Abstract

The zone plate is an optical device that depends on interference, not reflection or refraction, for its image-forming properties. Although the irradiance at the focus is only 110 that of a lens with the same aperture, a zone plate with 100 or more zones is capable of resolution equal to that of the lens. Zone plates can be used in spectral regions where conventional optics are unavailable and for special applications in the visible spectrum. This paper derives the third-order and chromatic aberrations of the zone plate. The image may be diffraction limited only if the illumination is relatively monochromatic. Like the pinhole camera, the zone plate turns out not to suffer from linear distortion, even at very wide fields.

© 1972 Optical Society of America

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References

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  1. M. Young, Appl. Opt. 10, 2763 (1971), and Refs. 2–6 therein.
    [Crossref] [PubMed]
  2. M. Young, Am. J. Phys. 40, 715 (1972).
    [Crossref]
  3. P. A. Newman and V. E. Rible, Appl. Opt. 5, 1226 (1966).
  4. H. Dammann and K. Görtler, Opt. Commun. 3, 312 (1971).
    [Crossref]
  5. G. Groh, Appl. Opt. 7, 1643 (1968).
    [Crossref] [PubMed]
  6. A. V. Baez, J. Opt. Soc. Am. 51, 405 (1961).
    [Crossref]
  7. W. G. Ferrier, Contemp. Phys. 10, 413 (1969).
    [Crossref]
  8. R. W. Wood, Physical Optics (Dover, New York, 1957), pp. 37–39.
  9. O. E. Myers, Am. J. Phys. 19, 359 (1951).
    [Crossref]
  10. C. L. Miles, Appl. Opt. 7, 976 (1968).
    [Crossref] [PubMed]
  11. H. H. M. Chau, Appl. Opt. 8, 1209 (1969).
    [Crossref] [PubMed]
  12. F. A. Jenkins and H. E. White, Fundamentals of Optics, 3rd ed. (McGraw-Hill, New York, 1957), pp. 360–361.
  13. This point seems to have been overlooked in Ref. 9. Similarly, Ref. 14 treated only the geometric zone plate.
  14. K. Kamiya, Sci. Light (Tokyo) 12, 35 (1963).
  15. A. Boivin, J. Opt. Soc. Am. 42, 60 (1952).
    [Crossref]
  16. M. Sussman, Am. J. Phys. 28, 394 (1960).
    [Crossref]
  17. M. Bottema, J. Opt. Soc. Am. 59, 1632 (1969).
    [Crossref]
  18. D. J. Stigliani, R. Mittra, and R. G. Semonin, J. Opt. Soc. Am. 57, 610 (1967).
    [Crossref]
  19. J. N. Latta, Appl. Opt. 10, 599 (1971).
    [Crossref] [PubMed]
  20. E. B. Champagne, J. Opt. Soc. Am. 57, 51 (1967).
    [Crossref]
  21. R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).
    [Crossref]
  22. L. C. Martin, Technical Optics, Vol. 1 (Pitman, London, 1948), Ch. IV.

1972 (1)

M. Young, Am. J. Phys. 40, 715 (1972).
[Crossref]

1971 (3)

1969 (3)

1968 (2)

1967 (2)

1966 (1)

P. A. Newman and V. E. Rible, Appl. Opt. 5, 1226 (1966).

1965 (1)

1963 (1)

K. Kamiya, Sci. Light (Tokyo) 12, 35 (1963).

1961 (1)

1960 (1)

M. Sussman, Am. J. Phys. 28, 394 (1960).
[Crossref]

1952 (1)

1951 (1)

O. E. Myers, Am. J. Phys. 19, 359 (1951).
[Crossref]

Baez, A. V.

Boivin, A.

Bottema, M.

Champagne, E. B.

Chau, H. H. M.

Dammann, H.

H. Dammann and K. Görtler, Opt. Commun. 3, 312 (1971).
[Crossref]

Ferrier, W. G.

W. G. Ferrier, Contemp. Phys. 10, 413 (1969).
[Crossref]

Görtler, K.

H. Dammann and K. Görtler, Opt. Commun. 3, 312 (1971).
[Crossref]

Groh, G.

Jenkins, F. A.

F. A. Jenkins and H. E. White, Fundamentals of Optics, 3rd ed. (McGraw-Hill, New York, 1957), pp. 360–361.

Kamiya, K.

K. Kamiya, Sci. Light (Tokyo) 12, 35 (1963).

Latta, J. N.

Martin, L. C.

L. C. Martin, Technical Optics, Vol. 1 (Pitman, London, 1948), Ch. IV.

Meier, R. W.

Miles, C. L.

Mittra, R.

Myers, O. E.

O. E. Myers, Am. J. Phys. 19, 359 (1951).
[Crossref]

Newman, P. A.

P. A. Newman and V. E. Rible, Appl. Opt. 5, 1226 (1966).

Rible, V. E.

P. A. Newman and V. E. Rible, Appl. Opt. 5, 1226 (1966).

Semonin, R. G.

Stigliani, D. J.

Sussman, M.

M. Sussman, Am. J. Phys. 28, 394 (1960).
[Crossref]

White, H. E.

F. A. Jenkins and H. E. White, Fundamentals of Optics, 3rd ed. (McGraw-Hill, New York, 1957), pp. 360–361.

Wood, R. W.

R. W. Wood, Physical Optics (Dover, New York, 1957), pp. 37–39.

Young, M.

Am. J. Phys. (3)

M. Young, Am. J. Phys. 40, 715 (1972).
[Crossref]

O. E. Myers, Am. J. Phys. 19, 359 (1951).
[Crossref]

M. Sussman, Am. J. Phys. 28, 394 (1960).
[Crossref]

Appl. Opt. (6)

Contemp. Phys. (1)

W. G. Ferrier, Contemp. Phys. 10, 413 (1969).
[Crossref]

J. Opt. Soc. Am. (6)

Opt. Commun. (1)

H. Dammann and K. Görtler, Opt. Commun. 3, 312 (1971).
[Crossref]

Sci. Light (Tokyo) (1)

K. Kamiya, Sci. Light (Tokyo) 12, 35 (1963).

Other (4)

R. W. Wood, Physical Optics (Dover, New York, 1957), pp. 37–39.

L. C. Martin, Technical Optics, Vol. 1 (Pitman, London, 1948), Ch. IV.

F. A. Jenkins and H. E. White, Fundamentals of Optics, 3rd ed. (McGraw-Hill, New York, 1957), pp. 360–361.

This point seems to have been overlooked in Ref. 9. Similarly, Ref. 14 treated only the geometric zone plate.

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Figures (2)

Fig. 1
Fig. 1

A zone plate with radius rn illuminated with parallel light. f is the focal length and F the optical path of a marginal ray through the focal point.

Fig. 2
Fig. 2

As in Fig. 1, with the illumination incident at angle α to the zone-plate axis.

Equations (23)

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r n = ( n λ f + n 2 λ 2 / 4 ) 1 2 .
r n ( n λ f ) 1 2 ,
OPD = ( f 2 + r n 2 ) 1 2 - f
= ( r n 2 / 2 f ) - ( r n 4 / 8 f 3 ) + .
4 n 2 I 0 / ( 2 k + 1 ) π 2 .
OPD = ( n λ / 2 ) + r n 4 / 8 f 3
n 2 = 2 f / λ
n λ / 2 = ( n λ / 2 ) ± λ / 4 ,
n λ / Δ λ ,
1 / f = ( 1 / f 1 ) + ( 1 / f 2 ) - ( d / f 1 f 2 )
d = f 1 + f 2 1 + λ / λ .
OPD = r n sin α + f [ 1 + ( tan α - r n / f ) 2 ] 1 2 - f [ 1 + tan 2 α ] 1 2 ,
OPD = r n 2 / 2 f - r n 4 / 8 f 3 + r n 3 α / 2 f 2 - 3 r n 2 α 2 / 4 f .
r n 3 α / 2 f 2 - 3 r n 2 α 2 / 4 f .
α = ( 3 n ) - 1 2
α = ( n λ / f ) - 1 2 ( 1 / 2 n )
OPD = r n 2 / 2 f - r n 4 / 8 f 3 + r n 3 α / 2 f 2 - r n 2 α 2 / 2 f .
+ 3 r n 4 ( q - f ) / 8 f 2 q 2 = 3 8 ( n λ / q ) 2 ( q - f ) ,
( r n 3 α 2 ) ( 1 q 2 - 1 p 2 ) cos ϕ             ( coma ) ,
- ( r n 2 α 2 / 2 f ) cos 2 ϕ             ( astigmatism ) ,
- ( r n 2 α 2 / 4 f )             ( field curvature ) .
( 1 + x 2 ) 1 2 = 1 + x 2 / 2 - x 4 / 8 ,
- r n ( tan α - sin α ) + r n 3 tan α / 2 f 2 - 3 r n 2 tan 2 α / 4 f + r n tan 3 α / 2.