Abstract

We discuss an extension of our previous research that uses image-plane optical masks to achieve superresolution in confocal scanning microscopy to the coherent optics of digital versatile disc readers. The theory and the design of superresolving optics for such high-numerical-aperture scanning coherent imaging systems is presented. A superresolving optical reader would permit superdense optical data storage, giving an improvement over the equivalent conventional storage densities by at least a factor of 2.

© 2000 Optical Society of America

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References

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  1. T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).
  2. G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schoumaker-Immink, Principles of Optical Disc Systems (Adam Hilger, Boston, 1985).
  3. M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 2, 727–746 (1982).
    [CrossRef]
  4. M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
    [CrossRef]
  5. M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
    [CrossRef]
  6. M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV. The case of uncertain localisation or nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
    [CrossRef]
  7. J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British patent89/13129 (6July1989).
  8. M. Bertero, P. Boccacci, R. E. Davies, F. Malfanti, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks,” Inverse Probl. 8, 1–23 (1992).
    [CrossRef]
  9. R. E. Davies, “Inverse problems in confocal scanning microscopy,” Ph.D. dissertation (Department of Physics, King’s College, University of London, 1990).
  10. M. R. Young, S. H. Jiang, R. E. Davies, J. G. Walker, E. R. Pike, M. Bertero, “Experimental confirmation of superresolution in confocal scanning microscopy using holographic masks,” J. Microsc. 165, 131–138 (1992).
    [CrossRef]
  11. J. Grochmalicki, E. R. Pike, J. G. Walker, “Experimental confirmation of super-resolution in incoherent scanning microscopy,” J. Eur. Opt. Soc. A Pure Appl. Opt. 2, 565–568 (1993).
    [CrossRef]
  12. I. Akduman, U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, “Superresolving masks for incoherent high-numerical-aperture scanning microscopy in three dimensions,” J. Opt. Soc. Am. A 15, 2275–2287 (1998).
    [CrossRef]
  13. U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, M. Bertero, “Superresolution in optical data storage,” J. Opt. A Pure Appl. Opt. 1, 794–800 (1999).
    [CrossRef]
  14. H. H. Hopkins, “The Airy disc formula for systems of high relative aperture,” Proc. R. Soc. London 69, 116–128 (1943).
  15. C. Sheppard, T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. London A 379, 145–158 (1982).
    [CrossRef]
  16. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  17. V. S. Ignatowsky, “Diffraction by an objective lens with arbitrary aperture,” Trans. Opt. Inst. Petrograd I(IV), 1–36 (1921) (in Russian).
  18. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
    [CrossRef]
  19. J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Boston, 1986).
  20. C. J. R. Sheppard, A. Choudhury, J. Gannaway, “Electromagnetic field near the focus of wide-angular lens and mirror systems,” Microwaves Opt. Acoust. 1, 129–132 (1977).
    [CrossRef]
  21. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  22. J. G. Dil, B. A. J. Jacobs, “Apparent size of reflecting obstacles of the order of one wavelength,” J. Opt. Soc. Am. 69, 950–960 (1979).
    [CrossRef]

1999 (1)

U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, M. Bertero, “Superresolution in optical data storage,” J. Opt. A Pure Appl. Opt. 1, 794–800 (1999).
[CrossRef]

1998 (1)

1993 (1)

J. Grochmalicki, E. R. Pike, J. G. Walker, “Experimental confirmation of super-resolution in incoherent scanning microscopy,” J. Eur. Opt. Soc. A Pure Appl. Opt. 2, 565–568 (1993).
[CrossRef]

1992 (2)

M. Bertero, P. Boccacci, R. E. Davies, F. Malfanti, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks,” Inverse Probl. 8, 1–23 (1992).
[CrossRef]

M. R. Young, S. H. Jiang, R. E. Davies, J. G. Walker, E. R. Pike, M. Bertero, “Experimental confirmation of superresolution in confocal scanning microscopy using holographic masks,” J. Microsc. 165, 131–138 (1992).
[CrossRef]

1984 (2)

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV. The case of uncertain localisation or nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

1982 (3)

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 2, 727–746 (1982).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

C. Sheppard, T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. London A 379, 145–158 (1982).
[CrossRef]

1979 (1)

1977 (1)

C. J. R. Sheppard, A. Choudhury, J. Gannaway, “Electromagnetic field near the focus of wide-angular lens and mirror systems,” Microwaves Opt. Acoust. 1, 129–132 (1977).
[CrossRef]

1959 (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

1943 (1)

H. H. Hopkins, “The Airy disc formula for systems of high relative aperture,” Proc. R. Soc. London 69, 116–128 (1943).

1921 (1)

V. S. Ignatowsky, “Diffraction by an objective lens with arbitrary aperture,” Trans. Opt. Inst. Petrograd I(IV), 1–36 (1921) (in Russian).

Akduman, I.

Bertero, M.

U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, M. Bertero, “Superresolution in optical data storage,” J. Opt. A Pure Appl. Opt. 1, 794–800 (1999).
[CrossRef]

M. Bertero, P. Boccacci, R. E. Davies, F. Malfanti, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks,” Inverse Probl. 8, 1–23 (1992).
[CrossRef]

M. R. Young, S. H. Jiang, R. E. Davies, J. G. Walker, E. R. Pike, M. Bertero, “Experimental confirmation of superresolution in confocal scanning microscopy using holographic masks,” J. Microsc. 165, 131–138 (1992).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV. The case of uncertain localisation or nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 2, 727–746 (1982).
[CrossRef]

J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British patent89/13129 (6July1989).

Boccacci, P.

M. Bertero, P. Boccacci, R. E. Davies, F. Malfanti, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks,” Inverse Probl. 8, 1–23 (1992).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

Bouwhuis, G.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schoumaker-Immink, Principles of Optical Disc Systems (Adam Hilger, Boston, 1985).

Braat, J.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schoumaker-Immink, Principles of Optical Disc Systems (Adam Hilger, Boston, 1985).

Brand, U.

U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, M. Bertero, “Superresolution in optical data storage,” J. Opt. A Pure Appl. Opt. 1, 794–800 (1999).
[CrossRef]

I. Akduman, U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, “Superresolving masks for incoherent high-numerical-aperture scanning microscopy in three dimensions,” J. Opt. Soc. Am. A 15, 2275–2287 (1998).
[CrossRef]

Brianzi, P.

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

Choudhury, A.

C. J. R. Sheppard, A. Choudhury, J. Gannaway, “Electromagnetic field near the focus of wide-angular lens and mirror systems,” Microwaves Opt. Acoust. 1, 129–132 (1977).
[CrossRef]

Davies, R. E.

M. Bertero, P. Boccacci, R. E. Davies, F. Malfanti, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks,” Inverse Probl. 8, 1–23 (1992).
[CrossRef]

M. R. Young, S. H. Jiang, R. E. Davies, J. G. Walker, E. R. Pike, M. Bertero, “Experimental confirmation of superresolution in confocal scanning microscopy using holographic masks,” J. Microsc. 165, 131–138 (1992).
[CrossRef]

R. E. Davies, “Inverse problems in confocal scanning microscopy,” Ph.D. dissertation (Department of Physics, King’s College, University of London, 1990).

De Mol, C.

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV. The case of uncertain localisation or nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

Dil, J. G.

Gannaway, J.

C. J. R. Sheppard, A. Choudhury, J. Gannaway, “Electromagnetic field near the focus of wide-angular lens and mirror systems,” Microwaves Opt. Acoust. 1, 129–132 (1977).
[CrossRef]

Grochmalicki, J.

U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, M. Bertero, “Superresolution in optical data storage,” J. Opt. A Pure Appl. Opt. 1, 794–800 (1999).
[CrossRef]

I. Akduman, U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, “Superresolving masks for incoherent high-numerical-aperture scanning microscopy in three dimensions,” J. Opt. Soc. Am. A 15, 2275–2287 (1998).
[CrossRef]

J. Grochmalicki, E. R. Pike, J. G. Walker, “Experimental confirmation of super-resolution in incoherent scanning microscopy,” J. Eur. Opt. Soc. A Pure Appl. Opt. 2, 565–568 (1993).
[CrossRef]

Hester, G.

U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, M. Bertero, “Superresolution in optical data storage,” J. Opt. A Pure Appl. Opt. 1, 794–800 (1999).
[CrossRef]

I. Akduman, U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, “Superresolving masks for incoherent high-numerical-aperture scanning microscopy in three dimensions,” J. Opt. Soc. Am. A 15, 2275–2287 (1998).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, “The Airy disc formula for systems of high relative aperture,” Proc. R. Soc. London 69, 116–128 (1943).

Huijser, A.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schoumaker-Immink, Principles of Optical Disc Systems (Adam Hilger, Boston, 1985).

Ignatowsky, V. S.

V. S. Ignatowsky, “Diffraction by an objective lens with arbitrary aperture,” Trans. Opt. Inst. Petrograd I(IV), 1–36 (1921) (in Russian).

Jacobs, B. A. J.

Jiang, S. H.

M. R. Young, S. H. Jiang, R. E. Davies, J. G. Walker, E. R. Pike, M. Bertero, “Experimental confirmation of superresolution in confocal scanning microscopy using holographic masks,” J. Microsc. 165, 131–138 (1992).
[CrossRef]

Malfanti, F.

M. Bertero, P. Boccacci, R. E. Davies, F. Malfanti, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks,” Inverse Probl. 8, 1–23 (1992).
[CrossRef]

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

Parker, P.

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

Pasman, J.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schoumaker-Immink, Principles of Optical Disc Systems (Adam Hilger, Boston, 1985).

Pike, E. R.

U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, M. Bertero, “Superresolution in optical data storage,” J. Opt. A Pure Appl. Opt. 1, 794–800 (1999).
[CrossRef]

I. Akduman, U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, “Superresolving masks for incoherent high-numerical-aperture scanning microscopy in three dimensions,” J. Opt. Soc. Am. A 15, 2275–2287 (1998).
[CrossRef]

J. Grochmalicki, E. R. Pike, J. G. Walker, “Experimental confirmation of super-resolution in incoherent scanning microscopy,” J. Eur. Opt. Soc. A Pure Appl. Opt. 2, 565–568 (1993).
[CrossRef]

M. Bertero, P. Boccacci, R. E. Davies, F. Malfanti, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks,” Inverse Probl. 8, 1–23 (1992).
[CrossRef]

M. R. Young, S. H. Jiang, R. E. Davies, J. G. Walker, E. R. Pike, M. Bertero, “Experimental confirmation of superresolution in confocal scanning microscopy using holographic masks,” J. Microsc. 165, 131–138 (1992).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV. The case of uncertain localisation or nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 2, 727–746 (1982).
[CrossRef]

J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British patent89/13129 (6July1989).

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

Schoumaker-Immink, K.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schoumaker-Immink, Principles of Optical Disc Systems (Adam Hilger, Boston, 1985).

Sheppard, C.

C. Sheppard, T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. London A 379, 145–158 (1982).
[CrossRef]

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

Sheppard, C. J. R.

C. J. R. Sheppard, A. Choudhury, J. Gannaway, “Electromagnetic field near the focus of wide-angular lens and mirror systems,” Microwaves Opt. Acoust. 1, 129–132 (1977).
[CrossRef]

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Boston, 1986).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

van Rosmalen, G.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schoumaker-Immink, Principles of Optical Disc Systems (Adam Hilger, Boston, 1985).

Walker, J. G.

J. Grochmalicki, E. R. Pike, J. G. Walker, “Experimental confirmation of super-resolution in incoherent scanning microscopy,” J. Eur. Opt. Soc. A Pure Appl. Opt. 2, 565–568 (1993).
[CrossRef]

M. R. Young, S. H. Jiang, R. E. Davies, J. G. Walker, E. R. Pike, M. Bertero, “Experimental confirmation of superresolution in confocal scanning microscopy using holographic masks,” J. Microsc. 165, 131–138 (1992).
[CrossRef]

M. Bertero, P. Boccacci, R. E. Davies, F. Malfanti, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks,” Inverse Probl. 8, 1–23 (1992).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV. The case of uncertain localisation or nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British patent89/13129 (6July1989).

Wilson, T.

C. Sheppard, T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. London A 379, 145–158 (1982).
[CrossRef]

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

Wolf, E.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

Young, M. R.

M. R. Young, S. H. Jiang, R. E. Davies, J. G. Walker, E. R. Pike, M. Bertero, “Experimental confirmation of superresolution in confocal scanning microscopy using holographic masks,” J. Microsc. 165, 131–138 (1992).
[CrossRef]

Inverse Probl. (1)

M. Bertero, P. Boccacci, R. E. Davies, F. Malfanti, E. R. Pike, J. G. Walker, “Superresolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks,” Inverse Probl. 8, 1–23 (1992).
[CrossRef]

J. Eur. Opt. Soc. A Pure Appl. Opt. (1)

J. Grochmalicki, E. R. Pike, J. G. Walker, “Experimental confirmation of super-resolution in incoherent scanning microscopy,” J. Eur. Opt. Soc. A Pure Appl. Opt. 2, 565–568 (1993).
[CrossRef]

J. Microsc. (1)

M. R. Young, S. H. Jiang, R. E. Davies, J. G. Walker, E. R. Pike, M. Bertero, “Experimental confirmation of superresolution in confocal scanning microscopy using holographic masks,” J. Microsc. 165, 131–138 (1992).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

U. Brand, J. Grochmalicki, G. Hester, E. R. Pike, M. Bertero, “Superresolution in optical data storage,” J. Opt. A Pure Appl. Opt. 1, 794–800 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Microwaves Opt. Acoust. (1)

C. J. R. Sheppard, A. Choudhury, J. Gannaway, “Electromagnetic field near the focus of wide-angular lens and mirror systems,” Microwaves Opt. Acoust. 1, 129–132 (1977).
[CrossRef]

Opt. Acta (4)

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination,” Opt. Acta 2, 727–746 (1982).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

M. Bertero, P. Brianzi, P. Parker, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis: III. The effect of sampling and truncation of the data,” Opt. Acta 31, 181–201 (1984).
[CrossRef]

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis: IV. The case of uncertain localisation or nonuniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[CrossRef]

Proc. R. Soc. London (1)

H. H. Hopkins, “The Airy disc formula for systems of high relative aperture,” Proc. R. Soc. London 69, 116–128 (1943).

Proc. R. Soc. London A (2)

C. Sheppard, T. Wilson, “The image of a single point in microscopes of large numerical aperture,” Proc. R. Soc. London A 379, 145–158 (1982).
[CrossRef]

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

Trans. Opt. Inst. Petrograd (1)

V. S. Ignatowsky, “Diffraction by an objective lens with arbitrary aperture,” Trans. Opt. Inst. Petrograd I(IV), 1–36 (1921) (in Russian).

Other (7)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

J. G. Walker, E. R. Pike, M. Bertero, “Scanning optical microscope,” British patent89/13129 (6July1989).

R. E. Davies, “Inverse problems in confocal scanning microscopy,” Ph.D. dissertation (Department of Physics, King’s College, University of London, 1990).

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. Schoumaker-Immink, Principles of Optical Disc Systems (Adam Hilger, Boston, 1985).

J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Boston, 1986).

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

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Figures (5)

Fig. 1
Fig. 1

Images of the vector-kernel functions for a NA of 0.6. The notations e i denote the components of E 0, and notations g i denote the components of the first row of the matrix K.

Fig. 2
Fig. 2

Singular spectrum for the images of Fig. 1. with a NA of 0.6.

Fig. 3
Fig. 3

Image (Fig. 1) singular functions for a NA of 0.6 for k = 1, 2, 3, 4, 10, 20 corresponding to the v k of Eqs. (4.1) (see text).

Fig. 4
Fig. 4

Optical masks calculated for higher and higher superresolution from 4, 10, and 20 singular functions.

Fig. 5
Fig. 5

Test specimens (a) 1 and (b) 2.

Equations (36)

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

NA=n sin α,
E1=p-p · rr
E1=p · nn+p · gg,
E2=p · nn+p · gh.
r=sin θ cos ϕ, sin θ sin ϕ, cos θ,
k=0, 0, 1,
n=sin ϕ, -cos ϕ, 0,
g=cos θ cos ϕ, cos θ sin ϕ, -sin θ,
h=cos ϕ, sin ϕ, 0.
E2x=pxcos θ cos2 ϕ+sin2 ϕ+pycos θ-1sin ϕ cos ϕ-pz sin θ cos ϕ,
E2y=pxcos θ-1sin ϕ cos ϕ+pycos θ sin2 ϕ+cos2 ϕ-pz sin θ sin ϕ,
E3ρi  SE2θ, ϕcos θ1/2 exp-ikn · ρids,
n · ρi=ρi cosϕ-ϕisin θ.
E3vi, ϕi  02πdϕ 0αdθE2θ, ϕsin θcos θ1/2×exp-ivi cosϕ-ϕisin θsin α,
02πdβ cos β expit cosβ-γ=2πiJ1tcos γ,
02πdβ sin β expit cosβ-γ=2πiJ1tsin γ,
02πdβ sin β cos β expit cosβ-γ=-πJ2tsin 2γ,
02πdβ cos2 β expit cosβ-γ=πJ0t-πJ2tcos 2γ,
02πdβ sin2 β expit cosβ-γ=πJ0t+πJ2tcos 2γ.
I0q; α=0αdθcos θ1/2sin θ1+cos θJ0q sin θsin α,
I1q; α=0αdθcos θ1/2 sin2 θ J1q sin θsin α,
I2q; α=0αdθcos θ1/2 sin θ1-cos θJ2q sin θsin α.
E3x=pxI0+cos 2ϕiI2+py sin 2ϕiI2-2ipz cos ϕiI1,
E3y=px sin 2ϕiI2+pyI0-cos 2ϕiI2-2ipz sin ϕiI1,
K=I0+cos 2ϕiI2sin 2ϕiI2-2i cos ϕiI1sin 2ϕiI2I0-cos 2ϕiI2-2i sin ϕiI1,
E3vi, ϕi=Kvi, ϕip.
g=K * E0f,
E0=ExI0+cos 2ϕ0I2+Ey sin 2ϕ0I2Ex sin 2ϕ0I2+EyI0-cos 2ϕ0I2-2iI1Ex cos ϕ0+Ey sin ϕ0,
Auk=αkvk,  A*vk=αkuk,
f0=k=0L-11αkvk, guk0,
vk, g= vk*vgvdv.
f0= Mvgvdv,
Mv=k=0L-11αk vk*vuk0.
g=m=13 Km * Emf,
hx, y=n,m hnΔ, mΔsincΩx-nΔ×sincΩy-mΔ,
gmΔ=Δ n fnΔgm-nΔ,

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