Abstract

A real-time full-color phase-only holographic display system generates holograms of 3D objects. The system includes a 3D object formed by voxels, an internet-based transmission capability that transmits the object information to the server, a real-time hologram generation unit, and a holographic display unit with incoherent illumination. The server calculates three phase holograms for RGB components using multiple GPUs. The resultant phase holograms are saved into an RGB bitmap image and loaded to the phase-only spatial light modulators (SLMs). SLMs are illuminated uniformly by LEDs, and reconstructed waves are aligned and overlapped by using high precision optics and stages. Experimental results are satisfactory.

© 2009 Optical Society of America

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2009

F. Yaras and L. Onural, “Color holographic reconstruction using multiple SLMs and LED illumination,” Proc. SPIE 7237, 72370O (2009).

2008

2007

D. E. Smalley, Q. Y. J. Smithwick, and J. V. M. Bove, “Holographic video display based on guided-wave acousto-optic devices,” Proc. SPIE 6488, 64880L (2007).

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

2006

2004

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, “3D electronic holography display system using a 100 mega-pixel spatial light modulator,” Proc. SPIE 5249, 297-308 (2004).

2000

Y. Barkana and M. Belkin, “Laser eye injuries,” Survey Ophthalmol. 44, 459-478 (2000).
[CrossRef]

1995

J. Watlington, M. Lucente, C. Sparrell, V. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

J. Amako, H. Miura, and T. Sonehara, “Speckle-noise reduction on kinoform reconstruction using a phase-only spatial light modulator,” Appl. Opt. 34, 3165-3171(1995).
[CrossRef]

1994

K. Taima, H. Ueda, H. Okamoto, T. Kubota, Y. Nakamura, H. Nishida, H. Takahashi, and E. Shimizu, “New approach to the interactive holographic display system,” Proc. SPIE 2176, 23-29 (1994).

1992

P. S. Hilaire, S. Benton, M. Lucente, and H. P. M., “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73-84 (1992).

J. M. Huntley and L. Benckert, “Speckle interferometry: noise reduction by correlation fringe averaging,” Appl. Opt. 31, 2412-2414 (1992).
[CrossRef]

1975

1972

1969

L. B. Lesem, P. M. Hirsch, and J. J. A. Jordan, “The kinoform: a new wave front reconstruction device,” IBM J. Res. Dev. 13, 150155 (1969).

1968

1965

Agour, M.

F. Yaras, M. Kovachev, R. Ilieva, M. Agour, and L. Onural, “Holographic reconstructions using phase-only spatial light modulators,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (2008), paper PD-1.

Ahrenberg, L.

Amako, J.

Barkana, Y.

Y. Barkana and M. Belkin, “Laser eye injuries,” Survey Ophthalmol. 44, 459-478 (2000).
[CrossRef]

Belkin, M.

Y. Barkana and M. Belkin, “Laser eye injuries,” Survey Ophthalmol. 44, 459-478 (2000).
[CrossRef]

Benckert, L.

Benton, S.

P. S. Hilaire, S. Benton, M. Lucente, and H. P. M., “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73-84 (1992).

Benzie, P.

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14, 7636-7641 (2006).
[CrossRef]

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, “Holographic 3DTV displays using spatial light modulators,” in Three-Dimensional Television--Capture, Transmission, Display, H. M. Ozaktas and L. Onural, eds. (Springer, 2008), pp. 529-555.

Bove, J. V.

D. E. Smalley, Q. Y. J. Smithwick, and J. V. M. Bove, “Holographic video display based on guided-wave acousto-optic devices,” Proc. SPIE 6488, 64880L (2007).

Bove, V.

J. Watlington, M. Lucente, C. Sparrell, V. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

Cameron, C. D.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, “3D electronic holography display system using a 100 mega-pixel spatial light modulator,” Proc. SPIE 5249, 297-308 (2004).

Coomber, S. D.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, “3D electronic holography display system using a 100 mega-pixel spatial light modulator,” Proc. SPIE 5249, 297-308 (2004).

Esmer, G. B.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, “Holographic 3DTV displays using spatial light modulators,” in Three-Dimensional Television--Capture, Transmission, Display, H. M. Ozaktas and L. Onural, eds. (Springer, 2008), pp. 529-555.

Fujii, T.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

Futterer, G.

S. Reichelt, R. Haussler, N. Leister, G. Futterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrows TV and monitors--solutions, challenges, and prospects,” in IEEE Lasers and Electro-Optics Society, 2008. LEOS 2008, 21st Annual Meeting of the IEEE (IEEE, 2008), pp. 194-195.

Gerritsen, H. J.

Goldfischer, L. I.

Hanák, I.

Hannan, W. J.

Haussler, R.

S. Reichelt, R. Haussler, N. Leister, G. Futterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrows TV and monitors--solutions, challenges, and prospects,” in IEEE Lasers and Electro-Optics Society, 2008. LEOS 2008, 21st Annual Meeting of the IEEE (IEEE, 2008), pp. 194-195.

Hilaire, P. S.

P. S. Hilaire, S. Benton, M. Lucente, and H. P. M., “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73-84 (1992).

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. J. A. Jordan, “The kinoform: a new wave front reconstruction device,” IBM J. Res. Dev. 13, 150155 (1969).

Huntley, J. M.

Ilieva, R.

F. Yaras, M. Kovachev, R. Ilieva, M. Agour, and L. Onural, “Holographic reconstructions using phase-only spatial light modulators,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (2008), paper PD-1.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, “Holographic 3DTV displays using spatial light modulators,” in Three-Dimensional Television--Capture, Transmission, Display, H. M. Ozaktas and L. Onural, eds. (Springer, 2008), pp. 529-555.

Ito, T.

Janda, M.

Jordan, J. J. A.

L. B. Lesem, P. M. Hirsch, and J. J. A. Jordan, “The kinoform: a new wave front reconstruction device,” IBM J. Res. Dev. 13, 150155 (1969).

Kang, H.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

F. Yaras, H. Kang, and L. Onural, “Real-time color holographic video display system,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (IEEE, 2009).

F. Yaraş, H. Kang, and L. Onural, “Real-time multiple SLM color holographic display using multiple GPU acceleration,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DWA4.

H. Kang, “Quality improvements of the coherent holographic stereogram for natural 3D display and its applications,” Ph.D. dissertation (Nihon University, 2008).

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

H. Kang, F. Yaras, and L. Onural, “Quality comparison and acceleration for digital hologram generation method based on segmentation,” in Proceedings of 3DTV Conference: The True Vision--Capture, Transmission and Display of 3D Video, (IEEE, 2009).

Kohler, C.

Kovachev, M.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, “Holographic 3DTV displays using spatial light modulators,” in Three-Dimensional Television--Capture, Transmission, Display, H. M. Ozaktas and L. Onural, eds. (Springer, 2008), pp. 529-555.

F. Yaras, M. Kovachev, R. Ilieva, M. Agour, and L. Onural, “Holographic reconstructions using phase-only spatial light modulators,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (2008), paper PD-1.

Kubota, T.

K. Taima, H. Ueda, H. Okamoto, T. Kubota, Y. Nakamura, H. Nishida, H. Takahashi, and E. Shimizu, “New approach to the interactive holographic display system,” Proc. SPIE 2176, 23-29 (1994).

Leister, N.

S. Reichelt, R. Haussler, N. Leister, G. Futterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrows TV and monitors--solutions, challenges, and prospects,” in IEEE Lasers and Electro-Optics Society, 2008. LEOS 2008, 21st Annual Meeting of the IEEE (IEEE, 2008), pp. 194-195.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. J. A. Jordan, “The kinoform: a new wave front reconstruction device,” IBM J. Res. Dev. 13, 150155 (1969).

Lucente, M.

J. Watlington, M. Lucente, C. Sparrell, V. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

P. S. Hilaire, S. Benton, M. Lucente, and H. P. M., “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73-84 (1992).

Magnor, M.

Mark, J.

Masuda, N.

Matsumura, M.

Miura, H.

Myers, E.

Nakamura, Y.

K. Taima, H. Ueda, H. Okamoto, T. Kubota, Y. Nakamura, H. Nishida, H. Takahashi, and E. Shimizu, “New approach to the interactive holographic display system,” Proc. SPIE 2176, 23-29 (1994).

Nishida, H.

K. Taima, H. Ueda, H. Okamoto, T. Kubota, Y. Nakamura, H. Nishida, H. Takahashi, and E. Shimizu, “New approach to the interactive holographic display system,” Proc. SPIE 2176, 23-29 (1994).

Okamoto, H.

K. Taima, H. Ueda, H. Okamoto, T. Kubota, Y. Nakamura, H. Nishida, H. Takahashi, and E. Shimizu, “New approach to the interactive holographic display system,” Proc. SPIE 2176, 23-29 (1994).

Onural, L.

F. Yaras and L. Onural, “Color holographic reconstruction using multiple SLMs and LED illumination,” Proc. SPIE 7237, 72370O (2009).

M. Janda, I. Hanák, and L. Onural, “Hologram synthesis for photorealistic reconstruction,” J. Opt. Soc. Am. A 25, 3083-3096 (2008).
[CrossRef]

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, “Holographic 3DTV displays using spatial light modulators,” in Three-Dimensional Television--Capture, Transmission, Display, H. M. Ozaktas and L. Onural, eds. (Springer, 2008), pp. 529-555.

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

H. Kang, F. Yaras, and L. Onural, “Quality comparison and acceleration for digital hologram generation method based on segmentation,” in Proceedings of 3DTV Conference: The True Vision--Capture, Transmission and Display of 3D Video, (IEEE, 2009).

F. Yaraş, H. Kang, and L. Onural, “Real-time multiple SLM color holographic display using multiple GPU acceleration,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DWA4.

F. Yaras, H. Kang, and L. Onural, “Real-time color holographic video display system,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (IEEE, 2009).

F. Yaras, M. Kovachev, R. Ilieva, M. Agour, and L. Onural, “Holographic reconstructions using phase-only spatial light modulators,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (2008), paper PD-1.

Osten, W.

Ramberg, E. G.

Reichelt, S.

S. Reichelt, R. Haussler, N. Leister, G. Futterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrows TV and monitors--solutions, challenges, and prospects,” in IEEE Lasers and Electro-Optics Society, 2008. LEOS 2008, 21st Annual Meeting of the IEEE (IEEE, 2008), pp. 194-195.

Reyhan, T.

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, “Holographic 3DTV displays using spatial light modulators,” in Three-Dimensional Television--Capture, Transmission, Display, H. M. Ozaktas and L. Onural, eds. (Springer, 2008), pp. 529-555.

Schwab, X.

Schwerdtner, A.

S. Reichelt, R. Haussler, N. Leister, G. Futterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrows TV and monitors--solutions, challenges, and prospects,” in IEEE Lasers and Electro-Optics Society, 2008. LEOS 2008, 21st Annual Meeting of the IEEE (IEEE, 2008), pp. 194-195.

Shimizu, E.

K. Taima, H. Ueda, H. Okamoto, T. Kubota, Y. Nakamura, H. Nishida, H. Takahashi, and E. Shimizu, “New approach to the interactive holographic display system,” Proc. SPIE 2176, 23-29 (1994).

Shiraki, A.

Slinger, C. W.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, “3D electronic holography display system using a 100 mega-pixel spatial light modulator,” Proc. SPIE 5249, 297-308 (2004).

Smalley, D. E.

D. E. Smalley, Q. Y. J. Smithwick, and J. V. M. Bove, “Holographic video display based on guided-wave acousto-optic devices,” Proc. SPIE 6488, 64880L (2007).

Smith, A. P.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, “3D electronic holography display system using a 100 mega-pixel spatial light modulator,” Proc. SPIE 5249, 297-308 (2004).

Smith, M. A.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, “3D electronic holography display system using a 100 mega-pixel spatial light modulator,” Proc. SPIE 5249, 297-308 (2004).

Smithwick, Q. Y. J.

D. E. Smalley, Q. Y. J. Smithwick, and J. V. M. Bove, “Holographic video display based on guided-wave acousto-optic devices,” Proc. SPIE 6488, 64880L (2007).

Sonehara, T.

Sparrell, C.

J. Watlington, M. Lucente, C. Sparrell, V. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

Stanley, M.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, “3D electronic holography display system using a 100 mega-pixel spatial light modulator,” Proc. SPIE 5249, 297-308 (2004).

Sugie, T.

Taima, K.

K. Taima, H. Ueda, H. Okamoto, T. Kubota, Y. Nakamura, H. Nishida, H. Takahashi, and E. Shimizu, “New approach to the interactive holographic display system,” Proc. SPIE 2176, 23-29 (1994).

Takahashi, H.

K. Taima, H. Ueda, H. Okamoto, T. Kubota, Y. Nakamura, H. Nishida, H. Takahashi, and E. Shimizu, “New approach to the interactive holographic display system,” Proc. SPIE 2176, 23-29 (1994).

Tamitani, I.

J. Watlington, M. Lucente, C. Sparrell, V. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

Tanaka, T.

Ueda, H.

K. Taima, H. Ueda, H. Okamoto, T. Kubota, Y. Nakamura, H. Nishida, H. Takahashi, and E. Shimizu, “New approach to the interactive holographic display system,” Proc. SPIE 2176, 23-29 (1994).

Watlington, J.

J. Watlington, M. Lucente, C. Sparrell, V. Bove, and I. Tamitani, “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc. SPIE 2406, 172-183 (1995).

Watson, J.

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14, 7636-7641 (2006).
[CrossRef]

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, “Holographic 3DTV displays using spatial light modulators,” in Three-Dimensional Television--Capture, Transmission, Display, H. M. Ozaktas and L. Onural, eds. (Springer, 2008), pp. 529-555.

Watson, P. J.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, “3D electronic holography display system using a 100 mega-pixel spatial light modulator,” Proc. SPIE 5249, 297-308 (2004).

Wims, A. M.

Wood, A. D.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, and A. D. Wood, “3D electronic holography display system using a 100 mega-pixel spatial light modulator,” Proc. SPIE 5249, 297-308 (2004).

Yamaguchi, T.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

H. Yoshikawa and T. Yamaguchi, “Fast hologram calculation for holographic video display,” Proc. SPIE 6027, 561-566(2006).

Yaras, F.

F. Yaras and L. Onural, “Color holographic reconstruction using multiple SLMs and LED illumination,” Proc. SPIE 7237, 72370O (2009).

F. Yaras, M. Kovachev, R. Ilieva, M. Agour, and L. Onural, “Holographic reconstructions using phase-only spatial light modulators,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (2008), paper PD-1.

F. Yaras, H. Kang, and L. Onural, “Real-time color holographic video display system,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (IEEE, 2009).

F. Yaraş, H. Kang, and L. Onural, “Real-time multiple SLM color holographic display using multiple GPU acceleration,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DWA4.

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

H. Kang, F. Yaras, and L. Onural, “Quality comparison and acceleration for digital hologram generation method based on segmentation,” in Proceedings of 3DTV Conference: The True Vision--Capture, Transmission and Display of 3D Video, (IEEE, 2009).

Yoshikawa, H.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

H. Yoshikawa and T. Yamaguchi, “Fast hologram calculation for holographic video display,” Proc. SPIE 6027, 561-566(2006).

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

Appl. Opt.

IBM J. Res. Dev.

L. B. Lesem, P. M. Hirsch, and J. J. A. Jordan, “The kinoform: a new wave front reconstruction device,” IBM J. Res. Dev. 13, 150155 (1969).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).

Opt. Express

Proc. SPIE

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[CrossRef]

Other

F. Yaras, M. Kovachev, R. Ilieva, M. Agour, and L. Onural, “Holographic reconstructions using phase-only spatial light modulators,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (2008), paper PD-1.

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F. Yaraş, H. Kang, and L. Onural, “Real-time multiple SLM color holographic display using multiple GPU acceleration,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DWA4.

F. Yaras, H. Kang, and L. Onural, “Real-time color holographic video display system,” in Proceedings of 3D TV Conference: The True Vision--Capture, Transmission and Display of 3D Video (IEEE, 2009).

M. Kovachev, R. Ilieva, P. Benzie, G. B. Esmer, L. Onural, J. Watson, and T. Reyhan, “Holographic 3DTV displays using spatial light modulators,” in Three-Dimensional Television--Capture, Transmission, Display, H. M. Ozaktas and L. Onural, eds. (Springer, 2008), pp. 529-555.

H. Kang, F. Yaraş, L. Onural, and H. Yoshikawa, “Real-time fringe pattern generation with high quality,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DTuB7.

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Figures (9)

Fig. 1
Fig. 1

Overall setup: BE, beam expander; R, red SLM; B, blue SLM; G, green SLM; D, driver unit of SLMs; N, network; BS, nonpolarized beam splitters.

Fig. 2
Fig. 2

Hologram calculation algorithm.

Fig. 3
Fig. 3

Illustration of N-point DFT as a weighted sum of complex sinusoids.

Fig. 4
Fig. 4

Pipelined computation using GPUs.

Fig. 5
Fig. 5

End-to-end system.

Fig. 6
Fig. 6

Rigid color 3D object.

Fig. 7
Fig. 7

Computer reconstruction using the ACPAS algorithm.

Fig. 8
Fig. 8

Single color reconstruction (a) by green laser (b) by green LED.

Fig. 9
Fig. 9

Optical reconstruction of a single frame of the 3D object.

Tables (3)

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Table 1 Overall System Specifications

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Table 2 Characteristics of LEDs

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Table 3 Performance Analysis of the System for 2 Mpixel Hologram Output [22]

Equations (5)

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I ACPAS ( ξ , η ) = i = 1 N a i r i exp { j 2 π [ ( ξ ξ c ) f i ξ c int + ( η η c ) f i η c int ] + j k r i + j ϕ c } ,
ϕ c = 2 π { ( f i ξ c f i ξ c int ) ( ξ c x i ) + ( f i η c f i η c int ) ( η c y i ) } ,
I ACPAS ( ξ , η ) = i = 1 N A i ( ξ , η ) exp ( j 2 π Φ i ( ξ , η ) ) ,
A i ( ξ , η ) = a i r i exp ( j k r i ) exp ( j ϕ c ) ,
Φ i ( ξ , η ) = ( ξ ξ c ) f i ξ c int + ( η η c ) f i η c int .

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