Abstract

A new method of optical imaging that can generate the section images of arbitrarily tilted planes has been developed from illumination-angle-scanning digital interference holography. A set of complex object fields are reconstructed from the holograms captured as the illumination angle is varied with uniform intervals. After the complex fields are modified with phase ramps that match the tilt (relative to the hologram plane) of a desired observation plane, the image of the object sliced along the tilted plane is obtained from their superposition. The axial resolution of a system employing this method is measured with a step height standard, and it is applied to the tomographic inspection of a microelectromechanical system.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (1)

2008 (3)

2007 (3)

2006 (2)

2005 (2)

2004 (1)

H. Y. Yun, S. J. Jeong, J. W. Kang, and C. K. Hong, “3-dimensional micro-structure inspection by phase shifting digital holography,” Key Eng. Mater. 270–273, 756–761(2004).
[CrossRef]

2002 (2)

G. Pedrini and H. J. Tiziani, “Short-coherence digital holography by use of a lensless holographic imaging system,” Appl. Opt. 41, 4489–4496 (2002).
[CrossRef] [PubMed]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef] [PubMed]

1999 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Charrière, F.

Chen, Z.

Choi, W.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Colomb, T.

Cuche, E.

Dasari, R. R.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Depeursinge, C.

Depeursinge, Christian

Fang-Yen, C.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Feld, M. S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gorski, W.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Herminjard, S.

Hong, C. K.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Jeong, S. J.

Kang, J. W.

H. Y. Yun, S. J. Jeong, J. W. Kang, and C. K. Hong, “3-dimensional micro-structure inspection by phase shifting digital holography,” Key Eng. Mater. 270–273, 756–761(2004).
[CrossRef]

Kim, M. K.

Kuehn, J.

Kühn, J.

Lauer, V.

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef] [PubMed]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Marian, A.

Marquet, P.

Montfort, F.

Moratal, C.

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Osten, W.

Pavillon, N.

Pedrini, G.

Potcoava, M. C.

M. C. Potcoava and M. K. Kim, “Optical tomography for biomedical applications by digital interference holography,” Meas. Sci. Technol. 19, 074010 (2008).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Rappaz, B.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tiziani, H. J.

Yu, L.

Yun, H. Y.

H. Y. Yun and C. K. Hong, “Interframe intensity correlation matrix for self-calibration in phase-shifting interferometry,” Appl. Opt. 44, 4860–4869 (2005).
[CrossRef] [PubMed]

H. Y. Yun, S. J. Jeong, J. W. Kang, and C. K. Hong, “3-dimensional micro-structure inspection by phase shifting digital holography,” Key Eng. Mater. 270–273, 756–761(2004).
[CrossRef]

Appl. Opt. (4)

J. Microsc. (1)

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef] [PubMed]

Key Eng. Mater. (1)

H. Y. Yun, S. J. Jeong, J. W. Kang, and C. K. Hong, “3-dimensional micro-structure inspection by phase shifting digital holography,” Key Eng. Mater. 270–273, 756–761(2004).
[CrossRef]

Meas. Sci. Technol. (1)

M. C. Potcoava and M. K. Kim, “Optical tomography for biomedical applications by digital interference holography,” Meas. Sci. Technol. 19, 074010 (2008).
[CrossRef]

Nat. Methods (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (5)

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

(a) Geometrical configuration of illumination. (b) Axial resolution δ and axial range Λ.

Fig. 2
Fig. 2

Two-level object (a) parallel to the x y plane and (b) tilted by γ relative to the reference plane. (c) Both the object and the reference plane tilted. (d)–(f) Section images obtained in the situations (a)–(c), respectively.

Fig. 3
Fig. 3

Schematic of an illumination-angle-scanning holographic microscopy: SF, spatial filter; L1, collimation lens; L2, condensing lens; BS, beam splitter; BP, back focal plane; MO, micro objective; CCD, charge coupled device; PztM, piezo electric transducer mirror.

Fig. 4
Fig. 4

(a) Phase image of SHS at θ = θ c = 20 ° . Section images (b) without and (c) with tilting adjustment. Section images of (c) the upper and (d) the lower surfaces of SHS with tilting adjustment. (e) Tomographic images sliced along the dotted lines in (c). (f) Intensity profiles along the dotted lines in (e).

Fig. 5
Fig. 5

Three-dimensional rendering of the SHS.

Fig. 6
Fig. 6

(a) Photograph of the gyroscopic chip. (b) Reconstructed intensity image of the inside of the dotted rectangle in (a). (c) Section image without tilting adjustment. Section images with tilting adjustment of (d) the whole area of the proof mass and the frame about 300 μm deep and (e) the electrodes about 600 μm deep.

Fig. 7
Fig. 7

Tomographic images of the gyroscope chip along the dotted lines (1)-(8) in Fig. 5. The white arrows indicate incompletely etched layers.

Equations (14)

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s k ( x , y , z ) = a ( x , y , z ) exp [ i ( k · r k z z 0 ) ] d z .
s k ( x , y , z h ) = F 1 { F [ s k ( x , y , z ) ] exp [ 2 π i f z ( z h z ) ] } d z ,
s k ( x , y , z h ) = F 1 [ A ( f x k x 2 π , f y k y 2 π , z ) ] exp { i [ k z ( z z 0 ) + 2 π f z ( z h z ) ] } d z ,
s k ( x , y , z h ) = F 1 [ A ( f x , f y , z ) ] exp [ i k z ( 2 z z 0 z h ) ] d z = a ( x , y , z ) exp [ i k z ( 2 z z 0 z h ) ] d z .
E k ( x , y , z h ) = a ( x , y , z ) exp [ i k z ( 2 z z 0 z h ) ] d z .
E k ( x , y , z 0 ) = a ( x , y , z ) exp [ 2 i k z ( z z 0 ) ] d z .
E total ( x , y , z 0 ) = k z a ( x , y , z ) exp [ 2 i k z ( z z 0 ) ] d z a ( x , y , z ) δ ( z z 0 ) d z a ( x , y , z 0 ) ,
g ( z z 0 ) n = 1 N exp [ 2 i k n ( z z 0 ) ] = n = ( N 1 ) / 2 ( N 1 ) / 2 exp [ 2 π i ( α c + n Δ α ) β ] = comb [ ( α α c ) Δ α ] rect [ ( α α c ) N Δ α ] exp ( 2 π i α β ) d α = F { comb [ ( α α c ) Δ α ] } * F { rect [ ( α α c ) N Δ α ] } ,
F { comb [ ( α α c ) Δ α ] } = Δ α exp ( 2 π i α c Δ α ) comb [ Δ α · β ] m = δ ( β m Δ α ) , F { rect [ ( α α c ) N Δ α ] } = N Δ α exp ( 2 π i α c N Δ α ) sinc ( N Δ α · β ) sinc ( N Δ α · β ) ,
g ( β ) m = sinc [ N Δ α ( β m Δ α ) ] .
E total ( x , y , z 0 ) a ( x , y , z ) m = sinc { N Δ k z π [ z ( z 0 + m π Δ k z ) ] } d z .
z = z 0 x cos α / cos γ y cos β / cos γ .
E total ( x , y , z ) = k z exp [ 2 i k z ( x cos α / cos γ + y cos β / cos γ ) ] a ( x , y , z ) exp [ 2 i k z ( z z 0 ) ] d z a ( x , y , z ) δ ( z z 0 + x cos α / cos γ + y cos β / cos γ ) d z a ( x , y , z 0 x cos α / cos γ y cos β / cos γ ) ,
Δ y = Δ y cos γ ,

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