Abstract

Fourier ptychography (FP) utilizes illumination control and computational post-processing to increase the resolution of bright-field microscopes. In effect, FP extends the fixed numerical aperture (NA) of an objective lens to form a larger synthetic system NA. Here, we build an FP microscope (FPM) using a 40X 0.75NA objective lens to synthesize a system NA of 1.45. This system achieved a two-slit resolution of 335 nm at a wavelength of 632 nm. This resolution closely adheres to theoretical prediction and is comparable to the measured resolution (315 nm) associated with a standard, commercially available 1.25 NA oil immersion microscope. Our work indicates that Fourier ptychography is an attractive method to improve the resolution-versus-NA performance, increase the working distance, and enlarge the field-of-view of high-resolution bright-field microscopes by employing lower NA objectives.

© 2015 Optical Society of America

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References

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2014 (6)

2013 (8)

G. Zheng, X. Ou, R. Horstmeyer, and C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21(13), 15131–15143 (2013).
[Crossref] [PubMed]

S. Chowdhury and J. Izatt, “Structured illumination quantitative phase microscopy for enhanced resolution amplitude and phase imaging,” Biomed. Opt. Express 4(10), 1795–1805 (2013).
[Crossref] [PubMed]

K. Lee, H.-D. Kim, K. Kim, Y. Kim, T. R. Hillman, B. Min, and Y. Park, “Synthetic Fourier transform light scattering,” Opt. Express 21(19), 22453–22463 (2013).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref] [PubMed]

D. L. van de Hoef, I. Coppens, T. Holowka, C. Ben Mamoun, O. Branch, and A. Rodriguez, “Plasmodium falciparum-Derived Uric Acid Precipitates Induce Maturation of Dendritic Cells,” PLoS ONE 8(2), e55584 (2013).
[Crossref] [PubMed]

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

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

2011 (1)

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6(12), 1929–1941 (2011).
[Crossref] [PubMed]

2010 (1)

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107(4), 1289–1294 (2010).
[Crossref] [PubMed]

2009 (2)

2006 (3)

2005 (1)

R. M. Touyz, G. Yao, M. T. Quinn, P. J. Pagano, and E. L. Schiffrin, “p47phox Associates With the Cytoskeleton Through Cortactin in Human Vascular Smooth Muscle Cells: Role in NAD(P)H Oxidase Regulation by Angiotensin II,” Arterioscler. Thromb. Vasc. Biol. 25(3), 512–518 (2005).
[Crossref] [PubMed]

2004 (1)

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

2003 (1)

2000 (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

1997 (1)

1994 (1)

1993 (1)

1992 (2)

D. J. Goldstein, “Resolution in light microscopy studied by computer simulation,” J. Microsc. 166(2), 185–197 (1992).
[Crossref]

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9(7), 1072–1085 (1992).
[Crossref]

1991 (1)

1978 (1)

R. Zimmermann, R. Iturriaga, and J. Becker-Birck, “Simultaneous determination of the total number of aquatic bacteria and the number thereof involved in respiration,” Appl. Environ. Microbiol. 36(6), 926–935 (1978).
[PubMed]

1972 (1)

I. T. Young, “The Classification of White Blood Cells,” IEEE Trans. Biomed. Eng. 19(4), 291–298 (1972).
[Crossref] [PubMed]

1968 (1)

1967 (1)

1966 (1)

1963 (1)

1962 (1)

1916 (1)

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Agard, D. A.

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett. 28(10), 801–803 (2003).
[Crossref] [PubMed]

Alexandrov, S. A.

Auth, T.

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107(4), 1289–1294 (2010).
[Crossref] [PubMed]

Barakat, R.

Becker-Birck, J.

R. Zimmermann, R. Iturriaga, and J. Becker-Birck, “Simultaneous determination of the total number of aquatic bacteria and the number thereof involved in respiration,” Appl. Environ. Microbiol. 36(6), 926–935 (1978).
[PubMed]

Ben Mamoun, C.

D. L. van de Hoef, I. Coppens, T. Holowka, C. Ben Mamoun, O. Branch, and A. Rodriguez, “Plasmodium falciparum-Derived Uric Acid Precipitates Induce Maturation of Dendritic Cells,” PLoS ONE 8(2), e55584 (2013).
[Crossref] [PubMed]

Best, C. A.

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107(4), 1289–1294 (2010).
[Crossref] [PubMed]

Bian, Z.

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Branch, O.

D. L. van de Hoef, I. Coppens, T. Holowka, C. Ben Mamoun, O. Branch, and A. Rodriguez, “Plasmodium falciparum-Derived Uric Acid Precipitates Induce Maturation of Dendritic Cells,” PLoS ONE 8(2), e55584 (2013).
[Crossref] [PubMed]

Brown, C. M.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6(12), 1929–1941 (2011).
[Crossref] [PubMed]

Chowdhury, S.

Cole, R. W.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6(12), 1929–1941 (2011).
[Crossref] [PubMed]

Coppens, I.

D. L. van de Hoef, I. Coppens, T. Holowka, C. Ben Mamoun, O. Branch, and A. Rodriguez, “Plasmodium falciparum-Derived Uric Acid Precipitates Induce Maturation of Dendritic Cells,” PLoS ONE 8(2), e55584 (2013).
[Crossref] [PubMed]

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

den Dekker, A. J.

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Dong, S.

Feld, M. S.

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107(4), 1289–1294 (2010).
[Crossref] [PubMed]

Feng, P.

Fienup, J. R.

García, J.

García-Martínez, P.

Gibson, S. F.

Goldstein, D. J.

D. J. Goldstein, “Resolution in light microscopy studied by computer simulation,” J. Microsc. 166(2), 185–197 (1992).
[Crossref]

Gov, N. S.

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107(4), 1289–1294 (2010).
[Crossref] [PubMed]

Grimes, D. N.

Guo, K.

Gustafsson, M. G. L.

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett. 28(10), 801–803 (2003).
[Crossref] [PubMed]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

Gutzler, T.

Hanser, B. M.

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett. 28(10), 801–803 (2003).
[Crossref] [PubMed]

Heintzmann, R.

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8(5), 342–344 (2014).
[Crossref]

Hell, S. W.

Hillman, T. R.

Holowka, T.

D. L. van de Hoef, I. Coppens, T. Holowka, C. Ben Mamoun, O. Branch, and A. Rodriguez, “Plasmodium falciparum-Derived Uric Acid Precipitates Induce Maturation of Dendritic Cells,” PLoS ONE 8(2), e55584 (2013).
[Crossref] [PubMed]

Horstmeyer, R.

Iturriaga, R.

R. Zimmermann, R. Iturriaga, and J. Becker-Birck, “Simultaneous determination of the total number of aquatic bacteria and the number thereof involved in respiration,” Appl. Environ. Microbiol. 36(6), 926–935 (1978).
[PubMed]

Izatt, J.

Jinadasa, T.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6(12), 1929–1941 (2011).
[Crossref] [PubMed]

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Kim, H.-D.

Kim, K.

Kim, Y.

Lanni, F.

Lee, D. J.

Lee, K.

Levin, E.

Lohmann, A. W.

Lu, R.

Lukosz, W.

Magistretti, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Marquet, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Marron, J. C.

Menzel, A.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

Mico, V.

Min, B.

Nanda, P.

Ou, X.

Pagano, P. J.

R. M. Touyz, G. Yao, M. T. Quinn, P. J. Pagano, and E. L. Schiffrin, “p47phox Associates With the Cytoskeleton Through Cortactin in Human Vascular Smooth Muscle Cells: Role in NAD(P)H Oxidase Regulation by Angiotensin II,” Arterioscler. Thromb. Vasc. Biol. 25(3), 512–518 (2005).
[Crossref] [PubMed]

Park, Y.

K. Lee, H.-D. Kim, K. Kim, Y. Kim, T. R. Hillman, B. Min, and Y. Park, “Synthetic Fourier transform light scattering,” Opt. Express 21(19), 22453–22463 (2013).
[Crossref] [PubMed]

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107(4), 1289–1294 (2010).
[Crossref] [PubMed]

Pavillon, N.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Paxman, R. G.

Popescu, G.

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107(4), 1289–1294 (2010).
[Crossref] [PubMed]

Quinn, M. T.

R. M. Touyz, G. Yao, M. T. Quinn, P. J. Pagano, and E. L. Schiffrin, “p47phox Associates With the Cytoskeleton Through Cortactin in Human Vascular Smooth Muscle Cells: Role in NAD(P)H Oxidase Regulation by Angiotensin II,” Arterioscler. Thromb. Vasc. Biol. 25(3), 512–518 (2005).
[Crossref] [PubMed]

Rodriguez, A.

D. L. van de Hoef, I. Coppens, T. Holowka, C. Ben Mamoun, O. Branch, and A. Rodriguez, “Plasmodium falciparum-Derived Uric Acid Precipitates Induce Maturation of Dendritic Cells,” PLoS ONE 8(2), e55584 (2013).
[Crossref] [PubMed]

Safran, S. A.

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107(4), 1289–1294 (2010).
[Crossref] [PubMed]

Sampson, D. D.

Schiffrin, E. L.

R. M. Touyz, G. Yao, M. T. Quinn, P. J. Pagano, and E. L. Schiffrin, “p47phox Associates With the Cytoskeleton Through Cortactin in Human Vascular Smooth Muscle Cells: Role in NAD(P)H Oxidase Regulation by Angiotensin II,” Arterioscler. Thromb. Vasc. Biol. 25(3), 512–518 (2005).
[Crossref] [PubMed]

Schulz, T. J.

Sedat, J. W.

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Figures (8)

Fig. 1
Fig. 1

Principle of Fourier ptychrography. The CTF of the microscope objective is a low pass filter with cutoff frequency kc. When the sample is illuminated by normal incident plane wave (yellow line), the spatial frequency of the sample in the range [-kc, kc] passes through the CTF to form an image. Illuminating the sample with a tilted plane wave with wavevector ki (blue line) shifts the sample spectrum. The CTF now defines the image’s spatial frequency support as [-ki-kc, -ki + kc]. After image capture, a phase retrieval algorithm stitches together the spatial frequency information from the unique support of each image. The resulting FP reconstruction is expected to exhibit a cutoff frequency of k max + k c , corresponding to an expanded system NA, N A sys =N A obj +N A illu .

Fig. 2
Fig. 2

High-NA FPM setup and synthesized Fourier domain spectrum. (a) Our primary high NA FPM system consists of a conventional microscope with a 20X 0.5NA objective lens and a ring illuminator, offering an illumination NA of 0.7. (b) Each captured image is merged in the Fourier domain, forming an enlarged passband. Center red circle: Fourier support of the original microscope; white circle: Fourier support of one LED; green circle: synthesized Fourier support of the FPM system. (c1) Known sample intensity; (c2) image captured by a conventional 20X microscope corresponding to red circle in (b); (c3-c4) two images captured with different off-axis LEDs on, corresponding to two of the white circles; (c5) FPM reconstruction, corresponding to the green circle.

Fig. 3
Fig. 3

Resolution calibration using customized two-slit targets, illumination wavelength λ = 632nm. (a) SEM, conventional microscope, and FPM images of the two-slit targets (180 nm width, 4500 nm length). (b) Line plots of vertical intensity distribution across both slits, showing a Sparrow resolution limit of 615 nm for 20X 0.5 NA objective (b1), 455 nm for 40X 0.75 NA objective (b2), 315 nm for 100X oil immersion 1.25 NA objective (b3), 385 nm for 1.2 NAsys FPM system (b4), and 335 nm for 1.45 NAsys FPM (b5). Line plots of about 81% dip-to-peak ratio are also shown for a rough estimation of Rayleigh resolution limit [43].

Fig. 4
Fig. 4

Microscope images of a malaria infected blood smear. (a) Full-sized 1.2 NAsys FPM reconstruction, which maintains the FOV and working distance of the 20X objective. The FOV of the 40X and 100X objective are marked with black and blue circles, respectively. (b1-b2) Two sub-regions from (a) (marked with red squares) captured by the 20X objective, (c1-c2) 40X 0.75 NA objective lens, and (d1-d2) 100X 1.25 NA objective lens. (e1-e2) 1.2 NAsys FPM, (f1-f2) 1.45 NAsys FPM images of cells from the same sub-regions. A malaria infected red blood cell from sub-region 2 are further zoomed in, showing particles (pointed by arrows) that are clearly resolved by 1.45 NAsys FPM and vaguely resolved by 100X oil immersion microscope.

Fig. 5
Fig. 5

The amplitude and phase from FPM images may be post-processed into different modality of microscope (a1-a2) 1.2 NAsys FPM intensity and phase image of the blood smear sample in Fig. 4. (b1-b2) Phase gradient images (similar appearance as DIC image), (c) Simulated dark field image using the data in (a).

Fig. 6
Fig. 6

Three dimensional spatial frequency space analysis of Fourier ptychography. (a1-a3) Normal angle illumination case, (b1-b3) oblique angle illumination case. Solid line red circles and arcs represents spatial frequency information of the sample captured with the microscope system under certain illumination, and dot rings depict the cross-sections of Ewald spheres.

Fig. 7
Fig. 7

Resolution calibration using a customized two-hole targets, illumination wavelength λ = 632nm. (a) SEM, FPM and conventional microscope image of holes (200nm diameter) on the target. (b) Line plots of vertical intensity distribution through the center of each hole pair, showing a Sparrow resolution of (b1) 635 nm for 20X 0.5 NA objective, (b2) 475 nm for 40X 0.75 NA objective, (b3) 405 nm for the 100X oil immersion 1.25 NA objective, and (b4) 405 nm for 1.2 NAsys FPM setup.

Fig. 8
Fig. 8

Two-point image formation. (a) General imaging system (adapted from [28]), (b) Finite corrected microscope system (adapted from [43]), (c) Infinite corrected microscope system.

Tables (5)

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Table 1 Sparrow resolution for microscope systems (λ = 632nm, two-slit targets)

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Table 2 Sparrow resolution for microscope systems (λ = 632nm, two-hole targets)

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Table 3 Sparrow resolution limit coefficient α in different circumstances

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Table 4 Sparrow resolution limit coefficient β in different circumstances

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Table 5 Sparrow resolution limit coefficient γ in different circumstances

Equations (6)

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

N A sys =N A obj +N A illu
k z = k 0 2 k px 2 k py 2 k 0 2 k ix 2 k iy 2
| k z | max =max( k 0 2 k 0 2 ( k 0 N A obj ) 2 , k 0 2 k 0 2 ( k 0 N A illu ) 2 )
ε'=α× q ka
ε α 2π × λ nsinθ =β× λ NA
ε=γ× λ N A obj

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