OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 3 — Mar. 1, 2003
  • pp: 411–420

Continuous parallax in discrete pixelated integral three-dimensional displays

Matthew C. Forman, Neil Davies, and Malcolm McCormick  »View Author Affiliations

JOSA A, Vol. 20, Issue 3, pp. 411-420 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (482 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An evaluation of the retention of continuous parallax in pixelated integral three-dimensional image displays is presented. The integral image capture process is first considered, to provide a starting point for the investigation. The complementary display system is then examined in detail. The viewing geometry of the display system is analyzed to provide a foundation for the work to follow, and an experimental investigation and simulations of the characteristics of emitted ray bundles are presented. Next, an analytical model of decoding lenslet array operation is derived, leading to an understanding of the process responsible for production of continuous parallax in replay. It is found that if the lateral resolution of the lenslet is matched to that of the display, continuous parallax is retained in the replayed image, where the finite aberration-limited resolution of the lenslet acts to produce a low-pass reconstruction filter. A condition is derived for optimal continuous parallax in replay, based on a relationship between pixel width and lenslet rms spot size.

© 2003 Optical Society of America

OCIS Codes
(110.0110) Imaging systems : Imaging systems
(110.6880) Imaging systems : Three-dimensional image acquisition
(350.3950) Other areas of optics : Micro-optics

Original Manuscript: May 14, 2002
Revised Manuscript: September 4, 2002
Manuscript Accepted: October 9, 2002
Published: March 1, 2003

Matthew C. Forman, Neil Davies, and Malcolm McCormick, "Continuous parallax in discrete pixelated integral three-dimensional displays," J. Opt. Soc. Am. A 20, 411-420 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Motoki, H. Isono, I. Yuyama, “Present status of three-dimensional television research,” Proc. IEEE 83, 1009–1021 (1995). [CrossRef]
  2. G. Lippmann, “Epreuves reversibles,” C. R. Acad. Sci. 146, 446–451 (1908).
  3. H. E. Ives, “Optical properties of a Lippmann lenticulated sheet,” J. Opt. Soc. Am. 21, 171–176 (1931). [CrossRef]
  4. C. B. Burkhardt, E. T. Doherty, “Beaded plate recording of integral photographs,” Appl. Opt. 8, 2329–2331 (1969). [CrossRef]
  5. R. L. de Montebello, “Wide angle integral photography—the integram technique,” in Three-Dimensional Imaging, S. A. Benton, ed., Proc. SPIE120, 73–91 (1970). [CrossRef]
  6. Yu. A. Dudnikov, B. K. Rozhkov, E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).
  7. F. Okano, H. Hoshino, J. Arai, I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997). [CrossRef] [PubMed]
  8. H. Arimoto, B. Javidi, “Integral three-dimensional imaging with computed reconstruction,” Opt. Lett. 26, 157–159 (2001). [CrossRef]
  9. Byoungho Lee, Sung-Wook Min, B. Javidi, “Theoretical analysis for three-dimensional integral imaging systems with double devices,” Appl. Opt. 41, 4856–4865 (2002). [CrossRef] [PubMed]
  10. N. Davies, M. McCormick, L. Yang, “Three dimensional imaging systems: a new development,” Appl. Opt. 27, 4520–4528 (1988). [CrossRef] [PubMed]
  11. N. Davies, M. McCormick, M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994). [CrossRef]
  12. M. Brewin, M. Forman, N. Davies, “Electronic capture and display of full parallax 3D images,” in Stereoscopic Displays and Virtual Reality Systems II, S. S. Fisher, J. O. Merritt, M. T. Bolas, eds., Proc. SPIE2409, 118–124 (1995). [CrossRef]
  13. N. A. Valyus, Stereoscopy (Focal Press, London, 1966).
  14. T. Okoshi, Three Dimensional Imaging Techniques (Academic, London, 1976).
  15. J. R. Moor, A. R. L. Travis, S. R. Lang, O. M. Castle, “The implementation of a multi-view autostereoscopic display,” in IEE Colloquium on Stereoscopic Television (Institute of Electrical Engineers, London, 1992), Digest No. 1992/173, pp. 4/5–4/16.
  16. I. Sexton, “Assorted problems with stereo displays (presentation),” 1996, http://www.cse.dmu.ac.uk/IRC/minutes/premins/sep15/ .
  17. J. Faubert, “Motion parallax, stereoscopy, and the perception of depth: practical and theoretical issues,” Three-Dimensional Video and Display: Devices and Systems, B. Javidi, ed., Vol. CR76 of SPIE Critical Review Series (SPIE Optical Engineering Press, Bellingham, Wash., 2001), pp. 168–191.
  18. C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58, 71–76 (1968). [CrossRef]
  19. Breault Research Organization, “ASAP version 7.0.3,” 2001, http://www.bro.com/ .
  20. Silonex Inc., “NORP-11, 12, 13 Series CdS Photocells data sheet,” 2002, http://www.silonex.com/ .
  21. M. A. Brewin, “Reduced information integral imaging,” Ph.D. thesis (De Montfort University, Leicester, UK, 1998).
  22. F. L. Pedrotti, S. J. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J.1993).
  23. E. H. Adelson, J. Y. A. Wang, “Single lens stereo with plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992). [CrossRef]

Cited By

Alert me when this paper is cited

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.

CrossCheck Deposited