## Axially moving a lenslet array for high-resolution 3D images in computational integral imaging |

Optics Express, Vol. 21, Issue 7, pp. 8873-8878 (2013)

http://dx.doi.org/10.1364/OE.21.008873

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### Abstract

This paper presents a new high-resolution computational integral imaging system employing a pickup with the axial movement of a lenslet array and a computation reconstruction algorithm with pixel-to-pixel mapping. In the proposed method, a lenslet array and its image sensor are moved together along the z-axis direction (or axial direction) and a series of elemental image arrays are obtained while moving. The elemental image arrays are then applied to pixel-to-pixel mapping without interpolation for the reconstruction of 3D slice images. Also, an analysis of the proposed reconstruction method is provided. To show the usefulness of the proposed method, experiments are conducted. The results indicate that the proposed method is superior to the existing method such as MALT in terms of image quality.

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## 1. Introduction

2. H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. **26**(3), 157–159 (2001). [CrossRef] [PubMed]

8. B. Lee, S.-Y. Jung, S.-W. Min, and J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. **26**(19), 1481–1482 (2001). [CrossRef] [PubMed]

2. H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. **26**(3), 157–159 (2001). [CrossRef] [PubMed]

9. J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. **27**(5), 324–326 (2002). [CrossRef] [PubMed]

16. A. Stern, B. Javidi, A. Stern, and B. Javidi, “Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. **42**(35), 7036–7042 (2003). [CrossRef] [PubMed]

9. J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. **27**(5), 324–326 (2002). [CrossRef] [PubMed]

12. H. Navarro, J. C. Barreiro, G. Saavedra, M. Martínez-Corral, and B. Javidi, “High-resolution far-field integral-imaging camera by double snapshot,” Opt. Express **20**(2), 890–895 (2012). [CrossRef] [PubMed]

13. R. Schulein, M. DaneshPanah, and B. Javidi, “3D imaging with axially distributed sensing,” Opt. Lett. **34**(13), 2012–2014 (2009). [CrossRef] [PubMed]

15. D.-H. Shin and B. Javidi, “Three-dimensional imaging and visualization of partially occluded objects using axially distributed stereo image sensing,” Opt. Lett. **37**(9), 1394–1396 (2012). [CrossRef] [PubMed]

*z*-direction or axial-direction. In the literature, axially moving a lenslet array was introduced for 3D display [8

8. B. Lee, S.-Y. Jung, S.-W. Min, and J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. **26**(19), 1481–1482 (2001). [CrossRef] [PubMed]

13. R. Schulein, M. DaneshPanah, and B. Javidi, “3D imaging with axially distributed sensing,” Opt. Lett. **34**(13), 2012–2014 (2009). [CrossRef] [PubMed]

15. D.-H. Shin and B. Javidi, “Three-dimensional imaging and visualization of partially occluded objects using axially distributed stereo image sensing,” Opt. Lett. **37**(9), 1394–1396 (2012). [CrossRef] [PubMed]

## 2. Overview of computational integral imaging

2. H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. **26**(3), 157–159 (2001). [CrossRef] [PubMed]

4. D.-H. Shin and H. Yoo, “Scale-variant magnification for computational integral imaging and its application to 3D object correlator,” Opt. Express **16**(12), 8855–8867 (2008). [CrossRef] [PubMed]

6. H. Yoo, “Artifact analysis and image enhancement in three-dimensional computational integral imaging using smooth windowing technique,” Opt. Lett. **36**(11), 2107–2109 (2011). [CrossRef] [PubMed]

10. S.-H. Hong and B. Javidi, “Improved resolution 3D object reconstruction using computational integral imaging with time multiplexing,” Opt. Express **12**(19), 4579–4588 (2004). [CrossRef] [PubMed]

*z/g*, where

*z*is the distance between the reconstruction plane and the virtual pinhole array and

*g*is the distance between the elemental images and the virtual pinhole array. Then, the magnified elemental images are superimposed on the reconstruction plane. After normalization to compensate intensity irregularity, a slice image for the 3D image is finally produced with respect to the reconstruction plane at a distance

*z*. To completely generate the volume data for 3D space, this process is repeatedly conducted adjusting the distance

*z*.

## 3. Ray analysis of axial movement of a lenslet array

*z*-direction) with a moving step.

**26**(3), 157–159 (2001). [CrossRef] [PubMed]

4. D.-H. Shin and H. Yoo, “Scale-variant magnification for computational integral imaging and its application to 3D object correlator,” Opt. Express **16**(12), 8855–8867 (2008). [CrossRef] [PubMed]

6. H. Yoo, “Artifact analysis and image enhancement in three-dimensional computational integral imaging using smooth windowing technique,” Opt. Lett. **36**(11), 2107–2109 (2011). [CrossRef] [PubMed]

7. D.-H. Shin and H. Yoo, “Computational integral imaging reconstruction method of 3D images using pixel-to-pixel mapping and image interpolation,” Opt. Commun. **282**(14), 2760–2767 (2009). [CrossRef]

7. D.-H. Shin and H. Yoo, “Computational integral imaging reconstruction method of 3D images using pixel-to-pixel mapping and image interpolation,” Opt. Commun. **282**(14), 2760–2767 (2009). [CrossRef]

## 4. Sufficient interpolation-free conditions

*δ*be the distance between two projected pixels in the reconstruction plane. If the value

*δ*is the pixel size, the reconstruction plane is completely covered by projected pixels. Then the empty pixels no longer exist. Thus, the maximum moving step ∆ avoiding empty pixels is given bywhere

*N*is the number of pixels in width of each elemental image. The condition derived above is a sufficient condition because the elemental images distributed longitudinally are only taken into account. Here, a sufficient number of elemental image arrays can be chosen by considering the worst case of emptiness, when reconstructing the slice image at the distance

*Nz*/

*g*. The length of the empty area between two pixels in this case is the same as

*N*times of the pixel size, thus

*N*projections are required to cover the empty area. Consequently,

*N*is the sufficient number of the arrays to cover any empty area.

7. D.-H. Shin and H. Yoo, “Computational integral imaging reconstruction method of 3D images using pixel-to-pixel mapping and image interpolation,” Opt. Commun. **282**(14), 2760–2767 (2009). [CrossRef]

## 5. Experiments and discussions

*z*= 3 mm and

*z*= 21 mm, respectively. The lenslet array with 30 × 30 lenslets is initially located at

*z*

_{1}= 0 mm. Each tiny lens has a size of 1.08 mm, a pixel array of 30 × 30, and a focal length of 3 mm. Then, each elemental image array has a size of 900 × 900 pixels. The lenslet array and a camera or a CCD array are moved together backward with a step of 3 mm, which is the same as the focal length, and multiple snapshots produces a series of twenty one elemental image arrays. For examples, the first and twenty-first elemental image arrays are shown in Figs. 4(b) and 4(c), respectively. It is seen that the recorded elemental images shows the car in different scales.

*z*= 21 mm, where the object was located originally. The conventional CIIR with an elemental image array provided a low image quality, as shown in Fig. 5(a). The MALT with the 21 elemental image arrays improved the quality of the reconstructed slice image, as depicted in Fig. 5(b). However, the slice image from MALT still suffers from blurring since MALT still has interpolation errors by magnification and the effect of the occluding object. On the contrary, the proposed method with the 21 arrays enhanced the image quality because pixel-to-pixel mapping without interpolation can reduce those errors, as indicated in Fig. 5(c). Especially, the zoomed area, showing the word ‘car’ in the object, indicated that the proposed method substantially improved the image quality of the slice image. Therefore, it is the much more useful in object recognition than the existing technique such as MALT.

## 6. Conclusions

## References and links

1. | G. Lippmann, “La photographic integrale,” C.R. Acad. Sci. |

2. | H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. |

3. | A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE |

4. | D.-H. Shin and H. Yoo, “Scale-variant magnification for computational integral imaging and its application to 3D object correlator,” Opt. Express |

5. | J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. |

6. | H. Yoo, “Artifact analysis and image enhancement in three-dimensional computational integral imaging using smooth windowing technique,” Opt. Lett. |

7. | D.-H. Shin and H. Yoo, “Computational integral imaging reconstruction method of 3D images using pixel-to-pixel mapping and image interpolation,” Opt. Commun. |

8. | B. Lee, S.-Y. Jung, S.-W. Min, and J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. |

9. | J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. |

10. | S.-H. Hong and B. Javidi, “Improved resolution 3D object reconstruction using computational integral imaging with time multiplexing,” Opt. Express |

11. | Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express |

12. | H. Navarro, J. C. Barreiro, G. Saavedra, M. Martínez-Corral, and B. Javidi, “High-resolution far-field integral-imaging camera by double snapshot,” Opt. Express |

13. | R. Schulein, M. DaneshPanah, and B. Javidi, “3D imaging with axially distributed sensing,” Opt. Lett. |

14. | D.-H. Shin, M. Cho, and B. Javidi, “Three-dimensional optical microscopy using axially distributed image sensing,” Opt. Lett. |

15. | D.-H. Shin and B. Javidi, “Three-dimensional imaging and visualization of partially occluded objects using axially distributed stereo image sensing,” Opt. Lett. |

16. | A. Stern, B. Javidi, A. Stern, and B. Javidi, “Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(110.3010) Imaging systems : Image reconstruction techniques

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: January 16, 2013

Revised Manuscript: March 28, 2013

Manuscript Accepted: March 31, 2013

Published: April 3, 2013

**Citation**

Hoon Yoo, "Axially moving a lenslet array for high-resolution 3D images in computational integral imaging," Opt. Express **21**, 8873-8878 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8873

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### References

- G. Lippmann, “La photographic integrale,” C.R. Acad. Sci.146, 446–451 (1908).
- H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett.26(3), 157–159 (2001). [CrossRef] [PubMed]
- A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE94(3), 591–607 (2006). [CrossRef]
- D.-H. Shin and H. Yoo, “Scale-variant magnification for computational integral imaging and its application to 3D object correlator,” Opt. Express16(12), 8855–8867 (2008). [CrossRef] [PubMed]
- 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]
- H. Yoo, “Artifact analysis and image enhancement in three-dimensional computational integral imaging using smooth windowing technique,” Opt. Lett.36(11), 2107–2109 (2011). [CrossRef] [PubMed]
- D.-H. Shin and H. Yoo, “Computational integral imaging reconstruction method of 3D images using pixel-to-pixel mapping and image interpolation,” Opt. Commun.282(14), 2760–2767 (2009). [CrossRef]
- B. Lee, S.-Y. Jung, S.-W. Min, and J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett.26(19), 1481–1482 (2001). [CrossRef] [PubMed]
- J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett.27(5), 324–326 (2002). [CrossRef] [PubMed]
- S.-H. Hong and B. Javidi, “Improved resolution 3D object reconstruction using computational integral imaging with time multiplexing,” Opt. Express12(19), 4579–4588 (2004). [CrossRef] [PubMed]
- Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express17(21), 19253–19263 (2009). [CrossRef] [PubMed]
- H. Navarro, J. C. Barreiro, G. Saavedra, M. Martínez-Corral, and B. Javidi, “High-resolution far-field integral-imaging camera by double snapshot,” Opt. Express20(2), 890–895 (2012). [CrossRef] [PubMed]
- R. Schulein, M. DaneshPanah, and B. Javidi, “3D imaging with axially distributed sensing,” Opt. Lett.34(13), 2012–2014 (2009). [CrossRef] [PubMed]
- D.-H. Shin, M. Cho, and B. Javidi, “Three-dimensional optical microscopy using axially distributed image sensing,” Opt. Lett.35(21), 3646–3648 (2010). [CrossRef] [PubMed]
- D.-H. Shin and B. Javidi, “Three-dimensional imaging and visualization of partially occluded objects using axially distributed stereo image sensing,” Opt. Lett.37(9), 1394–1396 (2012). [CrossRef] [PubMed]
- A. Stern, B. Javidi, A. Stern, and B. Javidi, “Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt.42(35), 7036–7042 (2003). [CrossRef] [PubMed]

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