Abstract

When measuring a three-dimensional shape with triangulation and projected interference fringes it is of interest to reduce speckle contrast without destroying the coherence of the projected light. A moving aperture is used to suppress the speckles and thereby reduce the phase error in the fringe image. It is shown that the phase error depends linearly on the ratio between the speckle contrast and the modulation of the fringes. In this investigation the spatial carrier method was used to extract the phase, where the phase error also depends on filtering the Fourier spectrum. An analytical expression for the phase error is derived. Both the speckle reduction and the theoretical expressions for the phase error are verified by simulations and experiments. It was concluded that a movement of the aperture by three aperture diameters during exposure of the image reduces the speckle contrast and hence the phase error by 60%. In the experiments, a phase error of 0.2 rad was obtained.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008

2007

2005

2004

2001

1999

1997

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610-615 (1997).
[CrossRef]

1995

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479-483(1995).
[CrossRef]

1994

1990

1985

1984

1983

1982

1975

T. S. McKechnie, “Reduction of speckle by a moving aperture: second order statistics,” Opt. Commun. 13, 29-34 (1975).
[CrossRef]

1967

S. H. Rowe and W. T. Welford, “Surface topography of non-optical surfaces by projected interference fringes,” Nature 216, 786-787 (1967).
[CrossRef]

Brophy, C. P.

Bryanston-Cross, P. J.

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479-483(1995).
[CrossRef]

Chen, M.

Da, F.

Dorsch, R. G.

Gai, S.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975).
[CrossRef]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, 1st ed. (Ben Roberts & Company, 2007).

Guo, H.

Halioua, M.

Hausler, G.

He, H.

Herrmann, J. M.

Huan, H.

Huntley, J. M.

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610-615 (1997).
[CrossRef]

Ina, H.

Kinell, L.

Kobayashi, S.

Liu, H.

Liu, H. C.

Lu, G.

McKechnie, T. S.

T. S. McKechnie, “Reduction of speckle by a moving aperture: second order statistics,” Opt. Commun. 13, 29-34 (1975).
[CrossRef]

T. S. McKechnie, “Speckle reduction,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975).
[CrossRef]

Mutoh, K.

Quan, C.

C. J. Tay, M. Thakur, and C. Quan, “Grating projection system for surface contour measurement,” Appl. Opt. 44, 1393-1400(2005).
[CrossRef] [PubMed]

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479-483(1995).
[CrossRef]

Rowe, S. H.

S. H. Rowe and W. T. Welford, “Surface topography of non-optical surfaces by projected interference fringes,” Nature 216, 786-787 (1967).
[CrossRef]

Saldner, H. O.

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610-615 (1997).
[CrossRef]

Sasaki, O.

Shang, H. M.

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479-483(1995).
[CrossRef]

Sjödahl, M.

Srinivasan, V.

Su, X.

Suzuki, T.

Takeda, M.

Tay, C. J.

C. J. Tay, M. Thakur, and C. Quan, “Grating projection system for surface contour measurement,” Appl. Opt. 44, 1393-1400(2005).
[CrossRef] [PubMed]

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479-483(1995).
[CrossRef]

Thakur, M.

Welford, W. T.

S. H. Rowe and W. T. Welford, “Surface topography of non-optical surfaces by projected interference fringes,” Nature 216, 786-787 (1967).
[CrossRef]

Wu, S.

Xian, T.

Yin, S.

Yu, F. T. S.

Appl. Opt.

L. Kinell and M. Sjödahl, “Robustness of reduced temporal phase unwrapping in the measurement of shape,” Appl. Opt. 40, 2297-2303 (2001).
[CrossRef]

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977-3982 (1983).
[CrossRef] [PubMed]

V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Appl. Opt. 24, 185-188 (1985).
[CrossRef] [PubMed]

T. Xian and X. Su, “Area modulation grating for sinusoidal structure illumination on phase-measuring profilometry,” Appl. Opt. 40, 1201-1206 (2001).
[CrossRef]

C. J. Tay, M. Thakur, and C. Quan, “Grating projection system for surface contour measurement,” Appl. Opt. 44, 1393-1400(2005).
[CrossRef] [PubMed]

H. Guo, H. He, and M. Chen, “Gamma correction for digital fringe projection profilometry,” Appl. Opt. 43, 2906-2914(2004).
[CrossRef] [PubMed]

F. Da and S. Gai, “Flexible three-dimensional measurement technique based on a digital light processing projector,” Appl. Opt. 47, 377-385 (2008).
[CrossRef] [PubMed]

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]

H. Huan, O. Sasaki, and T. Suzuki, “Multiperiod fringe projection interferometry using a backpropagation method for surface profile measurement,” Appl. Opt. 46, 7268-7274(2007).
[CrossRef] [PubMed]

R. G. Dorsch, G. Hausler, and J. M. Herrmann, “Laser triangulation: fundamental uncertainty in distance measurement,” Appl. Opt. 33, 1306-1314 (1994).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature

S. H. Rowe and W. T. Welford, “Surface topography of non-optical surfaces by projected interference fringes,” Nature 216, 786-787 (1967).
[CrossRef]

Opt. Commun.

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479-483(1995).
[CrossRef]

T. S. McKechnie, “Reduction of speckle by a moving aperture: second order statistics,” Opt. Commun. 13, 29-34 (1975).
[CrossRef]

Opt. Eng.

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610-615 (1997).
[CrossRef]

Other

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975).
[CrossRef]

T. S. McKechnie, “Speckle reduction,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975).
[CrossRef]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, 1st ed. (Ben Roberts & Company, 2007).

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Figures (7)

Fig. 1
Fig. 1

Simplified measurement model. The measurement object is situated in the object space. In the aperture plane one can see the moving aperture used for speckle reduction and an imaging lens.

Fig. 2
Fig. 2

Fourier plane representation of an image with fringes and speckles: M, fringe modulation; C, speckle contrast; s max , maximum spatial frequency; W, frequency window; f x , spatial frequency; f 0 , carrier frequency; unit irradiance is assumed.

Fig. 3
Fig. 3

(a) Experimental setup: λ / 2 , half-wave plate; PBS, polarized beam splitter; O, objective; μ, μ hole; CL, collimating lens; BS, beam splitter; M 1 M 3 , mirrors; ML, magnifying lens; P, polarizer; AP, aperture plane; IL, imaging lens. (b) The aperture plane of the imaging system: A, the aperture plate that can be rotated; B, the rectangular aperture; C, the circular apertures, the actual apertures that the light passes; D, the photosensor that registers each new revolution.

Fig. 4
Fig. 4

Contrast in the experimental and simulated images in comparison with the theoretical contrast for a moving aperture. Images were captured when the aperture had moved a total distance of 3, 7, 11, or 15 aperture diameters and when it had not moved at all.

Fig. 5
Fig. 5

Phase error for different given modulations: 0.4 (asterisks), 0.7 (squares), and 1 (circles). Markers on a dotted curve represent phase errors from the simulated images; markers on a solid curve represent the theoretically determined phase error. The theoretical values were calculated with the modulations that were determined from the images. Images were captured when the aperture had moved a total distance of 3, 7, 11, or 15 aperture diameters and when it had not moved at all.

Fig. 6
Fig. 6

Phase error in the experimental images (asterisks) in comparison with theoretically determined phase errors (circles). The theoretical values were calculated with the modulations that were determined from the images. Images were captured when the aperture had moved a total distance of 3, 7, 11, or 15 aperture diameters and when it had not moved at all.

Fig. 7
Fig. 7

(a), (b) Experimental fringe images; (c), (d) the corresponding phase maps. Since a tilted plane is subtracted from the phase maps they range between π and π radians. In (a) and (c) a stationary aperture was used; in (b) and (d) the aperture had moved a total distance of 11 aperture diameters.

Equations (7)

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

s ϕ = π 3 .
s ϕ = π C 3 ,
s ϕ = π C 3 M ,
s ϕ = π C M E w 3 E t .
C ( L ) = [ 2 L 0 L ( 1 l L ) | μ A ( l ) | 2 d l ] 1 / 2 ,
C I = I σ I ,
g ( x , y ) = 1 + M ( x , y ) · sin ( 2 π f 0 x ) ,

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