Abstract

We analyze by wave optics an integral method that produces three-dimensional (3D) images. The point light source is given at the pickup stage, and the light wave passing through each elemental lens is obtained at the display stage. The amplitude distributions of the waves from each elemental image are the same around a specific point where a 3D image is formed. Since the light waves approaching the image plane from different elemental lenses are incoherent, the synthesized value is the sum of the squared amplitudes of the waves. Therefore the modulation transfer function of this integral method is given by that of a single elemental lens.

© 2007 Optical Society of America

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References

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  1. G. Lippmann, Compt. Rend. 146, 446 (1908).
  2. H. E. Ives, J. Opt. Soc. Am. 21, 171 (1931).
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  3. F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
    [CrossRef]
  4. C. B. Buruckhardt, J. Opt. Soc. Am. 58, 71 (1968).
    [CrossRef]
  5. H. Hoshino, F. Okano, H. Isono, and I. Yuyama, J. Opt. Soc. Am. A 15, 2059 (1998).
    [CrossRef]
  6. F. Okano, J. Arai, and H. Hoshino, 'Steroscopic image pickup device and steroscopic display device,' Japan Patent 3836550, June 2, 1998.
  7. A. Stern and B. Javidi, J. Opt. Soc. Am. A 21, 1602 (2004).
    [CrossRef]

2004

1999

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
[CrossRef]

1998

1968

1931

1908

G. Lippmann, Compt. Rend. 146, 446 (1908).

Arai, J.

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
[CrossRef]

F. Okano, J. Arai, and H. Hoshino, 'Steroscopic image pickup device and steroscopic display device,' Japan Patent 3836550, June 2, 1998.

Buruckhardt, C. B.

Hoshino, H.

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
[CrossRef]

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, J. Opt. Soc. Am. A 15, 2059 (1998).
[CrossRef]

F. Okano, J. Arai, and H. Hoshino, 'Steroscopic image pickup device and steroscopic display device,' Japan Patent 3836550, June 2, 1998.

Isono, H.

Ives, H. E.

Javidi, B.

Lippmann, G.

G. Lippmann, Compt. Rend. 146, 446 (1908).

Okano, F.

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
[CrossRef]

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, J. Opt. Soc. Am. A 15, 2059 (1998).
[CrossRef]

F. Okano, J. Arai, and H. Hoshino, 'Steroscopic image pickup device and steroscopic display device,' Japan Patent 3836550, June 2, 1998.

Stern, A.

Yuyama, I.

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
[CrossRef]

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, J. Opt. Soc. Am. A 15, 2059 (1998).
[CrossRef]

Compt. Rend.

G. Lippmann, Compt. Rend. 146, 446 (1908).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, Opt. Eng. 38, 1072 (1999).
[CrossRef]

Other

F. Okano, J. Arai, and H. Hoshino, 'Steroscopic image pickup device and steroscopic display device,' Japan Patent 3836550, June 2, 1998.

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Figures (1)

Fig. 1
Fig. 1

(a). Schematic of the pickup stage of the integral method. Light waves from an object form elemental images on the pickup plate. (b) Schematic of the display stage. Light waves from the elemental images form a 3D optical image where the object was.

Equations (19)

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x = x m + m P a .
u i , m ( x i , m ) = 1 j λ L s exp ( j k x i , m 2 2 L s ) object δ ( x m x δ , m ) exp ( j k x m 2 2 L s ) exp ( j k x m x i , m L s ) d x m = 1 j λ L s exp ( j k x i , m 2 2 L s ) exp ( j k x δ , m 2 2 L s ) e ( j k x δ , m x i , m L s ) ,
h p , m ( x p , m ) = 1 j λ g exp ( j k x p , m 2 2 g ) w a 2 w a 2 u i , m ( x i , m ) exp ( x i , m 2 2 f ) exp ( j k x i , m 2 2 g ) exp ( j k x i , m x p , m g ) d x i , m ,
h p , m ( x δ p , m ) = 1 λ 2 g L s w a 2 w a 2 exp [ j k ( 1 L s + 1 g 1 f ) x i , m 2 2 ] exp ( j k x δ p , m x i , m ) d x i , m = h p , m ( x δ p , m ) ,
x δ p , m x δ , m L s + x p , m g .
x p , m = ( g L s ) x δ , m .
x δ d , m = ( g L s ) x δ , m .
u d , m ( x i , m ) = 1 j λ g exp ( j k x i , m 2 2 g ) elemental image δ ( x d , m x δ d , m ) exp ( j k x d , m 2 2 g ) exp ( j k x d , m x i , m g ) d x d , m = 1 j λ g exp ( j k x i , m 2 2 g ) exp ( j k x δ d , m 2 2 g ) exp ( j k x δ d , m x i , m g ) .
h d , m ( x m ) = 1 j λ L e exp ( j k x m 2 2 L e ) w a 2 w a 2 u d , m ( x i , m ) exp ( x i , m 2 2 f ) exp ( j k x i , m 2 2 L e ) exp ( j k x i , m x m L e ) d x i , m ,
h d , m ( x m ) = 1 λ 2 L e g w a 2 w a 2 exp ( j k 1 2 L f x i , m 2 ) exp [ j k ( x δ , m L s + x m L e ) x i , m ] d x i , m = 1 λ 2 L e g w a 2 w a exp { j k 1 2 L f [ x i , m + L f ( x δ , m L s + x m L e ) ] 2 } d x i , m ,
1 L f 1 g + 1 L e 1 f .
h d , m ( x δ e ) = 1 λ 2 L e g w a 2 w a 2 exp { j k 1 2 L f [ x i , m + L f ( x δ m P a L s + x m P a L e ) ] 2 } d x i , m = h d , m ( x δ e ) ,
x δ e x δ m P a L s + x m P a L e ,
x = m P a ( 1 + L e L s ) L e L s x δ .
( x δ , z i L s ) = ( x δ , L s ) = ( x δ , z δ ) .
h d , m ( x ) = 1 λ 2 L e g w a 2 w a 2 exp { j k 1 2 L f [ x i , m + L f L s ( x δ x ) ] 2 } d x i , m .
h d , m ( x ) 2 = M h d , m ( x ) 2 ,
MTF d F ( h d , m ( x p , m ) 2 ) ,
MTF p F ( h p , m ( x p , m ) 2 ) .

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