Open Access
Add to BibSonomyAbstract
We propose a method for enhancing depth-of-field, in which the spot size on a marginal depth plane is reduced. This method is implemented in a projection-type integral imaging system using a negative lens array without a diffuser. Numerical simulation results show that the spot size is merely 5.7% of that in a conventional system. Thus, the depth-of-field in the proposed system is enhanced by 17.5 times over that in a conventional system. Optical experiments confirm good agreement between the results and numerical predictions.
©2012 Optical Society of America
1. Introduction
A conventional integral imaging (II) system uses a positive lens array to integrate and reconstruct elemental images for 3D display technology [1–6]. In accordance with the principle of II, the reconstructed 3D object is located around the central depth plane (CDP) [3,7], where the depth-of-field (DOF) is severely limited by the aperture diaphragm of the lens array and resolution of the elemental images. Although researchers have proposed methods for the multi-layer enhancement of the DOF in animated technologies for 3D displays [8–20], these approaches are highly complicated and expensive. Enhancing DOF four times with these methods necessitates four layers and 200 Hz of refresh frequency, conditions that approach those used in conventional methods.
In this paper, we propose an approach to enhancing DOF, in which the spot size on the marginal depth plane (MDP) is reduced. This method uses a projection-type II system with a negative lens array without a diffuser. Numerical simulation results show that the spot size of the proposed system is 5.7% of that in a conventional system, in which a positive lens array and a diffuser are used under the same parameters. The DOF generated by the proposed method is enhanced by 17.5 times over that of a conventional system. Optical experimental results demonstrate the feasibility of our system.
The DOF of a conventional II system is determined by the spot size of the integrated points on the MDP (Fig. 1 ). Spot size is determined by the aperture diaphragm (Eq. (1)). The spot size of the imaged points on the MDP is denoted by Spo, which can be calculated by
where a is the distance from the lens array to the CDP, l denotes the distance from the CDP to the MDP, and p represents the aperture diaphragm of a conventional system. In a conventional system, p generally denotes the pitch of the lens. The DOF is small because it is limited by the spot size on the MDP. In conventional approaches, DOF can be enhanced by multi-layers [14–20], but this method is inefficient.2. Direct projection-type II system with a negative lens array
In the proposed method, we enhance DOF by reducing the spot size on the MDP. The enhancement is achieved in a projection-type II system with a negative lens array without a diffuser. Removing the diffuser changes the mode of elemental images. In a conventional II system, elemental images are projected and displayed on the diffuser. In the proposed method, however, elemental images are directly projected to the location in the space [2]. Under this condition, the aperture diaphragm also changes. The principle of the proposed system is depicted in Fig. 2 . A projector is used to project the elemental images onto the front of the lens array. The 3D images are accordingly integrated by the negative lens array. The parameters are shown in Table 1 .
Table 1. Parameters of the Proposed System
The spot size of the image point on the MDP is represented by SNe, which is limited by the aperture diaphragm of the proposed system. However, this aperture diaphragm is also the exit pupil of the projector (Fig. 2, Eq. (2)) [2]. Thus, the SNe can be calculated by
In the conventional II method, the aperture diaphragm is the pitch of the lens in the lens array. Thus, the p in Eq. (1) is replaced by a complex function g/lp × Pp, determined by the parameters of the projector and negative lens array. In this condition, distances lp and g can be adjusted to reduce spot size and increase DOF, respectively.
We carried out a numerical simulation to demonstrate the spot size of the image point in the two II systems (i.e., the proposed negative lens array system without a diffuser and the positive lens array system with a diffuser). The parameters of the simulation are shown in Table 2 and the results are shown in Fig. 3 .
Table 2. Simulation Parameters
A numerical simulation was performed to show the spot size of the image point in the two II systems (i.e., the proposed negative lens array system without a diffuser and positive lens array systems with a diffuser). The parameters of the simulation are shown in Table 2 and the results are shown in Fig. 3.
The simulation results show that the size of an image point in our proposed system is 0.17 mm when a is 84 mm and l is 36 mm. This value is 5.7% of that in the conventional system. The reduced spot size can be used to enhance the DOF of the II system. By contrast, when the maximum spot size is the same for the two II systems (e.g., 1 mm), the DOF is 24 mm in the positive lens array system and 420 mm in our system. The DOF in the latter is 17.5 times higher than that in the conventional system.
3. Optical experiments and results
Optical experiments demonstrate the feasibility of our system (Fig. 4 ). The parameters are shown in Tables 2 and 3 .
Fig. 4 Sketch of the proposed II system without a diffuser. (a) Optical experiment, (b) color stripes with different pitches.
Table 3. Experimental Parameters
The proposed II system requires only a projector and a negative lens array (Fig. 4(a)). By contrast, a conventional II system is made of a projector, a positive lens array, and a diffuser (Fig. 5 ). Color strips with different pitches (Fig. 4(b)) are used to test the spot size of the integrated images reconstructed by the II systems. A screen is used to capture the color strips integrated by the two systems. The results integrated by the proposed system are marked red, and those integrated by the conventional system are marked blue. The negative lens array is a mould of the positive lens array. The parameters of the two lens arrays are nearly the same, except for focus length.
Fig. 5 Reconstructed images on the CDP and MDP of the proposed system (red) and the conventional system (blue).
First, the color stripes with different pitches were reconstructed on the CDP and MDP, where l is 36 mm. The integrated images are shown in Fig. 5. The elemental images were calculated in accordance with Lens law, on a computer.
The optical experiment yields the following results. Both the integrated images on the CDP can be clearly seen in the two systems (Fig. 5). On the MDP, however, the spot sizes of the integrated points differ, as discussed above. The reconstructed image on the MDP of the proposed system shows that the stripe with a 0.17 mm pitch is fuzzy but can be separated. In the conventional system, the reconstructed stripe with a 3 mm pitch is fuzzy but can be separated. At an l of 36 mm, the spot size generated by the proposed method is 0.17 mm, considerably smaller than that of the conventional system.
Second, the same stripes are integrated on the MDP with l values ranging from 0 to 420 mm. The optical results are shown in Fig. 6 .
Fig. 6 Reconstructed images on different MDPs of the proposed system (red) and the conventional system (blue).
In the conventional system, the stripe with a 1 mm pitch is fuzzy and can be separated at an l of 12 mm. In the proposed system, the reconstructed stripe is fuzzy up to an l of 210 mm, identical to the stripe on the MDP (l = 12 mm) of the conventional system.
The same result is derived for the stripe with a 2 mm pitch. The reconstructed stripe on the MDP (l = 420 mm) of the proposed system is fuzzy, identical to the stripe on the MDP (l = 24 mm) of the conventional system.
The optical experiments confirm good agreement between the results and numerical predictions. Limited by a stripe with a 1 mm pitch, the DOF in the proposed system is 420 mm, an enhancement of 17.5 times relative to the conventional system. Limited by a stripe with a 2 mm pitch, the DOF in the proposed system is 840 mm, an improvement over the 48 mm generated by the conventional system.
4. Conclusion
We proposed and demonstrated an II system with a negative lens array and a projector without a diffuser; the system is designed to enhance DOF. The DOF in our system is 17.5 times that in the conventional system with a diffuser. Numerical simulation and optical experiments confirm the feasibility of our method, which can also be combined with the multi-layer method to effectively enhance DOF. This method serves as a new approach to the application of II systems in 3D display technologies.
Acknowledgments
This work was supported by the Ministry of Science and Technology of China under National Basic Research Program of China (973) grant No.2010CB327702.
References and links
1. G. Lippmann, “La photograhie integrale,” Comptes Rendus Acad. Sci. 146, 446–451 (1908).
2. S.- Park, B.-S. Song, and S.-W. Min, “Analysis of image visibility in projection-type integral imaging system without diffuser,” J. Opt. Soc. Kor. 14(2), 121–126 (2010). [CrossRef]
3. Y. Kim, S.-G. Park, S.-W. Min, and B. Lee, “Projection-type integral imaging system using multiple elemental image layers,” Appl. Opt. 50(7), B18–B24 (2011). [CrossRef] [PubMed]
4. J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009). [CrossRef] [PubMed]
5. R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D Multiperspective Display by Integral Imaging,” Proceedings of the IEEE Journal 97(6), 1067–1077 (2009). [CrossRef]
6. M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-Dimensional Optical Sensing and Visualization Using Integral Imaging,” Proceedings of the IEEE Journal 99(4), 556–575 (2011). [CrossRef]
7. J.-S. Jang and 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(20), 1924–1926 (2003). [CrossRef] [PubMed]
8. J.-S. Jang and B. Javidi, “Three-dimensional projection integral imaging using micro-convex-mirror arrays,” Opt. Express 12(6), 1077–1083 (2004). [CrossRef] [PubMed]
9. M. Okui, J. Arai, Y. Nojiri, and F. Okano, “Optical screen for direct projection of integral imaging,” Appl. Opt. 45(36), 9132–9139 (2006). [CrossRef] [PubMed]
10. D.-H. Shin, B. Lee, and E.-S. Kim, “Multidirectional curved integral imaging with large depth by additional use of a large-aperture lens,” Appl. Opt. 45(28), 7375–7381 (2006). [CrossRef] [PubMed]
11. H. Liao, M. Iwahara, T. Koike, N. Hata, I. Sakuma, and T. Dohi, “Scalable high-resolution integral videography autostereoscopic display with a seamless multiprojection system,” Appl. Opt. 44(3), 305–315 (2005). [CrossRef] [PubMed]
12. J.-S. Jang, Y.-S. Oh, and B. Javidi, “Spatiotemporally multiplexed integral imaging projector for large-scale high-resolution three-dimensional display,” Opt. Express 12(4), 557–563 (2004). [CrossRef] [PubMed]
13. H. Liao, M. Iwahara, N. Hata, and T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Express 12(6), 1067–1076 (2004). [CrossRef] [PubMed]
14. Y. Kim, J.-H. Park, H. Choi, J. Kim, S.-W. Cho, and B. Lee, “Depth-enhanced three-dimensional integral imaging by use of multilayered display devices,” Appl. Opt. 45(18), 4334–4343 (2006). [CrossRef] [PubMed]
15. H. Choi, Y. Kim, J.-H. Park, J. Kim, S.-W. Cho, and B. Lee, “Layered-panel integral imaging without the translucent problem,” Opt. Express 13(15), 5769–5776 (2005). [CrossRef] [PubMed]
16. Y. Kim, H. Choi, J. Kim, S.-W. Cho, Y. Kim, G. Park, and B. Lee, “Depth-enhanced integral imaging display system with electrically variable image planes using polymer-dispersed liquid-crystal layers,” Appl. Opt. 46(18), 3766–3773 (2007). [CrossRef] [PubMed]
17. J.-S. Jang, F. Jin, and B. Javidi, “Three-dimensional integral imaging with large depth of focus by use of real and virtual image fields,” Opt. Lett. 28(16), 1421–1423 (2003). [CrossRef] [PubMed]
18. Y. Kim, S. G. Park, S.-W. Min, and B. Lee, “Integral imaging system using a dual-mode technique,” Appl. Opt. 48(34), H71–H76 (2009). [CrossRef] [PubMed]
19. J.-J. Lee, B.-G. Lee, and H. Yoo, “Image quality enhancement of computational integral imaging reconstruction for partially occluded objects using binary weighting mask on occlusion areas,” Appl. Opt. 50(13), 1889–1893 (2011). [CrossRef] [PubMed]
20. J. Hong, J.-H. Park, S. Jung, and B. Lee, “Depth-enhanced integral imaging by use of optical path control,” Opt. Lett. 29(15), 1790–1792 (2004). [CrossRef] [PubMed]
