Abstract

We present a technique for synthesizing the Fourier hologram of a three-dimensional scene from its light field. The light field captures the volumetric information of an object, and an important advantage is that it does not require coherent illumination, as in conventional holography. In this work, we show how to obtain a high-resolution digital hologram with the light field obtained from a series of photographic images captured along the optical axis. The method is verified both by simulations and experimentally captured light field.

© 2016 Optical Society of America

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References

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2015 (2)

2014 (3)

X. Xiao, K. Wakunami, X. Chen, X. Shen, B. Javidi, J. Kim, and J. Nam, “Three-dimensional holographic display using dense ray sampling and integral imaging capture,” J. Disp. Technol. 10, 688–694 (2014).
[Crossref]

J.-H. Park, S.-K. Lee, N.-Y. Jo, H.-J. Kim, Y.-S. Kim, and H.-G. Lim, “Light ray field capture using focal plane sweeping and its optical reconstruction using 3D displays,” Opt. Express 22, 25444–25454 (2014).
[Crossref]

S.-G. Park, J. Yeom, Y. Jeong, N. Chen, J.-Y. Hong, and B. Lee, “Recent issues on integral imaging and its applications,” J. Inf. Disp. 15, 37–46 (2014).
[Crossref]

2013 (1)

2012 (2)

2011 (3)

2010 (2)

2009 (4)

2008 (1)

2007 (1)

2005 (1)

R. Ng, “Fourier slice photography,” ACM Trans. Graph. 24, 735–744 (2005).
[Crossref]

2003 (1)

2001 (1)

1967 (1)

R. V. Pole, “3-D imagery and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
[Crossref]

1936 (1)

A. Gershun, “The light field,” J. Math. Phys. XVIII, 51–151 (1936).

Abookasis, D.

Baasantseren, G.

Barreiro, J. C.

Chen, N.

Chen, X.

X. Xiao, K. Wakunami, X. Chen, X. Shen, B. Javidi, J. Kim, and J. Nam, “Three-dimensional holographic display using dense ray sampling and integral imaging capture,” J. Disp. Technol. 10, 688–694 (2014).
[Crossref]

Choi, H.-J.

Crozier, K. B.

Gershun, A.

A. Gershun, “The light field,” J. Math. Phys. XVIII, 51–151 (1936).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

Hahn, J.

Hanrahan, P.

M. Levoy and P. Hanrahan, “Light field rendering,” in SIGGRAPH ’96 Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1996), pp. 31–42.

Hong, J.

Hong, J.-Y.

S.-G. Park, J. Yeom, Y. Jeong, N. Chen, J.-Y. Hong, and B. Lee, “Recent issues on integral imaging and its applications,” J. Inf. Disp. 15, 37–46 (2014).
[Crossref]

Indebetouw, G.

Javidi, B.

X. Xiao, K. Wakunami, X. Chen, X. Shen, B. Javidi, J. Kim, and J. Nam, “Three-dimensional holographic display using dense ray sampling and integral imaging capture,” J. Disp. Technol. 10, 688–694 (2014).
[Crossref]

K. Wakunami, M. Yamaguchi, and B. Javidi, “High-resolution three-dimensional holographic display using dense ray sampling from integral imaging,” Opt. Lett. 37, 5103–5105 (2012).
[Crossref]

Jeong, K.-M.

Jeong, Y.

S.-G. Park, J. Yeom, Y. Jeong, N. Chen, J.-Y. Hong, and B. Lee, “Recent issues on integral imaging and its applications,” J. Inf. Disp. 15, 37–46 (2014).
[Crossref]

Jo, N.-Y.

Jung, J.-H.

Katz, B.

Ke, J.

Kim, H.

Kim, H.-J.

Kim, J.

X. Xiao, K. Wakunami, X. Chen, X. Shen, B. Javidi, J. Kim, and J. Nam, “Three-dimensional holographic display using dense ray sampling and integral imaging capture,” J. Disp. Technol. 10, 688–694 (2014).
[Crossref]

Kim, M.-S.

Kim, N.

Kim, Y.

Kim, Y.-S.

Lam, E. Y.

Lee, B.

Lee, S.-K.

Levoy, M.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235, 144–162 (2009).
[Crossref]

M. Levoy and P. Hanrahan, “Light field rendering,” in SIGGRAPH ’96 Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1996), pp. 31–42.

Li, Y.

Lim, H.-G.

Llavador, A.

Martínez-Corral, M.

McDowall, I.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235, 144–162 (2009).
[Crossref]

Min, S.-W.

Nam, J.

X. Xiao, K. Wakunami, X. Chen, X. Shen, B. Javidi, J. Kim, and J. Nam, “Three-dimensional holographic display using dense ray sampling and integral imaging capture,” J. Disp. Technol. 10, 688–694 (2014).
[Crossref]

Ng, R.

R. Ng, “Fourier slice photography,” ACM Trans. Graph. 24, 735–744 (2005).
[Crossref]

R. Ng, “Digital light field photography,” Ph.D. thesis (Stanford University, 2006).

Orth, A.

Park, J.-H.

Park, S.-G.

S.-G. Park, J. Yeom, Y. Jeong, N. Chen, J.-Y. Hong, and B. Lee, “Recent issues on integral imaging and its applications,” J. Inf. Disp. 15, 37–46 (2014).
[Crossref]

Pole, R. V.

R. V. Pole, “3-D imagery and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
[Crossref]

Poon, T.-C.

Rosen, J.

Saavedra, G.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley–Interscience, 2007).

Sánchez-Ortiga, E.

Shaked, N. T.

Shen, X.

X. Xiao, K. Wakunami, X. Chen, X. Shen, B. Javidi, J. Kim, and J. Nam, “Three-dimensional holographic display using dense ray sampling and integral imaging capture,” J. Disp. Technol. 10, 688–694 (2014).
[Crossref]

Stern, A.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley–Interscience, 2007).

Vo, H.

Wakunami, K.

X. Xiao, K. Wakunami, X. Chen, X. Shen, B. Javidi, J. Kim, and J. Nam, “Three-dimensional holographic display using dense ray sampling and integral imaging capture,” J. Disp. Technol. 10, 688–694 (2014).
[Crossref]

K. Wakunami, M. Yamaguchi, and B. Javidi, “High-resolution three-dimensional holographic display using dense ray sampling from integral imaging,” Opt. Lett. 37, 5103–5105 (2012).
[Crossref]

Xiao, X.

X. Xiao, K. Wakunami, X. Chen, X. Shen, B. Javidi, J. Kim, and J. Nam, “Three-dimensional holographic display using dense ray sampling and integral imaging capture,” J. Disp. Technol. 10, 688–694 (2014).
[Crossref]

Xu, Z.

Yamaguchi, M.

Yeom, J.

Zhang, X.

Zhang, Z.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235, 144–162 (2009).
[Crossref]

ACM Trans. Graph. (1)

R. Ng, “Fourier slice photography,” ACM Trans. Graph. 24, 735–744 (2005).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

R. V. Pole, “3-D imagery and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
[Crossref]

Biomed. Opt. Express (1)

J. Disp. Technol. (1)

X. Xiao, K. Wakunami, X. Chen, X. Shen, B. Javidi, J. Kim, and J. Nam, “Three-dimensional holographic display using dense ray sampling and integral imaging capture,” J. Disp. Technol. 10, 688–694 (2014).
[Crossref]

J. Inf. Disp. (1)

S.-G. Park, J. Yeom, Y. Jeong, N. Chen, J.-Y. Hong, and B. Lee, “Recent issues on integral imaging and its applications,” J. Inf. Disp. 15, 37–46 (2014).
[Crossref]

J. Math. Phys. (1)

A. Gershun, “The light field,” J. Math. Phys. XVIII, 51–151 (1936).

J. Microsc. (1)

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235, 144–162 (2009).
[Crossref]

J. Opt. Soc. Am. A (3)

Opt. Express (8)

Opt. Lett. (2)

Other (4)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley–Interscience, 2007).

R. Ng, “Digital light field photography,” Ph.D. thesis (Stanford University, 2006).

M. Levoy and P. Hanrahan, “Light field rendering,” in SIGGRAPH ’96 Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1996), pp. 31–42.

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Figures (9)

Fig. 1.
Fig. 1.

Light field definition.

Fig. 2.
Fig. 2.

Fourier hologram synthesis from the light field.

Fig. 3.
Fig. 3.

Relation between 3D object and its light field.

Fig. 4.
Fig. 4.

Object used in the simulation: (a) 3D object location and (b) 2D slice of light field L(x,θx) of the 3D object where y=0 and θy=0°.

Fig. 5.
Fig. 5.

(a) Magnitude and (b) phase profile of the Fourier hologram.

Fig. 6.
Fig. 6.

Reconstructed objects focused at different depth planes.

Fig. 7.
Fig. 7.

Object used in the simulation: (a) the 3D scene, and the 2D light field slice (b) L(x,tanθx) where y=0.55ymax and θy=0°, and (c) L(y,tanθy) where x=0.4xmax and θx=0°.

Fig. 8.
Fig. 8.

Magnitude and phase profiles of the Fourier holograms generated with light rays sampled with (a) 200×200, (b) 300×300, and (c) 500×500 angles.

Fig. 9.
Fig. 9.

Reconstructed images at different depths from holograms have a pixel resolution of (a) 200×200, (b) 300×300, (c) 500×500, and (d) the magnified images corresponding to the marked areas in (a)–(c).

Equations (11)

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H(u,v)=O(x,y,z)exp[jzπλf2(u2+v2)]×exp[j2πλf(xu+yv)]dxdydz,
H(ξ,η)=L(xl,yl,ξ,η,zl)×exp[j2πB(xlξ+ylη)]dxldyl,
O(x,y,z)n=1NO(x,y,zn)=n=1NO(x,y,z)δ(x,y,znz),
L(xl,yl,ξ,η,zl)=O(xl(zlzn)ξ,yl(zlzn)η,zlzn)=n=1NO(x,y,z)δ(xl+znξx,yl+znηy,zn).
L(xl,yl,ξ,η,zl)=O(xo,yo,zo)×δ(xl+zoξxo,yl+zoηyo).
Hp(ξ,η)=O(xo,yo,zo)exp[j2πBz(ξ2+η2)]×exp[j2πB(xoξ+yoη)].
H(ξ,η)=O(x,y,z)exp[j2πBz(ξ2+η2)]×exp[j2πB(xξ+yη)]dxdydz.
H(u,v)=H(ξ,η)|ξ=u/M,η=v/M=O(x,y,z)exp[j2πBzM2(u2+v2)]×exp[j2πBM(xu+yv)]dxdydz.
M=2fandB=2λ.
O(x,y,z)=H(u,v)exp[jπzλf2(u2+v2)]×exp[j2πλf(xu+yv)]dudv=H(u,v)exp[jπzλf21M12M2(u2+v2)]×exp[j2πλf1M1M2(xu+yv)]dudv.
M=pξandB=M22λf2,

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