Abstract

Free-viewpoint images obtained from phase-shifting synthetic aperture digital holography are given for scenes that include multiple objects and a concave object. The synthetic aperture technique is used to enlarge the effective sensor size and to make it possible to widen the range of changing perspective in the numerical reconstruction. The lensless Fourier setup and its aliasing-free zone are used to avoid aliasing errors arising at the sensor edge and to overcome a common problem in digital holography, namely, a narrow field of view. A change of viewpoint is realized by a double numerical propagation and by clipping the wave field by a given pupil. The computational complexity for calculating an image in the given perspective from the base complex-valued image is estimated at a double fast Fourier transform. The experimental results illustrate the natural change of appearance in cases of both multiple objects and a concave object.

© 2008 Optical Society of America

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References

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  1. K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holograph,” Appl. Opt. 47, D110-D116 (2007).
    [CrossRef]
  2. L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046-5051 (2001).
    [CrossRef]
  3. 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]
  4. S.-H. Hong and B. Javidi, “Three-dimensional visualization of partially occluded objects using integral imaging,” J. Disp. Technol. 1, 354-359 (2005).
    [CrossRef]
  5. A. W. Lohmann, “Three-dimensional properties of wave-fields,” Optik (Jena) 51, 105-117 (1978).
  6. T. Hamano and M. Kitamura, “Computer-generated holograms for reconstructing multi-3-D images by space-division recording method,” Proc. SPIE 3956, 23-32 (2000).
    [CrossRef]
  7. K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90-97 (2004).
    [CrossRef]
  8. A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation ,” Syst. Comput. Jpn. 38, 53-61 (2004).
  9. K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).
    [CrossRef]
  10. J. Maycock, C. P. McElhinney, B. M. Hennelly, T. J. Naughton, J. B. McDonald, and B. Javidi, “Reconstruction of partially occluded objects encoded in three-dimensional scenes by using digital holograms,” Appl. Opt. 45, 2975-2985 (2006).
    [CrossRef] [PubMed]
  11. R. Binet, J. Colineau, and J.-C. Lehureau, “Short-range synthetic aperture imaging at 633 nm by digital holography,” Appl. Opt. 41, 4775-4782 (2002).
    [CrossRef] [PubMed]
  12. V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Synthetic aperture superresolution with multiple off-axis holograms,” J. Opt. Soc. Am. A 23, 3162-3170 (2006).
    [CrossRef]
  13. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).
    [CrossRef] [PubMed]
  14. C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, “Digital recording and numerical reconstruction of lensless fourier holograms in optical metrology,” Appl. Opt. 38, 4812-4820(1999).
    [CrossRef]
  15. I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177-6186 (2001).
    [CrossRef]
  16. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), chap. 3.10.

2007 (2)

2006 (2)

2005 (2)

S.-H. Hong and B. Javidi, “Three-dimensional visualization of partially occluded objects using integral imaging,” J. Disp. Technol. 1, 354-359 (2005).
[CrossRef]

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).
[CrossRef]

2004 (2)

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90-97 (2004).
[CrossRef]

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation ,” Syst. Comput. Jpn. 38, 53-61 (2004).

2002 (1)

2001 (2)

2000 (1)

T. Hamano and M. Kitamura, “Computer-generated holograms for reconstructing multi-3-D images by space-division recording method,” Proc. SPIE 3956, 23-32 (2000).
[CrossRef]

1999 (1)

1997 (1)

1978 (1)

A. W. Lohmann, “Three-dimensional properties of wave-fields,” Optik (Jena) 51, 105-117 (1978).

Asundi, A. K.

Binet, R.

Colineau, J.

García, J.

García-Martínez, P.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), chap. 3.10.

Hamano, T.

T. Hamano and M. Kitamura, “Computer-generated holograms for reconstructing multi-3-D images by space-division recording method,” Proc. SPIE 3956, 23-32 (2000).
[CrossRef]

Hennelly, B. M.

Hong, S.-H.

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]

S.-H. Hong and B. Javidi, “Three-dimensional visualization of partially occluded objects using integral imaging,” J. Disp. Technol. 1, 354-359 (2005).
[CrossRef]

Hwang, Y. S.

Javidi, B.

Jüptner, W.

Kato, J.

Kitamura, M.

T. Hamano and M. Kitamura, “Computer-generated holograms for reconstructing multi-3-D images by space-division recording method,” Proc. SPIE 3956, 23-32 (2000).
[CrossRef]

Kondoh, A.

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation ,” Syst. Comput. Jpn. 38, 53-61 (2004).

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90-97 (2004).
[CrossRef]

Lehureau, J.-C.

Lohmann, A. W.

A. W. Lohmann, “Three-dimensional properties of wave-fields,” Optik (Jena) 51, 105-117 (1978).

Matsushima, K.

K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holograph,” Appl. Opt. 47, D110-D116 (2007).
[CrossRef]

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).
[CrossRef]

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90-97 (2004).
[CrossRef]

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation ,” Syst. Comput. Jpn. 38, 53-61 (2004).

Maycock, J.

McDonald, J. B.

McElhinney, C. P.

Miao, J.

Mico, V.

Mizuno, J.

Naughton, T. J.

Ohta, S.

Osten, W.

Peng, X.

Seebacher, S.

Wagner, C.

Xu, L.

Yamaguchi, I.

Zalevsky, Z.

Zhang, T.

Appl. Opt. (6)

Hidden surface removal in full-parallax CGHs by silhouette approximation (1)

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation ,” Syst. Comput. Jpn. 38, 53-61 (2004).

J. Disp. Technol. (1)

S.-H. Hong and B. Javidi, “Three-dimensional visualization of partially occluded objects using integral imaging,” J. Disp. Technol. 1, 354-359 (2005).
[CrossRef]

J. Display Technol. (1)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Optik (Jena) (1)

A. W. Lohmann, “Three-dimensional properties of wave-fields,” Optik (Jena) 51, 105-117 (1978).

Proc. SPIE (3)

T. Hamano and M. Kitamura, “Computer-generated holograms for reconstructing multi-3-D images by space-division recording method,” Proc. SPIE 3956, 23-32 (2000).
[CrossRef]

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE 5290, 90-97 (2004).
[CrossRef]

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), chap. 3.10.

Supplementary Material (2)

» Media 1: MOV (503 KB)     
» Media 2: MOV (1028 KB)     

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Figures (16)

Fig. 1
Fig. 1

Definition of the visual field in capturing wave fields and the viewing zone in numerical reconstruction.

Fig. 2
Fig. 2

Definition of the coordinate systems and schematic geometry used in numerical reconstruction.

Fig. 3
Fig. 3

Principle of numerical reconstruction from different viewpoints.

Fig. 4
Fig. 4

Definition of a pupil.

Fig. 5
Fig. 5

Experimental setup for capturing object waves by phase-shifting synthetic aperture digital holography.

Fig. 6
Fig. 6

Theoretical model for estimating the maximum spatial frequency of the interference fringe on the sensor surface.

Fig. 7
Fig. 7

Aliasing-free zone.

Fig. 8
Fig. 8

Numerical reconstruction without numerical propagation and the synthetic aperture technique. The number of pixels is 2048 × 2048 pixels.

Fig. 9
Fig. 9

Numerical reconstruction without synthetic aperture technique. The amplitude image of the wave field (a) without and (b) with numerical propagation. The propagation distance is d P = - 6.0 cm . Each image contains 2048 × 2048 pixels.

Fig. 10
Fig. 10

Schematic geometry of the object reconstructed in Fig. 9.

Fig. 11
Fig. 11

Example of a synthetic complex-valued image stitched from 5 × 5 segments.

Fig. 12
Fig. 12

(Multimedia online; ao.osa.org) Amplitude images | f ( x , y , 0 ; x e , y e ) | of a self-occluded object from different viewpoints (associated movie file, 499  Kbytes ).

Fig. 13
Fig. 13

(Multimedia online; ao.osa.org) Amplitude images | f ( x , y , - 3.0 cm ; x e , y e ) | of mutually occluded objects from different viewpoints (associated movie file, 1.0   Mbyte ).

Fig. 14
Fig. 14

Schematic geometry of the mutually occluded objects reconstructed in Fig. 13.

Fig. 15
Fig. 15

Visual field in the numerical reconstruction from different viewpoints.

Fig. 16
Fig. 16

Numerical reconstruction using different pupils: (a)–(c) Only the pupil size varies; (d)–(f) the pupil distance differs, but all pupils are placed in the same line of sight and have the same angle φ x , y as that used in Fig. 13.

Equations (14)

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R ( x s , y s ) = exp [ i k x s 2 + y s 2 2 d R ] ,
O R * ( x s , y s ) = f ( x , y , 0 ) exp [ i k 2 d R ( x 2 + y 2 ) ] exp [ - i 2 π λ d R ( x x s + y y s ) ] d x d y = F { f ( x , y , 0 ) ϕ * ( x , y ) } u = x s / λ d R , v = y s / λ d R ,
ϕ ( x , y ) = exp [ - i k 2 d R ( x 2 + y 2 ) ] ,
f ( x , y , 0 ) = F { O R * ( x s , y s ) } u s = - x / λ d R , v s = - y / λ d R × ϕ ( x , y ) ,
Δ x = λ d R N x δ x , Δ y = λ d R N y δ y ,
f ( x , y , d P ) = P d P { f ( x , y , 0 ) } = F - 1 { F 0 ( u , v ) exp [ i 2 π ( λ - 2 - u 2 - v 2 ) 1 / 2 d P ] } ,
f ^ ( x , y , d P ; x e , y e ) = f ( x , y , d P ) p ( x , y ; x e , y e ) .
f ^ ( x , y , 0 ; x e , y e ) = P - d B { f ^ ( x , y , d P ; x e , y e ) } ,
Λ = 2 π | k P - k R | ,
Λ min = λ 2 sin ( Δ θ / 2 ) ,
sin ( Δ θ / 2 ) = w / 4 d 2 + ( w / 4 ) 2 .
w 4 λ d 16 δ 2 - λ 2 .
p x × p y = ( p x × p y ) d P 2 / d P 2 ,
d P 2 x e , max + w x 2 tan θ x , 2 y e , max + w y 2 tan θ y ,

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