Abstract

Expressions are obtained for the three-dimensional intensity distribution in the error-free diffraction patterns of semitransparent and phase annuli. The results are discussed and illustrated graphically. Annular apertures have been used for improving the resolving power and focal depth of optical instruments; the most useful situation for a given central-obstruction ratio is where the central obstruction is completely opaque. However, by use of a phase annulus of the same dimension, with a phase step of π for the central region, some further improvement in the resolving power and focal depth is obtained for central-obstruction ratios up to 0.5. This improvement is illustrated experimentally.

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Boivin, A.

A. Boivin, J. Opt. Soc. Am. 42, 60 (1952).

Bouché, E. L.

E. L. Bouché and P. F. Kellen, J. Opt. Soc. Am. 53, 1350A (1963).

Dekanosidze, E. N.

E. N. Dekanosidze, Tables of Lommel's Functions of Two Variables (Pergamon Press, Inc., New York, 1960).

di Francia, G. Toraldo

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).

Dossier, B.

B. Dossier, Rev. Opt. 33, 57, 147, 267 (1954).

Kellen, P. F.

E. L. Bouché and P. F. Kellen, J. Opt. Soc. Am. 53, 1350A (1963).

Lansraux, G.

G. Lansraux, Rev Opt. 32, 475 (1953).

Linfoot, E. H.

E. H. Linfoot and E. Wolf, proc. phys. Soc. (London) B66, 145 (1953).

Rayleigh, Lord

Lord Rayleigh, Monthly Not. Roy. Astron. Soc. 33, 59 (1872) [reprinted in Sci. Papers 1, 163 (1964)].

Steel, W. H.

W. H. Steel, Rev. Opt. 32, 4 (1953).

Steward, G. C.

G. C. Steward, Phil Trans. Roy. Soc. (London) A225, 131 (1925).

Taylor, C. A.

C. A. Taylor and B. J. Thompson, J. Opt. Soc. Am. 48, 844 (1958).

Thompson, B. J.

C. A. Taylor and B. J. Thompson, J. Opt. Soc. Am. 48, 844 (1958).

Von Lommel, E.

E. Von Lommel, Abhandl. Bayer. Akad. 53, 233 (1885).

Welford, W. T.

W. T. Welford, J. Opt. Soc. Am. 50, 749 (1960).

Wolf, E.

E. H. Linfoot and E. Wolf, proc. phys. Soc. (London) B66, 145 (1953).

Other (13)

Lord Rayleigh, Monthly Not. Roy. Astron. Soc. 33, 59 (1872) [reprinted in Sci. Papers 1, 163 (1964)].

G. C. Steward, Phil Trans. Roy. Soc. (London) A225, 131 (1925).

E. H. Linfoot and E. Wolf, proc. phys. Soc. (London) B66, 145 (1953).

W. H. Steel, Rev. Opt. 32, 4 (1953).

C. A. Taylor and B. J. Thompson, J. Opt. Soc. Am. 48, 844 (1958).

W. T. Welford, J. Opt. Soc. Am. 50, 749 (1960).

G. Lansraux, Rev Opt. 32, 475 (1953).

B. Dossier, Rev. Opt. 33, 57, 147, 267 (1954).

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).

E. L. Bouché and P. F. Kellen, J. Opt. Soc. Am. 53, 1350A (1963).

E. Von Lommel, Abhandl. Bayer. Akad. 53, 233 (1885).

E. N. Dekanosidze, Tables of Lommel's Functions of Two Variables (Pergamon Press, Inc., New York, 1960).

A. Boivin, J. Opt. Soc. Am. 42, 60 (1952).

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