P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

J. Arai, M. Okui, M. Kobayashi, F. Okano, “Geometrical effects of positional errors in integral photography,” J. Opt. Soc. Am. A 21, 951–958 (2004).

[Crossref]

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).

[Crossref]

J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).

[Crossref]

F. Okano, H. Hoshino, J. Arai, I. Yayuma, “Real time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).

[Crossref]
[PubMed]

D. A. Atchinson, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000).

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).

[Crossref]

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).

[Crossref]

N. Davies, M. McCormick, L. Yang, “Three-dimensional imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988).

[Crossref]
[PubMed]

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).

[Crossref]

J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).

[Crossref]

H. Hoshino, F. Okano, H. Isono, I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).

[Crossref]

F. Okano, H. Hoshino, J. Arai, I. Yayuma, “Real time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).

[Crossref]
[PubMed]

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

J.-S. Jang, B. Javidi, “Three-dimensional integral imaging of micro-objects,” Opt. Lett. 29, 1230–1232 (2004).

[Crossref]
[PubMed]

J.-S. Jang, B. Javidi, “Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes,” Opt. Lett. 28, 1924–1926 (2003).

[Crossref]
[PubMed]

J.-S. Jang, B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. 42, 1869–1870 (2003).

[Crossref]

J.-S. Jang, B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27, 324–326 (2002).

[Crossref]

J.-S. Jang, B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27, 1144–1146 (2002).

[Crossref]

J.-S. Jang, B. Javidi, “Three-dimensional integral imaging of micro-objects,” Opt. Lett. 29, 1230–1232 (2004).

[Crossref]
[PubMed]

R. Martı́nez-Cuenca, G. Saavedra, M. Martı́nez-Corral, B. Javidi, “Enhanced depth of field integral imaging with sensor resolution constraints,” Opt. Express 12, 5237–5242 (2004).

[Crossref]
[PubMed]

M. Martı́nez-Corral, B. Javidi, R. Martı́nez-Cuenca, G. Saavedra, “Integral imaging with improved depth of field by use of amplitude modulated microlens array,” Appl. Opt. 43, 5806–5813 (2004).

[Crossref]

J.-S. Jang, B. Javidi, “Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes,” Opt. Lett. 28, 1924–1926 (2003).

[Crossref]
[PubMed]

A. Stern, B. Javidi, “Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. 42, 7036–7042 (2003).

[Crossref]
[PubMed]

S. Kishk, B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11, 3528–3541 (2003).

[Crossref]
[PubMed]

J.-S. Jang, B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. 42, 1869–1870 (2003).

[Crossref]

J.-S. Jang, B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27, 1144–1146 (2002).

[Crossref]

J.-S. Jang, B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27, 324–326 (2002).

[Crossref]

H. Choi, S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Multiple-viewing-zone integral imaging using dynamic barrier array for three-dimensional displays,” Opt. Express 11, 927–932 (2003).

[Crossref]
[PubMed]

J.-H. Park, S.-W. Min, S. Jung, B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. 40, 5217–5232 (2001).

[Crossref]

M. P. Keating, Geometric, Physical, and Visual Optics (Butterworth-Heinemann, Oxford, UK, 1988).

H. Choi, S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Multiple-viewing-zone integral imaging using dynamic barrier array for three-dimensional displays,” Opt. Express 11, 927–932 (2003).

[Crossref]
[PubMed]

J.-H. Park, S.-W. Min, S. Jung, B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. 40, 5217–5232 (2001).

[Crossref]

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. (Paris) 7, 821–825 (1908).

M. Martı́nez-Corral, B. Javidi, R. Martı́nez-Cuenca, G. Saavedra, “Integral imaging with improved depth of field by use of amplitude modulated microlens array,” Appl. Opt. 43, 5806–5813 (2004).

[Crossref]

R. Martı́nez-Cuenca, G. Saavedra, M. Martı́nez-Corral, B. Javidi, “Enhanced depth of field integral imaging with sensor resolution constraints,” Opt. Express 12, 5237–5242 (2004).

[Crossref]
[PubMed]

R. Martı́nez-Cuenca, G. Saavedra, M. Martı́nez-Corral, B. Javidi, “Enhanced depth of field integral imaging with sensor resolution constraints,” Opt. Express 12, 5237–5242 (2004).

[Crossref]
[PubMed]

M. Martı́nez-Corral, B. Javidi, R. Martı́nez-Cuenca, G. Saavedra, “Integral imaging with improved depth of field by use of amplitude modulated microlens array,” Appl. Opt. 43, 5806–5813 (2004).

[Crossref]

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).

[Crossref]

N. Davies, M. McCormick, L. Yang, “Three-dimensional imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988).

[Crossref]
[PubMed]

H. Choi, S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Multiple-viewing-zone integral imaging using dynamic barrier array for three-dimensional displays,” Opt. Express 11, 927–932 (2003).

[Crossref]
[PubMed]

J.-H. Park, S.-W. Min, S. Jung, B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. 40, 5217–5232 (2001).

[Crossref]

J. Arai, M. Okui, M. Kobayashi, F. Okano, “Geometrical effects of positional errors in integral photography,” J. Opt. Soc. Am. A 21, 951–958 (2004).

[Crossref]

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).

[Crossref]

J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).

[Crossref]

H. Hoshino, F. Okano, H. Isono, I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).

[Crossref]

F. Okano, H. Hoshino, J. Arai, I. Yayuma, “Real time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).

[Crossref]
[PubMed]

J. Arai, M. Okui, M. Kobayashi, F. Okano, “Geometrical effects of positional errors in integral photography,” J. Opt. Soc. Am. A 21, 951–958 (2004).

[Crossref]

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).

[Crossref]

H. Choi, S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Multiple-viewing-zone integral imaging using dynamic barrier array for three-dimensional displays,” Opt. Express 11, 927–932 (2003).

[Crossref]
[PubMed]

J.-H. Park, S.-W. Min, S. Jung, B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. 40, 5217–5232 (2001).

[Crossref]

M. Martı́nez-Corral, B. Javidi, R. Martı́nez-Cuenca, G. Saavedra, “Integral imaging with improved depth of field by use of amplitude modulated microlens array,” Appl. Opt. 43, 5806–5813 (2004).

[Crossref]

R. Martı́nez-Cuenca, G. Saavedra, M. Martı́nez-Corral, B. Javidi, “Enhanced depth of field integral imaging with sensor resolution constraints,” Opt. Express 12, 5237–5242 (2004).

[Crossref]
[PubMed]

D. A. Atchinson, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000).

J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).

[Crossref]

H. Hoshino, F. Okano, H. Isono, I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).

[Crossref]

D. H. McMahon, H. J. Caulfield, “A technique for producing wide-angle holographic displays,” Appl. Opt. 9, 91–96 (1970).

[Crossref]
[PubMed]

F. Okano, H. Hoshino, J. Arai, I. Yayuma, “Real time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).

[Crossref]
[PubMed]

J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).

[Crossref]

L. Erdmann, K. J. Gabriel, “High-resolution digital photography by use of a scanning microlens array,” Appl. Opt. 40, 5592–5599 (2001).

[Crossref]

A. Stern, B. Javidi, “Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. 42, 7036–7042 (2003).

[Crossref]
[PubMed]

T. Okoshi, “Optimum design and depth resolution of lens-sheat and projection-type three-dimensional displays,” Appl. Opt. 10, 2284–2291 (1971).

[Crossref]
[PubMed]

N. Davies, M. McCormick, L. Yang, “Three-dimensional imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988).

[Crossref]
[PubMed]

M. Martı́nez-Corral, B. Javidi, R. Martı́nez-Cuenca, G. Saavedra, “Integral imaging with improved depth of field by use of amplitude modulated microlens array,” Appl. Opt. 43, 5806–5813 (2004).

[Crossref]

J.-H. Park, S.-W. Min, S. Jung, B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. 40, 5217–5232 (2001).

[Crossref]

J. Arai, M. Okui, M. Kobayashi, F. Okano, “Geometrical effects of positional errors in integral photography,” J. Opt. Soc. Am. A 21, 951–958 (2004).

[Crossref]

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).

[Crossref]

H. Hoshino, F. Okano, H. Isono, I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).

[Crossref]

M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. (Paris) 7, 821–825 (1908).

J.-S. Jang, B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. 42, 1869–1870 (2003).

[Crossref]

N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).

[Crossref]

H. Choi, S.-W. Min, S. Jung, J.-H. Park, B. Lee, “Multiple-viewing-zone integral imaging using dynamic barrier array for three-dimensional displays,” Opt. Express 11, 927–932 (2003).

[Crossref]
[PubMed]

R. Martı́nez-Cuenca, G. Saavedra, M. Martı́nez-Corral, B. Javidi, “Enhanced depth of field integral imaging with sensor resolution constraints,” Opt. Express 12, 5237–5242 (2004).

[Crossref]
[PubMed]

H. Liao, M. Iwahara, N. Hata, T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Express 12, 1067–1076 (2004).

[Crossref]
[PubMed]

S. Kishk, B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11, 3528–3541 (2003).

[Crossref]
[PubMed]

J.-S. Jang, B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27, 1144–1146 (2002).

[Crossref]

J.-S. Jang, B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27, 324–326 (2002).

[Crossref]

J.-S. Jang, B. Javidi, “Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes,” Opt. Lett. 28, 1924–1926 (2003).

[Crossref]
[PubMed]

J.-S. Jang, B. Javidi, “Three-dimensional integral imaging of micro-objects,” Opt. Lett. 29, 1230–1232 (2004).

[Crossref]
[PubMed]

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68, 548–564 (1980).

[Crossref]

S. A. Benton, ed., Selected Papers on Three-Dimensional Displays (SPIE Optical Engineering Press, Bellingham, Wash., 2001).

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, J.-P. Huignard, “Image reconstruction using electro-optic holography,” Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003 (IEEE Press, Piscataway, N.J., 2003), Vol. 1, pp. 172–173.

D. A. Atchinson, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000).

M. P. Keating, Geometric, Physical, and Visual Optics (Butterworth-Heinemann, Oxford, UK, 1988).

An exact calculation would give the reconstructed image as the convolution between O(x)and a properly scaled version of the self-convolution of function H∘(x; 0).Since the study of resolution is not the aim of this paper, the following calculations can be accurately performed by assuming nonsignificant differences between the object and the reconstructed image.