Abstract

We propose a new method for phase retrieval that uses partially coherent illumination created by any arbitrary source shape in Köhler geometry. Using a stack of defocused intensity images, we recover not only the phase and amplitude of the sample, but also an estimate of the unknown source shape, which describes the spatial coherence of the illumination. Our algorithm uses a Kalman filtering approach which is fast, accurate and robust to noise. The method is experimentally simple and flexible, so should find use in optical, electron, X-ray and other phase imaging systems which employ partially coherent light. We provide an experimental demonstration in an optical microscope with various condenser apertures.

© 2014 Optical Society of America

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2014 (5)

2013 (6)

2012 (1)

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

2011 (2)

2010 (3)

2007 (3)

2006 (3)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2, 258–261 (2006).
[Crossref]

T. Gureyev, Y. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569– 580 (2006).
[Crossref]

A. Martin, F.-R. Chen, W.-K. Hsieh, J.-J. Kai, S. Findlay, and L. Allen, “Spatial incoherence in phase retrieval based on focus variation,” Ultramicroscopy 106, 914–924 (2006).
[Crossref] [PubMed]

2004 (2)

T. Gureyev, D. Paganin, A. Stevenson, S. Mayo, and S. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[Crossref] [PubMed]

C. J. R. Sheppard, “Defocused transfer function for a partially coherent microscope and application to phase retrieval,” J. Opt. Soc. Am. A 21, 828–831 (2004).
[Crossref]

2001 (2)

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Optics Communications 199, 65–75 (2001).
[Crossref]

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54, 27–32 (2001).
[Crossref]

1999 (1)

1998 (1)

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[Crossref]

1996 (1)

K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

1994 (1)

M. Raymer, M. Beck, and D. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[Crossref] [PubMed]

1992 (1)

W. Coene, G. Janssen, M. O. de Beeck, and D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69, 3743 (1992).
[Crossref] [PubMed]

1990 (1)

K. Nugent, “A generalization of Schell’s theorem,” Opt. Commun. 79, 267–269 (1990).
[Crossref]

1984 (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

1983 (1)

1982 (1)

1960 (1)

R. E. Kalman, “A new approach to linear filtering and prediction problems,” J. Basic. Eng 82, 35–45 (1960).
[Crossref]

Acosta, E.

Alieva, T.

Allen, L.

A. Martin, F.-R. Chen, W.-K. Hsieh, J.-J. Kai, S. Findlay, and L. Allen, “Spatial incoherence in phase retrieval based on focus variation,” Ultramicroscopy 106, 914–924 (2006).
[Crossref] [PubMed]

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Optics Communications 199, 65–75 (2001).
[Crossref]

Alpers, A.

Anastasio, M. A.

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

Barbastathis, G.

Barnea, Z.

K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Beck, M.

M. Raymer, M. Beck, and D. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
[Crossref] [PubMed]

Bishop, G.

G. Welch and G. Bishop, “An introduction to the Kalman filter,” (1995).

Boistel, R.

Börrnert, F.

A. Lubk, G. Guzzinati, F. Börrnert, and J. Verbeeck, “Transport of intensity phase retrieval of arbitrary wave fields including vortices,” Phys. Rev. Lett. 111, 173902 (2013).
[Crossref] [PubMed]

Bunk, O.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2, 258–261 (2006).
[Crossref]

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

Candes, E. J.

E. J. Candes, T. Strohmer, and V. Voroninski, “Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming,” Comm. Pure Appl. Math. 66, 1241–1274 (2013).
[Crossref]

Carney, P. S.

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

Chen, F.-R.

A. Martin, F.-R. Chen, W.-K. Hsieh, J.-J. Kai, S. Findlay, and L. Allen, “Spatial incoherence in phase retrieval based on focus variation,” Ultramicroscopy 106, 914–924 (2006).
[Crossref] [PubMed]

Clark, J.

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

Claus, R. A.

Z. Jingshan, R. A. Claus, J. Dauwels, L. Tian, and L. Waller, “Transport of intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes,” Opt. Express 22, 10661–10674 (2014).
[Crossref] [PubMed]

Z. Jingshan, L. Tian, R. A. Claus, J. Dauwels, and L. Waller, “Partially coherent phase recovery by Kalman filtering,” in “Frontiers in Optics,” (Optical Society of America, 2013), pp. FW6A–9.

Cloetens, P.

Coene, W.

W. Coene, G. Janssen, M. O. de Beeck, and D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69, 3743 (1992).
[Crossref] [PubMed]

Connolly, B.

Cookson, D.

K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

Dauwels, J.

David, C.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2, 258–261 (2006).
[Crossref]

Davidoiu, V.

de Beeck, M. O.

W. Coene, G. Janssen, M. O. de Beeck, and D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69, 3743 (1992).
[Crossref] [PubMed]

Depeursinge, C.

Dini, D. H.

D. H. Dini and D. P. Mandic, “Class of widely linear complex Kalman filters,” IEEE Trans. Neural Netw. Learning Syst. pp. 775–786 (2012).
[Crossref]

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

Fienup, J. R.

Findlay, S.

A. Martin, F.-R. Chen, W.-K. Hsieh, J.-J. Kai, S. Findlay, and L. Allen, “Spatial incoherence in phase retrieval based on focus variation,” Ultramicroscopy 106, 914–924 (2006).
[Crossref] [PubMed]

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

Gaylord, T. K.

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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

Guigay, J. P.

Gureyev, T.

T. Gureyev, Y. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569– 580 (2006).
[Crossref]

T. Gureyev, D. Paganin, A. Stevenson, S. Mayo, and S. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[Crossref] [PubMed]

K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

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K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54, 27–32 (2001).
[Crossref]

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A. Lubk, G. Guzzinati, F. Börrnert, and J. Verbeeck, “Transport of intensity phase retrieval of arbitrary wave fields including vortices,” Phys. Rev. Lett. 111, 173902 (2013).
[Crossref] [PubMed]

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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Lee, D.

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R. Socha, X. Shi, and D. LeHoty, “Simultaneous source mask optimization,” in “Photomask and Next Generation Lithography Mask Technology XII,” (International Society for Optics and Photonics, 2005), pp. 180–193.
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A. Lubk, G. Guzzinati, F. Börrnert, and J. Verbeeck, “Transport of intensity phase retrieval of arbitrary wave fields including vortices,” Phys. Rev. Lett. 111, 173902 (2013).
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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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T. Gureyev, Y. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569– 580 (2006).
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K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
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T. Gureyev, Y. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569– 580 (2006).
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T. Gureyev, D. Paganin, A. Stevenson, S. Mayo, and S. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
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T. Gureyev, Y. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569– 580 (2006).
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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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T. Gureyev, D. Paganin, A. Stevenson, S. Mayo, and S. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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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,” (International Society for Optics and Photonics, 2009), pp. 72740A.

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A. Lubk, G. Guzzinati, F. Börrnert, and J. Verbeeck, “Transport of intensity phase retrieval of arbitrary wave fields including vortices,” Phys. Rev. Lett. 111, 173902 (2013).
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[Crossref]

T. Gureyev, D. Paganin, A. Stevenson, S. Mayo, and S. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
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Figures (3)

Fig. 1
Fig. 1

We recover both phase and illumination coherence from a stack of images taken through-focus. (Left) Our brightfield microscope with z axis motion stage and an extra 2f system for imaging the source plane. (Right) Sample dataset of through-focus images.

Fig. 2
Fig. 2

Experimental comparison of phase recovered by the coherent Kalman filter as compared to the partially coherent Kalman filter, both with known and unknown sources. (Top) Measured source shape, with estimated source in white. (Second row) Phase recovered by the coherent Kalman filter is blurred for less coherent sources. (Third row) Phase recovered by the partially coherent Kalman filter (with known source). (Bottom) Phase recovered by the partially coherent Kalman filter with unknown source.

Fig. 3
Fig. 3

Convergence of source size estimation.

Tables (2)

Tables Icon

Table 1 Sparse Kalman filter method for partially coherent phase recovery.

Equations (13)

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I ( x , y , z ) = | A ( x , y , z ) | 2 S ( f z x , f z y ) ,
b n 1 = K a n 1 ,
b n = H n b n 1 ,
I n = C n | a n | 2 + v ,
I n = C n | a ^ n | 2 + C n diag ( a ^ n * ) ( a n a ^ n ) + C n diag ( a ^ n ) ( a n * a ^ n * ) + v ,
state : [ b n b n * ] = [ H n 0 0 H n * ] [ b n 1 b n 1 * ]
observation : I n = [ J n J n * ] [ b n b n * ] C n | a ^ n | 2 + v ,
R n = diag ( C n | a ^ n | 2 ) , and J n = C n diag ( a ^ n * ) K H .
a ^ n = K H b ^ n
Q n = Q ^ n ( Q ^ n + P ^ n ) ( Q ^ n + P ^ n + ( Q ^ n ) * + ( P ^ n ) * + S n 2 ) 1 ( Q ^ n + ( P ^ n ) * )
P n = P ^ n ( Q ^ n + P ^ n ) ( Q ^ n + P ^ n + ( Q ^ n ) * + ( P ^ n ) * + S n 2 ) 1 ( P ^ n + ( Q ^ n ) * )
b n = b ^ n + ( Q n + P n ) K diag ( a ^ n ) C n R n 1 ( I n C n | a ^ n | 2 ) .
arg min θ n = 1 N ( I n C n ( θ ) | a n | 2 ) T ( I n C n ( θ ) | a n | 2 ) ,

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