## Three-dimensional visualization of objects in scattering medium by use of computational integral imaging

Optics Express, Vol. 16, Issue 17, pp. 13080-13089 (2008)

http://dx.doi.org/10.1364/OE.16.013080

Acrobat PDF (1051 KB)

### Abstract

In this paper, we propose a method to three-dimensionally visualize objects in a scattering medium using integral imaging. Our approach is based on a particular use of the interference phenomenon between the ballistic photons getting through the scattering medium and the scattered photons being scattered by the medium. For three-dimensional (3D) sensing of the scattered objects, the synthetic aperture integral imaging system under coherent illumination records the scattered elemental images of the objects. Then, the computational geometrical ray propagation algorithm is applied to the scattered elemental images in order to eliminate the interference patterns between scattered and object beams. The original 3D information of the scattered objects is recovered by multiple imaging channels, each with a unique perspective of the object. We present both simulation and experimental results with virtual and real objects to demonstrate the proposed concepts.

© 2008 Optical Society of America

## 1. Introduction

15. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phy. Lett. **11**, 77–79 (1967). [CrossRef]

17. Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proceedings of IEEE **94**, 636–654 (2006). [CrossRef]

14. Y. S. Hwang, S. -H. Hong, and B. Javidi, “Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging,” J. Display Technol. **3**, 64–70 (2007). [CrossRef]

10. B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express **14**, 12096–12108 (2006). [CrossRef] [PubMed]

18. I. Moon and B. Javidi, “Volumetric 3D recognition of biological microorganisms using multivariate statistical method and digital holography,” J. Biomed. Opt. **11**, 064004 (2006). [CrossRef]

21. L. Yu and Z. Chen, “Improved tomographic imaging of wavelength scanning digital holographic microscopy by use of digital spectral shaping,” Opt. Express **15**, 878–886 (2007). [CrossRef] [PubMed]

25. R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools,” J. Display Technol. **1**, 321–327 (2005). [CrossRef]

30. J. Rosen and D. Abookasis, “Seeing through biological tissues using the fly eye principle,” Opt. Express **11**, 3605–3611 (2003). [CrossRef] [PubMed]

## 2. Principle of synthetic aperture integral imaging (SAII) recording and reconstruction

11. A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proceedings of the IEEE **94**, 591–607 (2006). [CrossRef]

28. M. Levoy, “Light fields and computional imaging,” IEEE Computer **39**, 46–55 (2006). [CrossRef]

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

*i*and

*j*are the index of the each elemental image,

*N*and

_{x}*N*are the number of elemental images in

_{y}*x*and

*y*directions,

*M*(·) is a magnified elemental image,

_{Eij}*p*and

_{x}*p*are the shifted value of the sensor channels in

_{y}*x*and

*y*directions, and

*N*is the number of the overlapped pixels for the magnified elemental images as shown in Fig. 1. The total image size projected by each magnified elemental image at a reconstruction II plan is given by

_{s}## 3. Synthetic aperture coherent integral imaging (SACII) system for 3D visualization of objects in scattering media

*S*|

^{2}and |

*E*|

^{2}are the scattered and object beam intensities,

*n*is the elemental image number, and

*r⃗*is a position vector in the elemental image, and

_{p}*k⃗*is the wave-number. In general, the fluctuation of |

*S*|

^{2}is slow compared with |

*E*|

^{2}due to scattering. The second term in Eq. (2) contains the perspective information of a 3D object. In this paper, we assume that the 3D object between two scattering layers is distorted. The original 3D object is recovered from the distorted perspective images of the 3D object by using multiple imaging channels based on integral imaging. The 2|

*S*||

*E*|cos[(

*k⃗*-

_{S}*k⃗*)∙

_{E}*r⃗*] term in Eq. (2) denotes interference patterns between original object and scattered beams. We consider that this term is the primary cause for the distortion of the original object in the proposed SACII system. The set of the corresponding pixels in different imaging channels can be modeled as samples of a random intensity distribution due to the random variation of cosine term in Eq. (2). In other words, each pixel get the scattering contribution from a scattered waves with a random k vector, and thus by adding up the pixel values, the effect of the scatter wave will diminish whereas the effect of the ballistic wave will constructively add up. Therefore, it can be assumed that the object distortion is a result of the interferences due to many scattered waves with different phases.

_{p}*N*measurements through multiple imaging channels so that the image of the scattered object at the

*p*

_{th}pixel position, corresponding to one point in the object space, can be described as follows:

*I*(

^{s}_{p}*i*) and

*I*(

^{o}_{p}*i*) are scattered and original object beam intensities, respectively and

*w*(

_{p}*i*) is random variable following independent and identically distributed (IID) statistical model [31]. Due to the fact that the

*w*(

_{p}*i*) is IID, the recorded samples,

*I*(

^{s}_{p}*i*), are also statistically independent. In order to recover the original intensity of one point of the object, one can use the statistical independence of

*I*(

^{s}_{p}*i*) by adding up the corresponding

*N*samples of a single object point captured by

*N*different imaging channels [See Fig. 1] such that the expectation of the cosine term in Eq. (2) diminishes to zero given the fact that the argument of cosine follows uniform distribution from -π to π [32–33

32. Neal C. Gallagher, “Optimum quantization in digital holography,” Appl. Opt. **17**, 109–115 (1978). [CrossRef] [PubMed]

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

*N*is total number of elemental image. According to Eq. (4), we believe that sufficient number of elemental images allow the optical imaging through scattering medium even if the unscattered beam information is weak owing to the fact that the distortion term in Eq. (2) is averaged out to zero resulting in the original unscattered beam.

## 4. Experimental results

### A. Computer simulations for 3D visualization of scattered objects

*z*=156cm, 168cm, 180cm, 192cm, and 204cm (see Fig. 3), where

_{0}*z*is the distance between the virtual pin-hole array and the image plane.

_{0}*z*=156cm, 168cm, 180cm, 192cm, and 204cm for the 3D reconstruction.

_{0}^{-6}, where we calculated the MSE between 3D images reconstructed at the 180cm. It is shown in the experimental results that the proposed SACII method can reduce the interference due to scattering in Eq. (2) so that the objects in the scattering medium can be three-dimensionally restored.

### B. Optical experiments for 3D visualization of scattered objects

*z*=130, 150, and 170mm by using the virtual ray propagation algorithm, where

_{0}*z*is the distance between the virtual pin-hole array and the reconstructed image plane. Figure 9 shows the sectional images reconstructed from the non-scattered and scattered elemental image sets by using the SACII algorithm, respectively. It is noted that the MSE between the original and restored II data in the area marked in white as shown in Fig. 9 was approximately 0.017, where we calculated the MSE between sectional mages reconstructed at z

_{0}_{0}=150mm. Figure 10 shows the data distributions of the original II and restored II data in the area marked in white as shown in Fig. 9, where 500 pixel points were randomly selected over the area. It is noted that the distortion indexes (ratio of standard deviation to mean) for the original and restored II data were approximately 0.0618 and 0.0398, respectively. It is shown that the standard deviation of the restored II data was much less than the scattered elemental image in Fig. 8(b), which illustrates that the proposed SACII method averages out the modulation terms due to scattering in Eq. (2) and can visualize the 3D objects in the scattering medium. We believe that the experimental results support the concept proposed in this paper.

## 5. Conclusions

## Acknowledgments

## References and links

1. | G. Lippmann, “La photographie intégrale,” Compte-Rendus |

2. | A. P. Sokolov, ed., |

3. | H. E. Ives, “Optical properties of a Lippman lenticulated sheet,” J. Opt. Soc. Am. |

4. | Y. Igarishi, H. Murata, and M. Ueda, “3D display system using a computer-generated integral photograph,” Jpn. J. Appl. Phys. |

5. | H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A |

6. | R. Martinez, A. Pons, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Optically-corrected elemental images for undistorted integral image display,” Opt. Express |

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

8. | A. Stern and B. Javidi, “3-D computational synthetic aperture integral imaging (COMPSAII),” Opt. Express |

9. | B. Tavakoli, B. Javidi, and E. Watson, “Three dimensional visualization by photon counting computational Integral Imaging,” Opt. Express |

10. | B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express |

11. | A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proceedings of the IEEE |

12. | A. Castro, Y. Frauel, and B. Javidi, “Integral imaging with large depth of field using an asymmetric phase mask,” Opt. Express |

13. | O. Matoba, E. Tajahuerce, and B. Javidi, “Real-time three-dimensional object recognition with multiple perspectives imaging,” Appl. Opt. |

14. | Y. S. Hwang, S. -H. Hong, and B. Javidi, “Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging,” J. Display Technol. |

15. | J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phy. Lett. |

16. | L. Martínez-León and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express |

17. | Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proceedings of IEEE |

18. | I. Moon and B. Javidi, “Volumetric 3D recognition of biological microorganisms using multivariate statistical method and digital holography,” J. Biomed. Opt. |

19. | T. Kreis, ed., |

20. | W. Osten, T. Baumbach, and W. Juptner, “Comparative digital holography,” Opt. Lett. , |

21. | L. Yu and Z. Chen, “Improved tomographic imaging of wavelength scanning digital holographic microscopy by use of digital spectral shaping,” Opt. Express |

22. | L. Yu and Z. Chen, “Digital holographic tomography based on spectral interferometry,” Opt. Lett. |

23. | J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. |

24. | L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic 3D imaging using the angular spectrum method,” Opt. Lett. |

25. | R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools,” J. Display Technol. |

26. | B. Javidi, S. H. Hong, and O. Matoba, “Multidimensional optical sensor and imaging system,” Appl. Opt. |

27. | T. Okoshi, ed., |

28. | M. Levoy, “Light fields and computional imaging,” IEEE Computer |

29. | B. Javidi and F. Okano eds, |

30. | J. Rosen and D. Abookasis, “Seeing through biological tissues using the fly eye principle,” Opt. Express |

31. | N. Mukhopadhyay, ed., |

32. | Neal C. Gallagher, “Optimum quantization in digital holography,” Appl. Opt. |

33. | P. Réfrégier, ed., |

**OCIS Codes**

(110.6150) Imaging systems : Speckle imaging

(110.6880) Imaging systems : Three-dimensional image acquisition

(170.3880) Medical optics and biotechnology : Medical and biological imaging

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: March 19, 2008

Revised Manuscript: May 29, 2008

Manuscript Accepted: July 18, 2008

Published: August 12, 2008

**Virtual Issues**

Vol. 3, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Inkyu Moon and Bahram Javidi, "Three-dimensional visualization of objects in
scattering medium by use of computational
integral imaging," Opt. Express **16**, 13080-13089 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13080

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### References

- G. Lippmann, "La photographie intégrale," Compte-Rendus 146, 446-451 (1908).
- A. P. Sokolov, ed., Autostereoscopy and integral photography by Professor Lippmanns method (Moscow State Univ. Press, 1911).
- H. E. Ives, "Optical properties of a Lippman lenticulated sheet," J. Opt. Soc. Am. 21, 171-176 (1931). [CrossRef]
- Y. Igarishi, H. Murata, and M. Ueda, "3D display system using a computer-generated integral photograph," Jpn. J. Appl. Phys. 17, 1683-1684 (1978). [CrossRef]
- H. Hoshino, F. Okano, H. Isono, and I. Yuyama, "Analysis of resolution limitation of integral photography," J. Opt. Soc. Am. A 15, 2059-2065 (1998). [CrossRef]
- R. Martinez, A. Pons, G. Saavedra, M. Martinez-Corral, and B. Javidi, "Optically-corrected elemental images for undistorted integral image display," Opt. Express 14, 9657-9663 (2006). [CrossRef]
- H. Arimoto and B. Javidi, "Integral three-dimensional imaging with digital reconstruction," Opt. Lett. 26, 157-159 (2001). [CrossRef]
- A. Stern and B. Javidi, "3-D computational synthetic aperture integral imaging (COMPSAII)," Opt. Express 11, 2446-2451 (2003). [CrossRef] [PubMed]
- B. Tavakoli, B. Javidi, and E. Watson, "Three dimensional visualization by photon counting computational Integral Imaging," Opt. Express 16, 4426-4436 (2008). [CrossRef] [PubMed]
- B. Javidi, I. Moon, and S. Yeom, "Three-dimensional identification of biological microorganism using integral imaging," Opt. Express 14, 12096-12108 (2006). [CrossRef] [PubMed]
- A. Stern and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proceedings of the IEEE 94, 591-607 (2006). [CrossRef]
- A. Castro, Y. Frauel, and B. Javidi, "Integral imaging with large depth of field using an asymmetric phase mask," Opt. Express 15, 10266-10273 (2007). [CrossRef] [PubMed]
- O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001). [CrossRef]
- Y. S. Hwang, S. -H. Hong, and B. Javidi, "Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging," J. Display Technol. 3, 64-70 (2007). [CrossRef]
- J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phy. Lett. 11, 77-79 (1967). [CrossRef]
- L. Martínez-León and B. Javidi, "Synthetic aperture single-exposure on-axis digital holography," Opt. Express 16, 161-169 (2008). [CrossRef] [PubMed]
- Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, "Three dimensional imaging and display using computational holographic imaging," Proceedings of IEEE 94, 636-654 (2006). [CrossRef]
- I. Moon and B. Javidi, "Volumetric 3D recognition of biological microorganisms using multivariate statistical method and digital holography," J. Biomed. Opt. 11, 064004 (2006). [CrossRef]
- T. Kreis, ed., Handbook of holographic interferometry (Wiley, 2005).
- W. Osten, T. Baumbach, and W. Juptner, "Comparative digital holography," Opt. Lett. 27, 1764-1766 (2002). [CrossRef]
- L. Yu and Z. Chen, "Improved tomographic imaging of wavelength scanning digital holographic microscopy by use of digital spectral shaping," Opt. Express 15, 878-886 (2007). [CrossRef] [PubMed]
- L. Yu and Z. Chen, "Digital holographic tomography based on spectral interferometry," Opt. Lett. 32, 3005-3007 (2007). [CrossRef] [PubMed]
- J. H. Massig, "Digital off-axis holography with a synthetic aperture," Opt. Lett. 27, 2179-2181 (2002). [CrossRef]
- L. Yu and M. K. Kim, "Wavelength-scanning digital interference holography for tomographic 3D imaging using the angular spectrum method," Opt. Lett. 30, 2092-2094 (2005). [CrossRef] [PubMed]
- R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, "Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools," J. Display Technol. 1, 321- 327 (2005). [CrossRef]
- B. Javidi, S. H. Hong, and O. Matoba, "Multidimensional optical sensor and imaging system," Appl. Opt. 45, 2986-2994 (2006). [CrossRef] [PubMed]
- T. Okoshi, ed., Three-dimensional imaging techniques (Academic, 1976).
- M. Levoy, "Light fields and computional imaging," IEEE Computer 39, 46-55 (2006). [CrossRef]
- B. Javidi and F. Okano eds, Three dimensional television, video, and display technologies (Springer, 2002).
- J. Rosen and D. Abookasis, "Seeing through biological tissues using the fly eye principle," Opt. Express 11, 3605-3611 (2003). [CrossRef] [PubMed]
- N. Mukhopadhyay, ed., Probability and Statistical Inference (Marcel Dekker, 2000).
- Neal C. Gallagher, "Optimum quantization in digital holography," Appl. Opt. 17, 109-115 (1978). [CrossRef] [PubMed]
- P. Réfrégier, ed., Noise theory and application to physics: from fluctuations to information (Springer, 2004).

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