Abstract

Realizing high resolution across large volumes is challenging for 3D imaging techniques with high-speed acquisition. Here, we describe a new method for 3D intensity and phase recovery from 4D light field measurements, achieving enhanced resolution via Fourier ptychography. Starting from geometric optics light field refocusing, we incorporate phase retrieval and correct diffraction artifacts. Further, we incorporate dark-field images to achieve lateral resolution beyond the diffraction limit of the objective (5× larger NA) and axial resolution better than the depth of field, using a low-magnification objective with a large field of view. Our iterative reconstruction algorithm uses a multislice coherent model to estimate the 3D complex transmittance function of the sample at multiple depths, without any weak or single-scattering approximations. Data are captured by an LED array microscope with computational illumination, which enables rapid scanning of angles for fast acquisition. We demonstrate the method with thick biological samples in a modified commercial microscope, indicating the technique’s versatility for a wide range of applications.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (10)

M. H. Jenkins, J. M. Long, T. K. Gaylord, “Multifilter phase imaging with partially coherent light,” Appl. Opt. 53, D29–D39 (2014).
[Crossref]

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

L. Tian, X. Li, K. Ramchandran, L. Waller, “Multiplexed coded illumination for Fourier ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376–2389 (2014).
[Crossref]

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22, 12513–12523 (2014).
[Crossref]

L. Tian, J. Wang, L. Waller, “3D differential phase-contrast microscopy with computational illumination using an LED array,” Opt. Lett. 39, 1326–1329 (2014).
[Crossref]

Z. Liu, L. Tian, S. Liu, L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19, 106002 (2014).
[Crossref]

X. Ou, G. Zheng, C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960–4972 (2014).
[Crossref]

D. J. Lee, A. M. Weiner, “Optical phase imaging using a synthetic aperture phase retrieval technique,” Opt. Express 22, 9380–9394 (2014).
[Crossref]

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

2013 (4)

M. Broxton, L. Grosenick, S. Yang, N. Cohen, A. Andalman, K. Deisseroth, M. Levoy, “Wave optics theory and 3-D deconvolution for the light field microscope,” Opt. Express 21, 25418–25439 (2013).
[Crossref]

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

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

L. Tian, J. C. Petruccelli, Q. Miao, H. Kudrolli, V. Nagarkar, G. Barbastathis, “Compressive X-ray phase tomography based on the transport of intensity equation,” Opt. Lett. 38, 3418–3421 (2013).
[Crossref]

2012 (2)

A. M. Maiden, M. J. Humphry, J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
[Crossref]

L. Waller, G. Situ, J. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6, 474–479 (2012).
[Crossref]

2011 (3)

2010 (2)

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

T.-W. Su, S. O. Isikman, W. Bishara, D. Tseng, A. Erlinger, A. Ozcan, “Multi-angle lensless digital holography for depth resolved imaging on a chip,” Opt. Express 18, 9690–9711 (2010).
[Crossref]

2009 (5)

2008 (3)

2007 (1)

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

2006 (4)

T. Gureyev, D. Paganin, G. Myers, Y. Nesterets, S. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
[Crossref]

A. Stern, B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591–607 (2006).
[Crossref]

M. Levoy, “Light fields and computational imaging,” Computer 39, 46–55 (2006).
[Crossref]

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

2005 (1)

2004 (1)

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

2003 (1)

W. R. Zipfel, R. M. Williams, W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[Crossref]

2002 (1)

2001 (1)

2000 (1)

T. J. Holmes, N. O’connor, “Blind deconvolution of 3D transmitted light brightfield micrographs,” J. Microsc. 200, 114–127 (2000).
[Crossref]

1997 (1)

A. Kirkland, W. Saxton, G. Chand, “Multiple beam tilt microscopy for super resolved imaging,” J. Electron. Microsc. 46, 11–22 (1997).
[Crossref]

1996 (1)

H. N. Chapman, “Phase-retrieval X-ray microscopy by Wigner—distribution deconvolution,” Ultramicroscopy 66, 153–172 (1996).
[Crossref]

1995 (1)

A. Kirkland, W. Saxton, K.-L. Chau, K. Tsuno, M. Kawasaki, “Super-resolution by aperture synthesis: tilt series reconstruction in CTEM,” Ultramicroscopy 57, 355–374 (1995).
[Crossref]

1994 (1)

1993 (1)

1985 (1)

1984 (1)

D. Hamilton, C. Sheppard, T. Wilson, “Improved imaging of phase gradients in scanning optical microscopy,” J. Microsc. 135, 275–286 (1984).
[Crossref]

1982 (2)

A. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imag. 4, 336–350 (1982).

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[Crossref]

1980 (1)

H. Bartelt, K. Brenner, A. Lohmann, “The Wigner distribution function and its optical production,” Opt. Commun. 32, 32–38 (1980).
[Crossref]

1971 (1)

R. Gerchberg, W. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

1967 (1)

1964 (1)

1957 (1)

J. M. Cowley, A. F. Moodie, “The scattering of electrons by atoms and crystals. i. A new theoretical approach,” Acta Crystallogr. 10, 609–619 (1957).
[Crossref]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, M. Horowitz, “Light field microscopy,” SIGGRAPH ‘06, New York, USA, 2006, pp. 924–934.

Alexandrov, S. A.

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

Anastasio, M. A.

Andalman, A.

Arimoto, H.

Babacan, S. D.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Badizadegan, K.

Barbastathis, G.

Bartelt, H.

H. Bartelt, K. Brenner, A. Lohmann, “The Wigner distribution function and its optical production,” Opt. Commun. 32, 32–38 (1980).
[Crossref]

Bishara, W.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).

T.-W. Su, S. O. Isikman, W. Bishara, D. Tseng, A. Erlinger, A. Ozcan, “Multi-angle lensless digital holography for depth resolved imaging on a chip,” Opt. Express 18, 9690–9711 (2010).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Brenner, K.

H. Bartelt, K. Brenner, A. Lohmann, “The Wigner distribution function and its optical production,” Opt. Commun. 32, 32–38 (1980).
[Crossref]

Broxton, M.

Bunk, O.

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express 19, 21345–21357 (2011).
[Crossref]

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

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Candès, E. J.

E. J. Candès, X. Li, M. Soltanolkotabi, “Phase retrieval via Wirtinger flow: theory and algorithms,” arXiv:1407.1065 (2014).

E. J. Candès, X. Li, M. Soltanolkotabi, “Phase retrieval from coded diffraction patterns,” arXiv:1310.3240 (2013).

Carney, P. S.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Chand, G.

A. Kirkland, W. Saxton, G. Chand, “Multiple beam tilt microscopy for super resolved imaging,” J. Electron. Microsc. 46, 11–22 (1997).
[Crossref]

Chapman, H. N.

H. N. Chapman, “Phase-retrieval X-ray microscopy by Wigner—distribution deconvolution,” Ultramicroscopy 66, 153–172 (1996).
[Crossref]

Chau, K.-L.

A. Kirkland, W. Saxton, K.-L. Chau, K. Tsuno, M. Kawasaki, “Super-resolution by aperture synthesis: tilt series reconstruction in CTEM,” Ultramicroscopy 57, 355–374 (1995).
[Crossref]

Choi, W.

Cohen, N.

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Cowley, J. M.

J. M. Cowley, A. F. Moodie, “The scattering of electrons by atoms and crystals. i. A new theoretical approach,” Acta Crystallogr. 10, 609–619 (1957).
[Crossref]

Dasari, R. R.

Deisseroth, K.

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Devaney, A.

A. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imag. 4, 336–350 (1982).

Devaney, A. J.

Diaz, A.

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express 19, 21345–21357 (2011).
[Crossref]

Dierolf, M.

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

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Supplementary Material (2)

» Supplement Media 1: AVI (2135 KB)     
» Media 2: PDF (2390 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Our LED array microscope setup for collecting 4D space-angle data. The angles of illumination are scanned in 2D by turning on different LEDs in the array.

Fig. 2.
Fig. 2.

Experimental results for a two-slice sample consisting of two resolution targets placed at different depths ( 55 and 55 μm), with one rotated laterally with respect to the other. (a) Some raw images collected from varying illumination angles θ x . (b) Two space-angle ( x θ x ) plots, where features from different depths create tilted lines with depth-dependent slopes, surrounded by diffraction fringes. (c) Reconstructions using our multislice method are compared to light field refocusing and physically changing the microscope focus. Diffraction effects severely blur the light field results, whereas our multislice method is able to recover the full diffraction-limited resolution with improved image contrast, while also removing out-of-focus blur.

Fig. 3.
Fig. 3.

Experimental results using multislice Fourier ptychography to achieve enhanced resolution at two depths simultaneously. Using a 4 × objective, we achieve a resolution of 0.69 μm (five times better NA than the objective). (Top) Low-resolution raw image. (Bottom) Zoom-in at two depths comparing our multi-slice recovery to physical refocusing.

Fig. 4.
Fig. 4.

Experimental results for a continuous 3D sample (Spirogyra algae) with a 10 × objective (0.25 NA). (Left) 3D rendering of the recovered intensity. (Right) Some example slices of the reconstructed complex transmittance function, compared with physically focused bright-field images. Our method is able to recover both 3D intensity and phase, with resolution beyond the objective’s diffraction limit, while removing out-of-plane blur. (Multislice reconstruction results, see Media 1).]

Fig. 5.
Fig. 5.

Comparison of simulated and measured resolution in our microscope using a 10 × objective (0.25 NA). Light field refocusing suffers diffraction errors that reduce the resolution as defocus increases. Multislice reconstructions restore the diffraction-limited resolution of the system, set by the sum of the illumination and objective NAs.

Fig. 6.
Fig. 6.

3D CTF analysis of our LED array microscope. The waves scattered from a point using a single-LED illumination vector (solid lines) create spherical waves (dotted circles). Each intensity image captures only the wave vectors within the objective NA (solid arcs) and the final bandwidth is set by the total range for all LEDs.

Equations (17)

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g m ( n ) ( r ) = o m ( r ) f m ( n ) ( r ) ,
f m + 1 ( n ) ( r ) = P Δ z m { g m ( n ) ( r ) } ,
C ( n ) ( u ) = G ( n ) ( u ) P ( u ) H ( u ) ,
H ( u ) = exp ( i 2 π Δ z N 1 / λ 2 | u | 2 )
I ( n ) ( r ) = | F { C ( n ) } ( r ) | 2 .
I Δ z ( x , y ) = n I ( n ) ( x x n Δ z z i , y y n Δ z z i ) ,
min { o m ( r ) } , P ( u ) n r | I ( n ) ( r ) | F { C ( n ) } ( r ) | 2 | 2 .
C ^ ( n ) ( u ) = F 1 { I ( n ) F { C ( n ) } | F { C ( n ) } | } ,
G ^ ( n ) ( u ) = U ( G ( n ) , P , C ( n ) / H , C ^ ( n ) / H ) ,
P ^ ( u ) = U ( P , G ( n ) , C ( n ) / H , C ^ ( n ) / H ) .
ψ ^ = U ( ψ , ϕ , β , β ^ ) = ψ + | ϕ | ϕ * ( β ^ β ) | ϕ | max · ( | ϕ | 2 + δ ) ,
g ^ N ( n ) ( r ) = F 1 { G ^ ( n ) } ( r ) .
o ^ m ( n ) ( r ) = U ( o m ( n ) ( r ) , f m ( n ) ( r ) , g m ( n ) ( r ) , g ^ m ( n ) ( r ) ) ,
f ^ m ( n ) ( r ) = U ( f m ( n ) ( r ) , o m ( n ) ( r ) , g m ( n ) ( r ) , g ^ m ( n ) ( r ) ) .
g ^ m 1 ( n ) ( r ) = P Δ z m 1 { f ^ m ( n ) ( r ) } .
Δ u x = 2 ( NA obj + NA illum ) / λ .
Δ u z = ( 2 1 NA obj 2 1 NA illum 2 ) / λ .

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