Abstract

We propose a new method to compute the phase-only computer-generated hologram (CGH) that can modulate an image on a tilted plane. We used the fractional Fourier transformation to compute light propagation between the hologram plane and the tilted plane. The phase-only hologram was obtained by an iterative algorithm. We proposed a method to calculate the inverse optical propagation from the hologram plane to a tilted plane by coordinate rotation and a simple interpolation in the Fourier domain. The experimental results show that the projected image on the tilted plane can be reconstructed by a phase-only hologram generated by our iterative algorithm. We also show that the quality of the projected image on the tilted plane is better than the image projected by the phase hologram generated by traditional method.

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2012

K. Yamamoto, Y. Ichihashi, T. Senoh, R. Oi, T. Kurita, "Calculating the Fresnel diffraction of light from a shifted and tilted plane," Opt. Exp. 20, 12949 (2012).

C. Chang, J. Xia, W. Lei, "Holographic image projection using fractional Fourier transformation," Opt. Commun. 285, 24-28 (2012).

2010

Y. Z. Liu, J. W. Dong, Y. Y. Pu, B. C. Chen, H. X. He, H. Z. Wang, "High-speed full analytical holographic computations for true-life scenes," Opt. Exp. 18, 3345-3351 (2010).

2009

2008

2005

S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, D. Alfieri, "Angular spectrum method with correction of anamorphism for numerical reconstruction of digital holograms on tilted planes," Opt. Exp. 13, 9935-9940 (2005).

2003

K. Matsushima, H. Schimmel, F. Wyrowski, "Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves," J. Opt. Soc. Amer. A 20, 1755-1762 (2003).

1999

1998

T.-L. Kelly, J. Munch, "Improved kinoforms on spatial light modulators with less than phase modulation capability," Opt. Eng. 37, 1608-1611 (1998).

1995

H. M. Ozaktas, D. Mendlovic, "Fractional Fourier optics," J. Opt. Soc. Amer. A 12, (1995).

1994

1993

D. Mendlovic, H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation (1,2)," J. Opt. Soc. Amer. A 10, (1993).

A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Amer. A 10, 2181-2186 (1993).

1991

D. H. Bailey, P. N. Swarztrauber, "The fractional Fourier transform and applications," SIAM Rev. 33, 389-404 (1991).

1989

1988

1980

V. Namias, "The fractional order Fourier transform and its application to quantum mechanics," J. Inst. Maths Appl. 25, 241-265 (1980).

1978

J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 327-329 (1978).

1973

1972

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

1967

J. J. Burch, "A computer algorithm for the synthesis of spatial frequency filter," Proc. IEEE 55, 599-600 (1967).

A. W. Lohmann, D. P. Paris, "Binary Fraunhofer holograms, generated by computer," Appl. Opt. 6, 1739-1748 (1967).

Appl. Opt.

J. Inst. Maths Appl.

V. Namias, "The fractional order Fourier transform and its application to quantum mechanics," J. Inst. Maths Appl. 25, 241-265 (1980).

J. Opt. Soc. Amer. A

D. Mendlovic, H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation (1,2)," J. Opt. Soc. Amer. A 10, (1993).

J. Opt. Soc. Amer. A

A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Amer. A 10, 2181-2186 (1993).

J. Opt. Soc. Amer. A

H. M. Ozaktas, D. Mendlovic, "Fractional Fourier optics," J. Opt. Soc. Amer. A 12, (1995).

K. Matsushima, H. Schimmel, F. Wyrowski, "Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves," J. Opt. Soc. Amer. A 20, 1755-1762 (2003).

Opt. Eng.

T.-L. Kelly, J. Munch, "Improved kinoforms on spatial light modulators with less than phase modulation capability," Opt. Eng. 37, 1608-1611 (1998).

Opt. Lett.

J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 327-329 (1978).

Opt. Commun.

C. Chang, J. Xia, W. Lei, "Holographic image projection using fractional Fourier transformation," Opt. Commun. 285, 24-28 (2012).

Opt. Exp.

Y. Z. Liu, J. W. Dong, Y. Y. Pu, B. C. Chen, H. X. He, H. Z. Wang, "High-speed full analytical holographic computations for true-life scenes," Opt. Exp. 18, 3345-3351 (2010).

K. Yamamoto, Y. Ichihashi, T. Senoh, R. Oi, T. Kurita, "Calculating the Fresnel diffraction of light from a shifted and tilted plane," Opt. Exp. 20, 12949 (2012).

S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, D. Alfieri, "Angular spectrum method with correction of anamorphism for numerical reconstruction of digital holograms on tilted planes," Opt. Exp. 13, 9935-9940 (2005).

Optik

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

Proc. IEEE

J. J. Burch, "A computer algorithm for the synthesis of spatial frequency filter," Proc. IEEE 55, 599-600 (1967).

SIAM Rev.

D. H. Bailey, P. N. Swarztrauber, "The fractional Fourier transform and applications," SIAM Rev. 33, 389-404 (1991).

Other

C. Chang, J. Xia, W. Lei, "Computer-generated hologram based on fractional Fourier transformation iteration algorithm," Proc. China Display/Asia Display Conf. (2011) pp. 608-611.

M. Kitamura, T. Hamano, "Computer-generated holograms for multilevel 3-D images with complex amplitude modulation," Proc. SPIE Practical Holography XVI and Holographic Materials VIII (2002) pp. 196-204.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Co., 2004).

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