Abstract

A method to analyze extreme ultraviolet microscopy images of nanostructures that allows for the simultaneous determination of an object’s feature size and image resolution is presented. It is based on the correlation between the image and a set of templates of known resolution generated from the original image using Gaussian filters. The analysis was applied to images obtained with a Fresnel zone plate microscope that uses a 13.2nm wavelength laser light for illumination. The object’s feature size and the resolution obtained with this method are shown to be in very good agreement with independent measurements of both magnitudes.

© 2008 Optical Society of America

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  1. W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft x-ray microscopy at a spatial resolution better than 15nm,” Nature 435, 1210-1213 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2007 (5)

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact x-ray microscopy,” J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007).
[CrossRef]

M. S. Pattichis and A. C. Bovik, “Analyzing image structure by multidimensional frequency modulation,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 753-766 (2007).
[CrossRef] [PubMed]

H. Stollberg, P. Guttmann, P. A. C. Takman, and H. M. Hertz, “Size-selective colloidal-gold localization in transmission x-ray microscopy,” J. Microsc. 225, 80-87 (2007).
[CrossRef] [PubMed]

P. Wachulak, M. C. Marconi, R. Bartels, C. S. Menoni, and J. J. Rocca, “Volume extreme ultraviolet holographic imaging with numerical optical sectioning,” Opt. Express 15, 10622-10628 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (4)

Y. Wang, M. A. Larotonda, B. M. Luther, D. Alessi, M. Berrill, V. N. Shlyaptsev, and J. J. Rocca, “Demonstration of high-repetition-rate tabletop soft-x-ray lasers with saturated output at wavelengths down to 13.9nm and gain down to 10.9nm,” Phys. Rev. A 72, 053807 (2005).
[CrossRef]

J. J. Rocca, Y. Wang, M. A. Larotonda, B. M. Luther, M. Berrill, and D. Alessi, “Saturated 13.2nm high-repetition-rate laser in nickellike cadmium,” Opt. Lett. 30, 2581-2583 (2005).
[CrossRef] [PubMed]

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

J. Nunez, X. Otazu, and M. T. Merino, “A multiresolution-based method for the determination of the relative resolution between images: first application to remote sensing and medical images,” Int. J. Imaging Syst. Technol. 15, 225-235 (2005).
[CrossRef]

2003 (2)

H. Stollberg, J. B. De Monvel, A. Holmberg, and H. M. Hertz, “Wavelet-based image restoration for compact x-ray microscopy,” J. Microsc. 211, 154-160 (2003).
[CrossRef] [PubMed]

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

2000 (1)

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

1998 (1)

J. Heck, D. T. Attwood, W. Meyer-Ilse, and E. H. Anderson, “Resolution determination in x-ray microscopy: an analysis of the effects of partial coherence and illumination spectrum,” J. X-Ray Sci. Technol. 8, 95-104 (1998).

1982 (1)

T. Yatagai, S. Nakadate, M. Idesawa, and H. Saito, “Automatic fringe analysis using digital image processing techniques,” Opt. Eng. (Bellingham) 21, 432-435 (1982).

Alessi, D.

Y. Wang, M. A. Larotonda, B. M. Luther, D. Alessi, M. Berrill, V. N. Shlyaptsev, and J. J. Rocca, “Demonstration of high-repetition-rate tabletop soft-x-ray lasers with saturated output at wavelengths down to 13.9nm and gain down to 10.9nm,” Phys. Rev. A 72, 053807 (2005).
[CrossRef]

J. J. Rocca, Y. Wang, M. A. Larotonda, B. M. Luther, M. Berrill, and D. Alessi, “Saturated 13.2nm high-repetition-rate laser in nickellike cadmium,” Opt. Lett. 30, 2581-2583 (2005).
[CrossRef] [PubMed]

Anderson, E. H.

E. H. Anderson, “Specialized electron beam nanolithography for EUV and x-ray diffractive optics,” IEEE J. Quantum Electron. 42, 27-35 (2006).
[CrossRef]

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

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

J. Heck, D. T. Attwood, W. Meyer-Ilse, and E. H. Anderson, “Resolution determination in x-ray microscopy: an analysis of the effects of partial coherence and illumination spectrum,” J. X-Ray Sci. Technol. 8, 95-104 (1998).

Attwood, D.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

D. Attwood, Soft X-Ray and Extreme Ultraviolet Radiation, Principles and Applications (Cambridge U. Press, 2000), p. 357.

Attwood, D. T.

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

J. Heck, D. T. Attwood, W. Meyer-Ilse, and E. H. Anderson, “Resolution determination in x-ray microscopy: an analysis of the effects of partial coherence and illumination spectrum,” J. X-Ray Sci. Technol. 8, 95-104 (1998).

Bartels, R.

Berrill, M.

Y. Wang, M. A. Larotonda, B. M. Luther, D. Alessi, M. Berrill, V. N. Shlyaptsev, and J. J. Rocca, “Demonstration of high-repetition-rate tabletop soft-x-ray lasers with saturated output at wavelengths down to 13.9nm and gain down to 10.9nm,” Phys. Rev. A 72, 053807 (2005).
[CrossRef]

J. J. Rocca, Y. Wang, M. A. Larotonda, B. M. Luther, M. Berrill, and D. Alessi, “Saturated 13.2nm high-repetition-rate laser in nickellike cadmium,” Opt. Lett. 30, 2581-2583 (2005).
[CrossRef] [PubMed]

Birch, J.

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

Bovik, A. C.

M. S. Pattichis and A. C. Bovik, “Analyzing image structure by multidimensional frequency modulation,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 753-766 (2007).
[CrossRef] [PubMed]

Brewer, C.

Brizuela, E.

Chao, W. L.

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

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

de Groot, J.

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

De Monvel, J. B.

H. Stollberg, J. B. De Monvel, A. Holmberg, and H. M. Hertz, “Wavelet-based image restoration for compact x-ray microscopy,” J. Microsc. 211, 154-160 (2003).
[CrossRef] [PubMed]

Denbeaux, G.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

Eriksson, F.

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

Guttmann, P.

H. Stollberg, P. Guttmann, P. A. C. Takman, and H. M. Hertz, “Size-selective colloidal-gold localization in transmission x-ray microscopy,” J. Microsc. 225, 80-87 (2007).
[CrossRef] [PubMed]

Harteneck, B.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

Harteneck, B. D.

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

Heck, J.

J. Heck, D. T. Attwood, W. Meyer-Ilse, and E. H. Anderson, “Resolution determination in x-ray microscopy: an analysis of the effects of partial coherence and illumination spectrum,” J. X-Ray Sci. Technol. 8, 95-104 (1998).

Hemberg, O.

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

Hertz, H. M.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact x-ray microscopy,” J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

H. Stollberg, P. Guttmann, P. A. C. Takman, and H. M. Hertz, “Size-selective colloidal-gold localization in transmission x-ray microscopy,” J. Microsc. 225, 80-87 (2007).
[CrossRef] [PubMed]

H. Stollberg, J. B. De Monvel, A. Holmberg, and H. M. Hertz, “Wavelet-based image restoration for compact x-ray microscopy,” J. Microsc. 211, 154-160 (2003).
[CrossRef] [PubMed]

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

Holmberg, A.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact x-ray microscopy,” J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

H. Stollberg, J. B. De Monvel, A. Holmberg, and H. M. Hertz, “Wavelet-based image restoration for compact x-ray microscopy,” J. Microsc. 211, 154-160 (2003).
[CrossRef] [PubMed]

Idesawa, M.

T. Yatagai, S. Nakadate, M. Idesawa, and H. Saito, “Automatic fringe analysis using digital image processing techniques,” Opt. Eng. (Bellingham) 21, 432-435 (1982).

Jansson, P.

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

Johansson, G. A.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact x-ray microscopy,” J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

Johnson, L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

Kemao, Q.

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007).
[CrossRef]

Larotonda, M. A.

Liddle, J. A.

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

Lindblom, M.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact x-ray microscopy,” J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

Lu, Y.

Lucero, A.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

Luther, B. M.

Marconi, M. C.

Menoni, C. S.

Merino, M. T.

J. Nunez, X. Otazu, and M. T. Merino, “A multiresolution-based method for the determination of the relative resolution between images: first application to remote sensing and medical images,” Int. J. Imaging Syst. Technol. 15, 225-235 (2005).
[CrossRef]

Meyer-Ilse, W.

J. Heck, D. T. Attwood, W. Meyer-Ilse, and E. H. Anderson, “Resolution determination in x-ray microscopy: an analysis of the effects of partial coherence and illumination spectrum,” J. X-Ray Sci. Technol. 8, 95-104 (1998).

Nakadate, S.

T. Yatagai, S. Nakadate, M. Idesawa, and H. Saito, “Automatic fringe analysis using digital image processing techniques,” Opt. Eng. (Bellingham) 21, 432-435 (1982).

Nunez, J.

J. Nunez, X. Otazu, and M. T. Merino, “A multiresolution-based method for the determination of the relative resolution between images: first application to remote sensing and medical images,” Int. J. Imaging Syst. Technol. 15, 225-235 (2005).
[CrossRef]

Olynick, D. L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

Otazu, X.

J. Nunez, X. Otazu, and M. T. Merino, “A multiresolution-based method for the determination of the relative resolution between images: first application to remote sensing and medical images,” Int. J. Imaging Syst. Technol. 15, 225-235 (2005).
[CrossRef]

Parkinson, B.

Pattichis, M. S.

M. S. Pattichis and A. C. Bovik, “Analyzing image structure by multidimensional frequency modulation,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 753-766 (2007).
[CrossRef] [PubMed]

Rehbein, S.

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

Rocca, J. J.

Saito, H.

T. Yatagai, S. Nakadate, M. Idesawa, and H. Saito, “Automatic fringe analysis using digital image processing techniques,” Opt. Eng. (Bellingham) 21, 432-435 (1982).

Shlyaptsev, V. N.

Y. Wang, M. A. Larotonda, B. M. Luther, D. Alessi, M. Berrill, V. N. Shlyaptsev, and J. J. Rocca, “Demonstration of high-repetition-rate tabletop soft-x-ray lasers with saturated output at wavelengths down to 13.9nm and gain down to 10.9nm,” Phys. Rev. A 72, 053807 (2005).
[CrossRef]

Stollberg, H.

H. Stollberg, P. Guttmann, P. A. C. Takman, and H. M. Hertz, “Size-selective colloidal-gold localization in transmission x-ray microscopy,” J. Microsc. 225, 80-87 (2007).
[CrossRef] [PubMed]

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact x-ray microscopy,” J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

H. M. Hertz, G. A. Johansson, H. Stollberg, J. de Groot, O. Hemberg, A. Holmberg, S. Rehbein, P. Jansson, F. Eriksson, and J. Birch, “Tabletop x-ray microscopy: sources, optics and applications,” J. Phys. IV 104, 115-119 (2003).

H. Stollberg, J. B. De Monvel, A. Holmberg, and H. M. Hertz, “Wavelet-based image restoration for compact x-ray microscopy,” J. Microsc. 211, 154-160 (2003).
[CrossRef] [PubMed]

Takman, P. A. C.

H. Stollberg, P. Guttmann, P. A. C. Takman, and H. M. Hertz, “Size-selective colloidal-gold localization in transmission x-ray microscopy,” J. Microsc. 225, 80-87 (2007).
[CrossRef] [PubMed]

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact x-ray microscopy,” J. Microsc. 226, 175-181 (2007).
[CrossRef] [PubMed]

Vaschenko, G.

Veklerov, E.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. L. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970-2975 (2000).
[CrossRef]

Wachulak, P.

Wang, Y.

Yatagai, T.

T. Yatagai, S. Nakadate, M. Idesawa, and H. Saito, “Automatic fringe analysis using digital image processing techniques,” Opt. Eng. (Bellingham) 21, 432-435 (1982).

IEEE J. Quantum Electron. (1)

E. H. Anderson, “Specialized electron beam nanolithography for EUV and x-ray diffractive optics,” IEEE J. Quantum Electron. 42, 27-35 (2006).
[CrossRef]

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

M. S. Pattichis and A. C. Bovik, “Analyzing image structure by multidimensional frequency modulation,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 753-766 (2007).
[CrossRef] [PubMed]

Int. J. Imaging Syst. Technol. (1)

J. Nunez, X. Otazu, and M. T. Merino, “A multiresolution-based method for the determination of the relative resolution between images: first application to remote sensing and medical images,” Int. J. Imaging Syst. Technol. 15, 225-235 (2005).
[CrossRef]

J. Microsc. (3)

H. Stollberg, J. B. De Monvel, A. Holmberg, and H. M. Hertz, “Wavelet-based image restoration for compact x-ray microscopy,” J. Microsc. 211, 154-160 (2003).
[CrossRef] [PubMed]

H. Stollberg, P. Guttmann, P. A. C. Takman, and H. M. Hertz, “Size-selective colloidal-gold localization in transmission x-ray microscopy,” J. Microsc. 225, 80-87 (2007).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

EUV microscope image of (a) 100 nm full-period grating, (c) 200 nm full-period grating, and (e) 100 nm full-period elbow-shaped grating obtained with a 13.2 nm wavelength laser illumination. (b), (d), and (f) are the corresponding SEM images of the test objects.

Fig. 2
Fig. 2

(a) EUV image of the 200 nm full-period grating. (b) Skeleton obtained from the image shown in (a). (c) Binary template generated by convolution of the skeleton image with a circle with diameter D = 50 nm .

Fig. 3
Fig. 3

Set of templates obtained applying Gaussian filters of different FWHM yielding different resolutions of δ. (a) δ = 15 , (b) δ = 45 , (c) δ = 75 , (d) δ = 105 , (e) δ = 135 , and (f) δ = 165 nm .

Fig. 4
Fig. 4

Resolution derived from the optimum Gaussian filter size as a function of the Rayleigh resolution.

Fig. 5
Fig. 5

Correlation coefficients plotted in the feature size-resolution space showing a global maximum for each of the three different images in Fig. 1. The dashed lines indicate the coordinates of the global maxima for each of the data sets: (a) 100 nm full-period grating linewidth 31 ± 5 nm and resolution 54.8 ± 5 nm ; (b) 200 nm full-period grating, linewidth 53.6 ± 5 nm , and 59.2 ± 5 nm resolution; and (c) 100 nm full-period elbow-shaped grating, linewidth 29 ± 5 nm , and 58.3 ± 5 nm resolution.

Tables (1)

Tables Icon

Table 1 Comparison of the Results in Linewidth and Image Resolution Obtained by the Correlation Algorithm with Independent Methods for Three Different Images Obtained with the EUV Microscope and 13.2 nm Illumination

Equations (11)

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c ( x m , y n ) = m M n N δ ( x x m , y y n ) c ( x , y ) ,
i b ( x , y ) = c b ( x m , y n ) p ( w x , w y ) = [ m M n N δ ( x x m , y y n ) c b ( x , y ) ] p ( w x w y ) ,
I b ( f x , f y ) = [ m M n N exp ( j 2 π ( f x x m + f y y n ) ) C b ( f x , f y ) ] sin ( π f x w x ) π f x w x sin ( π f y w y ) π f y w y ,
F ( f x , f y , w f ) = exp ( π 2 w f 2 4 ln 2 ( f x 2 + f y 2 ) ) .
T ( f x , f y ) = I b ( f x , f y ) F ( f x , f y , w f ) ,
I b ( f x , f y ) = [ m M n N exp ( j 2 π ( f x x m + f y y n ) ) C b ( f x , f y ) ] exp ( π 2 w 0 2 4 ln 2 ( f x 2 + f y 2 ) ) .
T ( f x , f y ) = [ m M n N exp ( j 2 π ( f x m w 0 + f y n w 0 ) ) C b ( f x , f y ) ] exp ( π 2 w 0 2 4 ln 2 ( f x 2 + f y 2 ) ) exp ( π 2 w f 2 4 ln 2 ( f x 2 + f y 2 ) ) .
t ( x , y ) = [ m M n N δ ( x m w 0 , y n w 0 ) C b ( x , y ) ] exp ( 4 ln 2 w 0 2 ( x 2 + y 2 ) ) exp ( 4 ln 2 w f 2 ( x 2 + y 2 ) ) .
T ( f x , f y , w 0 , w f ) = exp ( π 2 w 0 2 + w f 2 4 ln 2 ( f x 2 + f y 2 ) ) = exp ( π 2 δ 2 4 ln 2 ( f x 2 + f y 2 ) ) ,
w f ( δ ) = w 0 ( δ w 0 ) 2 1 = w 0 η 2 1 .
w f ( δ ) = w 0 ( δ w 0 r ) 2 1 = ( w 0 r ) ( η r ) 2 1 .

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