Abstract

The image reconstructed in ordinary digital holography was unable to bring out desired resolution in comparison to photographic materials; thus making it less preferable for many interesting applications. A method is proposed to enhance the resolution of digital holography in all directions by placing a random phase plate between the specimen and the electronic camera and then using an iterative approach to do the reconstruction. With this method, the resolution is improved remarkably in comparison to ordinary digital holography. Theoretical analysis is supported by numerical simulation. The feasibility of the method is also studied experimentally.

© 2015 Optical Society of America

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References

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2014 (1)

M. Schnell, P. S. Carney, and R. Hillenbrand, “Synthetic optical holography for rapid nanoimaging,” Nat. Commun. 5, 3499 (2014).
[Crossref] [PubMed]

2013 (4)

2012 (1)

2009 (2)

M. Paturzo and P. Ferraro, “Correct self-assembling of spatial frequencies in super-resolution synthetic aperture digital holography,” Opt. Lett. 34(23), 3650–3652 (2009).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

2007 (1)

2006 (3)

2005 (1)

2004 (3)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

J. C. H. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

2002 (3)

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143–3145 (2002).
[Crossref]

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27(24), 2179–2181 (2002).
[Crossref] [PubMed]

2001 (1)

1986 (1)

1978 (1)

1972 (1)

R. W. Gercherg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

Alfieri, D.

Asundi, A. K.

Badizadegan, K.

Bean, R.

Berenguer, F.

Bianco, V.

Bo, F.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143–3145 (2002).
[Crossref]

Callens, N.

Carney, P. S.

M. Schnell, P. S. Carney, and R. Hillenbrand, “Synthetic optical holography for rapid nanoimaging,” Nat. Commun. 5, 3499 (2014).
[Crossref] [PubMed]

Chen, B.

Chen, Q.

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Clark, D. C.

Coppola, G.

Cross, M.

Dasari, R. R.

De Nicola, S.

Diaz, A.

Dubois, F.

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Feld, M. S.

Ferraro, P.

Fienup, J. R.

Finizio, A.

García, J.

García-Martínez, P.

Gercherg, R. W.

R. W. Gercherg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Grilli, S.

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

Haynie, D. T.

Hillenbrand, R.

M. Schnell, P. S. Carney, and R. Hillenbrand, “Synthetic optical holography for rapid nanoimaging,” Nat. Commun. 5, 3499 (2014).
[Crossref] [PubMed]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Howells, M.

J. C. H. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

Howells, M. R.

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Hoyos, M.

Isaacson, M.

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Javidi, B.

Kim, M. K.

Kurowski, P.

Liu, C.

X. Yu, M. Cross, C. Liu, D. C. Clark, D. T. Haynie, and M. K. Kim, “Measurement of the traction force of biological cells by digital holography,” Biomed. Opt. Express 3(1), 153–159 (2012).
[Crossref] [PubMed]

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143–3145 (2002).
[Crossref]

Liu, Z.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143–3145 (2002).
[Crossref]

Locatelli, M.

Ma, J.

Maiden, A. M.

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

Massig, J. H.

Menzel, A.

Meucci, R.

Miao, J.

Miccio, L.

Mico, V.

Monnom, O.

Osten, W.

Panepucci, R. R.

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Park, Y.

Paturzo, M.

Pedrini, G.

Pelagotti, A.

Peng, X.

Peterson, I.

Pierattini, G.

Poggi, P.

Popescu, G.

Pugliese, E.

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(11), 13592–13606 (2013).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

Schnell, M.

M. Schnell, P. S. Carney, and R. Hillenbrand, “Synthetic optical holography for rapid nanoimaging,” Nat. Commun. 5, 3499 (2014).
[Crossref] [PubMed]

Situ, G.

Spence, J. C. H.

J. C. H. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Striano, V.

Vila-Comamala, J.

Wackerman, C. C.

Wang, Y.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143–3145 (2002).
[Crossref]

Weierstall, U.

J. C. H. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Xu, L.

Yang, C.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Yourassowsky, C.

Yu, X.

Yuan, C.

Zalevsky, Z.

Zhang, F.

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Zhu, J.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143–3145 (2002).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143–3145 (2002).
[Crossref]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Biomed. Opt. Express (1)

Chin. Opt. Lett. (1)

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

Nat. Commun. (1)

M. Schnell, P. S. Carney, and R. Hillenbrand, “Synthetic optical holography for rapid nanoimaging,” Nat. Commun. 5, 3499 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (4)

Optik (Stuttg.) (1)

R. W. Gercherg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Phys. Rev. Lett. (2)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

Ultramicroscopy (3)

J. C. H. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 Schematic of the suggested method.
Fig. 2
Fig. 2 Ray diagrams of the object wave: (a) without a grating or a random phase plate in the setup. (b) with a grating used in the setup. (c) with a random phase plate used in the setup.
Fig. 3
Fig. 3 (a) and (b) are the assumed modulus and phase images of the specimen, respectively. (c) Hologram obtained with common digital holography. (d) Hologram of the suggested method. (e) and (f) are the reconstructed modulus and phase images in common digital holography, respectively. (g) and (h) are the reconstructed modulus and phase images with the suggested method, respectively.
Fig. 4
Fig. 4 (a) The line profiles of modulus along white dashed lines in Fig. 3(a), Fig. 3(e) and Fig. 3(g) and are indicated by blue, green and red line respectively. (b) The initial diffraction pattern on the recording plane. (c) The reconstructed diffraction pattern after 1000 iterations with the suggested method.
Fig. 5
Fig. 5 (a) The evaluation of the reconstruction error. (b) The reconstructed modulus and phase with three random phase plates of different pixel size of 59.2 × 59.2 μm 2 , 29.6 × 29.6 μm 2 and 14.8 × 14.8 μm 2 , respectively. (c) The evaluation of the reconstruction error changes with the number of iterations.
Fig. 6
Fig. 6 The experimental setup. The focal length of the lens is 100 mm and the beam splitter prism used is 25.4 mm in width. d1 is the distance between the pinhole and the random phase plate; d2 is the distance between the random phase plate and the beam splitter prism; d3 is the distance between the beam splitter prism and the CCD. d1 = 60.7mm, d2 = 44.5mm, d3 = 20.5mm.
Fig. 7
Fig. 7 The modulus (a) and the phase (b) distribution of the random phase plate measured through the PIE experiment.
Fig. 8
Fig. 8 (a) The hologram in ordinary holography experiment. (b) and (c) are the reconstructed modulus and phase in ordinary holography experiment, respectively. (d) The hologram in the suggested holography experiment. (e) and (f) are the reconstructed modulus and phase in the suggested holography experiment, respectively.
Fig. 9
Fig. 9 Digital holography results with a biological specimen of pumpkin stem. (a) The hologram in ordinary holography experiment. (b) and (c) are the reconstructed modulus and phase in ordinary holography experiment, respectively. (d) The hologram in the suggested holography experiment. (e) and (f) are the reconstructed modulus and phase in the suggested holography experiment, respectively.

Equations (7)

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

I= | O | 2 + | R | 2 +O R * + O * R
t ~ (x,y)= t ~ ( f x , f y ) e i2π( f x x+ f y y) d f x d f y
O n+1 = O n ' S hole +( O n α O n ' )(1 S hole )
Ψ n+1 = ψ n+1 t
ψ n+1 ' = ψ n+1 + | t | | t max | t * ( | t | 2 +β) ( Ψ n+1 ' Ψ n+1 )
E 0 (n)= r |O(r)γ O n (r)| 2 r |O(r) | 2
γ= r O(r) O n * (r) r | O n (r) | 2

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