Abstract

An approach is proposed for removing the wave front curvature introduced by the microscope imaging objective in digital holography, which otherwise hinders the phase contrast imaging at reconstruction planes. The unwanted curvature is compensated by evaluating a correcting wave front at the hologram plane with no need for knowledge of the optical parameters, focal length of the imaging lens, or distances in the setup. Most importantly it is shown that a correction effect can be obtained at all reconstruction planes. Three different methods have been applied to evaluate the correction wave front and the methods are discussed in detail. The proposed approach is demonstrated by applying digital holography as a method of coherent microscopy for imaging amplitude and phase contrast of microstructures.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. W. P. Jueptner, P. Werner, M. Kujawinska, W. Osten, L. A. Salbut, S. Seebacher, “Combined measurement of silicon microbeams by grating interferometry and digital holography,” International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 348–357 (1998).
    [CrossRef]
  24. P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.
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    [CrossRef]

2002 (2)

U. Schanrs, W. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[CrossRef]

2001 (6)

X. Lei, P. Xiaoyuan, A. K. Asundi, M. Jianmin, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

S. Seebacker, W. Osten, T. Baumbach, W. Juptner, “The determination of materials parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Correct-image reconstruction in the presence of severe anamorphism by means of digital holography,” Opt. Lett. 26, 974–977 (2001).
[CrossRef]

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001).
[CrossRef] [PubMed]

X. Lei, P. Xiaoyuan, M. Jianmin, A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5052 (2001).
[CrossRef]

2000 (2)

1999 (3)

1998 (1)

1997 (1)

1995 (2)

J. Gu, F. Chen, “Fast Fourier transform, iteration, and least-squares fit demodulation image processing for analysis of single-carrier fringe pattern,” J. Opt. Soc. Am. A 12, 2159–2165 (1995).
[CrossRef]

T. C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

1994 (2)

1992 (1)

1987 (1)

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

1972 (1)

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavski, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Asundi, A. K.

X. Lei, P. Xiaoyuan, A. K. Asundi, M. Jianmin, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

X. Lei, P. Xiaoyuan, M. Jianmin, A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5052 (2001).
[CrossRef]

Baumbach, T.

S. Seebacker, W. Osten, T. Baumbach, W. Juptner, “The determination of materials parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

Bevilacqua, F.

Chen, F.

Coppola, G.

P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.

Cuche, E.

De Nicola, S.

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[CrossRef]

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Correct-image reconstruction in the presence of severe anamorphism by means of digital holography,” Opt. Lett. 26, 974–977 (2001).
[CrossRef]

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001).
[CrossRef] [PubMed]

S. Grilli, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Experimental demonstration of the longitudinal phase-shift in digital holography,” Opt. Eng. (to be published).

P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.

P. Ferraro, S. De Nicola, A. Finizio, S. Grilli, G. Pierattini, “Digital holographic interferometry for characterization of transparent materials,” in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, R. Hoefling, W. P. Jueptner, M. Kujawinska, eds., Proc. SPIE4399, 9–16 (2001).
[CrossRef]

Depeursinge, C.

Doh, K. B.

T. C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Duncan, B. D.

Ferraro, P.

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[CrossRef]

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Correct-image reconstruction in the presence of severe anamorphism by means of digital holography,” Opt. Lett. 26, 974–977 (2001).
[CrossRef]

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001).
[CrossRef] [PubMed]

S. Grilli, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Experimental demonstration of the longitudinal phase-shift in digital holography,” Opt. Eng. (to be published).

P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.

P. Ferraro, S. De Nicola, A. Finizio, S. Grilli, G. Pierattini, “Digital holographic interferometry for characterization of transparent materials,” in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, R. Hoefling, W. P. Jueptner, M. Kujawinska, eds., Proc. SPIE4399, 9–16 (2001).
[CrossRef]

Finizio, A.

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[CrossRef]

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Correct-image reconstruction in the presence of severe anamorphism by means of digital holography,” Opt. Lett. 26, 974–977 (2001).
[CrossRef]

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001).
[CrossRef] [PubMed]

S. Grilli, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Experimental demonstration of the longitudinal phase-shift in digital holography,” Opt. Eng. (to be published).

P. Ferraro, S. De Nicola, A. Finizio, S. Grilli, G. Pierattini, “Digital holographic interferometry for characterization of transparent materials,” in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, R. Hoefling, W. P. Jueptner, M. Kujawinska, eds., Proc. SPIE4399, 9–16 (2001).
[CrossRef]

P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.

Grilli, S.

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001).
[CrossRef] [PubMed]

P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.

P. Ferraro, S. De Nicola, A. Finizio, S. Grilli, G. Pierattini, “Digital holographic interferometry for characterization of transparent materials,” in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, R. Hoefling, W. P. Jueptner, M. Kujawinska, eds., Proc. SPIE4399, 9–16 (2001).
[CrossRef]

S. Grilli, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Experimental demonstration of the longitudinal phase-shift in digital holography,” Opt. Eng. (to be published).

Gu, J.

Iodice, M.

P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.

Jianmin, M.

X. Lei, P. Xiaoyuan, A. K. Asundi, M. Jianmin, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

X. Lei, P. Xiaoyuan, M. Jianmin, A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5052 (2001).
[CrossRef]

Jueptner, W. P.

W. P. Jueptner, P. Werner, M. Kujawinska, W. Osten, L. A. Salbut, S. Seebacher, “Combined measurement of silicon microbeams by grating interferometry and digital holography,” International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 348–357 (1998).
[CrossRef]

Juptner, W.

U. Schanrs, W. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

S. Seebacker, W. Osten, T. Baumbach, W. Juptner, “The determination of materials parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

U. Schanrs, W. Juptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef]

Kim, M.

Kim, M. K.

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavski, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Kujawinska, M.

W. P. Jueptner, P. Werner, M. Kujawinska, W. Osten, L. A. Salbut, S. Seebacher, “Combined measurement of silicon microbeams by grating interferometry and digital holography,” International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 348–357 (1998).
[CrossRef]

Lei, X.

X. Lei, P. Xiaoyuan, A. K. Asundi, M. Jianmin, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

X. Lei, P. Xiaoyuan, M. Jianmin, A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5052 (2001).
[CrossRef]

Magro, C.

P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.

Marquet, P.

Massig, J. H.

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavski, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Meucci, R.

Onural, L.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Osten, W.

S. Seebacker, W. Osten, T. Baumbach, W. Juptner, “The determination of materials parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

W. P. Jueptner, P. Werner, M. Kujawinska, W. Osten, L. A. Salbut, S. Seebacher, “Combined measurement of silicon microbeams by grating interferometry and digital holography,” International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 348–357 (1998).
[CrossRef]

Pedrini, G.

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

Pierattini, G.

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[CrossRef]

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001).
[CrossRef] [PubMed]

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Correct-image reconstruction in the presence of severe anamorphism by means of digital holography,” Opt. Lett. 26, 974–977 (2001).
[CrossRef]

S. Grilli, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Experimental demonstration of the longitudinal phase-shift in digital holography,” Opt. Eng. (to be published).

P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.

P. Ferraro, S. De Nicola, A. Finizio, S. Grilli, G. Pierattini, “Digital holographic interferometry for characterization of transparent materials,” in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, R. Hoefling, W. P. Jueptner, M. Kujawinska, eds., Proc. SPIE4399, 9–16 (2001).
[CrossRef]

Poon, T. C.

T. C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

B. D. Duncan, T. C. Poon, “Gaussian beam analysis of optical scanning holography,” J. Opt. Soc. Am. A 9, 229–233 (1992).
[CrossRef]

Salbut, L. A.

W. P. Jueptner, P. Werner, M. Kujawinska, W. Osten, L. A. Salbut, S. Seebacher, “Combined measurement of silicon microbeams by grating interferometry and digital holography,” International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 348–357 (1998).
[CrossRef]

Schanrs, U.

Schedin, S.

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

Schilling, B. W.

T. C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Scott, P. D.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Seebacher, S.

W. P. Jueptner, P. Werner, M. Kujawinska, W. Osten, L. A. Salbut, S. Seebacher, “Combined measurement of silicon microbeams by grating interferometry and digital holography,” International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 348–357 (1998).
[CrossRef]

Seebacker, S.

S. Seebacker, W. Osten, T. Baumbach, W. Juptner, “The determination of materials parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

Shinoda, K.

T. C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Stadelmaier, A.

Suzuki, Y.

T. C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Tiziani, H. J.

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

Werner, P.

W. P. Jueptner, P. Werner, M. Kujawinska, W. Osten, L. A. Salbut, S. Seebacher, “Combined measurement of silicon microbeams by grating interferometry and digital holography,” International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 348–357 (1998).
[CrossRef]

Wu, M. H.

T. C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Xiaoyuan, P.

X. Lei, P. Xiaoyuan, A. K. Asundi, M. Jianmin, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

X. Lei, P. Xiaoyuan, M. Jianmin, A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5052 (2001).
[CrossRef]

Yamaguchi, I.

Yaroslavski, L. P.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavski, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Zhang, T.

Appl. Opt. (3)

J. Mod. Opt. (1)

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

J. Opt. Soc. Am. A (3)

Meas. Sci. Technol. (1)

U. Schanrs, W. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Opt. Eng. (3)

T. C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

X. Lei, P. Xiaoyuan, A. K. Asundi, M. Jianmin, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (2)

S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[CrossRef]

S. Seebacker, W. Osten, T. Baumbach, W. Juptner, “The determination of materials parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

Opt. Lett. (6)

Sov. Phys. Tech. Phys. (1)

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavski, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Other (4)

W. P. Jueptner, P. Werner, M. Kujawinska, W. Osten, L. A. Salbut, S. Seebacher, “Combined measurement of silicon microbeams by grating interferometry and digital holography,” International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 348–357 (1998).
[CrossRef]

P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, S. Grilli, M. Iodice, C. Magro, G. Pierattini, “Digital holography for characterization and testing of MEMS structures,” in Proceedings of IEEE/LEOS International Conference on Optical MEMS 2002, (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 125–126.

S. Grilli, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Experimental demonstration of the longitudinal phase-shift in digital holography,” Opt. Eng. (to be published).

P. Ferraro, S. De Nicola, A. Finizio, S. Grilli, G. Pierattini, “Digital holographic interferometry for characterization of transparent materials,” in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, R. Hoefling, W. P. Jueptner, M. Kujawinska, eds., Proc. SPIE4399, 9–16 (2001).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for recording digital holograms: PBS—Polarizing beam splitter, M—mirror, PZT—Piezoelectric transducer actuator, MO—microscope objective, BE—beam expander.

Fig. 2
Fig. 2

(a) Digital hologram of a silicon optical waveguide on a silicon substrate, A—portion of the hologram used to correct the disturbing curvature in the reconstructed phase, B—portion of the hologram of the object under investigation: the waveguide, (b) amplitude-contrast image of the waveguide, (c) phase-contrast image of the waveguide in the presence of disturbing curvature.

Fig. 3
Fig. 3

(a) Wrapped phase modulo 2π of the portion A of the hologram of Fig. 2(a), (b) phase-contrast wrapped modulo 2π of the portion B of the hologram of Fig. 2(a).

Fig. 4
Fig. 4

(a) Unwrapped phase of the portion A of the hologram of Fig. 2(a), (b) phase correction wave front calculated by extrapolating to the region B the fitted sphere of region A.

Fig. 5
Fig. 5

Phase-contrast image of the silicon waveguide where the curvature has been corrected by subtracting the compensating wave front as calculated from the portion A of the hologram of Fig. 2(a). Note that the curvature has not completely been removed.

Fig. 6
Fig. 6

(a) Wrapped phase modulo 2π of the correction wave front calculated at the CCD plane by a manual digital adjusting procedure, (b) phase-contrast image of the silicon waveguide in which the inherent curvature has been completely compensated.

Fig. 7
Fig. 7

(a) Hologram of the polysilicon micro cantilever beams, (b) hologram recorded on a reference surface in proximity to the micro-machined beams, (c) phase-contrast image, wrapped modulo 2π, of the polysilicon beams reconstructed at distance d = 100 mm, (d) unwrapped phase with out-of-plane deformation and dimensions expressed in microns.

Equations (12)

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UCCDx, y=I1-I3+iI2-I4.
Φx, y=arctanI4-I2I3-I1.
Φcorrx, y=2πλx2+y22R,
oν, μ   hx, yrx, yexpiπdλx2+y2exp-2iπxν+yμdxdy,
expiϕcorrν, μ  expiΦcorrx, yexpiπdλx2+y2exp-2iπxν+yμdxdy,
Φoν, μ=argOν, μexpiϕcorrν, μ
Φcorrx, y=2πλx-x02+y-y022R1,
Φcorr2x, y=2πλx2+σy22R2,
Φcorr3x, y=2πλx2+y22R3,
Φcorr4x, y=2πλxγ+yρ,
Φcorrx, y=Φcorr1x, y+Φcorr2x, y+Φcorr3x, y+Φcorr4x, y,
Φoν, μ=argO1ν, μO2ν, μ.

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