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Applied Optics

Applied Optics


  • Vol. 10, Iss. 10 — Oct. 1, 1971
  • pp: 2284–2291

Optimum Design and Depth Resolution of Lens-Sheet and Projection-Type Three-Dimensional Displays

T. Okoshi  »View Author Affiliations

Applied Optics, Vol. 10, Issue 10, pp. 2284-2291 (1971)

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The primary purpose of this paper is to propose a comprehensive optimum-design theory of lenticular-sheet three-dimensional pictures. The proposed theory features the use of depth resolution of a 3–D image as the measure of the 3–D picture quality. The optimum parameters in the picture taking process, the optimum lens pitch and the depth-resolution limitation, are discussed. The obtained results are also applicable to a specific type of integral photography and to the projection-type 3–D display including projection-type holography. It is found that the optimum pitch of the lens sheet or the lens-type direction selective screen ranges between 0.1 mm and 0.5 mm in most cases, whereas it ranges between 0.2 mm and 1 mm for the triple-mirror screen.

© 1971 Optical Society of America

Original Manuscript: March 22, 1971
Published: October 1, 1971

T. Okoshi, "Optimum Design and Depth Resolution of Lens-Sheet and Projection-Type Three-Dimensional Displays," Appl. Opt. 10, 2284-2291 (1971)

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  1. C. B. Burckhardt, J. Opt. Soc. Am. 58, 71 (1968). [CrossRef]
  2. The term lens sheet in the title is used generically in this paper for both LS and IP.
  3. T. Okoshi, A. Yano, Y. Fukumori, Appl. Opt. 10, 482 (1971). [CrossRef] [PubMed]
  4. T. Okoshi, A. Yano, Opt. Commun. 3, 85(1971). [CrossRef]
  5. The symbols are chosen to facilitate the comparison with related papers such as Refs. 1, 2, and 3.
  6. In practice, some part of the image (usually 10–40%) is reconstructed in front of the lenticular sheet. It is only for mathematical simplicity that in Fig. 2 the whole image is assumed to be reconstructed behind the sheet.
  7. An alternative, probably more reasonable definition will be Δ′=(Δs2+Δd2)12. The definition in the text (algebraic sum) is used here only for its simplicity. The difference from the second definition only makes the estimation of the over-all resolution a little more pessimistic. It is easy to show that the ratio (Δ/Δ′) is between 1 and √2.
  8. C. B. Burckhardt, R. J. Collier, E. T. Doherty, Appl. Opt. 7, 627 (1968). [CrossRef] [PubMed]
  9. In a triple mirror without curvature, the six reflected components are in the same phase with each other for any direction of incidence. Therefore, the theoretical diffraction limitation is smaller than in a curved triple mirror.

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