Abstract

In this Letter, we study the reconstruction of digital holograms of microscopic objects using a fixed-point representation of the numercial-reconstruction process. For different bit levels in our fixed-point reconstruction algorithm, we investigate the errors introduced to both the reconstructed image intensity and the unwrapped quantitative phase information. Experimental results based on a microscopic lens array are provided.

© 2010 Optical Society of America

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2009

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, Lab Chip 9, 777 (2009).
[CrossRef] [PubMed]

N. Pandey, D. P. Kelly, T. J. Naughton, and B. M. Hennelly, Proc. SPIE 7442, 744205 (2009).
[CrossRef]

2008

“IEEE Standard for Floating-Point Arithmetic,” IEEE Std 754-2008, pp. 1-58, (2008).

2006

2005

G. A. Mills and I. Yamaguchi, Appl. Opt. 44, 1216 (2005).
[CrossRef] [PubMed]

B. M. Hennelly and J. T. Sheridan, J. Opt. Soc. Am. A Opt. Image Sci. Vis 22, 917 (2005).
[CrossRef] [PubMed]

2004

G. Coppola, P. Ferraro, M. Iodice, S. D. Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

D. Carl, B. Kemper, G. Wernicke, and G. V. Bally, Appl. Opt. 43, 6536 (2004).
[CrossRef]

2002

Peter R. Hobson and John Watson, J. Opt. A 4, S34 (2002).
[CrossRef]

2000

B. Parhami, Computer Arithmetic, Algorithms and Hardware Designs (Oxford U. Press, 2000).

A. Stadelmaier and J. H. Massig, Opt. Lett. 25, 1630 (2000).
[CrossRef]

1996

1992

C. Van Loan, Computational Frameworks for the Fast Fourier Transform (SIAM, 1992).
[CrossRef]

1974

A. Aho, J. Hopcroft, and J. Ullman, Design and Analysis of Computer Algorithms (Addison-Wesley, 1974).

Aho, A.

A. Aho, J. Hopcroft, and J. Ullman, Design and Analysis of Computer Algorithms (Addison-Wesley, 1974).

Bally, G. V.

Callens, N.

Carl, D.

Coppola, G.

G. Coppola, P. Ferraro, M. Iodice, S. D. Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Dubois, F.

Erlinger, A.

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, Lab Chip 9, 777 (2009).
[CrossRef] [PubMed]

Ferraro, P.

G. Coppola, P. Ferraro, M. Iodice, S. D. Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Finizio, A.

G. Coppola, P. Ferraro, M. Iodice, S. D. Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Galizzi, G. E.

Garcia-Sucerquia, J.

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Grilli, S.

G. Coppola, P. Ferraro, M. Iodice, S. D. Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Hennelly, B. M.

N. Pandey, D. P. Kelly, T. J. Naughton, and B. M. Hennelly, Proc. SPIE 7442, 744205 (2009).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, J. Opt. Soc. Am. A Opt. Image Sci. Vis 22, 917 (2005).
[CrossRef] [PubMed]

Hobson, Peter R.

Peter R. Hobson and John Watson, J. Opt. A 4, S34 (2002).
[CrossRef]

Hopcroft, J.

A. Aho, J. Hopcroft, and J. Ullman, Design and Analysis of Computer Algorithms (Addison-Wesley, 1974).

Iodice, M.

G. Coppola, P. Ferraro, M. Iodice, S. D. Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Javidi, B.

Jericho, M. H.

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Jericho, S. K.

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Kaufmann, G. H.

Kelly, D. P.

N. Pandey, D. P. Kelly, T. J. Naughton, and B. M. Hennelly, Proc. SPIE 7442, 744205 (2009).
[CrossRef]

Kemper, B.

Kerr, D.

Kreuzer, H. J.

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Massig, J. H.

Mills, G. A.

Naughton, T. J.

N. Pandey, D. P. Kelly, T. J. Naughton, and B. M. Hennelly, Proc. SPIE 7442, 744205 (2009).
[CrossRef]

A. E. Shortt, T. J. Naughton, and B. Javidi, Opt. Express 14, 5129 (2006).
[CrossRef] [PubMed]

Nicola, S. D.

G. Coppola, P. Ferraro, M. Iodice, S. D. Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Ozcan, A.

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, Lab Chip 9, 777 (2009).
[CrossRef] [PubMed]

Pandey, N.

N. Pandey, D. P. Kelly, T. J. Naughton, and B. M. Hennelly, Proc. SPIE 7442, 744205 (2009).
[CrossRef]

Parhami, B.

B. Parhami, Computer Arithmetic, Algorithms and Hardware Designs (Oxford U. Press, 2000).

Schockaert, C.

Seo, S.

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, Lab Chip 9, 777 (2009).
[CrossRef] [PubMed]

Sheridan, J. T.

B. M. Hennelly and J. T. Sheridan, J. Opt. Soc. Am. A Opt. Image Sci. Vis 22, 917 (2005).
[CrossRef] [PubMed]

Shortt, A. E.

Stadelmaier, A.

Su, T. W.

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, Lab Chip 9, 777 (2009).
[CrossRef] [PubMed]

Tseng, D. K.

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, Lab Chip 9, 777 (2009).
[CrossRef] [PubMed]

Ullman, J.

A. Aho, J. Hopcroft, and J. Ullman, Design and Analysis of Computer Algorithms (Addison-Wesley, 1974).

Van Loan, C.

C. Van Loan, Computational Frameworks for the Fast Fourier Transform (SIAM, 1992).
[CrossRef]

Watson, John

Peter R. Hobson and John Watson, J. Opt. A 4, S34 (2002).
[CrossRef]

Wernicke, G.

Xu, W.

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Yamaguchi, I.

Yourassowsky, C.

Appl. Opt.

J. Opt. A

Peter R. Hobson and John Watson, J. Opt. A 4, S34 (2002).
[CrossRef]

J. Opt. Soc. Am. A Opt. Image Sci. Vis

B. M. Hennelly and J. T. Sheridan, J. Opt. Soc. Am. A Opt. Image Sci. Vis 22, 917 (2005).
[CrossRef] [PubMed]

Lab Chip

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, Lab Chip 9, 777 (2009).
[CrossRef] [PubMed]

Meas. Sci. Technol.

G. Coppola, P. Ferraro, M. Iodice, S. D. Nicola, A. Finizio, and S. Grilli, Meas. Sci. Technol. 15, 529 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

N. Pandey, D. P. Kelly, T. J. Naughton, and B. M. Hennelly, Proc. SPIE 7442, 744205 (2009).
[CrossRef]

Rev. Sci. Instrum.

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Other

“IEEE Standard for Floating-Point Arithmetic,” IEEE Std 754-2008, pp. 1-58, (2008).

B. Parhami, Computer Arithmetic, Algorithms and Hardware Designs (Oxford U. Press, 2000).

A. Aho, J. Hopcroft, and J. Ullman, Design and Analysis of Computer Algorithms (Addison-Wesley, 1974).

C. Van Loan, Computational Frameworks for the Fast Fourier Transform (SIAM, 1992).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Setup for DHM. The optical and the numerical channel in digital holographic imaging are shown.

Fig. 2
Fig. 2

Reconstructions for (a) 20 bits fixed point, (b) 24 bits fixed point, and (c) 64 bit (double precision) floating point. The surface profiles (third row) are shown for the horizontal black line in the second row.

Fig. 3
Fig. 3

Number of computations required in reconstruction and the rms error in the surface profile. Experimental results show that each additional bit reduces the error by half.

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