Abstract

Image formation with partially coherent radiation is evaluated with the Hopkins formula and then applied to x-ray microscopy. Image characteristics expected from instruments with circular and annular pupils in partially coherent conditions are considered for two-point objects and a knife-edge object. The theoretically expected values for image characteristics that are easy accessible by an experiment, such as the width of a knife edge, are given for various x-ray microscopes.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Meyer-Ilse, D. Attwood, M. Koike, “The X-ray Microscopy Resource Center at the Advanced Light Source,” in Proceedings of the Fourth International Conference on Biophysics and Synchrotron Radiation, B. Chance, J. Deisenhofer, S. Ebashi, D. T. Goodhead, J. R. Heliwell, H. E. Huxley, T. Iizuka, J. Kirz, T. Mitsui, E. Rubenstein, N. Sakabe, T. Sasaki, G. Schmahl, H. B. Stuhrmann, K. Wüthrich, G. Zaccai, eds. (Clarendon, London, 1994), pp. 625–636.
  2. W. Meyer-Ilse, M. Koike, R. Beguiristan, J. Maser, D. Attwood, “X-ray Microscopy Resource Center at the Advanced Light Source,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1741, 112–115 (1993).
  3. G. Schmahl, D. Rudolph, B. Niemann, O. Christ, “Zone-plate x-ray microscopy,” Q. Rev. Biophys. 13, 297–315 (1980).
    [Crossref] [PubMed]
  4. G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).
  5. C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
    [Crossref]
  6. J. Soret, “Über die durch Kreisgitter erzeugten Diffraktionsphänomene,” Ann. Phys. Chem. 156, 99–113 (1875).
  7. B. Niemann, D. Rudolph, G. Schmahl, “Soft x-ray imaging zone plates with large zone numbers for microscopic and spectroscopic applications,” Opt. Commun. 12, 160–163 (1974).
    [Crossref]
  8. C. Jacobsen, S. Lindaas, S. Williams, X. Zhang, “Scanning luminescence x-ray microscopy: imaging fluorescence dyes at sub optical resolution,” J. Microsc. 172, 121–129 (1992).
    [Crossref]
  9. A. Irtel von Brenndorff, M. M. Moronne, C. Larabell, P. Selvin, “Soft x-ray stimulated high resolution luminescence microscopy,” in X-Ray Microscopy IV, A. I. Erko, V. Aristov, eds. (Bogordski Peschatnik, Chernogolovka, Russia, 1994).
  10. B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions, photoabsorption, scattering, transmission and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
    [Crossref]
  11. C. J. R. Sheppard, T. Wilson, “On the equivalence of scanning and conventional microscopes,” Optik 73, 39–43 (1986).
  12. C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
    [Crossref]
  13. H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
    [Crossref]
  14. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).
  15. C. Jacobsen, J. Kirz, S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47, 55–79 (1992).
    [Crossref]
  16. K. K. H. Toh, “Two-dimensional images with effects of lens aberrations in optical lithography,” Memorandum University of California at Berkeley/Electronics Research Laboratory M88/30 (University of California, Berkeley, Calif., 1988).
  17. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988).

1993 (2)

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions, photoabsorption, scattering, transmission and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

1992 (2)

C. Jacobsen, S. Lindaas, S. Williams, X. Zhang, “Scanning luminescence x-ray microscopy: imaging fluorescence dyes at sub optical resolution,” J. Microsc. 172, 121–129 (1992).
[Crossref]

C. Jacobsen, J. Kirz, S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47, 55–79 (1992).
[Crossref]

1991 (1)

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

1986 (1)

C. J. R. Sheppard, T. Wilson, “On the equivalence of scanning and conventional microscopes,” Optik 73, 39–43 (1986).

1980 (1)

G. Schmahl, D. Rudolph, B. Niemann, O. Christ, “Zone-plate x-ray microscopy,” Q. Rev. Biophys. 13, 297–315 (1980).
[Crossref] [PubMed]

1977 (1)

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[Crossref]

1974 (1)

B. Niemann, D. Rudolph, G. Schmahl, “Soft x-ray imaging zone plates with large zone numbers for microscopic and spectroscopic applications,” Opt. Commun. 12, 160–163 (1974).
[Crossref]

1953 (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[Crossref]

1875 (1)

J. Soret, “Über die durch Kreisgitter erzeugten Diffraktionsphänomene,” Ann. Phys. Chem. 156, 99–113 (1875).

Anderson, E.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

Attwood, D.

W. Meyer-Ilse, D. Attwood, M. Koike, “The X-ray Microscopy Resource Center at the Advanced Light Source,” in Proceedings of the Fourth International Conference on Biophysics and Synchrotron Radiation, B. Chance, J. Deisenhofer, S. Ebashi, D. T. Goodhead, J. R. Heliwell, H. E. Huxley, T. Iizuka, J. Kirz, T. Mitsui, E. Rubenstein, N. Sakabe, T. Sasaki, G. Schmahl, H. B. Stuhrmann, K. Wüthrich, G. Zaccai, eds. (Clarendon, London, 1994), pp. 625–636.

W. Meyer-Ilse, M. Koike, R. Beguiristan, J. Maser, D. Attwood, “X-ray Microscopy Resource Center at the Advanced Light Source,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1741, 112–115 (1993).

Beguiristan, R.

W. Meyer-Ilse, M. Koike, R. Beguiristan, J. Maser, D. Attwood, “X-ray Microscopy Resource Center at the Advanced Light Source,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1741, 112–115 (1993).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

Browne, M. T.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

Buckley, C. J.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

Choudhury, A.

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[Crossref]

Christ, O.

G. Schmahl, D. Rudolph, B. Niemann, O. Christ, “Zone-plate x-ray microscopy,” Q. Rev. Biophys. 13, 297–315 (1980).
[Crossref] [PubMed]

David, C.

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

Davis, J. C.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions, photoabsorption, scattering, transmission and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

Diehl, M.

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988).

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions, photoabsorption, scattering, transmission and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

Guttmann, P.

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

Henke, B. L.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions, photoabsorption, scattering, transmission and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[Crossref]

Irtel von Brenndorff, A.

A. Irtel von Brenndorff, M. M. Moronne, C. Larabell, P. Selvin, “Soft x-ray stimulated high resolution luminescence microscopy,” in X-Ray Microscopy IV, A. I. Erko, V. Aristov, eds. (Bogordski Peschatnik, Chernogolovka, Russia, 1994).

Jacobsen, C.

C. Jacobsen, J. Kirz, S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47, 55–79 (1992).
[Crossref]

C. Jacobsen, S. Lindaas, S. Williams, X. Zhang, “Scanning luminescence x-ray microscopy: imaging fluorescence dyes at sub optical resolution,” J. Microsc. 172, 121–129 (1992).
[Crossref]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

Kern, D.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

Kirz, J.

C. Jacobsen, J. Kirz, S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47, 55–79 (1992).
[Crossref]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

Koike, M.

W. Meyer-Ilse, D. Attwood, M. Koike, “The X-ray Microscopy Resource Center at the Advanced Light Source,” in Proceedings of the Fourth International Conference on Biophysics and Synchrotron Radiation, B. Chance, J. Deisenhofer, S. Ebashi, D. T. Goodhead, J. R. Heliwell, H. E. Huxley, T. Iizuka, J. Kirz, T. Mitsui, E. Rubenstein, N. Sakabe, T. Sasaki, G. Schmahl, H. B. Stuhrmann, K. Wüthrich, G. Zaccai, eds. (Clarendon, London, 1994), pp. 625–636.

W. Meyer-Ilse, M. Koike, R. Beguiristan, J. Maser, D. Attwood, “X-ray Microscopy Resource Center at the Advanced Light Source,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1741, 112–115 (1993).

Larabell, C.

A. Irtel von Brenndorff, M. M. Moronne, C. Larabell, P. Selvin, “Soft x-ray stimulated high resolution luminescence microscopy,” in X-Ray Microscopy IV, A. I. Erko, V. Aristov, eds. (Bogordski Peschatnik, Chernogolovka, Russia, 1994).

Lindaas, S.

C. Jacobsen, S. Lindaas, S. Williams, X. Zhang, “Scanning luminescence x-ray microscopy: imaging fluorescence dyes at sub optical resolution,” J. Microsc. 172, 121–129 (1992).
[Crossref]

Maser, J.

W. Meyer-Ilse, M. Koike, R. Beguiristan, J. Maser, D. Attwood, “X-ray Microscopy Resource Center at the Advanced Light Source,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1741, 112–115 (1993).

Meyer-Ilse, W.

W. Meyer-Ilse, D. Attwood, M. Koike, “The X-ray Microscopy Resource Center at the Advanced Light Source,” in Proceedings of the Fourth International Conference on Biophysics and Synchrotron Radiation, B. Chance, J. Deisenhofer, S. Ebashi, D. T. Goodhead, J. R. Heliwell, H. E. Huxley, T. Iizuka, J. Kirz, T. Mitsui, E. Rubenstein, N. Sakabe, T. Sasaki, G. Schmahl, H. B. Stuhrmann, K. Wüthrich, G. Zaccai, eds. (Clarendon, London, 1994), pp. 625–636.

W. Meyer-Ilse, M. Koike, R. Beguiristan, J. Maser, D. Attwood, “X-ray Microscopy Resource Center at the Advanced Light Source,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1741, 112–115 (1993).

Moronne, M. M.

A. Irtel von Brenndorff, M. M. Moronne, C. Larabell, P. Selvin, “Soft x-ray stimulated high resolution luminescence microscopy,” in X-Ray Microscopy IV, A. I. Erko, V. Aristov, eds. (Bogordski Peschatnik, Chernogolovka, Russia, 1994).

Niemann, B.

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

G. Schmahl, D. Rudolph, B. Niemann, O. Christ, “Zone-plate x-ray microscopy,” Q. Rev. Biophys. 13, 297–315 (1980).
[Crossref] [PubMed]

B. Niemann, D. Rudolph, G. Schmahl, “Soft x-ray imaging zone plates with large zone numbers for microscopic and spectroscopic applications,” Opt. Commun. 12, 160–163 (1974).
[Crossref]

Rivers, M.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

Rudolph, D.

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

G. Schmahl, D. Rudolph, B. Niemann, O. Christ, “Zone-plate x-ray microscopy,” Q. Rev. Biophys. 13, 297–315 (1980).
[Crossref] [PubMed]

B. Niemann, D. Rudolph, G. Schmahl, “Soft x-ray imaging zone plates with large zone numbers for microscopic and spectroscopic applications,” Opt. Commun. 12, 160–163 (1974).
[Crossref]

Schmahl, G.

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

G. Schmahl, D. Rudolph, B. Niemann, O. Christ, “Zone-plate x-ray microscopy,” Q. Rev. Biophys. 13, 297–315 (1980).
[Crossref] [PubMed]

B. Niemann, D. Rudolph, G. Schmahl, “Soft x-ray imaging zone plates with large zone numbers for microscopic and spectroscopic applications,” Opt. Commun. 12, 160–163 (1974).
[Crossref]

Schneider, G.

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

Selvin, P.

A. Irtel von Brenndorff, M. M. Moronne, C. Larabell, P. Selvin, “Soft x-ray stimulated high resolution luminescence microscopy,” in X-Ray Microscopy IV, A. I. Erko, V. Aristov, eds. (Bogordski Peschatnik, Chernogolovka, Russia, 1994).

Sheppard, C. J. R.

C. J. R. Sheppard, T. Wilson, “On the equivalence of scanning and conventional microscopes,” Optik 73, 39–43 (1986).

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[Crossref]

Soret, J.

J. Soret, “Über die durch Kreisgitter erzeugten Diffraktionsphänomene,” Ann. Phys. Chem. 156, 99–113 (1875).

Thieme, J.

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

Toh, K. K. H.

K. K. H. Toh, “Two-dimensional images with effects of lens aberrations in optical lithography,” Memorandum University of California at Berkeley/Electronics Research Laboratory M88/30 (University of California, Berkeley, Calif., 1988).

Wilhein, T.

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

Williams, S.

C. Jacobsen, S. Lindaas, S. Williams, X. Zhang, “Scanning luminescence x-ray microscopy: imaging fluorescence dyes at sub optical resolution,” J. Microsc. 172, 121–129 (1992).
[Crossref]

C. Jacobsen, J. Kirz, S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47, 55–79 (1992).
[Crossref]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

Wilson, T.

C. J. R. Sheppard, T. Wilson, “On the equivalence of scanning and conventional microscopes,” Optik 73, 39–43 (1986).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

Zhang, X.

C. Jacobsen, S. Lindaas, S. Williams, X. Zhang, “Scanning luminescence x-ray microscopy: imaging fluorescence dyes at sub optical resolution,” J. Microsc. 172, 121–129 (1992).
[Crossref]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

Ann. Phys. Chem. (1)

J. Soret, “Über die durch Kreisgitter erzeugten Diffraktionsphänomene,” Ann. Phys. Chem. 156, 99–113 (1875).

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions, photoabsorption, scattering, transmission and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

J. Microsc. (1)

C. Jacobsen, S. Lindaas, S. Williams, X. Zhang, “Scanning luminescence x-ray microscopy: imaging fluorescence dyes at sub optical resolution,” J. Microsc. 172, 121–129 (1992).
[Crossref]

Opt. Acta (1)

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[Crossref]

Opt. Commun. (2)

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[Crossref]

B. Niemann, D. Rudolph, G. Schmahl, “Soft x-ray imaging zone plates with large zone numbers for microscopic and spectroscopic applications,” Opt. Commun. 12, 160–163 (1974).
[Crossref]

Optik (2)

G. Schmahl, D. Rudolph, B. Niemann, P. Guttmann, J. Thieme, G. Schneider, C. David, M. Diehl, T. Wilhein, “X-ray microscopy studies,” Optik 93, 95–102 (1993).

C. J. R. Sheppard, T. Wilson, “On the equivalence of scanning and conventional microscopes,” Optik 73, 39–43 (1986).

Proc. R. Soc. London Ser. A (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[Crossref]

Q. Rev. Biophys. (1)

G. Schmahl, D. Rudolph, B. Niemann, O. Christ, “Zone-plate x-ray microscopy,” Q. Rev. Biophys. 13, 297–315 (1980).
[Crossref] [PubMed]

Ultramicroscopy (1)

C. Jacobsen, J. Kirz, S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47, 55–79 (1992).
[Crossref]

Other (6)

K. K. H. Toh, “Two-dimensional images with effects of lens aberrations in optical lithography,” Memorandum University of California at Berkeley/Electronics Research Laboratory M88/30 (University of California, Berkeley, Calif., 1988).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

W. Meyer-Ilse, D. Attwood, M. Koike, “The X-ray Microscopy Resource Center at the Advanced Light Source,” in Proceedings of the Fourth International Conference on Biophysics and Synchrotron Radiation, B. Chance, J. Deisenhofer, S. Ebashi, D. T. Goodhead, J. R. Heliwell, H. E. Huxley, T. Iizuka, J. Kirz, T. Mitsui, E. Rubenstein, N. Sakabe, T. Sasaki, G. Schmahl, H. B. Stuhrmann, K. Wüthrich, G. Zaccai, eds. (Clarendon, London, 1994), pp. 625–636.

W. Meyer-Ilse, M. Koike, R. Beguiristan, J. Maser, D. Attwood, “X-ray Microscopy Resource Center at the Advanced Light Source,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1741, 112–115 (1993).

A. Irtel von Brenndorff, M. M. Moronne, C. Larabell, P. Selvin, “Soft x-ray stimulated high resolution luminescence microscopy,” in X-Ray Microscopy IV, A. I. Erko, V. Aristov, eds. (Bogordski Peschatnik, Chernogolovka, Russia, 1994).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

(a) Schematic optical layout of an XM. (b) Schematic optical layout of an SXM.

Fig. 2
Fig. 2

Image contrast of a two-point object imaged with ∊j = ∊k = 0 and coherence parameters m of 0, 0.5, 1, and infinity; d is in units of λ/NAo.

Fig. 3
Fig. 3

Influence of m on the image contrast of a two-point object for four selected point distances d imaged with circular pupils (∊j = ∊k = 0); d is in units of λ/NAo.

Fig. 4
Fig. 4

Image contrast of a two-point object versus the inverse of the point distance d (in units of λ/NA) for m = 1 and (a) ∊k = 0 for different mutual intensities (0 ≤ ∊j ≤ 0.9), (b) ∊j = 0 for different central stops on the objective lens (0 ≤ ∊k ≤ 0.9).

Fig. 5
Fig. 5

Image contrast of a two-point object for four selected point distances d imaged with m = 1: (a) ∊k = 0, different mutual intensities (0 ≤ ∊j ≤ 0.9); (b) ∊j = 0, different central stops on the objective lens (0 ≤ ∊k ≤ 0.9).

Fig. 6
Fig. 6

Distance L between two points that form an image with 15.3% contrast as a function of the coherence parameter m at (a) ∊k = 0, different mutual intensities (0 ≤ ∊j ≤ 0.9), (b) ∊j = 0, different central stops on the objective lens (0 ≤ ∊k ≤ 0.9).

Fig. 7
Fig. 7

Response from imaging an edge with partially coherent light and the differentiated response at (a) m = 0.54, ∊j = 0.33, and ∊k = 0 (same as XM-1, 30 nm in Table 1); (b) m = 1, ∊j = 0, and ∊k = 0.45 (same as SXM in Table 1).

Fig. 8
Fig. 8

Point images for the parameters in Fig. 7(a) (m = 0.54, ∊j = 0.33, and ∊k = 0, continuous curve) and Fig. 7(b) (m = 1, ∊j = 0, and ∊k = 0.45, dashed curve).

Tables (1)

Tables Icon

Table 1 Image Characteristics of a Knife-Edge Object and a Two-Point Object for Different Optical Setups

Equations (5)

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

I ( x 1 , y 1 ) = - - - - J ( x 0 - x 0 , y 0 - y 0 ) × F ( x 0 , y 0 ) F * ( x 0 , y 0 ) K ( x 1 - x 0 , y 1 - y 0 ) × K * ( x 1 - x 0 , y 1 - y 0 ) d x 0 d y 0 d x 0 d y 0 .
K ( x , y ) = 2 ( 1 - k 2 ) [ J 1 ( ν ) ν - k J 1 ( k ν ) ν ]             with ν = 2 π ( x 2 + y 2 ) 1 / 2 .
J ( x , y ) = 2 ( 1 - j 2 ) [ J 1 ( m ν ) m ν - j J 1 ( j m ν ) m ν ]             with ν = 2 π ( x 2 + y 2 ) 1 / 2 ,
m = λ o / NA o λ c / NA c ,
F ( x , y ) = δ ( - ½ d - x , y ) + δ ( ½ d - x , y ) .

Metrics