Abstract

Two new concepts are deduced—those of hoxels and spatial spectrum by vector expression of four- dimensional Fourier transform integrals of the wave function or probability amplitude of any quantized energy probability distribution sampled by photons of this nature. Spatial spectrum collecting and recovering processes through hoxels by camera–projector arrays and holographic functional screens are proposed in detail to recover this three-dimensional holographic nature as a reinvention of holography. A real-time holographic display by simple aggregation of a digital camera–projector array is demonstrated as a rudimentary holographic television by holographic concepts, but without the need for coherent interference, as in conventional holography, or the encoded spatial frequency pattern of digital holography.

© 2010 Optical Society of America

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References

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  1. T. Okoshi, Three-Dimensional Imaging Techniques (Academic, 1976).
  2. J. A. Norling, “The stereoscopic art—a reprint,” SMPTE J. 60, 286–308 (1953).
  3. F. E. Ives, “Parallax stereogram and process of making same,” U.S. patent 725,567 (14 April 1903).
  4. M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. 7, 821–825 (1908).
  5. C. B. Burckhardt and E. T. Doherty, “Beaded plate recording of integral photographs,” Appl. Opt. 8, 2329–2331 (1969).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. D. Gabor, “Microscopy by reconstructed wavefronts and communication theory,” Proc. Phys. Soc. A194, 454–487(1949).
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    [CrossRef]
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    [CrossRef]
  10. E. N. Leith and J. Upatnieks, “Wavefront reconstruction with diffused illumination and three-dimensional objects,” J. Opt. Soc. Am. 54, 1295–1301 (1964).
    [CrossRef]
  11. Y. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543–545 (1962).
  12. Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave field of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1963).
  13. Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave field of its scattered radiation. II,” Opt. Spectrosc. 18, 152–157 (1965).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. L. Huff and R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).
  22. C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
    [CrossRef]
  23. M. L. Huebschman, B. Munjuluri, and H. R. Garner, “Dynamic holographic 3-D image projection,” Opt. Express 11, 437–445(2003).
    [CrossRef] [PubMed]
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  25. S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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  28. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

2009 (1)

2008 (3)

H. I. Bjelkhagen and R. K. Kostuk, eds., Practical Holography XXII: Materials and Applications (SPIE, 2008).

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Zebra Imaging, Inc., http://www.zebraimaging.com (2008).

2004 (1)

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

2003 (1)

1992 (3)

L. L. Cross and C. Cross, “HoloStories: reminiscences and a prognostication on holography,” Leonardo 25, 421–424 (1992).
[CrossRef]

M. A. Klug, M. W. Halle, and P. M. Hubel, “Full color ultragrams,” Proc. SPIE 1667, 110–119 (1992).
[CrossRef]

P. St. Hilaire, M. Lucente, and S. A. Benton, “Synthetic aperture holography: a novel approach to three dimensional displays,” J. Opt. Soc. Am. A 9, 1969–1978 (1992).
[CrossRef]

1980 (1)

L. Huff and R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).

1976 (1)

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, 1976).

1969 (2)

C. B. Burckhardt and E. T. Doherty, “Beaded plate recording of integral photographs,” Appl. Opt. 8, 2329–2331 (1969).
[CrossRef] [PubMed]

S. A. Benton, “Hologram reconstruction with extended light sources,” J. Opt. Soc. Am. 59, 1545–1546 (1969).

1968 (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

1967 (2)

1965 (1)

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave field of its scattered radiation. II,” Opt. Spectrosc. 18, 152–157 (1965).

1964 (1)

1963 (2)

E. N. Leith and J. Upatnieks, “Wavefront reconstruction with continuous-tone objects,” J. Opt. Soc. Am. 53, 1377–1381(1963).
[CrossRef]

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave field of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1963).

1962 (2)

Y. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543–545 (1962).

E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130(1962).
[CrossRef]

1953 (1)

J. A. Norling, “The stereoscopic art—a reprint,” SMPTE J. 60, 286–308 (1953).

1949 (1)

D. Gabor, “Microscopy by reconstructed wavefronts and communication theory,” Proc. Phys. Soc. A194, 454–487(1949).

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–779(1948).
[CrossRef] [PubMed]

1908 (1)

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

1891 (1)

G. Lippmann, “La photographie des couleurs,” C. R. Hebd. Seances Acad. Sci. 112, 274–275 (1891).

Benton, S. A.

Bjelkhagen, H. I.

H. I. Bjelkhagen and R. K. Kostuk, eds., Practical Holography XXII: Materials and Applications (SPIE, 2008).

Blanche, P. A.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Burckhardt, C. B.

Cameron, C. D.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Choi, S.

Coomber, S. D.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Cross, C.

L. L. Cross and C. Cross, “HoloStories: reminiscences and a prognostication on holography,” Leonardo 25, 421–424 (1992).
[CrossRef]

Cross, L. L.

L. L. Cross and C. Cross, “HoloStories: reminiscences and a prognostication on holography,” Leonardo 25, 421–424 (1992).
[CrossRef]

Denisyuk, Y. N.

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave field of its scattered radiation. II,” Opt. Spectrosc. 18, 152–157 (1965).

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave field of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1963).

Y. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543–545 (1962).

Doherty, E. T.

Dou, W.

Fan, F. C.

Flores, D.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Fusek, R. L.

L. Huff and R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).

Gabor, D.

D. Gabor, “Microscopy by reconstructed wavefronts and communication theory,” Proc. Phys. Soc. A194, 454–487(1949).

D. Gabor, “A new microscopic principle,” Nature 161, 777–779(1948).
[CrossRef] [PubMed]

Garner, H. R.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Gu, T.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Halle, M. W.

M. A. Klug, M. W. Halle, and P. M. Hubel, “Full color ultragrams,” Proc. SPIE 1667, 110–119 (1992).
[CrossRef]

Hubel, P. M.

M. A. Klug, M. W. Halle, and P. M. Hubel, “Full color ultragrams,” Proc. SPIE 1667, 110–119 (1992).
[CrossRef]

Huebschman, M. L.

Huff, L.

L. Huff and R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).

Ives, F. E.

F. E. Ives, “Parallax stereogram and process of making same,” U.S. patent 725,567 (14 April 1903).

Jeong, T. H.

Jiang, C. C.

Klug, M. A.

M. A. Klug, M. W. Halle, and P. M. Hubel, “Full color ultragrams,” Proc. SPIE 1667, 110–119 (1992).
[CrossRef]

Kostuk, R. K.

H. I. Bjelkhagen and R. K. Kostuk, eds., Practical Holography XXII: Materials and Applications (SPIE, 2008).

Leith, E. N.

Li, G.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Lin, W.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Lippmann, G.

G. Lippmann, “La photographie des couleurs,” C. R. Hebd. Seances Acad. Sci. 112, 274–275 (1891).

Lippmann, M. G.

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

Lohmann, A. W.

Lucente, M.

Miller, R. J.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Munjuluri, B.

Norling, J. A.

J. A. Norling, “The stereoscopic art—a reprint,” SMPTE J. 60, 286–308 (1953).

Norwood, R. A.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Okoshi, T.

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, 1976).

Paris, D.

Payne, D. A.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Peyghambarian, N.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Rokutanda, S.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Shang, X.

Slinger, C. W.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Smith, A. P.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Smith, M. G.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

St. Hilaire, P.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

P. St. Hilaire, M. Lucente, and S. A. Benton, “Synthetic aperture holography: a novel approach to three dimensional displays,” J. Opt. Soc. Am. A 9, 1969–1978 (1992).
[CrossRef]

Stanley, M.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Tay, S.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Thomas, J.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Tunc, A. V.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Upatnieks, J.

Voorakaranam, R.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Wang, P.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Watson, P. J.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

Xu, D.

Yamamoto, M.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

Yu, C.

Appl. Opt. (2)

C. R. Hebd. Seances Acad. Sci. (1)

G. Lippmann, “La photographie des couleurs,” C. R. Hebd. Seances Acad. Sci. 112, 274–275 (1891).

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (1)

J. Phys. (1)

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

Leonardo (1)

L. L. Cross and C. Cross, “HoloStories: reminiscences and a prognostication on holography,” Leonardo 25, 421–424 (1992).
[CrossRef]

Nature (2)

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef] [PubMed]

D. Gabor, “A new microscopic principle,” Nature 161, 777–779(1948).
[CrossRef] [PubMed]

Opt. Eng. (1)

L. Huff and R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).

Opt. Express (1)

Opt. Lett. (1)

Opt. Spectrosc. (2)

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave field of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1963).

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave field of its scattered radiation. II,” Opt. Spectrosc. 18, 152–157 (1965).

Proc. Phys. Soc. (1)

D. Gabor, “Microscopy by reconstructed wavefronts and communication theory,” Proc. Phys. Soc. A194, 454–487(1949).

Proc. SPIE (2)

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

M. A. Klug, M. W. Halle, and P. M. Hubel, “Full color ultragrams,” Proc. SPIE 1667, 110–119 (1992).
[CrossRef]

SMPTE J. (1)

J. A. Norling, “The stereoscopic art—a reprint,” SMPTE J. 60, 286–308 (1953).

Sov. Phys. Dokl. (1)

Y. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543–545 (1962).

Other (5)

F. E. Ives, “Parallax stereogram and process of making same,” U.S. patent 725,567 (14 April 1903).

Zebra Imaging, Inc., http://www.zebraimaging.com (2008).

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, 1976).

H. I. Bjelkhagen and R. K. Kostuk, eds., Practical Holography XXII: Materials and Applications (SPIE, 2008).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Supplementary Material (1)

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Figures (22)

Fig. 1
Fig. 1

Quantized energy probability distribution and wave function by photons.

Fig. 2
Fig. 2

Position vector r and propagation vector k .

Fig. 3
Fig. 3

Hoxel definition, in which each light ray represents a monochromatic plane wave radiated from a corresponding point on object O, with its average wavelength λ a .

Fig. 4
Fig. 4

Spatial spectrum definition, in which each light ray represents the parallel perspective of each hoxel near the object O; the final result is a color image in digital form.

Fig. 5
Fig. 5

Visual information of this nature with spatial spectrum language.

Fig. 6
Fig. 6

Spatial spectrum collection.

Fig. 7
Fig. 7

Recovery of 3D information of a space.

Fig. 8
Fig. 8

M × N hot spots are seen directly.

Fig. 9
Fig. 9

Discrete spatial spectrum distribution of hoxel H j k .

Fig. 10
Fig. 10

Output with large angular expanding input by a single spatial spectrum.

Fig. 11
Fig. 11

Output with huge angular expanding input by an M × N individual spatial spectrum.

Fig. 12
Fig. 12

Output of spatial spectrum through a holographic functional screen.

Fig. 13
Fig. 13

Output of HPO.

Fig. 14
Fig. 14

Relation between expanding of a single spectrum and integral spectra.

Fig. 15
Fig. 15

Laser speckle technology.

Fig. 16
Fig. 16

Holographic lens array.

Fig. 17
Fig. 17

Recovering fidelity.

Fig. 18
Fig. 18

Table of recovering fidelity ( 2 Z ) under different ω m n and h.

Fig. 19
Fig. 19

Sketch of experiment.

Fig. 20
Fig. 20

Spatial spectrum collecting system.

Fig. 21
Fig. 21

Spatial spectrum recovering system.

Fig. 22
Fig. 22

Pictures taken from functional screen. (a) Demonstration of dynamic performance display (Media 1) from the same viewing angle; the image is ambiguous beyond the depth of recovering fidelity. (b) Demonstration of stationary performance display for HPO in different viewing angles.

Equations (5)

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I ( r , t ) = f * f = | f ( r , t ) | 2 ,
f ( r , t ) = 0 + F ( k , v ) exp [ j 2 π ( k · r + v t ) ] d k d v .
I ( k , v ) = F * F = | F ( k , v | 2 ,
F ( k , v ) = 0 + f ( r , t ) exp [ j 2 π ( k · r + v t ) ] d r d t .
2 Δ Z = 2 Δ h / ω m n .

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