Abstract

We develop and test a pupil function determination algorithm, termed embedded pupil function recovery (EPRY), which can be incorporated into the Fourier ptychographic microscopy (FPM) algorithm and recover both the Fourier spectrum of sample and the pupil function of imaging system simultaneously. This EPRY-FPM algorithm eliminates the requirement of the previous FPM algorithm for a priori knowledge of the aberration in the imaging system to reconstruct a high quality image. We experimentally demonstrate the effectiveness of this algorithm by reconstructing high resolution, large field-of-view images of biological samples. We also illustrate that the pupil function we retrieve can be used to study the spatially varying aberration of a large field-of-view imaging system. We believe that this algorithm adds more flexibility to FPM and can be a powerful tool for the characterization of an imaging system’s aberration.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2014 (1)

2013 (5)

2010 (1)

F. Hüe, J. Rodenburg, A. Maiden, F. Sweeney, P. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[CrossRef]

2009 (2)

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

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

2008 (3)

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

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

2005 (1)

H. M. L. Faulkner, J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy,” Ultramicroscopy 103(2), 153–164 (2005).
[CrossRef] [PubMed]

2004 (1)

J. M. Rodenburg, H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[CrossRef]

1999 (1)

1997 (2)

J. R. Fienup, “Invariant error metrics for image reconstruction,” Appl. Opt. 36(32), 8352–8357 (1997).
[CrossRef] [PubMed]

M. Watanabe, S. K. Nayar, “Telecentric optics for focus analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 19(12), 1360–1365 (1997).
[CrossRef]

1996 (1)

1994 (1)

1992 (1)

J. Rodenburg, R. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Philos. Trans. R. Soc. Lond. A 339(1655), 521–553 (1992).
[CrossRef]

1982 (1)

1969 (1)

W. Hoppe, “Diffraction in inhomogeneous primary wave fields. 1. Principle of phase determination from electron diffraction interference,” Acta Crystallogr. A 25, 495–501 (1969).
[CrossRef]

Bates, R.

J. Rodenburg, R. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Philos. Trans. R. Soc. Lond. A 339(1655), 521–553 (1992).
[CrossRef]

Bian, Z.

Bunk, O.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, 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, F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Dierolf, M.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, 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, F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Dong, S.

Dorsch, R.

Faulkner, H. M. L.

H. M. L. Faulkner, J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy,” Ultramicroscopy 103(2), 153–164 (2005).
[CrossRef] [PubMed]

J. M. Rodenburg, H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[CrossRef]

Ferreira, C.

Fienup, J. R.

Guizar-Sicairos, M.

Hoppe, W.

W. Hoppe, “Diffraction in inhomogeneous primary wave fields. 1. Principle of phase determination from electron diffraction interference,” Acta Crystallogr. A 25, 495–501 (1969).
[CrossRef]

Horstmeyer, R.

Hüe, F.

F. Hüe, J. Rodenburg, A. Maiden, F. Sweeney, P. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[CrossRef]

Lohmann, A.

Mahajan, V. N.

Maiden, A.

F. Hüe, J. Rodenburg, A. Maiden, F. Sweeney, P. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[CrossRef]

Maiden, A. M.

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

Marriott, P.

J. Marrison, L. Räty, P. Marriott, P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[CrossRef] [PubMed]

Marrison, J.

J. Marrison, L. Räty, P. Marriott, P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[CrossRef] [PubMed]

Mendlovic, D.

Menzel, A.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, 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, F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Midgley, P.

F. Hüe, J. Rodenburg, A. Maiden, F. Sweeney, P. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[CrossRef]

Nayar, S. K.

M. Watanabe, S. K. Nayar, “Telecentric optics for focus analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 19(12), 1360–1365 (1997).
[CrossRef]

Nomura, H.

O’Toole, P.

J. Marrison, L. Räty, P. Marriott, P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[CrossRef] [PubMed]

Ou, X.

Pfeiffer, F.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, 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, F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Räty, L.

J. Marrison, L. Räty, P. Marriott, P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[CrossRef] [PubMed]

Rodenburg, J.

F. Hüe, J. Rodenburg, A. Maiden, F. Sweeney, P. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[CrossRef]

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

J. Rodenburg, R. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Philos. Trans. R. Soc. Lond. A 339(1655), 521–553 (1992).
[CrossRef]

Rodenburg, J. M.

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

H. M. L. Faulkner, J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy,” Ultramicroscopy 103(2), 153–164 (2005).
[CrossRef] [PubMed]

J. M. Rodenburg, H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[CrossRef]

Sato, T.

Sweeney, F.

F. Hüe, J. Rodenburg, A. Maiden, F. Sweeney, P. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[CrossRef]

Thibault, P.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, 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, F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Watanabe, M.

M. Watanabe, S. K. Nayar, “Telecentric optics for focus analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 19(12), 1360–1365 (1997).
[CrossRef]

Yang, C.

Zalevsky, Z.

Zheng, G.

Acta Crystallogr. A (1)

W. Hoppe, “Diffraction in inhomogeneous primary wave fields. 1. Principle of phase determination from electron diffraction interference,” Acta Crystallogr. A 25, 495–501 (1969).
[CrossRef]

Adv. Imaging Electron Phys. (1)

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

Appl. Opt. (4)

Appl. Phys. Lett. (1)

J. M. Rodenburg, H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[CrossRef]

Biomed. Opt. Express (1)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

M. Watanabe, S. K. Nayar, “Telecentric optics for focus analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 19(12), 1360–1365 (1997).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

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

Opt. Express (3)

Opt. Lett. (1)

Philos. Trans. R. Soc. Lond. A (1)

J. Rodenburg, R. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Philos. Trans. R. Soc. Lond. A 339(1655), 521–553 (1992).
[CrossRef]

Phys. Rev. B (1)

F. Hüe, J. Rodenburg, A. Maiden, F. Sweeney, P. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[CrossRef]

Sci. Rep. (1)

J. Marrison, L. Räty, P. Marriott, P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[CrossRef] [PubMed]

Science (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Ultramicroscopy (3)

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

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

H. M. L. Faulkner, J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy,” Ultramicroscopy 103(2), 153–164 (2005).
[CrossRef] [PubMed]

Other (3)

A. Maiden, J. Rodenburg, and M. Humphry, “A new method of high resolution, quantitative phase scanning microscopy,” in: M.T. Postek, D.E. Newbury, S.F. Platek, D.C. Joy (Eds.), SPIE Proceedings of Scanning Microscopy, 7729, 2010.
[CrossRef]

J. Wesner, J. Heil, and Th. Sure, “Reconstructing the pupil function of microscope objectives from the intensity PSF,” in Current Developments in Lens Design and Optical Engineering III, R. E. Fischer, W. J. Smith, and R. B. Johnson, eds., Proc. SPIE 4767, 32–43 (2002).

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).

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Figures (6)

Fig. 1
Fig. 1

Flowchart of EPRY-FPM algorithm.

Fig. 2
Fig. 2

Sample for simulation and reconstruction results. (a1-a2) Sample modulus and phase used to generate simulated data set. (a3) Phase of the pupil function used to generate simulated data set, intensity of the pupil function is a circular shape low pass filter same size as the phase circle. (b1-b2) Reconstructed modulus and phase using the original uncorrected FPM algorithm. (b3) Initial guess of the pupil phase used in both uncorrected FPM and EPRY-FPM, the initial guess of the pupil intensity is a circular shape low pass filter same size as the phase circle. (c1-c2) Reconstructed modulus and phase using EPRY-FPM algorithm; the initial guess of the sample spectrum is the same as the one used in uncorrected FPM algorithm. (c3) Reconstructed pupil function phase, showing a similar distribution as (a3). (d) Plot of convergence of both algorithms using the normalized mean square error metric.

Fig. 3
Fig. 3

Reconstruction from uncorrected FPM and EPRY-FPM algorithms using FPM blood smear data set. The initial guess of the pupil function is a circular shape low pass filter with no phase, and the reconstructed region is located 35% from the center of the FOV. (a1-a2) Reconstructed sample intensity and phase using uncorrected FPM algorithm. (b1-b2) Reconstructed sample intensity and phase using EPRY-FPM algorithm. (c1-c2) Reconstructed pupil function modulus and phase using EPRY-FPM algorithm. (d) Zernike decomposition of pupil function phase, the amplitude of the lowest 30 modes (representing the 30 lowest order aberrations) are shown.

Fig. 4
Fig. 4

Full FOV high resolution monochrome image (red LED illumination) reconstruction of blood smear: the entire FOV is segmented into small tiles, and the aberration is treated as constant in each tile. EPRY-FPM algorithm is run on each tile and the reconstructed high resolution images are mosaicked together. The insets show the detail of the reconstructed image and also the wavefront aberration at those locations.

Fig. 5
Fig. 5

Full FOV high resolution color image reconstruction of pathology slide: each color channel are reconstructed using the same method described in Fig. 4, and three channels are combined to generate RGB image. (a1, b1, c1) reconstructed sample intensity of three regions in the FOV. (a2, b2, c2) reconstructed red channel wavefront aberration of the three regions. (a3, b3, c3) reconstructed green channel wavefront aberration of the three regions. (a4, b4, c4) reconstructed blue channel wavefront aberration of the three regions.

Fig. 6
Fig. 6

Characterization of achievable resolution by three methods using USAF target: (a1-a4) Images at different FOV reconstructed by using uncorrected FPM method. (b1-b4) Images at different FOV reconstructed by using corrected FPM method. (c1-c4) Images at different FOV reconstructed by using EPRY-FPM method without pre-characterized aberration.

Equations (6)

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

I U n = | 1 { [ e ( r ) ] [ p ( r ) ] } | 2 = | 1 { S ( u U n ) P ( u ) } | 2
Φ ' n ( r ) = I U n ( r ) Φ n ( r ) | Φ n ( r ) |
S n + 1 ( u ) = S n ( u ) + α P n * ( u + U n ) | P n ( u + U n ) | max 2 [ ϕ ' n ( u + U n ) ϕ n ( u + U n ) ]
P n + 1 ( u ) = P n ( u ) + β S n * ( u - U n ) | S n ( u - U n ) | max 2 [ ϕ ' n ( u ) ϕ n ( u ) ]
E 2 ( m ) = Σ u | S ( u ) α S m ( u ) | 2 Σ u | S ( u ) | 2
α = Σ u S ( u ) S * m ( u ) Σ u | S n ( u ) | 2

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