Abstract

The complete characterization of spatial coherence is extremely difficult because the mutual coherence function (MCF) is a complex-valued function of four independent Cartesian coordinates. This difficulty limits the ability to control and to optimize the spatial coherence in a broad range of key applications. Here we propose an efficient and robust scheme for measuring the complete MCF of an arbitrary partially coherent beam using self-referencing holography, which does not require any prior knowledge or making any assumptions about the MCF. We further apply our method to lensless diffractive imaging, and experimentally demonstrate the reconstruction of a phase object under spatially partially coherent illumination. This application is particularly useful for imaging at short wavelengths, where the illumination sources lack spatial coherence and no high-quality imaging optics are available.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

X. Liu, F. Wang, L. Liu, Y. Chen, Y. Cai, and S. A. Ponomarenko, “Complex degree of coherence measurement for classical statistical fields,” Opt. Lett. 42, 77–80 (2017).
[Crossref] [PubMed]

A. Konijnenberg, W. Coene, and H. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

2016 (3)

D. Morrill, D. Li, and D. Pacifici, “Measuring subwavelength spatial coherence with plasmonic interferometry,” Nat. Photon. 10, 681–687 (2016).
[Crossref]

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimized flat-field epi-illumination,” Nat. Photon. 10, 705–708 (2016).
[Crossref]

K. A. Sharma, T. G. Brown, and M. A. Alonso, “Phase-space approach to lensless measurements of optical field correlations,” Opt. Express 24, 16099–16110 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (7)

2013 (3)

J. L. Codona, “Differential optical transfer function wavefront sensing,” Opt. Eng. 52, 097105 (2013).
[Crossref]

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

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

2012 (2)

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

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

2011 (1)

P. Gao, B. Yao, I. Harder, N. Lindlein, and F. J. Torcal-Milla, “Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement,” Opt. letters 36, 4305–4307 (2011).
[Crossref]

2009 (1)

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

2008 (1)

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard X-ray holographic diffraction imaging,” Phys. review letters 100, 245503 (2008).
[Crossref]

2007 (1)

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

2005 (1)

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

2004 (1)

S. Eisebitt, J. Lüning, W. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature. 432, 885–888 (2004).
[Crossref] [PubMed]

2000 (1)

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[Crossref]

1992 (1)

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform X-ray holography,” Science 256, 1009 (1992).
[Crossref] [PubMed]

Alonso, M. A.

Anderson, E. H.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform X-ray holography,” Science 256, 1009 (1992).
[Crossref] [PubMed]

Archetti, A.

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimized flat-field epi-illumination,” Nat. Photon. 10, 705–708 (2016).
[Crossref]

Assoufid, L.

S. Marathe, X. Shi, M. J. Wojcik, N. G. Kujala, R. Divan, D. C. Mancini, A. T. Macrander, and L. Assoufid, “Probing transverse coherence of X-ray beam with 2D phase grating interferometer,” Opt. Express 22, 14041–14053 (2014).
[Crossref] [PubMed]

X. Shi, S. Marathe, M. J. Wojcik, N. G. Kujala, A. T. Macrander, and L. Assoufid, “Circular grating interferometer for mapping transverse coherence area of X-ray beams,” Appl. Phys. Lett. 105, 041116 (2014).
[Crossref]

Autenrieth, T.

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard X-ray holographic diffraction imaging,” Phys. review letters 100, 245503 (2008).
[Crossref]

Bagheri, S.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Balaur, E.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Brown, T. G.

Bunk, O.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Burdet, N.

Burkhardt, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Burr, G.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Cai, Y.

Carpaij, R.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Chen, Y.

Cho, S.

Chushkin, Y.

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard X-ray holographic diffraction imaging,” Phys. review letters 100, 245503 (2008).
[Crossref]

Clark, J. N.

N. Burdet, X. Shi, D. Parks, J. N. Clark, X. Huang, S. D. Kevan, and I. K. Robinson, “Evaluation of partial coherence correction in X-ray ptychography,” Opt. Express 23, 5452 (2015).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Codona, J. L.

J. L. Codona, “Differential optical transfer function wavefront sensing,” Opt. Eng. 52, 097105 (2013).
[Crossref]

Coene, W.

A. Konijnenberg, W. Coene, and H. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

Corliss, D.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

David, C.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

de Jonge, M. D.

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

Diaz, A.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Dilanian, R. A.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Divan, R.

Divitt, S.

Douglass, K. M.

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimized flat-field epi-illumination,” Nat. Photon. 10, 705–708 (2016).
[Crossref]

Eberhardt, W.

S. Eisebitt, J. Lüning, W. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature. 432, 885–888 (2004).
[Crossref] [PubMed]

Eisebitt, S.

S. Eisebitt, J. Lüning, W. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature. 432, 885–888 (2004).
[Crossref] [PubMed]

Engelen, A.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Fakhry, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Faure, T.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Flagello, D.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Fleischer, J. W.

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

Flewett, S.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

Gallagher, E.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Gao, P.

P. Gao, B. Yao, I. Harder, N. Lindlein, and F. J. Torcal-Milla, “Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement,” Opt. letters 36, 4305–4307 (2011).
[Crossref]

Gbur, G.

Gianoncelli, A.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Groenendijk, R.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Grübel, G.

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard X-ray holographic diffraction imaging,” Phys. review letters 100, 245503 (2008).
[Crossref]

Gutt, C.

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard X-ray holographic diffraction imaging,” Phys. review letters 100, 245503 (2008).
[Crossref]

Hageman, J.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Halle, S.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Harder, I.

P. Gao, B. Yao, I. Harder, N. Lindlein, and F. J. Torcal-Milla, “Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement,” Opt. letters 36, 4305–4307 (2011).
[Crossref]

Harder, R.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Hartung, F.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Hellwig, O.

S. Eisebitt, J. Lüning, W. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature. 432, 885–888 (2004).
[Crossref] [PubMed]

Hennerkes, C.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Hibbs, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Hoffnagle, J.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Howells, M. R.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform X-ray holography,” Science 256, 1009 (1992).
[Crossref] [PubMed]

Huang, X.

N. Burdet, X. Shi, D. Parks, J. N. Clark, X. Huang, S. D. Kevan, and I. K. Robinson, “Evaluation of partial coherence correction in X-ray ptychography,” Opt. Express 23, 5452 (2015).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Jacobsen, C.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform X-ray holography,” Science 256, 1009 (1992).
[Crossref] [PubMed]

Kaulich, B.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Kazinczi, R.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Kern, D. P.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform X-ray holography,” Science 256, 1009 (1992).
[Crossref] [PubMed]

Kevan, S. D.

Kim, Y.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

King, B.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[Crossref]

Kirz, J.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform X-ray holography,” Science 256, 1009 (1992).
[Crossref] [PubMed]

Kneer, B.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Konijnenberg, A.

A. Konijnenberg, W. Coene, and H. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

Korotkova, O.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[Crossref]

Kujala, N. G.

X. Shi, S. Marathe, M. J. Wojcik, N. G. Kujala, A. T. Macrander, and L. Assoufid, “Circular grating interferometer for mapping transverse coherence area of X-ray beams,” Appl. Phys. Lett. 105, 041116 (2014).
[Crossref]

S. Marathe, X. Shi, M. J. Wojcik, N. G. Kujala, R. Divan, D. C. Mancini, A. T. Macrander, and L. Assoufid, “Probing transverse coherence of X-ray beam with 2D phase grating interferometer,” Opt. Express 22, 14041–14053 (2014).
[Crossref] [PubMed]

Lai, K.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Lai, S.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[Crossref]

Lambert, A.

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimized flat-field epi-illumination,” Nat. Photon. 10, 705–708 (2016).
[Crossref]

Leupold, O.

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard X-ray holographic diffraction imaging,” Phys. review letters 100, 245503 (2008).
[Crossref]

Li, D.

D. Morrill, D. Li, and D. Pacifici, “Measuring subwavelength spatial coherence with plasmonic interferometry,” Nat. Photon. 10, 681–687 (2016).
[Crossref]

Lindlein, N.

P. Gao, B. Yao, I. Harder, N. Lindlein, and F. J. Torcal-Milla, “Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement,” Opt. letters 36, 4305–4307 (2011).
[Crossref]

Liu, L.

X. Liu, F. Wang, L. Liu, Y. Chen, Y. Cai, and S. A. Ponomarenko, “Complex degree of coherence measurement for classical statistical fields,” Opt. Lett. 42, 77–80 (2017).
[Crossref] [PubMed]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[Crossref]

Liu, X.

Lörgen, M.

S. Eisebitt, J. Lüning, W. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature. 432, 885–888 (2004).
[Crossref] [PubMed]

Lüning, J.

S. Eisebitt, J. Lüning, W. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature. 432, 885–888 (2004).
[Crossref] [PubMed]

Macrander, A. T.

X. Shi, S. Marathe, M. J. Wojcik, N. G. Kujala, A. T. Macrander, and L. Assoufid, “Circular grating interferometer for mapping transverse coherence area of X-ray beams,” Appl. Phys. Lett. 105, 041116 (2014).
[Crossref]

S. Marathe, X. Shi, M. J. Wojcik, N. G. Kujala, R. Divan, D. C. Mancini, A. T. Macrander, and L. Assoufid, “Probing transverse coherence of X-ray beam with 2D phase grating interferometer,” Opt. Express 22, 14041–14053 (2014).
[Crossref] [PubMed]

Maiden, A.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Mancini, D. C.

Manley, S.

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimized flat-field epi-illumination,” Nat. Photon. 10, 705–708 (2016).
[Crossref]

Marathe, S.

S. Marathe, X. Shi, M. J. Wojcik, N. G. Kujala, R. Divan, D. C. Mancini, A. T. Macrander, and L. Assoufid, “Probing transverse coherence of X-ray beam with 2D phase grating interferometer,” Opt. Express 22, 14041–14053 (2014).
[Crossref] [PubMed]

X. Shi, S. Marathe, M. J. Wojcik, N. G. Kujala, A. T. Macrander, and L. Assoufid, “Circular grating interferometer for mapping transverse coherence area of X-ray beams,” Appl. Phys. Lett. 105, 041116 (2014).
[Crossref]

Maul, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

McIntyre, G.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

McNulty, I.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform X-ray holography,” Science 256, 1009 (1992).
[Crossref] [PubMed]

Melville, D.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Menzel, A.

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

Morrill, D.

D. Morrill, D. Li, and D. Pacifici, “Measuring subwavelength spatial coherence with plasmonic interferometry,” Nat. Photon. 10, 681–687 (2016).
[Crossref]

Morrison, G.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Neifeld, M. A.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[Crossref]

Novotny, L.

Nugent, K. A.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

Pacifici, D.

D. Morrill, D. Li, and D. Pacifici, “Measuring subwavelength spatial coherence with plasmonic interferometry,” Nat. Photon. 10, 681–687 (2016).
[Crossref]

Parks, D.

Partanen, H.

Paterson, D.

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

Peele, A. G.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

Pfeiffer, F.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Ponomarenko, S. A.

Quiney, H. M.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Rehbein, S.

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard X-ray holographic diffraction imaging,” Phys. review letters 100, 245503 (2008).
[Crossref]

Roberts, A.

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

Robinson, I. K.

N. Burdet, X. Shi, D. Parks, J. N. Clark, X. Huang, S. D. Kevan, and I. K. Robinson, “Evaluation of partial coherence correction in X-ray ptychography,” Opt. Express 23, 5452 (2015).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Rodenburg, J.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Rohmund, F.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Rosenbluth, A. E.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Russ, C.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Schlotter, W.

S. Eisebitt, J. Lüning, W. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature. 432, 885–888 (2004).
[Crossref] [PubMed]

Schulze-Briese, C.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Sharma, K. A.

Shi, X.

Sieben, C.

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimized flat-field epi-illumination,” Nat. Photon. 10, 705–708 (2016).
[Crossref]

Situ, G.

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

Stadler, L.-M.

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard X-ray holographic diffraction imaging,” Phys. review letters 100, 245503 (2008).
[Crossref]

Stöhr, J.

S. Eisebitt, J. Lüning, W. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature. 432, 885–888 (2004).
[Crossref] [PubMed]

Tervo, J.

Thibault, P.

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

Tian, K.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Tirapu-Azpiroz, J.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Torcal-Milla, F. J.

P. Gao, B. Yao, I. Harder, N. Lindlein, and F. J. Torcal-Milla, “Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement,” Opt. letters 36, 4305–4307 (2011).
[Crossref]

Tran, C. Q.

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

Turunen, J.

Urbach, H.

A. Konijnenberg, W. Coene, and H. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

van der Veen, J. F.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Vartanyants, I.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Vine, D. J.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Wagner, A.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Waller, L.

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

Wang, F.

Weitkamp, T.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Whitehead, L. W.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Williams, G. J.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

Wojcik, M. J.

S. Marathe, X. Shi, M. J. Wojcik, N. G. Kujala, R. Divan, D. C. Mancini, A. T. Macrander, and L. Assoufid, “Probing transverse coherence of X-ray beam with 2D phase grating interferometer,” Opt. Express 22, 14041–14053 (2014).
[Crossref] [PubMed]

X. Shi, S. Marathe, M. J. Wojcik, N. G. Kujala, A. T. Macrander, and L. Assoufid, “Circular grating interferometer for mapping transverse coherence area of X-ray beams,” Appl. Phys. Lett. 105, 041116 (2014).
[Crossref]

Wood, J. K.

Yao, B.

P. Gao, B. Yao, I. Harder, N. Lindlein, and F. J. Torcal-Milla, “Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement,” Opt. letters 36, 4305–4307 (2011).
[Crossref]

Zhao, C.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[Crossref]

Zimmermann, J.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

Appl. Phys. Lett. (1)

X. Shi, S. Marathe, M. J. Wojcik, N. G. Kujala, A. T. Macrander, and L. Assoufid, “Circular grating interferometer for mapping transverse coherence area of X-ray beams,” Appl. Phys. Lett. 105, 041116 (2014).
[Crossref]

J. Opt. Soc. Am. A (2)

Nat. Commun. (2)

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Nat. Photon. (3)

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

K. M. Douglass, C. Sieben, A. Archetti, A. Lambert, and S. Manley, “Super-resolution imaging of multiple cells by optimized flat-field epi-illumination,” Nat. Photon. 10, 705–708 (2016).
[Crossref]

D. Morrill, D. Li, and D. Pacifici, “Measuring subwavelength spatial coherence with plasmonic interferometry,” Nat. Photon. 10, 681–687 (2016).
[Crossref]

Nature. (2)

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

S. Eisebitt, J. Lüning, W. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature. 432, 885–888 (2004).
[Crossref] [PubMed]

Opt. Commun. (1)

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[Crossref]

Opt. Eng. (1)

J. L. Codona, “Differential optical transfer function wavefront sensing,” Opt. Eng. 52, 097105 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Opt. letters (1)

P. Gao, B. Yao, I. Harder, N. Lindlein, and F. J. Torcal-Milla, “Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement,” Opt. letters 36, 4305–4307 (2011).
[Crossref]

Optica (1)

Phys. Rev. A (1)

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[Crossref]

Phys. Rev. Lett. (3)

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent X rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

C. Q. Tran, G. J. Williams, A. Roberts, S. Flewett, A. G. Peele, D. Paterson, M. D. de Jonge, and K. A. Nugent, “Experimental measurement of the four-dimensional coherence function for an undulator X-ray source,” Phys. Rev. Lett. 98, 224801 (2007).
[Crossref] [PubMed]

Phys. review letters (1)

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard X-ray holographic diffraction imaging,” Phys. review letters 100, 245503 (2008).
[Crossref]

Science (1)

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform X-ray holography,” Science 256, 1009 (1992).
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Ultramicroscopy (1)

A. Konijnenberg, W. Coene, and H. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

Other (1)

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process,” in “SPIE Advanced Lithography,” vol. 7274 (International Society for Optics and Photonics, 2009), p. 72740.

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Figures (6)

Fig. 1
Fig. 1 The influence of spatial partial coherence on the propagation of light field and the diffractive imaging (experiment results). (a): Schematic plot of the experimental setup. We let a partially coherent beam propagate through an aperture which is superposed with a transmissive object, and observe the far-field diffracted intensity distribution. (b): The comparison between the intensity measurements of the coherent beam and the partially coherent beam. The blur of the diffraction pattern carries information about the spatial coherence properties of the beam.
Fig. 2
Fig. 2 The relations between the quadratic term (the original unperturbed diffraction pattern) and the two interference terms in the inverse Fourier transform of the perturbed diffraction pattern versus the location of the perturbation point r0. We use different colors to mark different values of r0. The gray square at the origin denotes the quadratic term which is twice as large as the aperture. The black square and the white square denote the transmission function and its complex-conjugate in the two interference terms respectively.
Fig. 3
Fig. 3 The experimental setup. The partially coherent beam is generated by focusing coherent laser beam onto a rotating difusser. By varying the intensity distribution of the focal spot, we can change the spatial coherence properties of the generated beam. We then collimate the generated beam and use it to illuminate a SLM, on which we simulate the effect of the aperture as well as the phase object. Finally, we measure intensity distribution of the Fourier transform (FT) of the light field at the SLM using a FT lens.
Fig. 4
Fig. 4 Experimental results for varying the location of the perturbation point for a GSM beam. (a,b,c): results for three different overlapping conditions, which require different number of measurements to retrieve the two interference terms. The squares in the figure are the products of the correlation function J(r, r0) and the aperture plane’s transmission function O(r). The red panda and the blue panda represent the trasmission function and its complex-conjugate in the two interference terms respectively.
Fig. 5
Fig. 5 Experimental results of varying the degree of coherence of the GSM beam. The locations of the perturbation points are chosen such that we can observe the whole Gaussian profile. (a1), (b1): amplitudes of the two interference terms. (a2), (b2): results of fitting to the amplitude’s cross-section. (a3), (b3): the phase of the two interference terms.
Fig. 6
Fig. 6 Experimental results of varying degree of coherence of the Gaussian-Airy correlation beam. (a1,b1 and a3,b3): the amplitude and the phase of the two interference terms in the presence of the phase object. (a2,b2 and a4,b4): the amplitude and the phase of the two interference terms in the absence of the phase object. (a5,b5): the phase of the results after modulation compensation.

Equations (9)

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I 0 ( k ) = T ( r 1 ) T ( r 2 ) * J ( r 1 , r 2 ) exp [ i 2 π k ( r 1 r 2 ) ] d 2 r 1 d 2 r 2 ,
T ( r ) = T ( r ) + γ δ ( r r 0 ) .
I ( k ) = [ T ( r 1 ) + γ δ ( r 1 r 0 ) ] [ T ( r 2 ) + γ δ ( r 2 r 0 ) ] * × J ( r 1 , r 2 ) exp [ i 2 π k ( r 1 r 2 ) ] d 2 r 1 d 2 r 2 .
I ( k ) = T ( r 1 ) T ( r 2 ) * J ( r 1 , r 2 ) exp [ i 2 π k ( r 1 r 2 ) ] d 2 r 1 d 2 r 2 + [ γ δ ( r 1 r 0 ) ] [ γ δ ( r 2 r 0 ) ] * × J ( r 1 , r 2 ) exp [ i 2 π k ( r 1 r 2 ) ] d 2 r 1 d 2 r 2 + [ γ δ ( r 2 r 0 ) ] * T ( r 1 ) J ( r 1 , r 2 ) exp [ i 2 π k ( r 1 r 2 ) ] d 2 r 1 d 2 r 2 + [ γ δ ( r 1 r 0 ) ] T ( r 2 ) * J ( r 1 , r 2 ) exp [ i 2 π k ( r 1 r 2 ) ] d 2 r 1 d 2 r 2 = I 0 ( k ) + | ( γ 1 ) T ( r 0 ) | 2 J ( r 0 , r 0 ) + γ * T ( r 1 ) J ( r 1 , r 0 ) exp [ i 2 π k ( r 1 r 0 ) ] d 2 r 1 + γ T ( r 2 ) * J ( r 0 , r 2 ) exp [ i 2 π k ( r 0 r 2 ) ] d 2 r 2 ,
{ r = r 1 r 0 r = r 0 r 2 { r 1 = r 0 + r r 2 = r 0 r ,
I ( k ) = I 0 ( k ) + | γ | 2 J ( r 0 , r 0 ) + γ * [ T ( r 0 + r ) J ( r 0 + r , r 0 ) ] exp [ i 2 π k r ] d 2 r + γ [ T ( r 0 r ) J ( r 0 r , r 0 ) ] * exp [ i 2 π k r ] d 2 r .
{ 1 { I C ( k ) I 0 ( k ) } = C * A + C B * 1 { I D ( k ) I 0 ( k ) } = D * A + D B * ,
{ A = T ( r 0 + r ) J ( r 0 + r , r 0 ) B = T ( r 0 r ) J ( r 0 r , r 0 ) , and { C = ( γ C 1 ) T ( r 0 ) D = ( γ D 1 ) T ( r 0 ) ,
{ A = [ D 1 { I C ( k ) I 0 ( k ) } C 1 { I D ( k ) I 0 ( k ) } ] [ C * D D * C ] 1 B = [ D * 1 { I C ( k ) I 0 ( k ) } C * 1 { I D ( k ) I 0 ( k ) } ] [ D * C C * D ] 1 .

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