Abstract

Line-field Fourier-domain interferometry that is capable of a fast three-dimensional (3-D) shape measurement is proposed. This system is constructed from a combination of a conventional Fourier-domain interferometer and a one-dimensional imaging system. This system directs a line-shaped focus onto a specimen, and a two-dimensional shape can be calculated from a single-shot image of the CCD camera without any mechanical scan. An aspherical mirror and a Japanese coin are presented as a 3-D shape measurement example.

© 2005 Optical Society of America

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References

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Appl. Opt.

J. Biomed. Opt.

G. Häusler and M. W. Lindner, �??Coherence radar and spectral radar�??new tools for dermatological diagnosis,�?? J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and F. Fercher, �??In vivo human retinal imaging by Fourier domain optical coherence tomography,�?? J. Biomed. Opt. 7, 457-463 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

Opt. Commun.

Y. Yasuno, M. Nakama, Y. Sutoh, M. Mori, and T. Yatagai, �??Optical coherence tomography by spectral interferometric joint transform correlator,�?? Opt. Commun. 186, 51-56 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Other

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1980).

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Figures (5)

Fig. 1.
Fig. 1.

Optical scheme of the line-field Fourier-domain interferometry. LS, light source. L1, L2, L3 denote spherical lenses of focal length 100, 100, 150 mm, respectively. CL, cylindrical lens of focal length 100 mm. S, specimen. M, mirror. G, grating with 1200 lp/mm

Fig. 2.
Fig. 2.

Perspective of optical setup on (a) the x-z plane and (b) the y-z plane. CL, cylindrical lens; L1 and L3, lenses; S, specimen; G, grating.

Fig. 3.
Fig. 3.

3-D shapes of an aspherical mirror. Contour lines are at each 10-µm interval.

Fig. 4.
Fig. 4.

Photograph of a Japanese 10-yen coin. The area of the yellow rectangle is measured using our system.

Fig. 5.
Fig. 5.

3-D and 2-D shapes of a Japanese 10-yen coin.

Equations (6)

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I ̂ ( ω ) = E ̂ r ( ω ) 2 + E ̂ p ( ω ) 2 + E ̂ r * ( ω ) E ̂ p ( ω ) + E ̂ r ( ω ) E ̂ p * ( ω ) ,
I ( t ) = Γ [ E r ( t ) ] + Γ [ E p ( t ) ] + Γ [ E r * ( t ) , E p ( t ) ] + Γ [ E r ( t ) , E p * ( t ) ] ,
I ( t ) = Γ [ E r ( t ) ] + Γ [ E r ( t 2 h c ) ]
+ Γ [ E r * ( t ) , E r ( t 2 h c ) ] + Γ [ E r * ( t ) , E r ( t 2 h c ) ]
= Γ [ E r ( t ) ] + Γ [ E r ( t 2 h c ) ]
+ Γ [ E r * ( t ) ] δ ( t 2 h c ) + Γ [ E r * ( t ) ] δ ( t + 2 h c ) ,

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