Abstract

This paper presents what is to the author’s knowledge a new theory for phase-only holograms. It explains many phenomena observed in the reconstruction of phase-only Fourier holograms and in particular the existence and nature of noise. Using this theory it was demonstrated that any reconstruction is the convolution of the target reconstruction with a two-dimensional set of impulses. The nature of this convolution function depends on the target reconstruction and in particular the spacing between the spots. In the simplest case of a two-spot generating hologram the convolution function was calculated analytically. The theory is also verified with examples from spot generating holograms, symbology, and image projection holograms.

© 2010 Optical Society of America

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2008 (2)

2005 (2)

A. G. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. 343, 511–526 (2005).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Robert, 2005).

2004 (2)

2001 (1)

2000 (2)

1995 (1)

1994 (1)

1986 (2)

1983 (1)

S. Kirkpatrick, C. Gelatt, and J. M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

1971 (1)

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Abushagur, M. A. G.

Akahori, H.

Ashkin, A.

Bjorkholm, J. E.

Bonas, I. G.

Christmas, J.

Chu, H. H.

Chu, S.

Collings, N.

Cooper, J.

Courtial, J.

Crossland, A. W.

Crossland, W.

Crossland, W. A.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

A. Georgiou, J. Christmas, J. Moore, A. Jeziorska, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal on silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. 47, 4793–4803 (2008).
[CrossRef]

A. G. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. 343, 511–526 (2005).

A. Georgiou and W. A. Crossland, “Image projection using phase-only holograms,” in Photon04 Conference Proceedings (2004).

W. A. Crossland, I. G. Manolis, M. M. Redmond, K. L. Tan, T. D. Wilkinson, M. J. Holmes, T. R. Parker, H. H. Chu, J. Croucher, V. A. Handerek, S. T. Warr, B. Robertson, I. G. Bonas, R. Franklin, C. Stace, H. J. White, R. A. Woolley, and H. G., “Holographic optical switching: the “ROSES” demonstrator,” J. Lightwave Technol. 18, 1845–1854 (2000).
[CrossRef]

Croucher, J.

Dammann, H.

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Davey, A.

Dziedzic, J. M.

Fienup, J. R.

Franklin, R.

G., H.

Gelatt, C.

S. Kirkpatrick, C. Gelatt, and J. M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Georgiou, A.

A. Georgiou, J. Christmas, J. Moore, A. Jeziorska, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal on silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. 47, 4793–4803 (2008).
[CrossRef]

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

A. Georgiou and W. A. Crossland, “Image projection using phase-only holograms,” in Photon04 Conference Proceedings (2004).

Georgiou, A. G.

A. G. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. 343, 511–526 (2005).

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Robert, 2005).

J. W. Goodman, Statistical Optics (Wiley, 2000).

Gortler, K.

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Handerek, V. A.

Holmes, M. J.

Ilias, M. G.

Jeziorska, A.

Johnson, E. G.

Jordan, P.

Kirkpatrick, S.

S. Kirkpatrick, C. Gelatt, and J. M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Komarcevic, M.

A. G. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. 343, 511–526 (2005).

Laczik, Z.

Leach, J.

Manolis, I. G.

Mears, R.

Moore, J.

O’Brien, D.

Padgett, M.

Parker, T. R.

Redmond, M. M.

Robertson, B.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Sinclair, G.

Stace, C.

Tan, K. L.

Vecchi, J. M. P.

S. Kirkpatrick, C. Gelatt, and J. M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Warr, S. T.

White, H. J.

Wilkinson, T.

Wilkinson, T. D.

Woolley, R. A.

Appl. Opt. (3)

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Mol. Cryst. Liq. Cryst. (1)

A. G. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. 343, 511–526 (2005).

Opt. Commun. (1)

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Optik (Stuttgart) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Science (1)

S. Kirkpatrick, C. Gelatt, and J. M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Robert, 2005).

J. W. Goodman, Statistical Optics (Wiley, 2000).

A. Georgiou and W. A. Crossland, “Image projection using phase-only holograms,” in Photon04 Conference Proceedings (2004).

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