comput. Sci. Eng.

O. B. Abouelatta, “3D surface roughness measurement using a light sectioning vision system,” Lect. Notes Comput. Sci. Eng. 2183(1), 698–703 (2010).

Meas. Sci. Technol.

D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
[CrossRef]

Micron

A. Bogner, P. H. Jouneau, G. Thollet, D. Basset, and C. Gauthies, “A history of scanning electron microscopy,” Micron 38, 390–401 (2007).
[CrossRef]

Mon. Weather Rev.

H. L. Mitchell and P. L. Houtekamer, “An adaptive ensemble Kalman filter,” Mon. Weather Rev. 128, 416–433 (2000).
[CrossRef]

Opt. Eng.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

M. F. M. Costa, “Surface inspection by an optical triangulation method,” Opt. Eng. 35, 2743 (1996).
[CrossRef]

Opt. Lasers Eng.

X. Luo, Y. Wang, C. Peifeng, and L. Zhou, “Investigation of CO2 laser beam modulation by rotating polygon,” Opt. Lasers Eng. 49, 132–136 (2011).
[CrossRef]

Opt. Quantum Electron.

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992).
[CrossRef]

Phys. Today

D. Rugar and P. K. Hansma, “Atomic force microscopy,” Phys. Today 43, 23–30 (1990).
[CrossRef]

Proc. Inst. Mech. Eng.

D. Y. Yim and S. W. Kim, “Optimum sampling interval for Ra roughness measurement,” Proc. Inst. Mech. Eng. 205, 139–142 (1991).

Proc. R. Soc. A

X. Jiang, P. J. Scott, D. J. Whitehouse, and L. Blunt, “Paradigm shifts in surface metrology. Part II. the current shift,” Proc. R. Soc. A 463, 2071–2099 (2007).
[CrossRef]

Proc. SPIE

J. Loomis, A. Lightman, A. Poe, and R. Caldwell, “Automated dimensional analysis using a light-sectioning microscope,” Proc. SPIE 1036, 88–99 (1988).

Surf. Sci.

G. Binnig and H. Rohrer, “Scanning tunneling microscope,” Surf. Sci. 126, 236–244 (1983).
[CrossRef]

TriboTest

W. Wang and P. L. Wong, “The dynamic measurement of surface topography using a light-section technique,” TriboTest 9, 305–316 (2003).
[CrossRef]

Other

G. Schmaltz, Technische Oberflächenkunde (Springer-Verlag, 1936), p. 73.

K. J. Stout and L. Blunt, Three-Dimensional Surface Topography2nd ed., (Penton, 2000).

“Geometrical product specifications (GPS)—surface texture: areal—Part 2: terms, definitions and surface texture parameters,” ISO/DIS 25178-2 (International Organization for Standardization, 2006).

H. R. Tizhoosh, “Fast fuzzy edge detection,” in Proceedings of Fuzzy Information Processing Society (2002), pp. 239–242.

R. C. Gonzalez and R. E. Woods, Digital Image Processing(Addison-Wesley, 1992).

“Geometrical product specifications (GPS)—surface texture: profile method—metrological characteristics of phase correct filters,” ISO 11562 (International Organization for Standardization, 1996).

L. Blunt and X. Jiang, “Advanced techniques for assessment surface topography: development of a basis for the 3D surface texture standards,” in SURFSTAND, 1st ed. (Kogan Page Science, 2003), pp. 17–40.

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Figures (10)

Fig. 1.
Fig. 1.

Diagram of surface topographic measuring system using light-sectioning method.

Fig. 2.
Fig. 2.

Schematic diagram of the measuring subsystem. The sample surface is labeled “Asperity;” this term defines roughness of surface, or unevenness.

Fig. 3.
Fig. 3.

Optical layout of light-sectioning method of the measuring subsystem: (1) light source, (2) green filter, (3) collector lens, (4) slit diaphragm, (5) front focal plane of tube lens (M2), (6), (10) tube lens, (7) condenser lens, (8) reference plane, (9) objective lens, (11) back focal plane of tube lens (M5), (12) front focal plane of eyepiece (M6), (13) eyepiece, and (14) primary image plane.

Fig. 4.
Fig. 4.

Variation of axial rays position with the undulating surface: (a) a concave surface; (b) a convex surface.

Fig. 5.
Fig. 5.

Height deviations D versus variances of width of slit image on CCD camera; W1 and W2 are the edges of the slit image on the CCD camera.

Fig. 6.
Fig. 6.

A microscopy picture of a lasertex cold-rolled steel sheet surface. Lasertex is a laser-ablation technique. Differently shaped craters are formed in a patterned structure on the steel surface by controlling the pulsed-laser power density, pulse-repetition rate, and pulse duration.

Fig. 7.
Fig. 7.

Slit image of the lasertex-treated sheet steel surface and the results of image processing: (a) a slit image captured by CCD camera; (b) binary image result of the slit image; (c) an edge as extracted on the side of W2; (d) the edge after being smoothed.

Fig. 8.
Fig. 8.

A reconstructed topography of the lasertex cold-rolled steel sheet.

Fig. 9.
Fig. 9.

Sk family parameters of the textured steel sheet.

Fig. 10.
Fig. 10.

Reconstructed topography of (a) a standard block and (b) a simulation surface.

Tables (3)

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Table 1. Amplitude Parameters of the Lasertex Cold-Rolled Steel Sheet from Fig. 8

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Table 2. Field Parameters of the Textured Steel Sheet (ISO/DIS 25178-2)

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Table 3. Comparison of the Experimental Results Between Standard Block and Simulation Surface

Equations (9)

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[A1B1C1D1]=[1L301][101/f31][1L201][101/f21][1L101][101/f11],
[A2B2C2D2]=[1L701][101/f61][1L601][101/f51][1L501][101/f41][1L401],
[Hφ]=[A2B2C2D2][h2θ2],
[h1θ1]=[A1B1C1D1][h0θ0],
[A1B1C1D1]=[1L3+2D01][101/f31][1L201][101/f21][1L101][101/f11],
[h2θ2]=[h1+2Dθ1].
{W1=0.387761.0758*DW2=0.224435.4087*D,
W2=nHDNP,
D=(nHDNP0.2244)/35.4087.

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