Abstract

Fourier ptychography (FP) is a recently developed imaging approach that facilitates high-resolution imaging beyond the cutoff frequency of the employed optics. In the original FP approach, a periodic LED array is used for sample illumination, and therefore, the scanning pattern is a uniform grid in the Fourier space. Such a uniform sampling scheme leads to 3 major problems for FP, namely: 1) it requires a large number of raw images, 2) it introduces the raster grid artefacts in the reconstruction process, and 3) it requires a high-dynamic-range detector. Here, we investigate scanning sequences and sampling patterns to optimize the FP approach. For most biological samples, signal energy is concentrated at low-frequency region, and as such, we can perform non-uniform Fourier sampling in FP by considering the signal structure. In contrast, conventional ptychography perform uniform sampling over the entire real space. To implement the non-uniform Fourier sampling scheme in FP, we have designed and built an illuminator using LEDs mounted on a 3D-printed plastic case. The advantages of this illuminator are threefold in that: 1) it reduces the number of image acquisitions by at least 50% (68 raw images versus 137 in the original FP setup), 2) it departs from the translational symmetry of sampling to solve the raster grid artifact problem, and 3) it reduces the dynamic range of the captured images 6 fold. The results reported in this paper significantly shortened acquisition time and improved quality of FP reconstructions. It may provide new insights for developing Fourier ptychographic imaging platforms and find important applications in digital pathology.

© 2015 Optical Society of America

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References

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    [Crossref]

2015 (2)

2014 (10)

S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856–20870 (2014).
[Crossref] [PubMed]

X. Huang, H. Yan, R. Harder, Y. Hwu, I. K. Robinson, and Y. S. Chu, “Optimization of overlap uniformness for ptychography,” Opt. Express 22(10), 12634–12644 (2014).
[Crossref] [PubMed]

L. Bian, J. Suo, G. Situ, G. Zheng, F. Chen, and Q. Dai, “Content adaptive illumination for Fourier ptychography,” Opt. Lett. 39(23), 6648–6651 (2014).
[Crossref] [PubMed]

S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22(11), 13586–13599 (2014).
[Crossref] [PubMed]

S. Dong, R. Shiradkar, P. Nanda, and G. Zheng, “Spectral multiplexing and coherent-state decomposition in Fourier ptychographic imaging,” Biomed. Opt. Express 5(6), 1757–1767 (2014).
[Crossref] [PubMed]

P. Memmolo, V. Bianco, F. Merola, L. Miccio, M. Paturzo, and P. Ferraro, “Breakthroughs in Photonics 2013, Holographic Imaging,” IEEE Photon. J. 6(2), 0701106 (2014).

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
[Crossref] [PubMed]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
[Crossref] [PubMed]

S. Dong, K. Guo, P. Nanda, R. Shiradkar, and G. Zheng, “FPscope: a field-portable high-resolution microscope using a cellphone lens,” Biomed. Opt. Express 5(10), 3305–3310 (2014).
[Crossref] [PubMed]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (1)

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

2010 (1)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

2009 (2)

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

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

2008 (3)

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16(10), 7264–7278 (2008).
[Crossref] [PubMed]

J. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

2004 (1)

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]

2002 (1)

1982 (1)

1978 (1)

1972 (1)

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

1969 (1)

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A 25, 502–507 (1969).
[Crossref]

Ao, Z.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
[Crossref] [PubMed]

Bauschke, H. H.

Bian, L.

Bian, Z.

Bianco, V.

P. Memmolo, V. Bianco, F. Merola, L. Miccio, M. Paturzo, and P. Ferraro, “Breakthroughs in Photonics 2013, Holographic Imaging,” IEEE Photon. J. 6(2), 0701106 (2014).

Bunk, O.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Chen, F.

Chu, Y. S.

Chung, J.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
[Crossref] [PubMed]

Combettes, P. L.

Cote, R.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
[Crossref] [PubMed]

Dai, Q.

Datar, R.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
[Crossref] [PubMed]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Dierolf, M.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Dong, S.

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]

Ferraro, P.

P. Memmolo, V. Bianco, F. Merola, L. Miccio, M. Paturzo, and P. Ferraro, “Breakthroughs in Photonics 2013, Holographic Imaging,” IEEE Photon. J. 6(2), 0701106 (2014).

Fienup, J. R.

Gerchberg, R. W.

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

Guizar-Sicairos, M.

Guo, K.

Harder, R.

Hoppe, W.

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A 25, 502–507 (1969).
[Crossref]

Horstmeyer, R.

Huang, X.

Humphry, M. J.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Hwu, Y.

Jefimovs, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

Kewish, C. M.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

Kraus, B.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Li, X.

Liao, J.

Luke, D. R.

Maiden, A. M.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[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]

Memmolo, P.

P. Memmolo, V. Bianco, F. Merola, L. Miccio, M. Paturzo, and P. Ferraro, “Breakthroughs in Photonics 2013, Holographic Imaging,” IEEE Photon. J. 6(2), 0701106 (2014).

Menzel, A.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Merola, F.

P. Memmolo, V. Bianco, F. Merola, L. Miccio, M. Paturzo, and P. Ferraro, “Breakthroughs in Photonics 2013, Holographic Imaging,” IEEE Photon. J. 6(2), 0701106 (2014).

Miccio, L.

P. Memmolo, V. Bianco, F. Merola, L. Miccio, M. Paturzo, and P. Ferraro, “Breakthroughs in Photonics 2013, Holographic Imaging,” IEEE Photon. J. 6(2), 0701106 (2014).

Nanda, P.

Ou, X.

Paturzo, M.

P. Memmolo, V. Bianco, F. Merola, L. Miccio, M. Paturzo, and P. Ferraro, “Breakthroughs in Photonics 2013, Holographic Imaging,” IEEE Photon. J. 6(2), 0701106 (2014).

Pfeiffer, F.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Ramchandran, K.

Rawal, S.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
[Crossref] [PubMed]

Robinson, I. K.

Rodenburg, J.

J. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

Rodenburg, J. M.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[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]

Sarahan, M. C.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Schlichting, I.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

Shiradkar, R.

Situ, G.

Strube, G.

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A 25, 502–507 (1969).
[Crossref]

Suo, J.

Thibault, P.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Tian, L.

Von König, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[Crossref]

Waller, L.

Wang, Y. M.

Williams, A.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
[Crossref] [PubMed]

Xin, H.

Yan, H.

Yang,

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
[Crossref] [PubMed]

Yang, C.

Zheng, G.

S. Dong, P. Nanda, K. Guo, J. Liao, and G. Zheng, “Incoherent Fourier ptychographic photography using structured light,” Photon. Res. 3(1), 19–23 (2015).
[Crossref]

K. Guo, Z. Bian, S. Dong, P. Nanda, Y. M. Wang, and G. Zheng, “Microscopy illumination engineering using a low-cost liquid crystal display,” Biomed. Opt. Express 6(2), 574–579 (2015).
[Crossref]

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Supplementary Material (3)

» Media 1: MP4 (11033 KB)     
» Media 2: MP4 (2132 KB)     
» Media 3: MP4 (2132 KB)     

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Figures (9)

Fig. 1
Fig. 1

FP reconstructions with different recovery sequences. (a) Input intensity and phase images. FP reconstructions with random order (b), illumination NA order (c) and total energy order (d). (e) The RMS error of the FP reconstruction versus loop number.

Fig. 2
Fig. 2

FP reconstructions with different recovery sequences. The sample image is modulated by a sinusoidal pattern, and the energy concentrates at two positions in the Fourier domain. FP reconstructions with random order (a), illumination NA order (b) and total energy order (c). (d) The RMS error of the FP reconstruction versus loop number.

Fig. 3
Fig. 3

FP reconstructions with different sampling patterns in the Fourier space. (a1)-(a5) The LED sampling pattern in the Fourier space. (b1)-(b5) The FP reconstructions corresponding to (a1)-(a5). (c) The overlapping percentages as a function of illumination NA. Different curves correspond to different cases in (a1)-(a5) (see the color code). (d) The RMS error as a function of sampling density ratio. A higher sampling density ratio helps the solution converging faster to the global minimum.

Fig. 4
Fig. 4

Raster grid artefact problem in FP. (a) A non-uniform sampling pattern and (b) a uniform sampling pattern. (c) The RMS errors are plotted as a function as iteration number. (d)-(e) The recovered sample images and pupil function corresponding to (a). (f)-(g) The recovered sample images and pupil function corresponding to (b). We can see the raster grid artefact problem in the recovered pupil function in (g2).

Fig. 5
Fig. 5

The Fourier ptychographic illuminator. (a) The illuminator is placed under the sample. (b) 4 LED elements and the first LED ring were mounted far away from the sample to achieve a higher sampling density at the low-frequency region. (c) The side view of the illuminator.

Fig. 6
Fig. 6

The measured intensity of the LED elements as function of illumination NA. (a) LED array illumination and (b) the reported ring-illuminator. The reported illuminator is able to reduce the dynamic range of the raw FP image sequence 6 fold.

Fig. 7
Fig. 7

Comparison of FP reconstructions using the LED matrix (a-b) and the reported FP illuminator (c-d). The total numbers of LED elements are the same for both case (62 LEDs). (a) The sampling pattern of the periodic LED array in the Fourier space. (b) The FP reconstructions using the periodic LED array: (b1) mouse brain slice, (b2) blood smear, (b3) pathology slide, and (b4) USAF resolution target. (c) The sampling pattern of the reported FP illuminator in the Fourier space. (d) The FP reconstructions using the reported FP illuminator. Also refer to Media 1.

Fig. 8
Fig. 8

FP reconstructions using the LED array (a) and the reported FP illuminator (b-c). (d) The conventional microscope images using a 40X objective lens.

Fig. 9
Fig. 9

(a) FP reconstructions using the LED matrix. The image quality degrades due to the raster grid artefact problem. (b) FP reconstructions using the reported FP illuminator. The sampling pattern is not translational symmetric, and thus, it solves the raster grid artefact problem.

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