Abstract

In recent years, the interferometric imaging method has been applied to analyze the structure of various specimens, such as crystals and biological tissues. However, the interferometric imaging method may require a relatively complex optical recording system, such as a reference wave and temporal coherence. In this paper, we propose a method based on noninterferometric imaging for quantitative phase retrieval of complex-valued specimens. A strategy using different focal lengths in the lens function is developed, and a series of diffraction intensity maps is recorded. Numerical simulation results are presented to demonstrate the feasibility and effectiveness of the proposed method.

© 2011 Optical Society of America

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2010 (9)

N. T. Shaked, Y. Zhu, N. Badie, N. Bursac, and A. Wax, “Reflective interferometric chamber for quantitative phase imaging of biological sample dynamics,” J. Biomed. Opt. 15, 030503 (2010).
[CrossRef] [PubMed]

C. E. Rommel, C. Dierker, L. Schmidt, S. Przibilla, G. von Bally, B. Kemper, and J. Schnekenburger, “Contrast-enhanced digital holographic imaging of cellular structures by manipulating the intracellular refractive index,” J. Biomed. Opt. 15, 041509 (2010).
[CrossRef] [PubMed]

V. Micó and Z. Zalevsky, “Superresolved digital in-line holographic microscopy for high-resolution lensless biological imaging,” J. Biomed. Opt. 15, 046027 (2010).
[CrossRef] [PubMed]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting digital holographic microscopy,” Biomed. Opt. Express 1, 610–616 (2010).
[CrossRef]

R. P. Yu and D. M. Paganin, “Blind phase retrieval for aberrated linear shift-invariant imaging systems,” New J. Phys. 12, 073040 (2010).
[CrossRef]

C. Falldorf, M. Agour, C. V. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system,” Appl. Opt. 49, 1826–1830 (2010).
[CrossRef] [PubMed]

P. F. Almoro, J. Glückstad, and S. G. Hanson, “Single-plane multiple speckle pattern phase retrieval using a deformable mirror,” Opt. Express 18, 19304–19313 (2010).
[CrossRef] [PubMed]

W. Chen and X. Chen, “Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain,” Opt. Express 18, 13536–13541(2010).
[CrossRef] [PubMed]

J. A. Rodrigo, H. Duadi, T. Alieva, and Z. Zalevsky, “Multi-stage phase retrieval algorithm based upon the gyrator transform,” Opt. Express 18, 1510–1520 (2010).
[CrossRef] [PubMed]

2009 (3)

W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17, 19662–19673 (2009).
[CrossRef] [PubMed]

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

2008 (2)

2007 (5)

K. Qian, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

W. Choi, C. F. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12, 054009 (2007).
[CrossRef] [PubMed]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).
[CrossRef]

A. Anand, G. Pedrini, W. Osten, and P. Almoro, “Wavefront sensing with random amplitude mask and phase retrieval,” Opt. Lett. 32, 1584–1586 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (2)

2004 (1)

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

2003 (4)

V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40–55 (2003).
[CrossRef]

J. Miao, K. O. Hodgson, T. Ishikawa, C. A. Larabell, M. A. LeGros, and Y. Nishino, “Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

L. Durak and O. Arikan, “Short-time Fourier transform: two fundamental properties and an optimal implementation,” IEEE Trans. Signal Process. 51, 1231–1242 (2003).
[CrossRef]

2002 (1)

1999 (4)

1998 (3)

1997 (1)

1994 (2)

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef] [PubMed]

1986 (2)

1985 (1)

1983 (1)

1982 (2)

1972 (1)

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

Agour, M.

Alieva, T.

Allen, L. J.

W. McBride, N. L. O. Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. A 61, 321–324 (2005).
[CrossRef] [PubMed]

Almoro, P.

Almoro, P. F.

Anand, A.

Arikan, O.

L. Durak and O. Arikan, “Short-time Fourier transform: two fundamental properties and an optimal implementation,” IEEE Trans. Signal Process. 51, 1231–1242 (2003).
[CrossRef]

Awatsuji, Y.

Badie, N.

N. T. Shaked, Y. Zhu, N. Badie, N. Bursac, and A. Wax, “Reflective interferometric chamber for quantitative phase imaging of biological sample dynamics,” J. Biomed. Opt. 15, 030503 (2010).
[CrossRef] [PubMed]

Badizadegan, K.

W. Choi, C. F. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Barnes, T. H.

Barty, A.

Beck, M.

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef] [PubMed]

Beetz, T.

Bergmann, R. B.

Bevilacqua, F.

Bredebusch, I.

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12, 054009 (2007).
[CrossRef] [PubMed]

Bursac, N.

N. T. Shaked, Y. Zhu, N. Badie, N. Bursac, and A. Wax, “Reflective interferometric chamber for quantitative phase imaging of biological sample dynamics,” J. Biomed. Opt. 15, 030503 (2010).
[CrossRef] [PubMed]

Chapman, H. N.

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Charrière, F.

Chen, W.

W. Chen and X. Chen, “Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain,” Opt. Express 18, 13536–13541(2010).
[CrossRef] [PubMed]

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Measurement of curvature and twist of a deformed object using digital holography,” Appl. Opt. 47, 2874–2881 (2008).
[CrossRef] [PubMed]

Chen, X.

Choi, W.

W. Choi, C. F. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Colomb, T.

Creath, K.

Cuche, E.

Cui, C.

Dasari, R. R.

W. Choi, C. F. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Depeursinge, C.

Dierker, C.

C. E. Rommel, C. Dierker, L. Schmidt, S. Przibilla, G. von Bally, B. Kemper, and J. Schnekenburger, “Contrast-enhanced digital holographic imaging of cellular structures by manipulating the intracellular refractive index,” J. Biomed. Opt. 15, 041509 (2010).
[CrossRef] [PubMed]

Domschke, W.

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12, 054009 (2007).
[CrossRef] [PubMed]

Duadi, H.

Durak, L.

L. Durak and O. Arikan, “Short-time Fourier transform: two fundamental properties and an optimal implementation,” IEEE Trans. Signal Process. 51, 1231–1242 (2003).
[CrossRef]

Elser, V.

Emery, Y.

Falldorf, C.

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, 023903 (2004).
[CrossRef] [PubMed]

Feld, M. S.

W. Choi, C. F. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Fienup, J. R.

Fu, Y.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

Fujii, M.

Gao, M.

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Gerchberg, R. W.

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

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).

Glückstad, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Guo, C. S.

Hanson, S. G.

He, H.

Hodgson, K. O.

J. Miao, K. O. Hodgson, T. Ishikawa, C. A. Larabell, M. A. LeGros, and Y. Nishino, “Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

Howells, M. R.

Ina, H.

Ishikawa, T.

J. Miao, K. O. Hodgson, T. Ishikawa, C. A. Larabell, M. A. LeGros, and Y. Nishino, “Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

Ito, K.

Jacobsen, C.

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Jüptner, W.

Kakue, T.

Kemper, B.

C. E. Rommel, C. Dierker, L. Schmidt, S. Przibilla, G. von Bally, B. Kemper, and J. Schnekenburger, “Contrast-enhanced digital holographic imaging of cellular structures by manipulating the intracellular refractive index,” J. Biomed. Opt. 15, 041509 (2010).
[CrossRef] [PubMed]

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12, 054009 (2007).
[CrossRef] [PubMed]

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Kobayashi, S.

Kopylow, C. V.

Kosmeier, S.

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12, 054009 (2007).
[CrossRef] [PubMed]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

Kubota, T.

Kuehn, J.

Langehanenberg, P.

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12, 054009 (2007).
[CrossRef] [PubMed]

Larabell, C. A.

J. Miao, K. O. Hodgson, T. Ishikawa, C. A. Larabell, M. A. LeGros, and Y. Nishino, “Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

Leary, N. L. O.

W. McBride, N. L. O. Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. A 61, 321–324 (2005).
[CrossRef] [PubMed]

LeGros, M. A.

J. Miao, K. O. Hodgson, T. Ishikawa, C. A. Larabell, M. A. LeGros, and Y. Nishino, “Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

Liao, J.

Lue, N.

W. Choi, C. F. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
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J. Miao, K. O. Hodgson, T. Ishikawa, C. A. Larabell, M. A. LeGros, and Y. Nishino, “Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. USA 100, 110–112 (2003).
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[CrossRef]

Nishino, Y.

J. Miao, K. O. Hodgson, T. Ishikawa, C. A. Larabell, M. A. LeGros, and Y. Nishino, “Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

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W. McBride, N. L. O. Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. A 61, 321–324 (2005).
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D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[CrossRef]

Oh, S.

W. Choi, C. F. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Osten, W.

Paganin, D.

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[CrossRef]

Paganin, D. M.

R. P. Yu and D. M. Paganin, “Blind phase retrieval for aberrated linear shift-invariant imaging systems,” New J. Phys. 12, 073040 (2010).
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D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).

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C. E. Rommel, C. Dierker, L. Schmidt, S. Przibilla, G. von Bally, B. Kemper, and J. Schnekenburger, “Contrast-enhanced digital holographic imaging of cellular structures by manipulating the intracellular refractive index,” J. Biomed. Opt. 15, 041509 (2010).
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K. Qian, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
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W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
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W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
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W. Chen, C. Quan, and C. J. Tay, “Measurement of curvature and twist of a deformed object using digital holography,” Appl. Opt. 47, 2874–2881 (2008).
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Raymer, M. G.

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
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H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
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Rommel, C. E.

C. E. Rommel, C. Dierker, L. Schmidt, S. Przibilla, G. von Bally, B. Kemper, and J. Schnekenburger, “Contrast-enhanced digital holographic imaging of cellular structures by manipulating the intracellular refractive index,” J. Biomed. Opt. 15, 041509 (2010).
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R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).

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J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
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J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
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Schmidt, L.

C. E. Rommel, C. Dierker, L. Schmidt, S. Przibilla, G. von Bally, B. Kemper, and J. Schnekenburger, “Contrast-enhanced digital holographic imaging of cellular structures by manipulating the intracellular refractive index,” J. Biomed. Opt. 15, 041509 (2010).
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C. E. Rommel, C. Dierker, L. Schmidt, S. Przibilla, G. von Bally, B. Kemper, and J. Schnekenburger, “Contrast-enhanced digital holographic imaging of cellular structures by manipulating the intracellular refractive index,” J. Biomed. Opt. 15, 041509 (2010).
[CrossRef] [PubMed]

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12, 054009 (2007).
[CrossRef] [PubMed]

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N. T. Shaked, Y. Zhu, N. Badie, N. Bursac, and A. Wax, “Reflective interferometric chamber for quantitative phase imaging of biological sample dynamics,” J. Biomed. Opt. 15, 030503 (2010).
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Shimozato, Y.

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W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Measurement of curvature and twist of a deformed object using digital holography,” Appl. Opt. 47, 2874–2881 (2008).
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Ura, S.

Vartanyants, I.

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
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C. E. Rommel, C. Dierker, L. Schmidt, S. Przibilla, G. von Bally, B. Kemper, and J. Schnekenburger, “Contrast-enhanced digital holographic imaging of cellular structures by manipulating the intracellular refractive index,” J. Biomed. Opt. 15, 041509 (2010).
[CrossRef] [PubMed]

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12, 054009 (2007).
[CrossRef] [PubMed]

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Wang, D.

Wang, H. T.

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N. T. Shaked, Y. Zhu, N. Badie, N. Bursac, and A. Wax, “Reflective interferometric chamber for quantitative phase imaging of biological sample dynamics,” J. Biomed. Opt. 15, 030503 (2010).
[CrossRef] [PubMed]

Weierstall, U.

Yamaguchi, I.

Yen, C. F.

W. Choi, C. F. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Yu, R. P.

R. P. Yu and D. M. Paganin, “Blind phase retrieval for aberrated linear shift-invariant imaging systems,” New J. Phys. 12, 073040 (2010).
[CrossRef]

Zalevsky, Z.

V. Micó and Z. Zalevsky, “Superresolved digital in-line holographic microscopy for high-resolution lensless biological imaging,” J. Biomed. Opt. 15, 046027 (2010).
[CrossRef] [PubMed]

J. A. Rodrigo, H. Duadi, T. Alieva, and Z. Zalevsky, “Multi-stage phase retrieval algorithm based upon the gyrator transform,” Opt. Express 18, 1510–1520 (2010).
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Zhang, L.

Zhang, R.

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Zhang, T.

Zhao, J.

Zhu, Y.

N. T. Shaked, Y. Zhu, N. Badie, N. Bursac, and A. Wax, “Reflective interferometric chamber for quantitative phase imaging of biological sample dynamics,” J. Biomed. Opt. 15, 030503 (2010).
[CrossRef] [PubMed]

Zhu, Y. Y.

Zou, J. M.

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Acta Crystallogr. A (1)

W. McBride, N. L. O. Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. A 61, 321–324 (2005).
[CrossRef] [PubMed]

Appl. Opt. (7)

Appl. Phys. Lett. (1)

W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

Biomed. Opt. Express (1)

IEEE Trans. Signal Process. (1)

L. Durak and O. Arikan, “Short-time Fourier transform: two fundamental properties and an optimal implementation,” IEEE Trans. Signal Process. 51, 1231–1242 (2003).
[CrossRef]

J. Biomed. Opt. (4)

C. E. Rommel, C. Dierker, L. Schmidt, S. Przibilla, G. von Bally, B. Kemper, and J. Schnekenburger, “Contrast-enhanced digital holographic imaging of cellular structures by manipulating the intracellular refractive index,” J. Biomed. Opt. 15, 041509 (2010).
[CrossRef] [PubMed]

V. Micó and Z. Zalevsky, “Superresolved digital in-line holographic microscopy for high-resolution lensless biological imaging,” J. Biomed. Opt. 15, 046027 (2010).
[CrossRef] [PubMed]

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12, 054009 (2007).
[CrossRef] [PubMed]

N. T. Shaked, Y. Zhu, N. Badie, N. Bursac, and A. Wax, “Reflective interferometric chamber for quantitative phase imaging of biological sample dynamics,” J. Biomed. Opt. 15, 030503 (2010).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

Nat. Methods (1)

W. Choi, C. F. Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef] [PubMed]

Nature (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

New J. Phys. (1)

R. P. Yu and D. M. Paganin, “Blind phase retrieval for aberrated linear shift-invariant imaging systems,” New J. Phys. 12, 073040 (2010).
[CrossRef]

Opt. Commun. (1)

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

Opt. Express (4)

Opt. Lasers Eng. (1)

K. Qian, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

Opt. Lett. (8)

Optik (Jena) (1)

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

Phys. Rev. A (1)

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

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

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef] [PubMed]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

J. Miao, K. O. Hodgson, T. Ishikawa, C. A. Larabell, M. A. LeGros, and Y. Nishino, “Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

Science (1)

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Other (5)

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed.(Academic, 1999).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (7)

Fig. 1
Fig. 1

Schematic experimental setup for the proposed noninterferometric imaging: CCD, charge-coupled device; Mask (or a SLM), a thin lens function embedded.

Fig. 2
Fig. 2

Flow chart of the proposed quantitative phase-retrieval algorithm based on noninterferometric imaging.

Fig. 3
Fig. 3

Focal lengths 40, 50, and 60 mm : (a) original amplitude map; (b) original phase map; (c) typical diffraction intensity map; (d) relationship between the number of iterations and the SSE; (e) extracted amplitude-contrast map; (f) extracted phase-contrast map; (g) comparison along the line between Figs. 3b, 3f.

Fig. 4
Fig. 4

Focal lengths 40 , 42 , and 44 mm : (a) relationship between the number of iterations and the SSE; (b) extracted phase-contrast map; (c) comparison along the line between Figs. 3b, 4b. Focal lengths 40, 41, and 42 mm : (d) relationship between the number of iterations and the SSE; (e) extracted phase-contrast map; (f) comparison along the line between Figs. 3b, 4e.

Fig. 5
Fig. 5

Focal lengths 40, 60, and 80 mm ): (a) relationship between the number of iterations and the SSE; (b) extracted phase-contrast map; (c) comparison along the line between Figs. 3b, 5b. Focal lengths 40, 70, and 100 mm : (d) relationship between the number of iterations and the SSE; (e) extracted phase-contrast map; (f) comparison along the line between Figs. 3b, 5e.

Fig. 6
Fig. 6

Focal lengths 40, 50, 60, and 70 mm : (a) relationship between the number of iterations and the SSE; (b) extracted amplitude-contrast map; (c) extracted phase-contrast map; (d) comparison along the line between Figs. 3b, 6c. Focal lengths 40, 50, 60, 70, and 80 mm : (e) relationship between the number of iterations and the SSE; (f) extracted amplitude-contrast map; (g) extracted phase-contrast map; (h) comparison along the line between Figs. 3b, 6g.

Fig. 7
Fig. 7

Noise contamination, SNR of 40: (a) relationship between the number of iterations and the SSE; (b) extracted amplitude-contrast map; (c) extracted phase-contrast map; (d) comparison along the line between Figs. 3b, 7c. Noise contamination, SNR of 30: (e) relationship between the number of iterations and the SSE; (f) extracted amplitude-contrast map; (g) extracted phase-contrast map; (h) comparison along the line between Figs. 3b, 7g.

Equations (6)

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

O ( ξ , η ) = j λ + + O ( x , y ) exp ( j k Ω ) Ω d x d y ,
O ( ξ , η ) = ASA d 1 [ O ( x , y ) ] ,
T ( ξ , η ) = exp [ j k 2 f ( ξ 2 + η 2 ) ] ,
A ( x , y ) ¯ = abs [ O ( x , y ) ¯ ] ,
P ( x , y ) ¯ = angle [ O ( x , y ) ¯ ] ,
SSE = [ ( { abs [ O ( x , y ) ] } A ( x , y ) ¯ ) 2 ] / ( { abs [ O ( x , y ) ] } 2 ) .

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