Abstract

We present a parameter analysis of the integral Fourier hologram that is generated from multiple orthographic view images of a three-dimensional object. The maximum view angle, the lens array pitch, and the projection angle step are analyzed to reveal their effects on the maximum size of the reconstructed object and its maximum spatial frequency. With these analyses, we propose a lens array shift method to enhance the resolution of the reconstructed object from the Fourier hologram. The principles are verified by computational and optical experiment.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. 48(34), H120–H136 (2009).
    [CrossRef] [PubMed]
  2. J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6320 .
    [CrossRef] [PubMed]
  3. S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11(26), 3528–3541 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-26-3528 .
    [CrossRef] [PubMed]
  4. J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27(5), 324–326 (2002).
    [CrossRef]
  5. L. Erdmann and K. J. Gabriel, “High-resolution digital integral photography by use of a scanning microlens array,” Appl. Opt. 40(31), 5592–5599 (2001).
    [CrossRef]
  6. Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19253 .
    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 9, pp. 351–353.
  8. A. Stern and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” J. Opt. Soc. Am. A 23(5), 1227–1235 (2006).
    [CrossRef]
  9. A. Stern and B. Javidi, “Sampling in the light of Wigner distribution,” J. Opt. Soc. Am. A 21(3), 360–366 (2004).
    [CrossRef]
  10. J.-H. Park, J. Kim, and B. Lee, “Three-dimensional optical correlator using a sub-image array,” Opt. Express 13(13), 5116–5126 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-5116 .
    [CrossRef] [PubMed]
  11. L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
    [CrossRef]
  12. J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8800 .
    [CrossRef] [PubMed]

2009

N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. 48(34), H120–H136 (2009).
[CrossRef] [PubMed]

J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6320 .
[CrossRef] [PubMed]

Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19253 .
[CrossRef]

2008

J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8800 .
[CrossRef] [PubMed]

2006

A. Stern and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” J. Opt. Soc. Am. A 23(5), 1227–1235 (2006).
[CrossRef]

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

2005

J.-H. Park, J. Kim, and B. Lee, “Three-dimensional optical correlator using a sub-image array,” Opt. Express 13(13), 5116–5126 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-5116 .
[CrossRef] [PubMed]

2004

A. Stern and B. Javidi, “Sampling in the light of Wigner distribution,” J. Opt. Soc. Am. A 21(3), 360–366 (2004).
[CrossRef]

2003

S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11(26), 3528–3541 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-26-3528 .
[CrossRef] [PubMed]

2002

J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27(5), 324–326 (2002).
[CrossRef]

2001

L. Erdmann and K. J. Gabriel, “High-resolution digital integral photography by use of a scanning microlens array,” Appl. Opt. 40(31), 5592–5599 (2001).
[CrossRef]

Baasantseren, G.

J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6320 .
[CrossRef] [PubMed]

J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8800 .
[CrossRef] [PubMed]

Erdmann, L.

L. Erdmann and K. J. Gabriel, “High-resolution digital integral photography by use of a scanning microlens array,” Appl. Opt. 40(31), 5592–5599 (2001).
[CrossRef]

Gabriel, K. J.

L. Erdmann and K. J. Gabriel, “High-resolution digital integral photography by use of a scanning microlens array,” Appl. Opt. 40(31), 5592–5599 (2001).
[CrossRef]

Jang, J.-S.

J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27(5), 324–326 (2002).
[CrossRef]

Javidi, B.

A. Stern and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” J. Opt. Soc. Am. A 23(5), 1227–1235 (2006).
[CrossRef]

A. Stern and B. Javidi, “Sampling in the light of Wigner distribution,” J. Opt. Soc. Am. A 21(3), 360–366 (2004).
[CrossRef]

S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11(26), 3528–3541 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-26-3528 .
[CrossRef] [PubMed]

J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27(5), 324–326 (2002).
[CrossRef]

Kang, J.-M.

J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8800 .
[CrossRef] [PubMed]

Katz, B.

N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. 48(34), H120–H136 (2009).
[CrossRef] [PubMed]

Kim, J.

J.-H. Park, J. Kim, and B. Lee, “Three-dimensional optical correlator using a sub-image array,” Opt. Express 13(13), 5116–5126 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-5116 .
[CrossRef] [PubMed]

Kim, M.-S.

J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6320 .
[CrossRef] [PubMed]

Kim, N.

J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6320 .
[CrossRef] [PubMed]

Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19253 .
[CrossRef]

J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8800 .
[CrossRef] [PubMed]

Kishk, S.

S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11(26), 3528–3541 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-26-3528 .
[CrossRef] [PubMed]

Kwon, K.-C.

Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19253 .
[CrossRef]

Lee, B.

J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8800 .
[CrossRef] [PubMed]

J.-H. Park, J. Kim, and B. Lee, “Three-dimensional optical correlator using a sub-image array,” Opt. Express 13(13), 5116–5126 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-5116 .
[CrossRef] [PubMed]

Lim, Y.-T.

Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19253 .
[CrossRef]

Park, G.

J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8800 .
[CrossRef] [PubMed]

Park, J.-H.

Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19253 .
[CrossRef]

J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6320 .
[CrossRef] [PubMed]

J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8800 .
[CrossRef] [PubMed]

J.-H. Park, J. Kim, and B. Lee, “Three-dimensional optical correlator using a sub-image array,” Opt. Express 13(13), 5116–5126 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-5116 .
[CrossRef] [PubMed]

Rosen, J.

N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. 48(34), H120–H136 (2009).
[CrossRef] [PubMed]

Shaked, N. T.

N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. 48(34), H120–H136 (2009).
[CrossRef] [PubMed]

Stern, A.

A. Stern and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” J. Opt. Soc. Am. A 23(5), 1227–1235 (2006).
[CrossRef]

A. Stern and B. Javidi, “Sampling in the light of Wigner distribution,” J. Opt. Soc. Am. A 21(3), 360–366 (2004).
[CrossRef]

Vincent, A.

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

Wang, D.

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

Zhang, L.

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

Appl. Opt.

N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. 48(34), H120–H136 (2009).
[CrossRef] [PubMed]

L. Erdmann and K. J. Gabriel, “High-resolution digital integral photography by use of a scanning microlens array,” Appl. Opt. 40(31), 5592–5599 (2001).
[CrossRef]

IEEE Trans. Circ. Syst. Video Tech.

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

J. Opt. Soc. Am. A

A. Stern and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” J. Opt. Soc. Am. A 23(5), 1227–1235 (2006).
[CrossRef]

A. Stern and B. Javidi, “Sampling in the light of Wigner distribution,” J. Opt. Soc. Am. A 21(3), 360–366 (2004).
[CrossRef]

Opt. Express

J.-H. Park, J. Kim, and B. Lee, “Three-dimensional optical correlator using a sub-image array,” Opt. Express 13(13), 5116–5126 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-5116 .
[CrossRef] [PubMed]

Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19253 .
[CrossRef]

J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6320 .
[CrossRef] [PubMed]

S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11(26), 3528–3541 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-26-3528 .
[CrossRef] [PubMed]

J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8800 .
[CrossRef] [PubMed]

Opt. Lett.

J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27(5), 324–326 (2002).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 9, pp. 351–353.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (20)

Fig. 1
Fig. 1

Fourier hologram generation using multiple orthographic view images.

Fig. 2
Fig. 2

Schematic of generation and reconstruction of the integral Fourier hologram.

Fig. 3
Fig. 3

Space domain representation of the object field at z=z0 and z=0 plane.

Fig. 4
Fig. 4

Space domain representation of the reconstruction at z=0 plane.

Fig. 5
Fig. 5

Space domain representation of the reconstructed object at z=z0 .

Fig. 6
Fig. 6

Spatial frequency domain representation of the object at z=z0 and z=0 planes.

Fig. 7
Fig. 7

Spatial frequency domain representation of the reconstruction at z=0 plane.

Fig. 8
Fig. 8

Spatial frequency domain representation of the final reconstruction at z=z0 plane.

Fig. 9
Fig. 9

Principle of lens array shift method. (a) Lens array shift in the vertical direction. (b) Synthesis of new set of the element images.

Fig. 10
Fig. 10

The object used in simulation

Fig. 11
Fig. 11

Space domain representation of the reconstructed objects with the parameters in Table 1. (a) Case (I), (b) case (II).

Fig. 12
Fig. 12

Reconstructed images from the integral Fourier holograms using parameters in 
Table 1. (a) Case (I), (b) Case (II).

Fig. 13
Fig. 13

Spatial frequency domain representation of the reconstructions at z=0 plane with the parameters in Table 2. (a) Case (I), (b) case (II). (c) case (III), (d) case (IV).

Fig. 14
Fig. 14

Reconstruction of the integral Fourier hologram with parameters of Table 2. (a) Case (I) (b) case (II), (c) case (III), (d) case (IV).

Fig. 15
Fig. 15

Experimental setup to capture the element images of two plane objects

Fig. 16
Fig. 16

Element images and generated orthographic images. (a)Conventional single set of element images (left figure) and orthographic images (right figure) generated from single set of element images. (b) Element images (left figure) synthesized from 4 sets of the elemental images captured with lens array shifting and orthographic images (right figure) generated from synthesized element images.

Fig. 17
Fig. 17

Reconstruction of two plane objects. (a) Reconstruction from conventional integral Fourier hologram generated from a single set of element images, (b) reconstruction from proposed integral Fourier hologram generated with lens array shift method.

Fig. 18
Fig. 18

Experimental setup to capture the element images. (a) The experimental setup to capture the real 3D object, (b) frontal image of the object. (c) the distances from the lens array to the different parts of the object.

Fig. 19
Fig. 19

Amplitude (left figures) and phase (right figures) of the generated Fourier hologram. (a) Conventional integral Fourier hologram. (b) Integral Fourier hologram by using Lens shift method.

Fig. 20
Fig. 20

Reconstruction of the 3D object’s Fourier hologram. (a) Conventional integral Fourier hologram generated from a single set of element images (b) Proposed integral Fourier hologram generated using lens shift method, (c) Comparison of the reconstructions at z=54mm

Tables (2)

Tables Icon

Table 1 Simulation parameters to verify the overlapping theorem

Tables Icon

Table 2 Simulation Parameters to verify the spatial frequency theorem

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

H ( u ) = H ( M s ) = P s t ( x p ) exp ( j 2 π b x p s ) d x p = O ( x , y , z ) exp [ j 2 π b M ( x u + z l M u 2 ) ] d x d z ,
M = 2 f l , b = 2 λ l .
O ( x , y , z ) = z 0 O ( x , y ; z 0 ) δ ( z z o ) ,
H ( u , v ) = exp [ j z 0 π λ f 2 ( u 2 + v 2 ) ] O ( x , y ; z 0 ) exp [ j 2 π λ f ( x u + y v ) ] d x d y ,
F T { H ( u , v ) } = F T { exp [ j z 0 π λ f 2 ( u 2 + v 2 ) ] O ( x , y ; z 0 ) exp [ j 2 π λ f ( x u + y v ) ] d x d y } = F T { exp [ j z o π λ f 2 ( u 2 + v 2 ) ] } F T { O ( x , y ; z 0 ) exp [ j 2 π λ f ( x u + y v ) ] d x d y } = exp [ j π λ z o ( x 2 + y 2 ) ] O ( x , y ; z 0 ) = O ( x , y ; z 0 ) exp [ j π λ z 0 ( ( x ξ ) 2 + ( y η ) 2 ) ] d x d y ,
L x λ f 2 Δ u = λ 4 Δ θ .
f x , max = f ξ ' , max = L u λ f = 2 θ max λ ,
B x = B ξ 1 2 Δ x p .
B x < 2 θ max λ .
2 θ max λ < 1 Δ x p B x .

Metrics