Abstract

Novel gradient focal point (GFP) methods by use of the gradient curvature cylindrical lens, the gradient thickness cylindrical lens and a tilted imaging sensor are proposed for the optical profiler. With the employed simple idea that the different divergence angle of an input beam to the lens generates the different focal position, the height information of one point can be obtained just in a single-shot by GFP approaches. The feasibility of the proposed system is demonstrated to be an alternative to optical profilers.

© 2012 OSA

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References

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2012 (1)

2011 (2)

R. Jang, C. S. Kang, J. A. Kim, J. W. Kim, J. E. Kim, and H. Y. Park, “High-speed measurement of three-dimensional surface profiles up to 10 μm using two-wavelength phase-shifting interferometry utilizing an injection locking technique,” Appl. Opt.50(11), 1541–1547 (2011).
[CrossRef] [PubMed]

J. A. Kim, C. S. Kang, J. Jin, C. Eom, R. Jang, and J. W. Kim, “Note: High speed optical profiler based on a phase-shifting technique using frequency-scanning lasers,” Rev. Sci. Instrum.82(8), 086111 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (1)

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum.80(7), 073706 (2009).
[CrossRef] [PubMed]

2007 (1)

2004 (1)

2003 (1)

2002 (1)

1998 (1)

B. Bowe and V. Toal, “White light interferometric surface profiler,” Opt. Eng.37(6), 1796–1799 (1998).
[CrossRef]

1994 (1)

Bowe, B.

B. Bowe and V. Toal, “White light interferometric surface profiler,” Opt. Eng.37(6), 1796–1799 (1998).
[CrossRef]

Charrière, F.

Chun, B. S.

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum.80(7), 073706 (2009).
[CrossRef] [PubMed]

Colomb, T.

Cuche, E.

Dakoff, A.

Dan, D.

Depeursinge, C.

Duan, T.

Emery, Y.

Eom, C.

J. A. Kim, C. S. Kang, J. Jin, C. Eom, R. Jang, and J. W. Kim, “Note: High speed optical profiler based on a phase-shifting technique using frequency-scanning lasers,” Rev. Sci. Instrum.82(8), 086111 (2011).
[CrossRef] [PubMed]

Gao, F.

Gao, P.

Gass, J.

Guo, R.

Gweon, D.

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum.80(7), 073706 (2009).
[CrossRef] [PubMed]

Hirabayashi, A.

Jang, R.

J. A. Kim, C. S. Kang, J. Jin, C. Eom, R. Jang, and J. W. Kim, “Note: High speed optical profiler based on a phase-shifting technique using frequency-scanning lasers,” Rev. Sci. Instrum.82(8), 086111 (2011).
[CrossRef] [PubMed]

R. Jang, C. S. Kang, J. A. Kim, J. W. Kim, J. E. Kim, and H. Y. Park, “High-speed measurement of three-dimensional surface profiles up to 10 μm using two-wavelength phase-shifting interferometry utilizing an injection locking technique,” Appl. Opt.50(11), 1541–1547 (2011).
[CrossRef] [PubMed]

Jiang, X.

Jin, J.

J. A. Kim, C. S. Kang, J. Jin, C. Eom, R. Jang, and J. W. Kim, “Note: High speed optical profiler based on a phase-shifting technique using frequency-scanning lasers,” Rev. Sci. Instrum.82(8), 086111 (2011).
[CrossRef] [PubMed]

Kang, C. S.

J. A. Kim, C. S. Kang, J. Jin, C. Eom, R. Jang, and J. W. Kim, “Note: High speed optical profiler based on a phase-shifting technique using frequency-scanning lasers,” Rev. Sci. Instrum.82(8), 086111 (2011).
[CrossRef] [PubMed]

R. Jang, C. S. Kang, J. A. Kim, J. W. Kim, J. E. Kim, and H. Y. Park, “High-speed measurement of three-dimensional surface profiles up to 10 μm using two-wavelength phase-shifting interferometry utilizing an injection locking technique,” Appl. Opt.50(11), 1541–1547 (2011).
[CrossRef] [PubMed]

Kim, J. A.

R. Jang, C. S. Kang, J. A. Kim, J. W. Kim, J. E. Kim, and H. Y. Park, “High-speed measurement of three-dimensional surface profiles up to 10 μm using two-wavelength phase-shifting interferometry utilizing an injection locking technique,” Appl. Opt.50(11), 1541–1547 (2011).
[CrossRef] [PubMed]

J. A. Kim, C. S. Kang, J. Jin, C. Eom, R. Jang, and J. W. Kim, “Note: High speed optical profiler based on a phase-shifting technique using frequency-scanning lasers,” Rev. Sci. Instrum.82(8), 086111 (2011).
[CrossRef] [PubMed]

Kim, J. E.

Kim, J. W.

R. Jang, C. S. Kang, J. A. Kim, J. W. Kim, J. E. Kim, and H. Y. Park, “High-speed measurement of three-dimensional surface profiles up to 10 μm using two-wavelength phase-shifting interferometry utilizing an injection locking technique,” Appl. Opt.50(11), 1541–1547 (2011).
[CrossRef] [PubMed]

J. A. Kim, C. S. Kang, J. Jin, C. Eom, R. Jang, and J. W. Kim, “Note: High speed optical profiler based on a phase-shifting technique using frequency-scanning lasers,” Rev. Sci. Instrum.82(8), 086111 (2011).
[CrossRef] [PubMed]

Kim, K.

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum.80(7), 073706 (2009).
[CrossRef] [PubMed]

Kim, M. K.

Kitagawa, K.

Kühn, J.

Lei, M.

Li, P.

Liu, Z.

Ma, B.

Marquet, P.

Min, J.

Montfort, F.

Muhamedsalih, H.

Ogawa, H.

Park, H. Y.

Shi, K.

Tiziani, H. J.

Toal, V.

B. Bowe and V. Toal, “White light interferometric surface profiler,” Opt. Eng.37(6), 1796–1799 (1998).
[CrossRef]

Uhde, H. M.

Wang, K.

Yan, S.

Yang, Y.

Yao, B.

Ye, T.

Yin, S.

Zheng, J.

Appl. Opt. (5)

Opt. Eng. (1)

B. Bowe and V. Toal, “White light interferometric surface profiler,” Opt. Eng.37(6), 1796–1799 (1998).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Rev. Sci. Instrum. (2)

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum.80(7), 073706 (2009).
[CrossRef] [PubMed]

J. A. Kim, C. S. Kang, J. Jin, C. Eom, R. Jang, and J. W. Kim, “Note: High speed optical profiler based on a phase-shifting technique using frequency-scanning lasers,” Rev. Sci. Instrum.82(8), 086111 (2011).
[CrossRef] [PubMed]

Other (4)

W. J. Smith, “Paraxial optics and calculations,” in Modern Optical Engineering, 4th ed. (SPIE Press, 2008), pp. 35–48.

T. S. Tkaczyk, “Microscope construction,” in Field Guide to Microscopy (SPIE Press, 2010), p. 36.

R. E. Fischer, B. T. Galeb, and P. R. Yoder, “Basic optics and optical system specification,” in Optical System Design, 2nd ed. (SPIE Press, 2008), pp. 17–20.

J. W. Goodman, “Fresnel and Fraunhofer diffraction,” in Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, 2005), pp. 76–79.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of GFP methods: (a) Gradient Curvature Cylindrical (GCC) lens, (b) Gradient Thickness Cylindrical (GTC) lens, (c) tilted plano-convex cylindrical lens and (d) tilted imaging sensor.

Fig. 2
Fig. 2

Changes of (a) bow tie-like spots and (b) intensity profiles according to the divergence angle of an input light; converged (left), collimated (center), and diverged (right) light.

Fig. 3
Fig. 3

Paraxial GFP system and paraxial rays in air space.

Fig. 4
Fig. 4

Image defocus simulation results according to (a) ± 1 mm and (b) ± 0.1 mm specimen defocuses in a double telecentric condition (solid line), 60 mm shorter (dash line) and 60 mm longer (dot line) than a doubly-telecentric condition: d2, distance between the objective lens and the cylindrical lens; f1, focal length of the objective lens is 10 mm; f2, focal length of the cylindrical lens is 100 mm.

Fig. 5
Fig. 5

Schematic diagram of GFP system for specifying design parameters: (a) focused rays on a tilted imaging sensor according to the specimen defocus and (b) design parameters of GFP system.

Fig. 6
Fig. 6

System implementations of (a) GCC lens method, (b) Tilted cylindrical lens method: OL, objective lens; BS, beam-splitter; CL, collimating lens.

Fig. 7
Fig. 7

Experimental results: (a) Bow tie-like spots (exaggerated in vertical direction) with respect to + 15 μm defocus (left), in-focus (center) and −15 μm defocus (right), (b) Intensity profiles with respect to + 15 μm defocus (dash line), in-focus (solid line) and −15 μm defocus (dot line) and (c) Peak position of the intensity profile according to ± 15 μm specimen defocuses in GCC lens method.

Fig. 8
Fig. 8

Experimental results: (a) Bow tie-like spots (exaggerated in vertical direction) with respect to + 50 μm defocus (left), in-focus (center) and −50 μm defocus (right), (b) Intensity profiles with respect to + 50 μm defocus (dash line), in-focus (solid line) and −50 μm defocus (dot line) and (c) Peak position of the intensity profile according to ± 50 μm specimen defocuses in GCC lens method.

Tables (1)

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Table 1 Dimensions of the Fabricated GCC Lens

Equations (13)

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d 3 = ( d 1 + d 2 d 1 d 2 f 1 ) / ( 1+ d 1 f 1 + d 1 f 2 + d 2 f 2 d 1 d 2 f 1 f 2 ) ,
d 3 = ( f 2 f 1 ) 2 d 1 +( f 2 + f 2 2 f 1 ).
Δ d 3 =± ( f 2 f 1 ) 2 Δ d 1 .
N= 2( Δ d obj ) /r
L=Np= 2p( Δ d obj ) /r ,
2( Δ d img )=2 ( f cyl / f obj ) 2 ( Δ d obj ),
2( Δ d img )=Lsinθ,
θ= sin 1 [ r p ( f cyl f obj ) 2 ].
r p ( f cyl f obj ) 2 1
f cyl f obj p/r .
A=2.44 f cyl λ/ D obj ,
f cyl ( D obj p ) / ( 2.44λ ) .
( D obj p ) / ( 2.44λ ) f cyl f obj p/r .

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