Abstract

Phase retrieval is an important tool to unveil wavefront of light, especially in high performance microscopy such as Fourier ptychographic microscopy (FPM). In general phase-retrieval methods, the resolution and the number of measurements are in a trade-off relationship. Inspired by FPM, we devise what we believe is a novel microscopic phase-retrieval method, termed single-shot FPM (SSFPM). In our approach, the imaging performance exceeds the trade-off relationship in that it enables phase retrieval for high resolution with a single measurement. By placing the lens array at the Fourier plane of the objective lens, multiple intensity profiles required for the FPM algorithm are collected in a single shot. To achieve enough redundancy of data for satisfying convergence condition of FPM, the specimen is simultaneously illuminated by multiple light-emitting diodes. SSFPM reconstructs quantitative phase profile and enhances the resolution sacrificed by applying lens-array imaging. We demonstrate the performance of SSFPM with numerical simulation and experiments. The prototype achieves lateral resolution of 3.10 μm over a field of view of 0.34  mm2. Without an interferometer or scanning devices, SSFPM can reconstruct high resolution of a complex profile with a single shot.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2017 (2)

2016 (9)

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

Z. Yang and Q. Zhan, “Single-shot smartphone-based quantitative phase imaging using a distorted grating,” PLoS ONE 11, e0159596 (2016).
[Crossref]

P. Sidorenko and O. Cohen, “Single-shot ptychography,” Optica 3, 9–14 (2016).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space,” Opt. Express 24, 15765–15781 (2016).
[Crossref]

R. Horstmeyer, J. Chung, X. Ou, G. Zheng, and C. Yang, “Diffraction tomography with Fourier ptychography,” Optica 3, 827–835 (2016).
[Crossref]

S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (2016).
[Crossref]

A. Llavador, J. Sola-Pikabea, G. Saavedra, B. Javidi, and M. Martínez-Corral, “Resolution improvements in integral microscopy with Fourier plane recording,” Opt. Express 24, 20792–20798 (2016).
[Crossref]

J. Kim, Y. Jeong, H. Kim, C.-K. Lee, B. Lee, J. Hong, Y. Kim, Y. Hong, S.-D. Lee, and B. Lee, “F-number matching method in light field microscopy using an elastic micro lens array,” Opt. Lett. 41, 2751–2754 (2016).
[Crossref]

2015 (5)

J.-Y. Hong, J. Yeom, J. Kim, S.-G. Park, Y. Jeong, and B. Lee, “Analysis of the pickup and display property of integral floating microscopy,” J. Inf. Display 16, 143–153 (2015).
[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2, 904–911 (2015).
[Crossref]

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]

C. Jang, J. Kim, D. C. Clark, S. Lee, B. Lee, and M. K. Kim, “Holographic fluorescence microscopy with incoherent digital holographic adaptive optics,” J. Biomed. Opt. 20, 111204 (2015).
[Crossref]

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]

2014 (6)

2013 (5)

2011 (1)

T. J. Fuchs and J. M. Buhmann, “Computational pathology: challenges and promises for tissue analysis,” Computer. Med. Imaging Graph. 35, 515–530 (2011).
[Crossref]

2010 (4)

2009 (1)

2008 (1)

2006 (4)

V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Synthetic aperture superresolution with multiple off-axis holograms,” J. Opt. Soc. Am. A 23, 3162–3170 (2006).
[Crossref]

J. R. Fienup, “Lensless coherent imaging by phase retrieval with an illumination pattern constraint,” Opt. Express 14, 498–508 (2006).
[Crossref]

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[Crossref]

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

2005 (1)

2004 (2)

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

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, “Single-step superresolution by interferometric imaging,” Opt. Express 12, 2589–2596 (2004).
[Crossref]

2000 (1)

1999 (1)

1997 (1)

1987 (1)

1983 (1)

1982 (1)

1972 (1)

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

1962 (1)

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

Aino, M.

Andalman, A.

Asundi, A.

Barbastathis, G.

Bian, Z.

Bishara, W.

Broxton, M.

Buhmann, J. M.

T. J. Fuchs and J. M. Buhmann, “Computational pathology: challenges and promises for tissue analysis,” Computer. Med. Imaging Graph. 35, 515–530 (2011).
[Crossref]

Chen, B.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

Chen, M.

Chen, Q.

Chung, J.

Clark, D. C.

C. Jang, J. Kim, D. C. Clark, S. Lee, B. Lee, and M. K. Kim, “Holographic fluorescence microscopy with incoherent digital holographic adaptive optics,” J. Biomed. Opt. 20, 111204 (2015).
[Crossref]

Cohen, N.

Cohen, O.

Colomb, T.

Coskun, A. F.

Cuche, E.

Deisseroth, K.

Denis, L.

Depeursinge, C.

Dong, S.

Emery, Y.

Faulkner, H.

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

Fienup, J. R.

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

Fournier, C.

Fuchs, T. J.

T. J. Fuchs and J. M. Buhmann, “Computational pathology: challenges and promises for tissue analysis,” Computer. Med. Imaging Graph. 35, 515–530 (2011).
[Crossref]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref]

Garcia, J.

García, J.

Garcia-Martinez, P.

García-Martínez, P.

Gerchberg, R. W.

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

Göröcs, Z.

Grosenick, L.

Guizar-Sicairos, M.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

Günaydin, H.

Guo, K.

Harder, R.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[Crossref]

Hong, J.

Hong, J.-Y.

J.-Y. Hong, J. Yeom, J. Kim, S.-G. Park, Y. Jeong, and B. Lee, “Analysis of the pickup and display property of integral floating microscopy,” J. Inf. Display 16, 143–153 (2015).
[Crossref]

Hong, K.

Hong, Y.

Horisaki, R.

Horowitz, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

Horstmeyer, R.

Humphry, M. J.

Im, H.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

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]

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]

Iwamoto, Y.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Jang, C.

C. Jang, J. Kim, D. C. Clark, S. Lee, B. Lee, and M. K. Kim, “Holographic fluorescence microscopy with incoherent digital holographic adaptive optics,” J. Biomed. Opt. 20, 111204 (2015).
[Crossref]

Javidi, B.

Jeong, S.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Jeong, Y.

Jung, J.-H.

Kim, H.

Kim, J.

J. Kim, Y. Jeong, H. Kim, C.-K. Lee, B. Lee, J. Hong, Y. Kim, Y. Hong, S.-D. Lee, and B. Lee, “F-number matching method in light field microscopy using an elastic micro lens array,” Opt. Lett. 41, 2751–2754 (2016).
[Crossref]

J.-Y. Hong, J. Yeom, J. Kim, S.-G. Park, Y. Jeong, and B. Lee, “Analysis of the pickup and display property of integral floating microscopy,” J. Inf. Display 16, 143–153 (2015).
[Crossref]

C. Jang, J. Kim, D. C. Clark, S. Lee, B. Lee, and M. K. Kim, “Holographic fluorescence microscopy with incoherent digital holographic adaptive optics,” J. Biomed. Opt. 20, 111204 (2015).
[Crossref]

J. Kim, J.-H. Jung, Y. Jeong, K. Hong, and B. Lee, “Real-time integral imaging system for light field microscopy,” Opt. Express 22, 10210–10220 (2014).
[Crossref]

Kim, M. K.

C. Jang, J. Kim, D. C. Clark, S. Lee, B. Lee, and M. K. Kim, “Holographic fluorescence microscopy with incoherent digital holographic adaptive optics,” J. Biomed. Opt. 20, 111204 (2015).
[Crossref]

M. K. Kim, “Principles and techniques of digital holographic microscopy,” J. Photon. Energy 1, 018005 (2010).
[Crossref]

Kim, Y.

Lahav, O.

Lee, B.

Lee, C.-K.

Lee, H.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Lee, S.

C. Jang, J. Kim, D. C. Clark, S. Lee, B. Lee, and M. K. Kim, “Holographic fluorescence microscopy with incoherent digital holographic adaptive optics,” J. Biomed. Opt. 20, 111204 (2015).
[Crossref]

Lee, S.-D.

Leith, E. N.

Levoy, M.

Li, X.

Liang, R.

S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (2016).
[Crossref]

Liu, H.

Liu, Z.

Llavador, A.

Lorenz, D.

Luo, Y.

Magistretti, P. J.

Maiden, A. M.

Marquet, P.

Martínez-Corral, M.

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]

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]

Mico, V.

Morrison, G. R.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[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]

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]

Nanda, P.

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
[Crossref]

Ogura, Y.

Ou, X.

Ozcan, A.

Pacheco, S.

S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (2016).
[Crossref]

Park, S.-G.

J.-Y. Hong, J. Yeom, J. Kim, S.-G. Park, Y. Jeong, and B. Lee, “Analysis of the pickup and display property of integral floating microscopy,” J. Inf. Display 16, 143–153 (2015).
[Crossref]

Pathania, D.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Petruccelli, J. C.

Pfeifer, M. A.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[Crossref]

Pivovarov, M.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Qu, W.

Ramchandran, K.

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. SSFPM setup. The specimen is illuminated by multiple LEDs (only three LEDs are illustrated for simplicity in these figures). (a) 3D schematic diagram of SSFPM; (b) its corresponding 2D diagram. In this setup, the multiple scattered waves are incoherently integrated and transmitted to a CCD through the objective lens, the 4f system, and the lens array.
Fig. 2.
Fig. 2. Principle of multiplexing strategy. The schematic diagram of (a1) single illumination and (b1) multiplexed illumination. (a2, b2) Fourier spectrum of specimen. The lens array is placed at the position to image subimages with single measurement. Measured intensity pattern in CCD with (a3) single illumination and (b3) multiplexed illumination. Note that the Fourier spectrum and intensity patterns are shown in logarithmic scale. (b2) Fourier spectrum with LED multiplexing, which appears as integration of spectrum of each LED from n=1 to n=N. The region depicted as red circle in (b2) is the summation of N red circles in b4. (b4) Fourier spectrum reconstructed by SSFPM. Each red circle is spaced at regular intervals Δki. The blue circle denotes an adjacent lens to the central lens. The gap between lenses is Δkm.
Fig. 3.
Fig. 3. Numerical simulation results of SSFPM. The input (a) intensity and (b) phase of complex specimen. (c) A measured intensity pattern which is calculated by the Eq. (4). Forty-nine subimages of different spatial frequency appear using a 7×7 square grid lens array. As 3×3 LEDs are turned on simultaneously, nine bright-field images are measured. (d) A magnified central subimage that has low resolution. Applying the measured pattern to the SSFPM, (e) intensity and (f) phase profiles are reconstructed.
Fig. 4.
Fig. 4. 1951 USAF resolution target imaging using SSFPM. (a) Original experimental data from 7×7 lens array when turning 3×3 LEDs simultaneously on; (b) image from a conventional ×10 microscope with coherent illumination. (c, d) The high resolution of reconstruction intensity and phase profiles, respectively. (e–g) The zoom-in intensity images of raw data, reconstruction image, and conventional microscope image.
Fig. 5.
Fig. 5. Biological specimen imaging using SSFPM. High resolution (a) intensity and (b) phase images of epidermal onion cells, with FOV of 0.34  mm2. The magnified (c1–e1) intensity images and (c2–e2) phase images corresponding to the regions of red, green, and blue boxes in (a) and (b). (c3–e3) The coherent microscopic images captured by a conventional microscope with a ×10 objective lens, for comparison. (c4–e4) The raw-data images taken by proposed SSFPM extracted from central bright subimage. The same objective lens (×10 magnification, NAobj=0.25, fobj=18  mm) and CCD sensor are used in all these allium cepa epidermal cells imaging experiments.
Fig. 6.
Fig. 6. Phase distribution of allium cepa epidermal cells using recovered phase profile by (a) SSFPM and (b) phase-shifting DH.

Tables (1)

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Algorithm 1 SSFPM algorithm

Equations (10)

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In(r)=|F{O˜(kkn)}·P˜(k)|2,
O˜n(k)=F{O(r)ejkn·r}·P˜(k).
In,m(r)=|Fl,m{O˜n(kkm))}·P˜l(k)|2,
IN,m(r)=n=1N|Fl,m{O˜n(kkm))}·P˜l(k)|2,
ϕ(0)(r)=IN,m0(r)·ejϕ(0),
ϕ˜(l)(k)=F{ϕ(l)(r)}
ϕ˜n,m(l)(k)=ϕ˜(l)(kkn)·P˜(k)·P˜l(kkm).
ϕn,m(l)(r)=F1{ϕ˜n,m(l)(k)}.
Ωn,m(l)(r)=IN,m(r)n=1N|ϕn,m(l)(r)|2·ϕn,m(l)(r).
ϕ˜n,m(l+1)(k)=ϕ˜n,m(l)(k)+P˜l(k)·(F{Ωn,m(l)(r)}ϕ˜n,m(l)(k))|P˜l(k)|max2.

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