Abstract

Full-field transmission hard X-ray microscopy (TXM) has been widely applied to study morphology and structures with high spatial precision and to dynamic processes. Zernike phase contrast (ZPC) in hard X-ray TXM is often utilized to get an in-line phase contrast enhancement for weak-absorbing materials with little contrast differences. Here, following forward image formation, we derive and simplify the contrast transfer functions (CTFs) of the Zernike phase imaging system in TXM based on a linear space-shift-invariant imaging mode under certain approximations. The CTFs in ZPC in their simplified forms show a high similarity to the one in free-space propagation X-ray imaging systems.

© 2016 Optical Society of America

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2015 (3)

E. Nazaretski, K. Lauer, H. Yan, N. Bouet, J. Zhou, R. Conley, X. Huang, W. Xu, M. Lu, K. Gofron, S. Kalbfleisch, U. Wagner, C. Rau, and Y. S. Chu, “Pushing the limits: an instrument for hard X-ray imaging below 20 nm,” J. Synchrotron Radiat. 22, 336–341 (2015).
[Crossref] [PubMed]

H. Chen, Z. Wang, K. Gao, Q. Hou, D. Wang, and Z. Wu, “Quantitative phase retrieval in X-ray Zernike phase contrast microscopy,” J. Synchrotron Radiat. 22, 1056–1061 (2015).
[Crossref] [PubMed]

I. Vartiainen, C. Holzner, I. Mohacsi, P. Karvinen, A. Diaz, G. Pigino, and C. David, “Artifact characterization and reduction in scanning X-ray Zernike phase contrast microscopy,” Opt. Express 23(10), 13278–13293 (2015).
[Crossref] [PubMed]

2014 (4)

Y. Yang, R. Heine, Y. Cheng, C.-C. Wang, Y.-F. Song, and T. Baumbach, “Approaching quantitative Zernike phase contrast in full-field transmission hard X-ray microscopy: Origin and reduction of artifacts,” Appl. Phys. Lett. 105, 094101 (2014).
[Crossref]

B. Bayerlein, P. Zaslansky, Y. Dauphin, A. Rack, P. Fratzl, and I. Zlotnikov, “Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth,” Nat. Mater. 13, 1102–1107 (2014).
[Crossref] [PubMed]

Y. Cheng, H. Suhonen, L. Helfen, J. Li, F. Xu, M. Grunze, P. A. Levkin, and T. Baumbach, “Direct three-dimensional imaging of polymer-water interfaces by nanoscale hard X-ray phase tomography,” Soft Matter 10, 2982–2990 (2014).
[Crossref] [PubMed]

T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking morphological dynamics,” Proc. Natl. Acad. Sci. USA 111, 3921–3926 (2014).
[Crossref] [PubMed]

2012 (2)

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3D imaging of structure and composition in extended objects,” PloS One 7, e50124 (2012).
[Crossref] [PubMed]

J. Nelson, S. Misra, Y. Yang, A. Jackson, Y. Liu, H. Wang, H. Dai, J. C. Andrews, Y. Cui, and M. F. Toney, “In operando X-ray diffraction and transmission X-ray microscopy of lithium sulfur batteries,” J. Am. Chem. Soc. 134, 6337–6343 (2012).
[Crossref] [PubMed]

2011 (2)

K. Nagayama, “Another 60 years in electron microscopy: development of phase-plate electron microscopy and biological applications,” J. Electron Microsc. 60, S43–S62 (2011).

Y. Liu, J. C. Andrews, J. Wang, F. Meirer, P. Zhu, Z. Wu, and P. Pianetta, “Phase retrieval using polychromatic illumination for transmission X-ray microscopy,” Opt. Express 19(2), 540 (2011).
[Crossref] [PubMed]

2010 (3)

J. Y. Huang, K. Jin, J. Lim, H. Kim, S. Jang, H. Choi, K. Gil, and S. Lee, “High-resolution and high-contrast bio-medical X-ray imaging by using synchrotron radiation in the PLS,” J. Korean Phys. Soc. 56, 2077 (2010).
[Crossref]

M. Langer, P. Cloetens, and F. Peyrin, “Regularization of phase retrieval with phase-attenuation duality prior for 3-D holotomography,” IEEE Trans. Image Process. 19, 2428–2436 (2010).
[Crossref] [PubMed]

S.-C. Chao, Y.-C. Yen, Y.-F. Song, Y.-M. Chen, H.-C. Wu, and N.-L. Wu, “A study on the interior microstructures of working Sn particle electrode of Li-ion batteries by in situ X-ray transmission microscopy,” Electrochem. Commun. 12, 234–237 (2010).
[Crossref]

2009 (2)

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

B. Arhatari, A. Peele, K. Hannah, P. Kappen, K. Nugent, G. Williams, G. Yin, Y. Chen, J. Chen, and Y. Song, “A coherence approach to phase-contrast microscopy II: Experiment,” Ultramicroscopy 109, 280–286 (2009).
[Crossref] [PubMed]

2008 (1)

K. A. Nugent, B. D. Arhatari, and A. G. Peele, “A coherence approach to phase-contrast microscopy: Theory,” Ultramicroscopy 108, 937–945 (2008).
[Crossref] [PubMed]

2007 (2)

T. Bacquart, G. Devès, A. Carmona, R. Tucoulou, S. Bohic, and R. Ortega, “Subcellular speciation analysis of trace element oxidation states using synchrotron radiation micro-X-ray absorption near-edge structure,” Anal. Chem. 79, 7353–7359 (2007).
[Crossref] [PubMed]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the fresnel region,” Opt. Lett. 32(12), 1617–1619 (2007).
[Crossref] [PubMed]

2006 (1)

P. Cloetens, R. Mache, M. Schlenker, and S. Lerbs-Mache, “Quantitative phase tomography of arabidopsis seeds reveals intercellular void network,” Proc. Natl. Acad. Sci. USA 103, 14626–14630 (2006).
[Crossref] [PubMed]

2005 (2)

A. Momose, “Recent advances in X-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355 (2005).
[Crossref]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210–1213 (2005).
[Crossref] [PubMed]

2004 (1)

C. A. Larabell and M. A. Le Gros, “X-ray tomography generates 3-D reconstructions of the yeast, Saccharomyces cerevisiae, at 60-nm resolution,” Mol. Biol. Cell 15, 957–962 (2004).
[Crossref]

2002 (1)

S. Sugitani and K. Nagayama, “Complex observation in electron microscopy: III. inverse theory of observation-scheme dependent information transfer,” J. Phys. Soc. Jpn. 71, 744 (2002).
[Crossref]

1999 (1)

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.- Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32, A145 (1999).
[Crossref]

1998 (1)

G. Schneider, “Cryo X-ray microscopy with high spatial resolution in amplitude and phase contrast,” Ultramicroscopy 75, 85–104 (1998).
[Crossref] [PubMed]

1997 (1)

P. Cloetens, M. Pateyron-Salomé, J. Buffiere, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[Crossref]

1977 (1)

J. P. Guigay, “Fourier transform analysis of fresnel diffraction patterns and in-line holograms,” Optik 49, 121–125 (1977).

Anderson, E. H.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210–1213 (2005).
[Crossref] [PubMed]

Andrews, J. C.

J. Nelson, S. Misra, Y. Yang, A. Jackson, Y. Liu, H. Wang, H. Dai, J. C. Andrews, Y. Cui, and M. F. Toney, “In operando X-ray diffraction and transmission X-ray microscopy of lithium sulfur batteries,” J. Am. Chem. Soc. 134, 6337–6343 (2012).
[Crossref] [PubMed]

Y. Liu, J. C. Andrews, J. Wang, F. Meirer, P. Zhu, Z. Wu, and P. Pianetta, “Phase retrieval using polychromatic illumination for transmission X-ray microscopy,” Opt. Express 19(2), 540 (2011).
[Crossref] [PubMed]

Arhatari, B.

B. Arhatari, A. Peele, K. Hannah, P. Kappen, K. Nugent, G. Williams, G. Yin, Y. Chen, J. Chen, and Y. Song, “A coherence approach to phase-contrast microscopy II: Experiment,” Ultramicroscopy 109, 280–286 (2009).
[Crossref] [PubMed]

Arhatari, B. D.

K. A. Nugent, B. D. Arhatari, and A. G. Peele, “A coherence approach to phase-contrast microscopy: Theory,” Ultramicroscopy 108, 937–945 (2008).
[Crossref] [PubMed]

Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210–1213 (2005).
[Crossref] [PubMed]

Bacquart, T.

T. Bacquart, G. Devès, A. Carmona, R. Tucoulou, S. Bohic, and R. Ortega, “Subcellular speciation analysis of trace element oxidation states using synchrotron radiation micro-X-ray absorption near-edge structure,” Anal. Chem. 79, 7353–7359 (2007).
[Crossref] [PubMed]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.- Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32, A145 (1999).
[Crossref]

P. Cloetens, M. Pateyron-Salomé, J. Buffiere, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[Crossref]

Baumbach, T.

Y. Cheng, H. Suhonen, L. Helfen, J. Li, F. Xu, M. Grunze, P. A. Levkin, and T. Baumbach, “Direct three-dimensional imaging of polymer-water interfaces by nanoscale hard X-ray phase tomography,” Soft Matter 10, 2982–2990 (2014).
[Crossref] [PubMed]

T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking morphological dynamics,” Proc. Natl. Acad. Sci. USA 111, 3921–3926 (2014).
[Crossref] [PubMed]

Y. Yang, R. Heine, Y. Cheng, C.-C. Wang, Y.-F. Song, and T. Baumbach, “Approaching quantitative Zernike phase contrast in full-field transmission hard X-ray microscopy: Origin and reduction of artifacts,” Appl. Phys. Lett. 105, 094101 (2014).
[Crossref]

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3D imaging of structure and composition in extended objects,” PloS One 7, e50124 (2012).
[Crossref] [PubMed]

Bayat, S.

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3D imaging of structure and composition in extended objects,” PloS One 7, e50124 (2012).
[Crossref] [PubMed]

Bayerlein, B.

B. Bayerlein, P. Zaslansky, Y. Dauphin, A. Rack, P. Fratzl, and I. Zlotnikov, “Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth,” Nat. Mater. 13, 1102–1107 (2014).
[Crossref] [PubMed]

Bohic, S.

T. Bacquart, G. Devès, A. Carmona, R. Tucoulou, S. Bohic, and R. Ortega, “Subcellular speciation analysis of trace element oxidation states using synchrotron radiation micro-X-ray absorption near-edge structure,” Anal. Chem. 79, 7353–7359 (2007).
[Crossref] [PubMed]

Boistel, R.

Bouet, N.

E. Nazaretski, K. Lauer, H. Yan, N. Bouet, J. Zhou, R. Conley, X. Huang, W. Xu, M. Lu, K. Gofron, S. Kalbfleisch, U. Wagner, C. Rau, and Y. S. Chu, “Pushing the limits: an instrument for hard X-ray imaging below 20 nm,” J. Synchrotron Radiat. 22, 336–341 (2015).
[Crossref] [PubMed]

Buffiere, J.

P. Cloetens, M. Pateyron-Salomé, J. Buffiere, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[Crossref]

Buffière, J.- Y.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.- Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32, A145 (1999).
[Crossref]

Carmona, A.

T. Bacquart, G. Devès, A. Carmona, R. Tucoulou, S. Bohic, and R. Ortega, “Subcellular speciation analysis of trace element oxidation states using synchrotron radiation micro-X-ray absorption near-edge structure,” Anal. Chem. 79, 7353–7359 (2007).
[Crossref] [PubMed]

Chao, S.-C.

S.-C. Chao, Y.-C. Yen, Y.-F. Song, Y.-M. Chen, H.-C. Wu, and N.-L. Wu, “A study on the interior microstructures of working Sn particle electrode of Li-ion batteries by in situ X-ray transmission microscopy,” Electrochem. Commun. 12, 234–237 (2010).
[Crossref]

Chao, W.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210–1213 (2005).
[Crossref] [PubMed]

Chen, H.

H. Chen, Z. Wang, K. Gao, Q. Hou, D. Wang, and Z. Wu, “Quantitative phase retrieval in X-ray Zernike phase contrast microscopy,” J. Synchrotron Radiat. 22, 1056–1061 (2015).
[Crossref] [PubMed]

Chen, J.

B. Arhatari, A. Peele, K. Hannah, P. Kappen, K. Nugent, G. Williams, G. Yin, Y. Chen, J. Chen, and Y. Song, “A coherence approach to phase-contrast microscopy II: Experiment,” Ultramicroscopy 109, 280–286 (2009).
[Crossref] [PubMed]

Chen, Y.

B. Arhatari, A. Peele, K. Hannah, P. Kappen, K. Nugent, G. Williams, G. Yin, Y. Chen, J. Chen, and Y. Song, “A coherence approach to phase-contrast microscopy II: Experiment,” Ultramicroscopy 109, 280–286 (2009).
[Crossref] [PubMed]

Chen, Y.-M.

S.-C. Chao, Y.-C. Yen, Y.-F. Song, Y.-M. Chen, H.-C. Wu, and N.-L. Wu, “A study on the interior microstructures of working Sn particle electrode of Li-ion batteries by in situ X-ray transmission microscopy,” Electrochem. Commun. 12, 234–237 (2010).
[Crossref]

Cheng, Y.

Y. Cheng, H. Suhonen, L. Helfen, J. Li, F. Xu, M. Grunze, P. A. Levkin, and T. Baumbach, “Direct three-dimensional imaging of polymer-water interfaces by nanoscale hard X-ray phase tomography,” Soft Matter 10, 2982–2990 (2014).
[Crossref] [PubMed]

Y. Yang, R. Heine, Y. Cheng, C.-C. Wang, Y.-F. Song, and T. Baumbach, “Approaching quantitative Zernike phase contrast in full-field transmission hard X-ray microscopy: Origin and reduction of artifacts,” Appl. Phys. Lett. 105, 094101 (2014).
[Crossref]

Choi, H.

J. Y. Huang, K. Jin, J. Lim, H. Kim, S. Jang, H. Choi, K. Gil, and S. Lee, “High-resolution and high-contrast bio-medical X-ray imaging by using synchrotron radiation in the PLS,” J. Korean Phys. Soc. 56, 2077 (2010).
[Crossref]

Chu, Y. S.

E. Nazaretski, K. Lauer, H. Yan, N. Bouet, J. Zhou, R. Conley, X. Huang, W. Xu, M. Lu, K. Gofron, S. Kalbfleisch, U. Wagner, C. Rau, and Y. S. Chu, “Pushing the limits: an instrument for hard X-ray imaging below 20 nm,” J. Synchrotron Radiat. 22, 336–341 (2015).
[Crossref] [PubMed]

Cloetens, P.

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3D imaging of structure and composition in extended objects,” PloS One 7, e50124 (2012).
[Crossref] [PubMed]

M. Langer, P. Cloetens, and F. Peyrin, “Regularization of phase retrieval with phase-attenuation duality prior for 3-D holotomography,” IEEE Trans. Image Process. 19, 2428–2436 (2010).
[Crossref] [PubMed]

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Y. Cheng, H. Suhonen, L. Helfen, J. Li, F. Xu, M. Grunze, P. A. Levkin, and T. Baumbach, “Direct three-dimensional imaging of polymer-water interfaces by nanoscale hard X-ray phase tomography,” Soft Matter 10, 2982–2990 (2014).
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T. Bacquart, G. Devès, A. Carmona, R. Tucoulou, S. Bohic, and R. Ortega, “Subcellular speciation analysis of trace element oxidation states using synchrotron radiation micro-X-ray absorption near-edge structure,” Anal. Chem. 79, 7353–7359 (2007).
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M. Langer, P. Cloetens, and F. Peyrin, “Regularization of phase retrieval with phase-attenuation duality prior for 3-D holotomography,” IEEE Trans. Image Process. 19, 2428–2436 (2010).
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Pigino, G.

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E. Nazaretski, K. Lauer, H. Yan, N. Bouet, J. Zhou, R. Conley, X. Huang, W. Xu, M. Lu, K. Gofron, S. Kalbfleisch, U. Wagner, C. Rau, and Y. S. Chu, “Pushing the limits: an instrument for hard X-ray imaging below 20 nm,” J. Synchrotron Radiat. 22, 336–341 (2015).
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F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3D imaging of structure and composition in extended objects,” PloS One 7, e50124 (2012).
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P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.- Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32, A145 (1999).
[Crossref]

Sano, Y.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

Schlenker, M.

P. Cloetens, R. Mache, M. Schlenker, and S. Lerbs-Mache, “Quantitative phase tomography of arabidopsis seeds reveals intercellular void network,” Proc. Natl. Acad. Sci. USA 103, 14626–14630 (2006).
[Crossref] [PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.- Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32, A145 (1999).
[Crossref]

P. Cloetens, M. Pateyron-Salomé, J. Buffiere, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[Crossref]

Schneider, G.

G. Schneider, “Cryo X-ray microscopy with high spatial resolution in amplitude and phase contrast,” Ultramicroscopy 75, 85–104 (1998).
[Crossref] [PubMed]

Song, Y.

B. Arhatari, A. Peele, K. Hannah, P. Kappen, K. Nugent, G. Williams, G. Yin, Y. Chen, J. Chen, and Y. Song, “A coherence approach to phase-contrast microscopy II: Experiment,” Ultramicroscopy 109, 280–286 (2009).
[Crossref] [PubMed]

Song, Y.-F.

Y. Yang, R. Heine, Y. Cheng, C.-C. Wang, Y.-F. Song, and T. Baumbach, “Approaching quantitative Zernike phase contrast in full-field transmission hard X-ray microscopy: Origin and reduction of artifacts,” Appl. Phys. Lett. 105, 094101 (2014).
[Crossref]

S.-C. Chao, Y.-C. Yen, Y.-F. Song, Y.-M. Chen, H.-C. Wu, and N.-L. Wu, “A study on the interior microstructures of working Sn particle electrode of Li-ion batteries by in situ X-ray transmission microscopy,” Electrochem. Commun. 12, 234–237 (2010).
[Crossref]

Sugitani, S.

S. Sugitani and K. Nagayama, “Complex observation in electron microscopy: III. inverse theory of observation-scheme dependent information transfer,” J. Phys. Soc. Jpn. 71, 744 (2002).
[Crossref]

Suhonen, H.

Y. Cheng, H. Suhonen, L. Helfen, J. Li, F. Xu, M. Grunze, P. A. Levkin, and T. Baumbach, “Direct three-dimensional imaging of polymer-water interfaces by nanoscale hard X-ray phase tomography,” Soft Matter 10, 2982–2990 (2014).
[Crossref] [PubMed]

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3D imaging of structure and composition in extended objects,” PloS One 7, e50124 (2012).
[Crossref] [PubMed]

Tamasaku, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

Toney, M. F.

J. Nelson, S. Misra, Y. Yang, A. Jackson, Y. Liu, H. Wang, H. Dai, J. C. Andrews, Y. Cui, and M. F. Toney, “In operando X-ray diffraction and transmission X-ray microscopy of lithium sulfur batteries,” J. Am. Chem. Soc. 134, 6337–6343 (2012).
[Crossref] [PubMed]

Tucoulou, R.

T. Bacquart, G. Devès, A. Carmona, R. Tucoulou, S. Bohic, and R. Ortega, “Subcellular speciation analysis of trace element oxidation states using synchrotron radiation micro-X-ray absorption near-edge structure,” Anal. Chem. 79, 7353–7359 (2007).
[Crossref] [PubMed]

van de Kamp, T.

T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking morphological dynamics,” Proc. Natl. Acad. Sci. USA 111, 3921–3926 (2014).
[Crossref] [PubMed]

Van den Bos, A.

M. Howells, C. Jacobsen, T. Warwick, and A. Van den Bos, “Principles and applications of zone plate X-ray microscopes,” in Science of Microscopy, (Springer, 2007), pp. 835–926.
[Crossref]

Vartiainen, I.

Wagner, U.

E. Nazaretski, K. Lauer, H. Yan, N. Bouet, J. Zhou, R. Conley, X. Huang, W. Xu, M. Lu, K. Gofron, S. Kalbfleisch, U. Wagner, C. Rau, and Y. S. Chu, “Pushing the limits: an instrument for hard X-ray imaging below 20 nm,” J. Synchrotron Radiat. 22, 336–341 (2015).
[Crossref] [PubMed]

Wang, C.-C.

Y. Yang, R. Heine, Y. Cheng, C.-C. Wang, Y.-F. Song, and T. Baumbach, “Approaching quantitative Zernike phase contrast in full-field transmission hard X-ray microscopy: Origin and reduction of artifacts,” Appl. Phys. Lett. 105, 094101 (2014).
[Crossref]

Wang, D.

H. Chen, Z. Wang, K. Gao, Q. Hou, D. Wang, and Z. Wu, “Quantitative phase retrieval in X-ray Zernike phase contrast microscopy,” J. Synchrotron Radiat. 22, 1056–1061 (2015).
[Crossref] [PubMed]

Wang, H.

J. Nelson, S. Misra, Y. Yang, A. Jackson, Y. Liu, H. Wang, H. Dai, J. C. Andrews, Y. Cui, and M. F. Toney, “In operando X-ray diffraction and transmission X-ray microscopy of lithium sulfur batteries,” J. Am. Chem. Soc. 134, 6337–6343 (2012).
[Crossref] [PubMed]

Wang, J.

Wang, Z.

H. Chen, Z. Wang, K. Gao, Q. Hou, D. Wang, and Z. Wu, “Quantitative phase retrieval in X-ray Zernike phase contrast microscopy,” J. Synchrotron Radiat. 22, 1056–1061 (2015).
[Crossref] [PubMed]

Warwick, T.

M. Howells, C. Jacobsen, T. Warwick, and A. Van den Bos, “Principles and applications of zone plate X-ray microscopes,” in Science of Microscopy, (Springer, 2007), pp. 835–926.
[Crossref]

Williams, G.

B. Arhatari, A. Peele, K. Hannah, P. Kappen, K. Nugent, G. Williams, G. Yin, Y. Chen, J. Chen, and Y. Song, “A coherence approach to phase-contrast microscopy II: Experiment,” Ultramicroscopy 109, 280–286 (2009).
[Crossref] [PubMed]

Wu, H.-C.

S.-C. Chao, Y.-C. Yen, Y.-F. Song, Y.-M. Chen, H.-C. Wu, and N.-L. Wu, “A study on the interior microstructures of working Sn particle electrode of Li-ion batteries by in situ X-ray transmission microscopy,” Electrochem. Commun. 12, 234–237 (2010).
[Crossref]

Wu, N.-L.

S.-C. Chao, Y.-C. Yen, Y.-F. Song, Y.-M. Chen, H.-C. Wu, and N.-L. Wu, “A study on the interior microstructures of working Sn particle electrode of Li-ion batteries by in situ X-ray transmission microscopy,” Electrochem. Commun. 12, 234–237 (2010).
[Crossref]

Wu, Z.

H. Chen, Z. Wang, K. Gao, Q. Hou, D. Wang, and Z. Wu, “Quantitative phase retrieval in X-ray Zernike phase contrast microscopy,” J. Synchrotron Radiat. 22, 1056–1061 (2015).
[Crossref] [PubMed]

Y. Liu, J. C. Andrews, J. Wang, F. Meirer, P. Zhu, Z. Wu, and P. Pianetta, “Phase retrieval using polychromatic illumination for transmission X-ray microscopy,” Opt. Express 19(2), 540 (2011).
[Crossref] [PubMed]

Xu, F.

Y. Cheng, H. Suhonen, L. Helfen, J. Li, F. Xu, M. Grunze, P. A. Levkin, and T. Baumbach, “Direct three-dimensional imaging of polymer-water interfaces by nanoscale hard X-ray phase tomography,” Soft Matter 10, 2982–2990 (2014).
[Crossref] [PubMed]

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3D imaging of structure and composition in extended objects,” PloS One 7, e50124 (2012).
[Crossref] [PubMed]

Xu, W.

E. Nazaretski, K. Lauer, H. Yan, N. Bouet, J. Zhou, R. Conley, X. Huang, W. Xu, M. Lu, K. Gofron, S. Kalbfleisch, U. Wagner, C. Rau, and Y. S. Chu, “Pushing the limits: an instrument for hard X-ray imaging below 20 nm,” J. Synchrotron Radiat. 22, 336–341 (2015).
[Crossref] [PubMed]

Yabashi, M.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

Yamakawa, D.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

Yamamura, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

Yamauchi, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

Yan, H.

E. Nazaretski, K. Lauer, H. Yan, N. Bouet, J. Zhou, R. Conley, X. Huang, W. Xu, M. Lu, K. Gofron, S. Kalbfleisch, U. Wagner, C. Rau, and Y. S. Chu, “Pushing the limits: an instrument for hard X-ray imaging below 20 nm,” J. Synchrotron Radiat. 22, 336–341 (2015).
[Crossref] [PubMed]

Yang, Y.

Y. Yang, R. Heine, Y. Cheng, C.-C. Wang, Y.-F. Song, and T. Baumbach, “Approaching quantitative Zernike phase contrast in full-field transmission hard X-ray microscopy: Origin and reduction of artifacts,” Appl. Phys. Lett. 105, 094101 (2014).
[Crossref]

J. Nelson, S. Misra, Y. Yang, A. Jackson, Y. Liu, H. Wang, H. Dai, J. C. Andrews, Y. Cui, and M. F. Toney, “In operando X-ray diffraction and transmission X-ray microscopy of lithium sulfur batteries,” J. Am. Chem. Soc. 134, 6337–6343 (2012).
[Crossref] [PubMed]

Yen, Y.-C.

S.-C. Chao, Y.-C. Yen, Y.-F. Song, Y.-M. Chen, H.-C. Wu, and N.-L. Wu, “A study on the interior microstructures of working Sn particle electrode of Li-ion batteries by in situ X-ray transmission microscopy,” Electrochem. Commun. 12, 234–237 (2010).
[Crossref]

Yin, G.

B. Arhatari, A. Peele, K. Hannah, P. Kappen, K. Nugent, G. Williams, G. Yin, Y. Chen, J. Chen, and Y. Song, “A coherence approach to phase-contrast microscopy II: Experiment,” Ultramicroscopy 109, 280–286 (2009).
[Crossref] [PubMed]

Yokoyama, H.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

Yumoto, H.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

Zaslansky, P.

B. Bayerlein, P. Zaslansky, Y. Dauphin, A. Rack, P. Fratzl, and I. Zlotnikov, “Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth,” Nat. Mater. 13, 1102–1107 (2014).
[Crossref] [PubMed]

Zhou, J.

E. Nazaretski, K. Lauer, H. Yan, N. Bouet, J. Zhou, R. Conley, X. Huang, W. Xu, M. Lu, K. Gofron, S. Kalbfleisch, U. Wagner, C. Rau, and Y. S. Chu, “Pushing the limits: an instrument for hard X-ray imaging below 20 nm,” J. Synchrotron Radiat. 22, 336–341 (2015).
[Crossref] [PubMed]

Zhu, P.

Zlotnikov, I.

B. Bayerlein, P. Zaslansky, Y. Dauphin, A. Rack, P. Fratzl, and I. Zlotnikov, “Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth,” Nat. Mater. 13, 1102–1107 (2014).
[Crossref] [PubMed]

Anal. Chem. (1)

T. Bacquart, G. Devès, A. Carmona, R. Tucoulou, S. Bohic, and R. Ortega, “Subcellular speciation analysis of trace element oxidation states using synchrotron radiation micro-X-ray absorption near-edge structure,” Anal. Chem. 79, 7353–7359 (2007).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

Y. Yang, R. Heine, Y. Cheng, C.-C. Wang, Y.-F. Song, and T. Baumbach, “Approaching quantitative Zernike phase contrast in full-field transmission hard X-ray microscopy: Origin and reduction of artifacts,” Appl. Phys. Lett. 105, 094101 (2014).
[Crossref]

Electrochem. Commun. (1)

S.-C. Chao, Y.-C. Yen, Y.-F. Song, Y.-M. Chen, H.-C. Wu, and N.-L. Wu, “A study on the interior microstructures of working Sn particle electrode of Li-ion batteries by in situ X-ray transmission microscopy,” Electrochem. Commun. 12, 234–237 (2010).
[Crossref]

IEEE Trans. Image Process. (1)

M. Langer, P. Cloetens, and F. Peyrin, “Regularization of phase retrieval with phase-attenuation duality prior for 3-D holotomography,” IEEE Trans. Image Process. 19, 2428–2436 (2010).
[Crossref] [PubMed]

J. Am. Chem. Soc. (1)

J. Nelson, S. Misra, Y. Yang, A. Jackson, Y. Liu, H. Wang, H. Dai, J. C. Andrews, Y. Cui, and M. F. Toney, “In operando X-ray diffraction and transmission X-ray microscopy of lithium sulfur batteries,” J. Am. Chem. Soc. 134, 6337–6343 (2012).
[Crossref] [PubMed]

J. Appl. Phys. (1)

P. Cloetens, M. Pateyron-Salomé, J. Buffiere, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[Crossref]

J. Electron Microsc. (1)

K. Nagayama, “Another 60 years in electron microscopy: development of phase-plate electron microscopy and biological applications,” J. Electron Microsc. 60, S43–S62 (2011).

J. Korean Phys. Soc. (1)

J. Y. Huang, K. Jin, J. Lim, H. Kim, S. Jang, H. Choi, K. Gil, and S. Lee, “High-resolution and high-contrast bio-medical X-ray imaging by using synchrotron radiation in the PLS,” J. Korean Phys. Soc. 56, 2077 (2010).
[Crossref]

J. Phys. D Appl. Phys. (1)

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.- Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32, A145 (1999).
[Crossref]

J. Phys. Soc. Jpn. (1)

S. Sugitani and K. Nagayama, “Complex observation in electron microscopy: III. inverse theory of observation-scheme dependent information transfer,” J. Phys. Soc. Jpn. 71, 744 (2002).
[Crossref]

J. Synchrotron Radiat. (2)

H. Chen, Z. Wang, K. Gao, Q. Hou, D. Wang, and Z. Wu, “Quantitative phase retrieval in X-ray Zernike phase contrast microscopy,” J. Synchrotron Radiat. 22, 1056–1061 (2015).
[Crossref] [PubMed]

E. Nazaretski, K. Lauer, H. Yan, N. Bouet, J. Zhou, R. Conley, X. Huang, W. Xu, M. Lu, K. Gofron, S. Kalbfleisch, U. Wagner, C. Rau, and Y. S. Chu, “Pushing the limits: an instrument for hard X-ray imaging below 20 nm,” J. Synchrotron Radiat. 22, 336–341 (2015).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. (1)

A. Momose, “Recent advances in X-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355 (2005).
[Crossref]

Mol. Biol. Cell (1)

C. A. Larabell and M. A. Le Gros, “X-ray tomography generates 3-D reconstructions of the yeast, Saccharomyces cerevisiae, at 60-nm resolution,” Mol. Biol. Cell 15, 957–962 (2004).
[Crossref]

Nat. Mater. (1)

B. Bayerlein, P. Zaslansky, Y. Dauphin, A. Rack, P. Fratzl, and I. Zlotnikov, “Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth,” Nat. Mater. 13, 1102–1107 (2014).
[Crossref] [PubMed]

Nat. Phys. (1)

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2009).
[Crossref]

Nature (1)

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210–1213 (2005).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Optik (1)

J. P. Guigay, “Fourier transform analysis of fresnel diffraction patterns and in-line holograms,” Optik 49, 121–125 (1977).

PloS One (1)

F. Xu, L. Helfen, H. Suhonen, D. Elgrabli, S. Bayat, P. Reischig, T. Baumbach, and P. Cloetens, “Correlative nanoscale 3D imaging of structure and composition in extended objects,” PloS One 7, e50124 (2012).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (2)

T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking morphological dynamics,” Proc. Natl. Acad. Sci. USA 111, 3921–3926 (2014).
[Crossref] [PubMed]

P. Cloetens, R. Mache, M. Schlenker, and S. Lerbs-Mache, “Quantitative phase tomography of arabidopsis seeds reveals intercellular void network,” Proc. Natl. Acad. Sci. USA 103, 14626–14630 (2006).
[Crossref] [PubMed]

Soft Matter (1)

Y. Cheng, H. Suhonen, L. Helfen, J. Li, F. Xu, M. Grunze, P. A. Levkin, and T. Baumbach, “Direct three-dimensional imaging of polymer-water interfaces by nanoscale hard X-ray phase tomography,” Soft Matter 10, 2982–2990 (2014).
[Crossref] [PubMed]

Ultramicroscopy (3)

K. A. Nugent, B. D. Arhatari, and A. G. Peele, “A coherence approach to phase-contrast microscopy: Theory,” Ultramicroscopy 108, 937–945 (2008).
[Crossref] [PubMed]

B. Arhatari, A. Peele, K. Hannah, P. Kappen, K. Nugent, G. Williams, G. Yin, Y. Chen, J. Chen, and Y. Song, “A coherence approach to phase-contrast microscopy II: Experiment,” Ultramicroscopy 109, 280–286 (2009).
[Crossref] [PubMed]

G. Schneider, “Cryo X-ray microscopy with high spatial resolution in amplitude and phase contrast,” Ultramicroscopy 75, 85–104 (1998).
[Crossref] [PubMed]

Other (4)

D. B. Murphy and M. W. Davidson, Fundamentals of Light Microscopy and Electronic Imaging (Wiley-Blackwell, 2012).
[Crossref]

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

J. Frank, Three-Dimensional Electron Microscopy of Macromolecular Assemblies (Academic, 1996).

M. Howells, C. Jacobsen, T. Warwick, and A. Van den Bos, “Principles and applications of zone plate X-ray microscopes,” in Science of Microscopy, (Springer, 2007), pp. 835–926.
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Schematic layout of image formation in a TXM setup. The phase ring is placed in the back focal plane of the objective lens (Fresnel zone plate). Ui is the wavefield behind the sample. Ub is the wavefield behind the phase ring (in the back focal plane of FZP). Uo is the wavefield arriving at the detector plane. The P wave (red) represents the zeroth-order diffraction; the S wave (green) is the higher-order diffraction that passes the phase ring untouched. The interference between the phase altered P wave and the S wave will lead to contrast enhancement in the intensity recorded at the imaging plane.

Fig. 2
Fig. 2

Contrast transfer function (CTF) simulation and comparison between absorption mode and Zernike phase contrast mode in a TXM system. (a) Simulation of the amplitude and phase CTFs under absorption mode with a defocusing distance of 150 µm; (b) amplitude and phase CTFs under Zernike phase contrast mode with the same defocusing distance; (c) absorption image of the object, showing merely the edges of the object; (d) phase contrast image of the same object with the large scale features preserved; (e) comparison of line profiles of both (c) and (d).

Equations (12)

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

U i ( r ) = T ( r ) U s o u r c e = exp [ B ( r ) + i ϕ ( r ) ] 1 B ( r ) + i ϕ ( r ) .
B ( r ) 1 , | ϕ ( r ) ϕ ( r + Δ r ) | 1.
U b ( f ) = { U i ( r ) } A p ( f ) H ( f ) .
A p ( f ) = { exp ( i θ p ) P ( m , λ ) = exp ( i 3 π 2 ) P ( m , λ ) or exp ( i π 2 ) P ( m , λ ) if f f p 1 if f > f p
H ( f ) = exp [ i π Δ z λ f 2 + g ( f ) ] .
U b ( f ) = { [ 1 B ( r ) ] + i ϕ ( r ) } A p ( f ) H ( f ) = { exp ( i θ p ) P ( m , λ ) δ ( f ) B ˜ ( f ) + i ϕ ˜ ( f ) } H ( f ) = { U i ( r ) } H ( f ) ,
{ I o ( f ) } = | { U o ( r ) } | 2 = U i ( r λ Δ z f 2 ) U i * ( r + λ Δ z f 2 ) exp ( i 2 π fr ) d r
I ˜ o ( f ) = δ ( f ) + 2 sin ( π λ Δ z f 2 ) ϕ ˜ ( f ) 2 cos ( π λ Δ z f 2 ) B ˜ ( f ) .
I ˜ o ( f ) = δ ( f ) P 2 + 2 sin ( π λ Δ z f 2 + θ p ) ϕ ˜ ( f ) P 2 cos ( π λ Δ z f 2 + θ p ) B ˜ ( f ) P .
I ˜ o ( f ) = δ ( f ) P 2 2 cos ( π λ Δ z f 2 ) ϕ ˜ ( f ) P 2 sin ( π λ Δ z f 2 ) B ˜ ( f ) P
I ˜ o ( f ) 2 sin ( π λ Δ z f 2 + θ p ) ϕ ˜ ( f ) P 2 cos ( π λ Δ z f 2 + θ p ) B ˜ ( f ) P
{ I o ( f ) } = U i ( r λ Δ z f 2 ) U i * ( r + λ Δ z f 2 ) exp ( i 2 π fr ) d r = [ i B ( r λ Δ z f 2 ) + i ϕ ( r λ Δ z f 2 ) ] [ i B ( r + λ Δ z f 2 ) + i ϕ ( r + λ Δ z f 2 ) ] * exp ( i 2 π fr ) d r = { 1 + i [ B ( r + λ Δ z f 2 ) B ( r λ Δ z f 2 ) ] [ ϕ ( r + λ Δ z f 2 ) + ϕ ( r λ Δ z f 2 ) ] } exp ( i 2 π fr ) d r = δ ( f ) + i B ˜ ( r ) [ exp ( i π λ Δ z f 2 ) exp ( i π λ Δ z f 2 ) ] ϕ ˜ ( r ) [ exp ( i π λ Δ z f 2 ) + exp ( i π λ Δ z f 2 ) ] = δ ( f ) 2 sin ( π λ Δ z f 2 ) B ˜ ( f ) 2 cos ( π λ Δ z f 2 ) ϕ ˜ ( f )

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