Abstract

In industrial applications of thin metallic wires it is important to characterize the surface defects of the wires. We present an optical technique for the automatic detection of surface defects on thin metallic wires (diameters, 50–2000 µm) that can be used in on-line systems for surface quality control. This technique is based on the intensity variations on the scattered cone generated when the wire is illuminated with a beam at oblique incidence. Our results are compared with those obtained by atomic-force microscopy and scanning-electron microscopy.

© 2000 Optical Society of America

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References

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  1. T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24(12), 61–69 (1991).
  2. J. F. Fardeau, “New laser sensor for wire diameter measurement,” Wire J. Intern. 22(1), 42–51 (1989).
  3. I. Serroukh, E. Bernabeu, L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 34, 1319–1325 (1999).
  4. G. W. Rowe, An Introduction to the Principles of Metalworking (Edward Arnold, London, 1965).
  5. L. M. Sanchez-Brea, J. A. Gomez-Pedrero, E. Bernabeu, “Measurement of surface defects on thin steel wires by atomic force microscopy,” Appl. Surf. Sci. 150, 125–130 (1999).
    [CrossRef]
  6. D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
    [CrossRef]
  7. C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
    [CrossRef]
  8. S. Gómez, K. Hale, J. Burrows, B. Griffiths, “Measurements of surface defects on optical components,” Meas. Sci. Technol. 9, 607–616 (1998).
    [CrossRef]
  9. K. I. Jolic, C. R. Nagarajah, W. Thompson, “Non-contact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
    [CrossRef]
  10. L. M. Sanchez-Brea, P. Siegmann, E. Bernabeu, F. Pérez-Quintian, M. A. Rebollo, C. A. Raffo, “Medición de la Rugosidad y localización de fallas en hilos metálicos por métodos ópticos,” presented at the 83rd Reunión Nacional de Física, La Plata, Argentina, 21–25 September 1998.
  11. F. Perez-Quintian, M. A. Rebollo, N. G. Gaggioli, C. A. Raffo, “Optical methods for on line surface wire testing,” presented at the Seventh European Conference on Nondestructive Testing, Copenhagen, Denmark, 26–29 May 1998.
  12. S. A. Stefani, C. R. Nagarajah, R. Willgoss, “A surface inspection technique for continuously extruded cylindrical products,” Meas. Sci. Technol. 10, N21–N25 (1999).
    [CrossRef]
  13. T. K. Millard, “Computer simulation of defect detection,” Wire Ind. 58, 141–145 (1991).
  14. C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Laser scattering from the surface of thin wires at oblique illumination,” in Optics and Optoelectronics Theory, Devices and Applications, O. Nijhawan, A. K. Gupta, A. K. Musla, K. Singh, eds. (Narosa, House, New Delhi, 1999), pp. 298–301.
  15. C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Localization of surface roughness of thin wires using laser scattering,” presented at the Fourteenth World Conference on Nondestructive Testing, New Delhi, 8–13 December 1996.
  16. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962).
    [CrossRef] [PubMed]
  17. H. Hönl, A. W. Maue, K. Westpfahl, “cap. B-II, Beugung un konvexen Körpern ohne Kanten,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV, p. 1.

1999 (3)

I. Serroukh, E. Bernabeu, L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 34, 1319–1325 (1999).

L. M. Sanchez-Brea, J. A. Gomez-Pedrero, E. Bernabeu, “Measurement of surface defects on thin steel wires by atomic force microscopy,” Appl. Surf. Sci. 150, 125–130 (1999).
[CrossRef]

S. A. Stefani, C. R. Nagarajah, R. Willgoss, “A surface inspection technique for continuously extruded cylindrical products,” Meas. Sci. Technol. 10, N21–N25 (1999).
[CrossRef]

1998 (2)

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

S. Gómez, K. Hale, J. Burrows, B. Griffiths, “Measurements of surface defects on optical components,” Meas. Sci. Technol. 9, 607–616 (1998).
[CrossRef]

1997 (1)

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

1994 (1)

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Non-contact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

1991 (2)

T. K. Millard, “Computer simulation of defect detection,” Wire Ind. 58, 141–145 (1991).

T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24(12), 61–69 (1991).

1989 (1)

J. F. Fardeau, “New laser sensor for wire diameter measurement,” Wire J. Intern. 22(1), 42–51 (1989).

1962 (1)

Alén, J. M.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Ananthalakshmi, A. V.

C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Laser scattering from the surface of thin wires at oblique illumination,” in Optics and Optoelectronics Theory, Devices and Applications, O. Nijhawan, A. K. Gupta, A. K. Musla, K. Singh, eds. (Narosa, House, New Delhi, 1999), pp. 298–301.

C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Localization of surface roughness of thin wires using laser scattering,” presented at the Fourteenth World Conference on Nondestructive Testing, New Delhi, 8–13 December 1996.

Babu Rao, C.

C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Localization of surface roughness of thin wires using laser scattering,” presented at the Fourteenth World Conference on Nondestructive Testing, New Delhi, 8–13 December 1996.

C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Laser scattering from the surface of thin wires at oblique illumination,” in Optics and Optoelectronics Theory, Devices and Applications, O. Nijhawan, A. K. Gupta, A. K. Musla, K. Singh, eds. (Narosa, House, New Delhi, 1999), pp. 298–301.

Bernabeu, E.

I. Serroukh, E. Bernabeu, L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 34, 1319–1325 (1999).

L. M. Sanchez-Brea, J. A. Gomez-Pedrero, E. Bernabeu, “Measurement of surface defects on thin steel wires by atomic force microscopy,” Appl. Surf. Sci. 150, 125–130 (1999).
[CrossRef]

L. M. Sanchez-Brea, P. Siegmann, E. Bernabeu, F. Pérez-Quintian, M. A. Rebollo, C. A. Raffo, “Medición de la Rugosidad y localización de fallas en hilos metálicos por métodos ópticos,” presented at the 83rd Reunión Nacional de Física, La Plata, Argentina, 21–25 September 1998.

Blanco-García, J.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Bugarín, J.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Burrows, J.

S. Gómez, K. Hale, J. Burrows, B. Griffiths, “Measurements of surface defects on optical components,” Meas. Sci. Technol. 9, 607–616 (1998).
[CrossRef]

Dorrío, B. V.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Doval, A. F.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Fardeau, J. F.

J. F. Fardeau, “New laser sensor for wire diameter measurement,” Wire J. Intern. 22(1), 42–51 (1989).

Fernández, A.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Fernández, J. L.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Gaggioli, N. G.

F. Perez-Quintian, M. A. Rebollo, N. G. Gaggioli, C. A. Raffo, “Optical methods for on line surface wire testing,” presented at the Seventh European Conference on Nondestructive Testing, Copenhagen, Denmark, 26–29 May 1998.

Gómez, S.

S. Gómez, K. Hale, J. Burrows, B. Griffiths, “Measurements of surface defects on optical components,” Meas. Sci. Technol. 9, 607–616 (1998).
[CrossRef]

Gomez-Pedrero, J. A.

L. M. Sanchez-Brea, J. A. Gomez-Pedrero, E. Bernabeu, “Measurement of surface defects on thin steel wires by atomic force microscopy,” Appl. Surf. Sci. 150, 125–130 (1999).
[CrossRef]

Griffiths, B.

S. Gómez, K. Hale, J. Burrows, B. Griffiths, “Measurements of surface defects on optical components,” Meas. Sci. Technol. 9, 607–616 (1998).
[CrossRef]

Hale, K.

S. Gómez, K. Hale, J. Burrows, B. Griffiths, “Measurements of surface defects on optical components,” Meas. Sci. Technol. 9, 607–616 (1998).
[CrossRef]

Herchenreder, T. A.

T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24(12), 61–69 (1991).

Hönl, H.

H. Hönl, A. W. Maue, K. Westpfahl, “cap. B-II, Beugung un konvexen Körpern ohne Kanten,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV, p. 1.

Jolic, K. I.

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Non-contact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

Keller, J. B.

Kesavamoorthy, R.

C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Localization of surface roughness of thin wires using laser scattering,” presented at the Fourteenth World Conference on Nondestructive Testing, New Delhi, 8–13 December 1996.

C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Laser scattering from the surface of thin wires at oblique illumination,” in Optics and Optoelectronics Theory, Devices and Applications, O. Nijhawan, A. K. Gupta, A. K. Musla, K. Singh, eds. (Narosa, House, New Delhi, 1999), pp. 298–301.

López, C.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Maue, A. W.

H. Hönl, A. W. Maue, K. Westpfahl, “cap. B-II, Beugung un konvexen Körpern ohne Kanten,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV, p. 1.

Millard, T. K.

T. K. Millard, “Computer simulation of defect detection,” Wire Ind. 58, 141–145 (1991).

T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24(12), 61–69 (1991).

Nagarajah, C. R.

S. A. Stefani, C. R. Nagarajah, R. Willgoss, “A surface inspection technique for continuously extruded cylindrical products,” Meas. Sci. Technol. 10, N21–N25 (1999).
[CrossRef]

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Non-contact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

Pérez-Amor, M.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Perez-Quintian, F.

F. Perez-Quintian, M. A. Rebollo, N. G. Gaggioli, C. A. Raffo, “Optical methods for on line surface wire testing,” presented at the Seventh European Conference on Nondestructive Testing, Copenhagen, Denmark, 26–29 May 1998.

Pérez-Quintian, F.

L. M. Sanchez-Brea, P. Siegmann, E. Bernabeu, F. Pérez-Quintian, M. A. Rebollo, C. A. Raffo, “Medición de la Rugosidad y localización de fallas en hilos metálicos por métodos ópticos,” presented at the 83rd Reunión Nacional de Física, La Plata, Argentina, 21–25 September 1998.

Raffo, C. A.

L. M. Sanchez-Brea, P. Siegmann, E. Bernabeu, F. Pérez-Quintian, M. A. Rebollo, C. A. Raffo, “Medición de la Rugosidad y localización de fallas en hilos metálicos por métodos ópticos,” presented at the 83rd Reunión Nacional de Física, La Plata, Argentina, 21–25 September 1998.

F. Perez-Quintian, M. A. Rebollo, N. G. Gaggioli, C. A. Raffo, “Optical methods for on line surface wire testing,” presented at the Seventh European Conference on Nondestructive Testing, Copenhagen, Denmark, 26–29 May 1998.

Rebollo, M. A.

F. Perez-Quintian, M. A. Rebollo, N. G. Gaggioli, C. A. Raffo, “Optical methods for on line surface wire testing,” presented at the Seventh European Conference on Nondestructive Testing, Copenhagen, Denmark, 26–29 May 1998.

L. M. Sanchez-Brea, P. Siegmann, E. Bernabeu, F. Pérez-Quintian, M. A. Rebollo, C. A. Raffo, “Medición de la Rugosidad y localización de fallas en hilos metálicos por métodos ópticos,” presented at the 83rd Reunión Nacional de Física, La Plata, Argentina, 21–25 September 1998.

Rowe, G. W.

G. W. Rowe, An Introduction to the Principles of Metalworking (Edward Arnold, London, 1965).

Sanchez-Brea, L. M.

I. Serroukh, E. Bernabeu, L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 34, 1319–1325 (1999).

L. M. Sanchez-Brea, J. A. Gomez-Pedrero, E. Bernabeu, “Measurement of surface defects on thin steel wires by atomic force microscopy,” Appl. Surf. Sci. 150, 125–130 (1999).
[CrossRef]

L. M. Sanchez-Brea, P. Siegmann, E. Bernabeu, F. Pérez-Quintian, M. A. Rebollo, C. A. Raffo, “Medición de la Rugosidad y localización de fallas en hilos metálicos por métodos ópticos,” presented at the 83rd Reunión Nacional de Física, La Plata, Argentina, 21–25 September 1998.

Serroukh, I.

I. Serroukh, E. Bernabeu, L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 34, 1319–1325 (1999).

Siegmann, P.

L. M. Sanchez-Brea, P. Siegmann, E. Bernabeu, F. Pérez-Quintian, M. A. Rebollo, C. A. Raffo, “Medición de la Rugosidad y localización de fallas en hilos metálicos por métodos ópticos,” presented at the 83rd Reunión Nacional de Física, La Plata, Argentina, 21–25 September 1998.

Stefani, S. A.

S. A. Stefani, C. R. Nagarajah, R. Willgoss, “A surface inspection technique for continuously extruded cylindrical products,” Meas. Sci. Technol. 10, N21–N25 (1999).
[CrossRef]

Tejedor, B. G.

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

Thompson, W.

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Non-contact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

Westpfahl, K.

H. Hönl, A. W. Maue, K. Westpfahl, “cap. B-II, Beugung un konvexen Körpern ohne Kanten,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV, p. 1.

Whitehouse, D. J.

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

Willgoss, R.

S. A. Stefani, C. R. Nagarajah, R. Willgoss, “A surface inspection technique for continuously extruded cylindrical products,” Meas. Sci. Technol. 10, N21–N25 (1999).
[CrossRef]

Appl. Surf. Sci. (1)

L. M. Sanchez-Brea, J. A. Gomez-Pedrero, E. Bernabeu, “Measurement of surface defects on thin steel wires by atomic force microscopy,” Appl. Surf. Sci. 150, 125–130 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (5)

S. A. Stefani, C. R. Nagarajah, R. Willgoss, “A surface inspection technique for continuously extruded cylindrical products,” Meas. Sci. Technol. 10, N21–N25 (1999).
[CrossRef]

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

C. López, A. F. Doval, B. V. Dorrío, J. Blanco-García, J. Bugarín, J. M. Alén, A. Fernández, J. L. Fernández, M. Pérez-Amor, B. G. Tejedor, “Fibre optic reflectometric technique for the automatic detection and measurement of surface cracks,” Meas. Sci. Technol. 9, 1413–1431 (1998).
[CrossRef]

S. Gómez, K. Hale, J. Burrows, B. Griffiths, “Measurements of surface defects on optical components,” Meas. Sci. Technol. 9, 607–616 (1998).
[CrossRef]

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Non-contact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

Opt. Eng. (1)

I. Serroukh, E. Bernabeu, L. M. Sanchez-Brea, “A geometrical model for wire optical diffraction selected by experimental statistical analysis,” Opt. Eng. 34, 1319–1325 (1999).

Wire Ind. (1)

T. K. Millard, “Computer simulation of defect detection,” Wire Ind. 58, 141–145 (1991).

Wire J. Intern. (2)

T. K. Millard, T. A. Herchenreder, “Automatic diameter measurement: state of the art,” Wire J. Intern. 24(12), 61–69 (1991).

J. F. Fardeau, “New laser sensor for wire diameter measurement,” Wire J. Intern. 22(1), 42–51 (1989).

Other (6)

G. W. Rowe, An Introduction to the Principles of Metalworking (Edward Arnold, London, 1965).

L. M. Sanchez-Brea, P. Siegmann, E. Bernabeu, F. Pérez-Quintian, M. A. Rebollo, C. A. Raffo, “Medición de la Rugosidad y localización de fallas en hilos metálicos por métodos ópticos,” presented at the 83rd Reunión Nacional de Física, La Plata, Argentina, 21–25 September 1998.

F. Perez-Quintian, M. A. Rebollo, N. G. Gaggioli, C. A. Raffo, “Optical methods for on line surface wire testing,” presented at the Seventh European Conference on Nondestructive Testing, Copenhagen, Denmark, 26–29 May 1998.

C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Laser scattering from the surface of thin wires at oblique illumination,” in Optics and Optoelectronics Theory, Devices and Applications, O. Nijhawan, A. K. Gupta, A. K. Musla, K. Singh, eds. (Narosa, House, New Delhi, 1999), pp. 298–301.

C. Babu Rao, A. V. Ananthalakshmi, R. Kesavamoorthy, “Localization of surface roughness of thin wires using laser scattering,” presented at the Fourteenth World Conference on Nondestructive Testing, New Delhi, 8–13 December 1996.

H. Hönl, A. W. Maue, K. Westpfahl, “cap. B-II, Beugung un konvexen Körpern ohne Kanten,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV, p. 1.

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Figures (9)

Fig. 1
Fig. 1

Diffraction and geometrical contributions to the scattering pattern according to the geometrical theory of diffraction for a perfect, smooth cylindrical wire of diameter 300 µm: solid curve, diffraction contribution; dashed curve, geometrical contribution. The wavelength is λ = 675 nm, and the incidence is normal to the wire axis. ϕ2 is the angle with respect to the maximum of the geometrical contribution.

Fig. 2
Fig. 2

(a) Transverse representation of the wire, showing the reflection of rays. (b) Sketch of the cone generated by the wire when the wire is illuminated with a laser beam at oblique incidence.

Fig. 3
Fig. 3

(a) Image of the ring detected by the CCD camera for a steel wire (diameter, 300 ± 1 µm) with scratches.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup.

Fig. 5
Fig. 5

(a) Reconstruction, by means of geometrical transformation, of the wire shown in Fig. 3. This reconstruction is an intensity image of the wire. (b) Defects detected by I D 1, z) when I T = -10 gl.

Fig. 6
Fig. 6

SEM image of the steel wire with defects of Fig. 3. We can see three scratches at the center of the image and another scratch at the right in the image.

Fig. 7
Fig. 7

AFM image of a steel wire (diameter, 399 ± 1 µm) with a high-quality surface. As we can observe, no defects are detected by the AFM. The resolution of the AFM is ±6 nm in height.

Fig. 8
Fig. 8

(a) Image of the ring detected by the CCD camera for the steel wire of Fig. 7. (b) Image of the geometrical reconstruction. (c) Defects detected by I D 1, z) when I T = -10 gl.

Fig. 9
Fig. 9

Γ(z) parameter (solid curve) for the wire with defects of Fig. 3 and (dashed curve) for the high-quality surface wire of Fig. 7.

Tables (1)

Tables Icon

Table 1 Width and Distance between Scratches (in micrometers) for the Wire with Surface Defects shown in Fig. 5a

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

k1=2π/λcos θ1zˆ-sin θ1xˆ,
nˆ=cos ϕ1xˆ+sin ϕ1yˆ,
k1=k1+k1,
k2=-k1,
k2=k1.
k2ϕ1, θ1=kcos θ1zˆ+sin θ1 cos 2ϕ1xˆ+sin θ1 sin 2ϕ1yˆ.
θ2=θ1, ϕ2=2ϕ1,
ϕ2=tan-1a0 sin ϕ1+ρ sin 2ϕ1a0 cos ϕ1+ρ cos 2ϕ1,
z=ρtan θ2.
tan θ1=hL-z,
z=ρLρ+h.
Itheorθ2, ϕ2=I0δθ2-θ1|cosϕ2/2|,
IDϕ1, z=Iϕ1, z-IFϕ1, z.
IDϕ1, z<IT.
Γz=1πΩ Dz, ϕ1dϕ1,
Dϕ1, z=1IDϕ1, z<IT0IDϕ1, z>IT
Ix, y=IL exp-x/Lx2-y/Ly2,

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