Abstract

A three-dimensional optical correlator using a lens array is proposed and demonstrated. The proposed method captures three-dimensional objects using the lens array and transforms them into sub-images. Through successive two-dimensional correlations between the sub-images, a three-dimensional optical correlation is accomplished. As a result, the proposed method is capable of detecting out-of-plane rotations of three-dimensional objects as well as three-dimensional shifts.

© 2005 Optical Society of America

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References

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  1. T.-C. Poon and T. Kim, “Optical image recognition of three-dimensional objects,” Appl. Opt. 38, 370–381 (1999).
    [Crossref]
  2. B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
    [Crossref]
  3. J. Rosen, “Three-dimensional optical Fourier transform and correlation,” Opt. Lett. 22, 964–966 (1997).
    [Crossref] [PubMed]
  4. J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. 37, 7438–7544 (1998).
    [Crossref]
  5. J. Esteve-Taboada, D. Mas, and J. Garcia, “Three-dimensional object recognition by Fourier transform profilometry,” Appl. Opt. 38, 4760–4765 (1999).
    [Crossref]
  6. O. Matoba, E. Tajahuerce, and B. Javidi, “Real-time three-dimensional object recognition with multiple perspectives imaging,” Appl. Opt. 40, 3318–3325 (2001).
    [Crossref]
  7. Y. Frauel and B. Javidi, “Digital three-dimensional image correlation by use of compter-reconstructed integral imaging,” Appl. Opt. 41, 5488–5496 (2002).
    [Crossref] [PubMed]
  8. J.-H. Park, S. Jung, H. Choi, and B Lee, “Detection of the longitudinal and the lateral positions of a three-dimensional object using a lens array and joint transform correlator,” Opt. Mem. Neur. Net. 11, 181–188 (2002).
  9. C. Wu, A. Aggoun, M. McCormick, and S.Y. Kung, “Depth extraction from unidirectional image using a modified multi-baseline technique,” in Conference on Stereoscopic Display and Virtual Reality Systems IX, A.J. Woods, J.O. Merritt, S.A. Benton, and M.T. Bolas eds., Proc. SPIE 4660, 135–145 (2002).
  10. J.-H. Park, S. Jung, H. Choi, Y. Kim, and B. Lee, “Depth extraction by use of a rectangular lens array and one-dimensional elemental image modification,” Appl. Opt. 43, 4882–4895 (2004).
    [Crossref] [PubMed]

2004 (1)

2002 (3)

Y. Frauel and B. Javidi, “Digital three-dimensional image correlation by use of compter-reconstructed integral imaging,” Appl. Opt. 41, 5488–5496 (2002).
[Crossref] [PubMed]

J.-H. Park, S. Jung, H. Choi, and B Lee, “Detection of the longitudinal and the lateral positions of a three-dimensional object using a lens array and joint transform correlator,” Opt. Mem. Neur. Net. 11, 181–188 (2002).

C. Wu, A. Aggoun, M. McCormick, and S.Y. Kung, “Depth extraction from unidirectional image using a modified multi-baseline technique,” in Conference on Stereoscopic Display and Virtual Reality Systems IX, A.J. Woods, J.O. Merritt, S.A. Benton, and M.T. Bolas eds., Proc. SPIE 4660, 135–145 (2002).

2001 (1)

2000 (1)

1999 (2)

1998 (1)

J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. 37, 7438–7544 (1998).
[Crossref]

1997 (1)

Aggoun, A.

C. Wu, A. Aggoun, M. McCormick, and S.Y. Kung, “Depth extraction from unidirectional image using a modified multi-baseline technique,” in Conference on Stereoscopic Display and Virtual Reality Systems IX, A.J. Woods, J.O. Merritt, S.A. Benton, and M.T. Bolas eds., Proc. SPIE 4660, 135–145 (2002).

Choi, H.

J.-H. Park, S. Jung, H. Choi, Y. Kim, and B. Lee, “Depth extraction by use of a rectangular lens array and one-dimensional elemental image modification,” Appl. Opt. 43, 4882–4895 (2004).
[Crossref] [PubMed]

J.-H. Park, S. Jung, H. Choi, and B Lee, “Detection of the longitudinal and the lateral positions of a three-dimensional object using a lens array and joint transform correlator,” Opt. Mem. Neur. Net. 11, 181–188 (2002).

Esteve-Taboada, J.

Frauel, Y.

Garcia, J.

Javidi, B.

Jung, S.

J.-H. Park, S. Jung, H. Choi, Y. Kim, and B. Lee, “Depth extraction by use of a rectangular lens array and one-dimensional elemental image modification,” Appl. Opt. 43, 4882–4895 (2004).
[Crossref] [PubMed]

J.-H. Park, S. Jung, H. Choi, and B Lee, “Detection of the longitudinal and the lateral positions of a three-dimensional object using a lens array and joint transform correlator,” Opt. Mem. Neur. Net. 11, 181–188 (2002).

Kim, T.

Kim, Y.

Kung, S.Y.

C. Wu, A. Aggoun, M. McCormick, and S.Y. Kung, “Depth extraction from unidirectional image using a modified multi-baseline technique,” in Conference on Stereoscopic Display and Virtual Reality Systems IX, A.J. Woods, J.O. Merritt, S.A. Benton, and M.T. Bolas eds., Proc. SPIE 4660, 135–145 (2002).

Lee, B

J.-H. Park, S. Jung, H. Choi, and B Lee, “Detection of the longitudinal and the lateral positions of a three-dimensional object using a lens array and joint transform correlator,” Opt. Mem. Neur. Net. 11, 181–188 (2002).

Lee, B.

Mas, D.

Matoba, O.

McCormick, M.

C. Wu, A. Aggoun, M. McCormick, and S.Y. Kung, “Depth extraction from unidirectional image using a modified multi-baseline technique,” in Conference on Stereoscopic Display and Virtual Reality Systems IX, A.J. Woods, J.O. Merritt, S.A. Benton, and M.T. Bolas eds., Proc. SPIE 4660, 135–145 (2002).

Park, J.-H.

J.-H. Park, S. Jung, H. Choi, Y. Kim, and B. Lee, “Depth extraction by use of a rectangular lens array and one-dimensional elemental image modification,” Appl. Opt. 43, 4882–4895 (2004).
[Crossref] [PubMed]

J.-H. Park, S. Jung, H. Choi, and B Lee, “Detection of the longitudinal and the lateral positions of a three-dimensional object using a lens array and joint transform correlator,” Opt. Mem. Neur. Net. 11, 181–188 (2002).

Poon, T.-C.

Rosen, J.

J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. 37, 7438–7544 (1998).
[Crossref]

J. Rosen, “Three-dimensional optical Fourier transform and correlation,” Opt. Lett. 22, 964–966 (1997).
[Crossref] [PubMed]

Tajahuerce, E.

Wu, C.

C. Wu, A. Aggoun, M. McCormick, and S.Y. Kung, “Depth extraction from unidirectional image using a modified multi-baseline technique,” in Conference on Stereoscopic Display and Virtual Reality Systems IX, A.J. Woods, J.O. Merritt, S.A. Benton, and M.T. Bolas eds., Proc. SPIE 4660, 135–145 (2002).

Appl. Opt. (6)

in Conference on Stereoscopic Display and Virtual Reality Systems IX (1)

C. Wu, A. Aggoun, M. McCormick, and S.Y. Kung, “Depth extraction from unidirectional image using a modified multi-baseline technique,” in Conference on Stereoscopic Display and Virtual Reality Systems IX, A.J. Woods, J.O. Merritt, S.A. Benton, and M.T. Bolas eds., Proc. SPIE 4660, 135–145 (2002).

Opt. Lett. (2)

Opt. Mem. Neur. Net. (1)

J.-H. Park, S. Jung, H. Choi, and B Lee, “Detection of the longitudinal and the lateral positions of a three-dimensional object using a lens array and joint transform correlator,” Opt. Mem. Neur. Net. 11, 181–188 (2002).

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Figures (10)

Fig. 1.
Fig. 1.

Conceptual diagram of the proposed method

Fig. 2.
Fig. 2.

Sub-image (a) geometry and (b) generation

Fig. 3.
Fig. 3.

Observing-angle-invariance of the sub-image: (a) ordinary image (or elemental image) (b) sub-image

Fig. 4.
Fig. 4.

Size-invariance of the sub-image: (a) ordinary image (b) sub-image

Fig. 5.
Fig. 5.

Procedure for detecting out-of-plane rotation and 3D shift

Fig. 6.
Fig. 6.

Examples of experimentally obtained elemental images and sub-images

Fig. 7.
Fig. 7.

Example of (a) JPS captured by CCD and (b) correlation peak calculated by Fourier transforming the captured JPS digitally.

Fig. 8.
Fig. 8.

Experimental result: intensity profile of the correlation peaks between one sub-image for a reference object located at (xr, yr, zr )=(0 mm, 0 mm, 25 mm) and each sub-image of a signal object located at (xs, ys, zs )=(5 mm, 0 mm, 40 mm) with θx-z =0°, 2°, 4°, and 6° and θy-z =0°

Fig. 9.
Fig. 9.

Experimental result: detected positions of the correlation peak with various locations of the signal object when the reference object is located at (xr, yr, zr )=(0 mm, 0 mm, 25 mm) and the signal object has no out-of-plane rotation.

Fig. 10.
Fig. 10.

Experimental result: detected positions of the correlation peak with various locations of the signal object when the reference object is located at (xr, yr, zr )=(0 mm, 0 mm, 25 mm) and the signal object has θx-z =4°, and θy-z =0° rotation.

Equations (6)

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θ sub , y z , i = tan 1 ( y i f ) ,
Δ u r , i , s , i = u r , i u s , i = y r y s + ( z r z s ) tan θ sub , y z , i φ .
Δ u r , i , s , j = y r y s + z r tan θ sub , y z , i z s tan θ sub , y z , j φ
= y r y s + z r tan θ sub , y z , i z s tan ( θ sub , y z , j + θ y z ) φ .
Δ θ = tan 1 ( y i + 1 f ) tan 1 ( y i f ) y i + 1 y i f = s f ,
Ω = 2 tan 1 ( φ 2 f ) φ f ,

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