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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Appl. Opt.

Opt. Lett.

Opt. Mem. Neur. Net.

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).

Proc. SPIE

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, M.T. Bolas eds., Proc. SPIE 4660, 135-145 (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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