Abstract

In this paper, a large-depth-of-field projected fringe profilometry using a supercontinuum light source generated by launching femto second laser pulses into a highly nonlinear photonic crystal fiber is presented. Since the supercontinuum light has high spatial coherence and a broad spectral range (from UV to near infrared), a high power (hundreds of mW) point white light source can be employed to generate modulated fringe patterns, which offers following major advantages: (1) large-depth-of-field, (2) ease of calibration, and (3) little speckle noise (a major problem for the laser system). Thus, a highly accurate, large-depth-of-field projected fringe profilometer can be realized. Both the theoretical description and experimental demonstration are provided.

© 2005 Optical Society of America

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  1. K. A. Haines and B. P. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
    [Crossref]
  2. M. Takeda and K. Muta, “Fourier transform profilometry for the automatic measurement of 3-D object shaped,” Appl. Opt. 24, 3977–3982 (1983).
    [Crossref]
  3. K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 350–393 (1988).
  4. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [Crossref] [PubMed]
  5. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Appl. Opt. 24, 185–188 (1985).
    [Crossref] [PubMed]
  6. V. Y. Su, G von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
    [Crossref]
  7. G. W. Lu, S. D. Wu, N. Palmer, and H. Y. Liu, “Application of phase-shift optical triangulation to precision gear gauging,” Proc. SPIE 3520, 52–63 (1998).
    [Crossref]
  8. H. Y. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Comm. 216, 65–80 (2003).
    [Crossref]
  9. W. H. Su, H. Y. Liu, K. Reichard, S. Yin, Francis, and T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
    [Crossref]
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    [Crossref]
  11. Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 32, 3598–3600 (1993).
    [Crossref] [PubMed]
  12. W. H. Su, K. Reichard, H. Y. Liu, and S. Yin, “Integration of segmented 3D profiles measured by calibration-based phase-shifting projected fringe profilometry (PSPFP),” Opt. Mem. Neural Net.12, (2003).
  13. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [Crossref] [PubMed]
  14. M. Seefeldt, A. Heuer, and R. Menzel, “Compact white-light source with an average output power of 2.4W and 900 nm spectral bandwidth,” Opt. Commun. 216, 199–202 (2003).
    [Crossref]
  15. T. Schreiber, J. Limpert, H. Zellmer, A. Tűnnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
    [Crossref]
  16. K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express. 12, 2096–2101 (2004).
    [Crossref] [PubMed]
  17. K. R. Spring and M. W. Dividson, “Depth of field and Depth of focus,” http://www.microscopyu.com/articles/formulas/formulasfielddepth.html.
  18. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Seventh edition, 1999), Chap. 4. and Chap. 8.8.2.
  19. J. B. Pawley etc., Handbook of biological confocal microscopy (New York: Plenum Press, 1990), Chap. 1.
  20. Robert E. Wheeler, “Notes on view camera geometry,” http://www.bobwheeler.com/photo/ViewCam.pdf, 2003.

2004 (1)

K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express. 12, 2096–2101 (2004).
[Crossref] [PubMed]

2003 (4)

M. Seefeldt, A. Heuer, and R. Menzel, “Compact white-light source with an average output power of 2.4W and 900 nm spectral bandwidth,” Opt. Commun. 216, 199–202 (2003).
[Crossref]

T. Schreiber, J. Limpert, H. Zellmer, A. Tűnnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[Crossref]

H. Y. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Comm. 216, 65–80 (2003).
[Crossref]

W. H. Su, H. Y. Liu, K. Reichard, S. Yin, Francis, and T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[Crossref]

1998 (1)

G. W. Lu, S. D. Wu, N. Palmer, and H. Y. Liu, “Application of phase-shift optical triangulation to precision gear gauging,” Proc. SPIE 3520, 52–63 (1998).
[Crossref]

1997 (1)

1993 (2)

Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 32, 3598–3600 (1993).
[Crossref] [PubMed]

V. Y. Su, G von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

1992 (1)

1988 (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 350–393 (1988).

1985 (1)

1984 (1)

1983 (1)

1965 (1)

K. A. Haines and B. P. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[Crossref]

Birks, T. A.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Seventh edition, 1999), Chap. 4. and Chap. 8.8.2.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 350–393 (1988).

Dividson, M. W.

K. R. Spring and M. W. Dividson, “Depth of field and Depth of focus,” http://www.microscopyu.com/articles/formulas/formulasfielddepth.html.

Francis,

W. H. Su, H. Y. Liu, K. Reichard, S. Yin, Francis, and T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[Crossref]

Haines, K. A.

K. A. Haines and B. P. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[Crossref]

Halioua, M.

Hansen, K. P.

T. Schreiber, J. Limpert, H. Zellmer, A. Tűnnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[Crossref]

Heuer, A.

M. Seefeldt, A. Heuer, and R. Menzel, “Compact white-light source with an average output power of 2.4W and 900 nm spectral bandwidth,” Opt. Commun. 216, 199–202 (2003).
[Crossref]

Hildebrand, B. P.

K. A. Haines and B. P. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[Crossref]

Knight, J. C.

Larkin, K. G.

Li, P.

K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express. 12, 2096–2101 (2004).
[Crossref] [PubMed]

Limpert, J.

T. Schreiber, J. Limpert, H. Zellmer, A. Tűnnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[Crossref]

Liu, H. C.

Liu, H. Y.

H. Y. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Comm. 216, 65–80 (2003).
[Crossref]

W. H. Su, H. Y. Liu, K. Reichard, S. Yin, Francis, and T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[Crossref]

G. W. Lu, S. D. Wu, N. Palmer, and H. Y. Liu, “Application of phase-shift optical triangulation to precision gear gauging,” Proc. SPIE 3520, 52–63 (1998).
[Crossref]

W. H. Su, K. Reichard, H. Y. Liu, and S. Yin, “Integration of segmented 3D profiles measured by calibration-based phase-shifting projected fringe profilometry (PSPFP),” Opt. Mem. Neural Net.12, (2003).

Liu, Z.

K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express. 12, 2096–2101 (2004).
[Crossref] [PubMed]

Lu, G. W.

G. W. Lu, S. D. Wu, N. Palmer, and H. Y. Liu, “Application of phase-shift optical triangulation to precision gear gauging,” Proc. SPIE 3520, 52–63 (1998).
[Crossref]

Menzel, R.

M. Seefeldt, A. Heuer, and R. Menzel, “Compact white-light source with an average output power of 2.4W and 900 nm spectral bandwidth,” Opt. Commun. 216, 199–202 (2003).
[Crossref]

Muta, K.

Oreb, B. F.

Palmer, N.

G. W. Lu, S. D. Wu, N. Palmer, and H. Y. Liu, “Application of phase-shift optical triangulation to precision gear gauging,” Proc. SPIE 3520, 52–63 (1998).
[Crossref]

Pawley, J. B.

J. B. Pawley etc., Handbook of biological confocal microscopy (New York: Plenum Press, 1990), Chap. 1.

Reichard, K.

W. H. Su, H. Y. Liu, K. Reichard, S. Yin, Francis, and T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[Crossref]

H. Y. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Comm. 216, 65–80 (2003).
[Crossref]

W. H. Su, K. Reichard, H. Y. Liu, and S. Yin, “Integration of segmented 3D profiles measured by calibration-based phase-shifting projected fringe profilometry (PSPFP),” Opt. Mem. Neural Net.12, (2003).

Russell, P. St. J.

Schreiber, T.

T. Schreiber, J. Limpert, H. Zellmer, A. Tűnnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[Crossref]

Seefeldt, M.

M. Seefeldt, A. Heuer, and R. Menzel, “Compact white-light source with an average output power of 2.4W and 900 nm spectral bandwidth,” Opt. Commun. 216, 199–202 (2003).
[Crossref]

Shi, K.

K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express. 12, 2096–2101 (2004).
[Crossref] [PubMed]

Spring, K. R.

K. R. Spring and M. W. Dividson, “Depth of field and Depth of focus,” http://www.microscopyu.com/articles/formulas/formulasfielddepth.html.

Srinivasan, V.

Su, V. Y.

V. Y. Su, G von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

Su, W. H.

H. Y. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Comm. 216, 65–80 (2003).
[Crossref]

W. H. Su, H. Y. Liu, K. Reichard, S. Yin, Francis, and T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[Crossref]

W. H. Su, K. Reichard, H. Y. Liu, and S. Yin, “Integration of segmented 3D profiles measured by calibration-based phase-shifting projected fringe profilometry (PSPFP),” Opt. Mem. Neural Net.12, (2003).

Surrel, Y.

Takeda, M.

Tunnermann, A.

T. Schreiber, J. Limpert, H. Zellmer, A. Tűnnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[Crossref]

von Bally, G

V. Y. Su, G von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

Vukicevic, D.

V. Y. Su, G von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

Wheeler, Robert E.

Robert E. Wheeler, “Notes on view camera geometry,” http://www.bobwheeler.com/photo/ViewCam.pdf, 2003.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Seventh edition, 1999), Chap. 4. and Chap. 8.8.2.

Wu, S. D.

G. W. Lu, S. D. Wu, N. Palmer, and H. Y. Liu, “Application of phase-shift optical triangulation to precision gear gauging,” Proc. SPIE 3520, 52–63 (1998).
[Crossref]

Yin, S.

K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express. 12, 2096–2101 (2004).
[Crossref] [PubMed]

W. H. Su, H. Y. Liu, K. Reichard, S. Yin, Francis, and T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[Crossref]

H. Y. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Comm. 216, 65–80 (2003).
[Crossref]

W. H. Su, K. Reichard, H. Y. Liu, and S. Yin, “Integration of segmented 3D profiles measured by calibration-based phase-shifting projected fringe profilometry (PSPFP),” Opt. Mem. Neural Net.12, (2003).

Yu, T. S.

W. H. Su, H. Y. Liu, K. Reichard, S. Yin, Francis, and T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[Crossref]

Zellmer, H.

T. Schreiber, J. Limpert, H. Zellmer, A. Tűnnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[Crossref]

Appl. Opt. (4)

J. Opt. Soc. Am. A (1)

Opt. Comm. (1)

H. Y. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Comm. 216, 65–80 (2003).
[Crossref]

Opt. Commun. (3)

V. Y. Su, G von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

M. Seefeldt, A. Heuer, and R. Menzel, “Compact white-light source with an average output power of 2.4W and 900 nm spectral bandwidth,” Opt. Commun. 216, 199–202 (2003).
[Crossref]

T. Schreiber, J. Limpert, H. Zellmer, A. Tűnnermann, and K. P. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71–78 (2003).
[Crossref]

Opt. Eng. (1)

W. H. Su, H. Y. Liu, K. Reichard, S. Yin, Francis, and T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[Crossref]

Opt. Express. (1)

K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express. 12, 2096–2101 (2004).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Lett. (1)

K. A. Haines and B. P. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[Crossref]

Proc. SPIE (1)

G. W. Lu, S. D. Wu, N. Palmer, and H. Y. Liu, “Application of phase-shift optical triangulation to precision gear gauging,” Proc. SPIE 3520, 52–63 (1998).
[Crossref]

Prog. Opt. (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 350–393 (1988).

Other (5)

W. H. Su, K. Reichard, H. Y. Liu, and S. Yin, “Integration of segmented 3D profiles measured by calibration-based phase-shifting projected fringe profilometry (PSPFP),” Opt. Mem. Neural Net.12, (2003).

K. R. Spring and M. W. Dividson, “Depth of field and Depth of focus,” http://www.microscopyu.com/articles/formulas/formulasfielddepth.html.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Seventh edition, 1999), Chap. 4. and Chap. 8.8.2.

J. B. Pawley etc., Handbook of biological confocal microscopy (New York: Plenum Press, 1990), Chap. 1.

Robert E. Wheeler, “Notes on view camera geometry,” http://www.bobwheeler.com/photo/ViewCam.pdf, 2003.

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Figures (6)

Fig. 1.
Fig. 1.

Geometrical illustration of depth of field.

Fig. 2.
Fig. 2.

Schematic diagram of a standard projection imaging system.

Fig. 3.
Fig. 3.

Appearance of projected fringes on a tested object using different types of illumination source: (a) a laser source; (b) an extended white light source; and (c) a point supercontinuum light source.

Fig. 4.
Fig. 4.

Schematic diagram of a phase-shifting projected fringe profilometric system using the supercontinuum light illumination

Fig. 5.
Fig. 5.

Fringes projected on a fan blade via supercontinuum light illumination.

Fig. 6.
Fig. 6.

Measured 3D surface profile of a fan blade

Equations (17)

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DOF tot = DOF w + DOF g
DOF w = k 1 λ N A 2
1 u + 1 v = 1 f
L n = u f 2 f 2 + ( u f ) F c
L f = u f 2 f 2 ( u f ) F c , for f 2 ( u f ) F c > 0
L f = , for f 2 ( u f ) F c 0
L DOF = L f L n = 2 u f 2 ( u f ) F c f 4 ( u f ) 2 F 2 c 2 , for f 2 ( u f ) F c > 0
L DOF = , for f 2 ( u f ) F c 0
L DOF = 2 F c m + 1 m 2 1 χ , for χ < 1
L DOF = , for χ 1
where χ = ( c m d ) 2
I 0 ( c , r ) = a ( c , r ) + b ( c , r ) cos [ 2 π c d + ϕ ( c , r ) ] ,
I 1 ( c , r ) = a ( c , r ) + b ( c , r ) cos [ 2 π c d + ϕ ( c , r ) + π 2 ] ,
I 2 ( c , r ) = a ( c , r ) + b ( c , r ) cos [ 2 π c d + ϕ ( c , r ) + π ] ,
I 3 ( c , r ) = a ( c , r ) + b ( c , r ) cos [ 2 π c d + ϕ ( c , r ) + 3 π 2 ] ,
ϕ ( c , r ) = arctan [ I 3 ( c , r ) I 1 ( c , r ) I 0 ( c , r ) I 2 ( c , r ) ] 2 π c d .
H A C = A C tan θ 0 = ( φ C φ A ) d 0 tan θ 0 2 π

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