Abstract

An innovative approach is proposed for calculating high resolution computer generated integral holograms by using the Fourier Ptychographic (FP) algorithm. The approach initializes a high resolution complex hologram with a random guess, and then stitches together low resolution multi-view images, synthesized from the elemental images captured by integral imaging (II), to recover the high resolution hologram through an iterative retrieval with FP constrains. This paper begins with an analysis of the principle of hologram synthesis from multi-projections, followed by an accurate determination of the constrains required in the Fourier ptychographic integral-holography (FPIH). Next, the procedure of the approach is described in detail. Finally, optical reconstructions are performed and the results are demonstrated. Theoretical analysis and experiments show that our proposed approach can reconstruct 3D scenes with high resolution.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2014 (5)

2013 (6)

2012 (2)

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific Reports 3, 1927 (2012).

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] [PubMed]

2010 (1)

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (5)

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Advances in Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinearoptimization approach,” Opt. Express 16, 7264–7278 (2008).
[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, 8800–8813 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (1)

2004 (1)

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys Rev Lett. 93, 023903 (2004).
[Crossref] [PubMed]

2003 (3)

1987 (1)

Abbey, B.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

Abookasis, D.

Baasantseren, G.

Bean, R.

Berenguer, F.

Bian, Z.

Bunk, O.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Chen, B.

Chen, Y.

Chung, J.

G. Zheng, X. Ou, R. Horstmeyer, J. Chung, and C. Yang, “Fourier ptychographic microscopy: A gigapixel superscope for biomedicine,” Opt. Photon. News 25, 26–33 (2014).
[Crossref]

Clark, J. N.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

Cloetens, P.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific Reports 3, 1927 (2012).

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

de Jonge, M.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

Diaz, A.

Dierolf, M.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific Reports 3, 1927 (2012).

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Dong, S.

Enders, B.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific Reports 3, 1927 (2012).

Faulkner, H. M.

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys Rev Lett. 93, 023903 (2004).
[Crossref] [PubMed]

Fienup, J. R.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, Greenwood Village, Colorado, USA, 2004), 3rd ed.

Guizar-Sicairos, M.

Guo, K.

Hong, S.-I.

Horstmeyer, R.

Ichikawa, T.

Itoh, M.

Jang, J.-S.

Javidi, B.

Jin, F.

Jo, N.-Y.

Kang, J.-M.

Kewish, C. M.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Kim, M.-S.

Kim, N.

Kim, Y.-S.

Lee, B.

Lee, S.-K.

Lim, H.-G.

McNulty, I.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

Menzel, A.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[Crossref] [PubMed]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Nanda, P.

Nugent, K. A.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

Ohsawa, Y.

Ou, X.

Park, G.

Park, J.-H.

Peele, A. G.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

Peterson, I.

Pfeifer, M. A.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

Pfeiffer, F.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific Reports 3, 1927 (2012).

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Robinson, I. K.

Rodenburg, J. M.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[Crossref] [PubMed]

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Advances in Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys Rev Lett. 93, 023903 (2004).
[Crossref] [PubMed]

Rosen, J.

Sakamoto, Y.

Sando, Y.

Schneider, P.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Shaked, N. T.

Shiradkar, R.

Stern, A.

Stockmar, M.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific Reports 3, 1927 (2012).

Thibault, P.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific Reports 3, 1927 (2012).

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Vila-Comamala, J.

Wakunami, K.

Wang, X.

Wepf, R.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Williams, G. J.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

Wu, X.

Xin, H.

Xu, Y.

Yamaguchi, K.

Yamaguchi, M.

Yang, C.

Yatagai, T.

Zanette, I.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific Reports 3, 1927 (2012).

Zhang, F.

Zhang, J.

Zheng, G.

S. Dong, R. Shiradkar, P. Nanda, and G. Zheng, “Spectral multiplexing and coherent-state decomposition in Fourier ptychographic imaging,” Biomed. Opt. Express 5, 1757–1767 (2014).
[Crossref] [PubMed]

S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22, 13586–13599 (2014).
[Crossref] [PubMed]

G. Zheng, X. Ou, R. Horstmeyer, J. Chung, and C. Yang, “Fourier ptychographic microscopy: A gigapixel superscope for biomedicine,” Opt. Photon. News 25, 26–33 (2014).
[Crossref]

G. Zheng, “Breakthroughs in photonics 2013: Fourier ptychographic imaging,” Photonics Journal, IEEE 6, 1–7 (2014).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nature Photonics 7, 739–745 (2013).
[Crossref]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38, 4845–4848 (2013).
[Crossref] [PubMed]

Advances in Imaging Electron Phys. (1)

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Advances in Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

Appl. Opt. (3)

Biomed. Opt. Express (1)

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

Nature (1)

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Nature Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nature Photonics 7, 739–745 (2013).
[Crossref]

Nature Physics (1)

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Physics 4, 394–398 (2008).
[Crossref]

Opt. Express (8)

N. T. Shaked, J. Rosen, and A. Stern, “Integral holography: white-light single-shot hologram acquisition,” Opt. Express 15, 5754–5760 (2007).
[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, 6320–6334 (2009).
[Crossref] [PubMed]

S.-K. Lee, S.-I. Hong, Y.-S. Kim, H.-G. Lim, N.-Y. Jo, and J.-H. Park, “Hologram synthesis of three-dimensional real objects using portable integral imaging camera,” Opt. Express 21, 23662–23670 (2013).
[Crossref] [PubMed]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[Crossref] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinearoptimization approach,” Opt. Express 16, 7264–7278 (2008).
[Crossref] [PubMed]

R. Horstmeyer and C. Yang, “A phase space model of Fourier ptychographic microscopy,” Opt. Express 22, 338–358 (2014).
[Crossref] [PubMed]

S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22, 13586–13599 (2014).
[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, 8800–8813 (2008).
[Crossref] [PubMed]

Opt. Lett. (5)

Opt. Photon. News (1)

G. Zheng, X. Ou, R. Horstmeyer, J. Chung, and C. Yang, “Fourier ptychographic microscopy: A gigapixel superscope for biomedicine,” Opt. Photon. News 25, 26–33 (2014).
[Crossref]

Photonics Journal, IEEE (1)

G. Zheng, “Breakthroughs in photonics 2013: Fourier ptychographic imaging,” Photonics Journal, IEEE 6, 1–7 (2014).
[Crossref]

Phys Rev Lett. (1)

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys Rev Lett. 93, 023903 (2004).
[Crossref] [PubMed]

Science (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Scientific Reports (1)

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific Reports 3, 1927 (2012).

Other (1)

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, Greenwood Village, Colorado, USA, 2004), 3rd ed.

Supplementary Material (1)

» Media 1: MP4 (22842 KB)     

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Figures (7)

Fig. 1
Fig. 1 Schemes of II model and multi-projection holography system. (a) The model of II, in which a 3D object parrot and its EIA are shown as well. (b) The multi-projection holography system, in which a high resolution hologram is composed of a set of low resolution regions which produce multi-view projections. (c) The conversion of EIA to OIA is of a link between II and multi-projection holography.
Fig. 2
Fig. 2 The principle of synthesizing high resolution holograms from low resolution multi-view images. (a) A numerical reconstruction of two point sources from a high resolution Fourier hologram (b) Reconstructions from the low-pass-filtered hologram array.
Fig. 3
Fig. 3 Procedure of complex hologram calculation using FP. The numbers in figure represent the steps of FP. The orange arrow presents a Fourier transform operation while the black arrow presents an inverse one. Several OIs with concave viewpoint are laid out in array format. The red, green and blue rectangles individually enclose a subregion corresponding to an OI labeled by the same color arrow.
Fig. 4
Fig. 4 Optical experimental setup.
Fig. 5
Fig. 5 3D scene reconstruction from FPIH. (a) Space alignment of letters in II system, (b) Reconstructed ‘A’ and ‘R’ letters at different distances ( Media 1 Media 2.
Fig. 6
Fig. 6 Reconstructions of a 3D object with fine structures from FPIH. (a) The variation curve of E with iteration times, (b) Reconstructed ‘parrot’ at the second diffraction order under η = 0 and non-iteration, (c) Reconstructed images at three diffraction orders under η = 0.5 and 10 iterations.
Fig. 7
Fig. 7 Resolution enhancement of FPIH. (a) The USAF resolution target, (b) Reconstruction at the zero diffraction order under η = 0 and non-iteration, (c) Reconstruction at the zero diffraction order under η = 0.5 and 50 iterations.

Tables (1)

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Table 1 Configurations of equipments

Equations (16)

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M II = f 0 z = Δ p Δ o
P ( u , v ) = exp [ j π λ f h ( 1 z 0 f h ) ( u 2 + v 2 ) ] { O ( x o , y o ; z o ) } d z o
1 { p ( u u x , v v y ) } = 1 { P ( u , v ) [ rect ( u v ) rect ( u v ) * δ ( u u x , v v x ) ] } O ( x o , y o , z o ) exp [ j 2 π ( ξ x x 0 + ξ y y o ) ] * exp [ j π λ f h 2 f h z o ( x o 2 + y o 2 ) ] * sinc ( a x 0 λ f h ) sinc ( b y 0 λ f h ) d z o
{ ξ x = u x / ( λ f h ) = sin θ x / λ ξ y = u y / ( λ f h ) = sin θ y / λ
| 1 { p ( u u x , v v y ) } | | L { O ( x o , y o , z o ) exp [ j 2 π ( ξ x x o + ξ y y o ) ] } d z o | O I ( θ x , θ y )
{ u x = f h sin θ x f h Δ p x / f 0 u x = f h sin θ y f h Δ p y / f 0
| 1 { p ( m m x , n n y ) } | = | 1 { p x , y } | = OI x , y
{ m x = ( f h Δ p x ) / ( f 0 Δ h ) n y = ( f h Δ p y ) / ( f 0 Δ h ) , N g = f h Δ p f 0 Δ h < min ( N s , N t )
N u × N v N x ( N s N g ) × N y ( N t N g )
N g = f h Δ h Δ o z
Δ o = λ f h Δ h N u
Δ o Δ o = λ f h 2 Δ h 2 N u N g z
O x , y = OI x , y O x , y | O x , y |
p x , y = η p x , y + ( 1 η ) p x , y
E ( k ) = 1 N x N y x , y s , t ( | O x , y | OI x , y ) 2 s , t OI x , y
H ( m , n ) = 0.5 { 1 + cos [ φ P ( m , n ) φ 0 ] }

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