Superresolution imaging via ptychography

doi:10.1364/JOSAA.28.000604

Superresolution imaging via ptychography

Andrew M. Maiden, Martin J. Humphry, Fucai Zhang, and John M. Rodenburg »View Author Affiliations

JOSA A, Vol. 28, Issue 4, pp. 604-612 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000604

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Abstract

Coherent diffractive imaging of objects is made considerably more practicable by using ptychography, where a set of diffraction patterns replaces a single measurement and introduces a high degree of redundancy into the recorded data. Here we demonstrate that this redundancy allows diffraction patterns to be extrapolated beyond the aperture of the recording device, leading to superresolved images, improving the limit on the finest feature separation by more than a factor of 3.

OCIS Codes
(100.5070) Image processing : Phase retrieval
(100.6640) Image processing : Superresolution
(170.0180) Medical optics and biotechnology : Microscopy

ToC Category:
Image Processing

History
Original Manuscript: December 8, 2010
Manuscript Accepted: January 27, 2011
Published: March 21, 2011

Virtual Issues
Vol. 6, Iss. 5 Virtual Journal for Biomedical Optics
April 21, 2011 Spotlight on Optics

Citation
Andrew M. Maiden, Martin J. Humphry, Fucai Zhang, and John M. Rodenburg, "Superresolution imaging via ptychography," J. Opt. Soc. Am. A 28, 604-612 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-4-604

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References

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” in Advances in Imaging and Electron Physics, P.W.Hawkes, ed. (Elsevier, 2008), Vol. 150, pp. 87–184. [CrossRef]
W. Hoppe, “Trace structure analysis, ptychography, phase tomography,” Ultramicroscopy 10, 187–198 (1982). [CrossRef]
P. D. Nellist, B. C. McCallum, and J. M. Rodenburg, “Resolution beyond the ‘information limit’ in transmission electron microscopy,” Nature 374, 630–632 (1995). [CrossRef]
H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004). [CrossRef] [PubMed]
J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004). [CrossRef]
M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008). [CrossRef] [PubMed]
P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008). [CrossRef] [PubMed]
A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009). [CrossRef] [PubMed]
J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107, 227–231 (2007). [CrossRef]
J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007). [CrossRef] [PubMed]
F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010). [CrossRef]
M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010). [CrossRef] [PubMed]
A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011). [CrossRef]
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]
A. Kirkland, W. Saxton, K. L. Chau, K. Tsuno, and M. Kawasaki, “Super-resolution by aperture synthesis: tilt series reconstruction in CTEM,” Ultramicroscopy 57, 355–374 (1995). [CrossRef]
M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000). [CrossRef] [PubMed]
J. W. Goodman, Introduction to Fourier Optics3rd ed.(Roberts, 2005), Chap. 6, pp. 162–167.
M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with Fourier-weighted projections,” J. Opt. Soc. Am. A 25, 701–709(2008). [CrossRef]
R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974). [CrossRef]
H. Ur and D. Gross, “Improved resolution from subpixel shifted pictures,” CVGIP Graph. Models Image Process. 54, 181–186(1992). [CrossRef]
G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express 17, 624–639 (2009). [CrossRef] [PubMed]
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, 035017 (2010). [CrossRef]
A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010). [CrossRef] [PubMed]
G. O. Reynolds, J. B. D. Velis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (American Institute of Physics, 1998), Chap. 13, p. 107.
Y. Takaki and H. Ohzu, “Fast numerical reconstruction technique for high-resolution hybrid holographic microscopy,” Appl. Opt. 38, 2204–2211 (1999). [CrossRef]
J. Miao, D. Sayre, and H. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998). [CrossRef]
V. Elser and R. P. Millane, “Reconstruction of an object from its symmetry-averaged diffraction pattern,” Acta Crystallogr. A 64, 273–279 (2008). [CrossRef] [PubMed]
J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987). [CrossRef]
J. R. Fienup, “Lensless coherent imaging by phase retrieval with an illumination pattern constraint,” Opt. Express 14, 498–508(2006). [CrossRef] [PubMed]

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[1] J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” in Advances in Imaging and Electron Physics, P.W.Hawkes, ed. (Elsevier, 2008), Vol. 150, pp. 87–184. [CrossRef]

[2] W. Hoppe, “Trace structure analysis, ptychography, phase tomography,” Ultramicroscopy 10, 187–198 (1982). [CrossRef]

[3] P. D. Nellist, B. C. McCallum, and J. M. Rodenburg, “Resolution beyond the ‘information limit’ in transmission electron microscopy,” Nature 374, 630–632 (1995). [CrossRef]

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

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

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

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

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

[9] J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107, 227–231 (2007). [CrossRef]

[10] J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007). [CrossRef] [PubMed]

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

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

[13] A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011). [CrossRef]

[14] 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]

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

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

[17] J. W. Goodman, Introduction to Fourier Optics3rd ed.(Roberts, 2005), Chap. 6, pp. 162–167.

[18] M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with Fourier-weighted projections,” J. Opt. Soc. Am. A 25, 701–709(2008). [CrossRef]

[19] R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974). [CrossRef]

[20] H. Ur and D. Gross, “Improved resolution from subpixel shifted pictures,” CVGIP Graph. Models Image Process. 54, 181–186(1992). [CrossRef]

[21] G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express 17, 624–639 (2009). [CrossRef] [PubMed]

[22] 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, 035017 (2010). [CrossRef]

[23] A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010). [CrossRef] [PubMed]

[24] G. O. Reynolds, J. B. D. Velis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (American Institute of Physics, 1998), Chap. 13, p. 107.

[25] Y. Takaki and H. Ohzu, “Fast numerical reconstruction technique for high-resolution hybrid holographic microscopy,” Appl. Opt. 38, 2204–2211 (1999). [CrossRef]

[26] J. Miao, D. Sayre, and H. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998). [CrossRef]

[27] V. Elser and R. P. Millane, “Reconstruction of an object from its symmetry-averaged diffraction pattern,” Acta Crystallogr. A 64, 273–279 (2008). [CrossRef] [PubMed]

[28] J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987). [CrossRef]

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

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Superresolution imaging via ptychography