Abstract

In projection-type integral imaging, positional errors in elemental images and elemental lenses affect three-dimensional (3D) image quality. We analyzed the relationships between the geometric distortion in elemental images caused by a projection lens and the spatial distortion in the reconstructed 3D image. As a result, we clarified that 3D images that were reconstructed far from the lens array were largely affected, and that the reconstructed images were significantly distorted in the depth direction at the corners of the displayed images.

© 2008 Optical Society of America

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References

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2006 (2)

2004 (4)

1997 (1)

1908 (1)

M. G. Lippmann, J. Fluid Mech. 7, 821 (1908).

Arai, J.

Dohi, T.

Hata, N.

Hoshino, H.

Iwahara, M.

Jang, J.-S.

Javidi, B.

Kim, J.

Kobayashi, M.

Lee, B.

Liao, H.

Lippmann, M. G.

M. G. Lippmann, J. Fluid Mech. 7, 821 (1908).

Min, S.-W.

Nojiri, Y.

Oh, Y.-S.

Okano, F.

Okui, M.

Yamashita, T.

Yuyama, I.

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Figures (4)

Fig. 1
Fig. 1

Principal light rays of elemental images and reconstructed image (solid lines without distortion; dotted lines with distortion).

Fig. 2
Fig. 2

Calculated and measured results of distortion in reconstructed images. An original elemental image was made by a computer in the experiment, and it reconstructed a point light source image at a z 0 = 130 mm distance from the lens array plane to the reconstructed image. The distorted elemental images with an artificial distortion rate D of ± 0.75 % , ± 0.25 % , and ± 1.25 % were made from the original elemental image. The elemental images with distortion were displayed on a direct-view liquid crystal display with an effective pixel count of 3840 ( H ) × 2160 ( V ) . The 3D positions of the reconstructed point images were found by using ground glass, and the x and z coordinates of the positions of the brightest reconstructed point image were measured.

Fig. 3
Fig. 3

Distortions of reconstructed images in the depth direction.

Fig. 4
Fig. 4

Distortions of reconstructed images in the x direction.

Tables (1)

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Table 1 Elemental Lenses and Image Specifications

Equations (6)

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x m ( z ) = x m e g z + m p = x 0 m p z 0 z + m p ,
x m ( z ) = x m d g z + m p = x m e + Δ x m g z + m p = ( x 0 m p z 0 Δ x m g ) z + m p ,
σ 2 ( z ) = 1 2 N + 1 m = n N n + N [ x m ( z ) x m ( z ) ¯ ] 2 = 1 2 N + 1 m = n N n + N { [ ( n m ) p z 0 + A m g ] z ( n m ) p } 2 ,
A m = Δ x ¯ Δ x m = 1 2 N + 1 m = n N n + N Δ x m Δ x m ,
z = m = n N n + N [ ( n m ) 2 p 2 z 0 + A m ( n m ) p g ] m = n N n + N [ ( n m ) p z 0 + A m g ] 2 ,
x = ( x 0 n p z 0 Δ x ¯ g ) z + n p .

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