## Holographic Image Projection on Tilted Planes by Phase-Only Computer Generated Hologram Using Fractional Fourier Transformation

Journal of Display Technology, Vol. 10, Issue 2, pp. 107-113 (2014)

Acrobat PDF (1415 KB)

### 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.

© 2013 IEEE

**Citation**

Chenliang Chang, Jun Xia, and Yanqiao Jiang, "Holographic Image Projection on Tilted Planes by
Phase-Only Computer Generated Hologram Using Fractional Fourier Transformation," J. Display Technol. **10**, 107-113 (2014)

http://www.opticsinfobase.org/jdt/abstract.cfm?URI=jdt-10-2-107

Sort: Year | Journal | Reset

### References

- A. W. Lohmann, D. P. Paris, "Binary Fraunhofer holograms, generated by computer," Appl. Opt. 6, 1739-1748 (1967).
- N. Yoshikawa, T. Yatagai, "Phase optimization of a kinoform by simulated annealing," Appl. Opt. 33, 863-868 (1994).
- 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).
- D. Leseberg, C. Frere, "Computer-generated holograms of 3-D objects composed of tilted planar segments," Appl. Opt. 27, 3020-3024 (1988).
- C. Frere, D. Leseberg, "Large objects reconstructed from computer-generated holograms," Appl. Opt. 28, 2422-2425 (1989).
- 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).
- 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).
- S. J. Jeong, C. K. Hong, "Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method," Appl. Opt. 47, 3064-3071 (2008).
- 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).
- L. Ahrenberg, P. Benzie, M. Magnor, J. Watson, "Computer generated holograms from three dimensional meshes using an analytic light transport model," Appl. Opt. 47, 1567-1574 (2008).
- 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).
- J. J. Burch, "A computer algorithm for the synthesis of spatial frequency filter," Proc. IEEE 55, 599-600 (1967).
- 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).
- J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 327-329 (1978).
- H. Akahori, "Comparison of deterministic phase coding with random phase coding in terms of dynamic range," Appl. Opt. 12, 2336-2343 (1973).
- J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, "Encoding amplitude information onto phase-only filters," Appl. Opt. 38, 5004-5013 (1999).
- T.-L. Kelly, J. Munch, "Improved kinoforms on spatial light modulators with less than phase modulation capability," Opt. Eng. 37, 1608-1611 (1998).
- C. Chang, J. Xia, W. Lei, "Holographic image projection using fractional Fourier transformation," Opt. Commun. 285, 24-28 (2012).
- 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.
- V. Namias, "The fractional order Fourier transform and its application to quantum mechanics," J. Inst. Maths Appl. 25, 241-265 (1980).
- D. H. Bailey, P. N. Swarztrauber, "The fractional Fourier transform and applications," SIAM Rev. 33, 389-404 (1991).
- H. M. Ozaktas, D. Mendlovic, "Fractional Fourier optics," J. Opt. Soc. Amer. A 12, (1995).
- 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).
- H. Zhang, J. H. Xie, J. Liu, Y. T. Wang, "Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection," Appl. Opt. 48, 5834-5841 (2009).

## Cited By |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.