Abstract

We experimentally demonstrated single-shot phase imaging with a coded aperture (SPICA), which connects digital holography and coherent diffractive imaging based on compressive sensing to realize the advantages of both methods simultaneously. SPICA allows the observation of a complex field with a simple, single-shot optical setup that does not need reference light and does not suffer from losses associated with the field-of-view and spatial resolution. Experiments showed the promising capabilities of SPICA for single-shot holographic imaging.

© 2015 Optical Society of America

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References

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2015 (3)

2014 (4)

2013 (2)

Y. Rivenson, A. Stern, and B. Javidi, “Overview of compressive sensing techniques applied in holography,” Appl. Opt. 52, A423–A432 (2013).
[Crossref] [PubMed]

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

2012 (3)

2011 (2)

S. Lim, D. L. Marks, and D. J. Brady, “Sampling and processing for compressive holography,” Appl. Opt. 50, H75–H86 (2011).
[Crossref] [PubMed]

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

2010 (3)

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nature Photonics 4, 833–839 (2010).
[Crossref]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[Crossref]

M. M. Marim, M. Atlan, E. Angelini, and J.-C. Olivo-Marin, “Compressed sensing with off-axis frequency-shifting holography,” Opt. Lett. 35, 871–873 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (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]

2007 (2)

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
[Crossref]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

2006 (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Info. Theory 52, 1289–1306 (2006).
[Crossref]

1997 (1)

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase un-wrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

1984 (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

1982 (1)

1962 (1)

Abbey, B.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Aino, M.

Angelini, E.

Arai, Y.

Atlan, M.

Balaur, E.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Banerjee, P. P.

Baraniuk, R.

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
[Crossref]

Bhaduri, B.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

Brady, D. J.

Bunk, O.

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]

Cadenazzi, G. A.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Chapman, H. N.

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nature Photonics 4, 833–839 (2010).
[Crossref]

Chen, C.-C.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Choi, K.

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]

Dierolf, M.

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]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Info. Theory 52, 1289–1306 (2006).
[Crossref]

Edwards, C.

Fahimian, B. P.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Faridian, A.

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Fienup, J. R.

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

Gao, P.

Goddard, L. L.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase un-wrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Henderson, C. A.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Horisaki, R.

Horstmeyer, R.

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

Ishikawa, T.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Javidi, B.

Jiang, H.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Kaku, T.

Körner, K.

Lee, T.-K.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Leith, E. N.

Lim, S.

Lu, C.-H.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Marim, M. M.

Marks, D. L.

McNulty, I.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Menzel, A.

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]

Miao, J.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Murnane, M. M.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

Naik, D.

Nakashima, A.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Nehmetallah, G.

Nguyen, T. H.

Nishimura, T.

T. Nishimura, Y. Ogura, and J. Tanida, “Optofluidic DNA computation based on optically manipulated micro-droplets,” Microfluidics and Nanofluidics 13, 1–7 (2012).
[Crossref]

Nugent, K. A.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nature Photonics 4, 833–839 (2010).
[Crossref]

Ogura, Y.

R. Horisaki, Y. Ogura, M. Aino, and J. Tanida, “Single-shot phase imaging with a coded aperture,” Opt. Lett. 39, 6466–6469 (2014).
[Crossref] [PubMed]

T. Nishimura, Y. Ogura, and J. Tanida, “Optofluidic DNA computation based on optically manipulated micro-droplets,” Microfluidics and Nanofluidics 13, 1–7 (2012).
[Crossref]

Olivo-Marin, J.-C.

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Osten, W.

Pedrini, G.

Peele, A. G.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Pfeiffer, F.

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]

Pham, H.

Popescu, G.

Putkunz, C. T.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Quiney, H. M.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Raines, K. S.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Rivenson, Y.

Y. Rivenson, A. Stern, and B. Javidi, “Overview of compressive sensing techniques applied in holography,” Appl. Opt. 52, A423–A432 (2013).
[Crossref] [PubMed]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[Crossref]

Robinson, I. K.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Singh, A. K.

Song, C.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Stern, A.

Streibl, N.

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

Tahara, T.

Takeda, M.

Tamanoi, F.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Tanida, J.

Thibault, P.

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]

Tian, L.

Upatnieks, J.

Urano, J.

H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proceedings of the National Academy of Sciences107, 11234–11239 (2010).
[Crossref]

Vine, D. J.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Waller, L.

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase un-wrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

Whitehead, L. W.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Wilke, M.

Williams, G. J.

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Figures (6)

Fig. 1
Fig. 1

Experimental set-up and computational reconstruction process of SPICA.

Fig. 2
Fig. 2

Experimental results with two wires. (a) The CA pattern and (b) the captured image. (c) The amplitude and (d) the phase of the retrieved field on the CA. (e) The amplitude and (f) the phase of the reconstructed field at zo1. (g) The amplitude and (h) the phase of the reconstructed field at zo2. Phases are normalized in the interval [−π,π]. Black lines in Figs. (e) and (g) show the positions of the line profiles in Fig. 3.

Fig. 3
Fig. 3

Line profiles of the reconstructed wires.

Fig. 4
Fig. 4

Experimental results obtained with a lens. (a) The captured image. (b) The amplitude and (c) the phase of the retrieved field on the CA. (d) The amplitude and (e) the phase of the reconstructed field.

Fig. 5
Fig. 5

Unwrapped phase maps of the reconstructed lens. (a) The three-dimensional map and (b) the line profile.

Fig. 6
Fig. 6

Experimental results with mixture of oil and water. (a) The captured image. (b) The amplitude and (c) the phase of the retrieved field on the CA. (d) The amplitude and (e) the phase of the reconstructed field. (f) The unwrapped phase of (e). (g) Image of the region surrounded by the square in Fig. (d) observed with a microscope, where the scale bar is 200 μm.

Equations (2)

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g = | P z s M P z o f | 2 ,
δ z o λ w ,

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