Abstract

Phase-reversal zone plates can be designed even for regions of the electromagnetic spectrum where the index of refraction is complex, with a real part close to 1.0. These devices are superior to Fresnel zone plates both in their light collection, and in their signal-to-noise characteristics. Materials with suitable optical and mechanical properties exist throughout most of the 1–800-Å wavelength range for their construction. Imperfections in fabrication, such as incorrect plate thickness, sloping zone edges, or an error in the width of alternate zones result in only moderate deterioration in optical performance.

© 1974 Optical Society of America

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  1. J. L. Soret, Arch. Sci. Phys. Nat. 52, 320 (1875). According to Wood, the first Fresnel zone plate was made by Lord Rayleigh in 1871, but this work was never published [see R. W. Wood, Physical Optics, 3rd ed. (Macmillan, New York, 1934), p. 37].
  2. Rayleigh, Wave Theory, in Encyclopedia Britannica, 9th ed., Vol. 24, 429 (1888).
  3. R. W. Wood, Philos. Mag. 45, 511 (1898).
  4. Ora E. Myers, Am. J. Phys. 19, 359 (1951).
    [Crossref]
  5. A. V. Baez, J. Opt. Soc. Am. 42, 756 (1952); J. Opt. Soc. Am. 51, 405 (1961).
    [Crossref]
  6. D. C. Pfeifer, L. D. Ferris, and W. M. Yen, J. Opt. Soc. Am. 63, 91 (1973).
    [Crossref]
  7. H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
    [Crossref]
  8. (a)D. Rudolph and G. Schmahl, in Symposium on New Techniques in Space Astronomy, edited by F. Labuhn and R. Lust, International Astronomical Union Symposium (Reidel, Dordrecht, Netherland, 1971), Vol. 41, p. 205; (b)J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Ref. 8 (a), p. 207.
  9. P. N. Keating, R. K. Mueller, and T. Sawatari, J. Opt. Soc. Am. 62, 945 (1972).
    [Crossref]
  10. G. Elwert and J. V. Feitzinger, Optik 31, 600 (1970); H. H. Fink, Optik 31, 150 (1970).
  11. G. Schmahl and D. Rudolph, Optik 29, 577 (1969). There appears to be a typographic error in Eq. (2) of this paper. The second term in the numerator should be n2λH2(3ξη+ξ2+η2)/4.
  12. M. Young, J. Opt. Soc. Am. 62, 972 (1972).
    [Crossref]
  13. D. J. Stigliani, R. Mittra, and R. G. Semonin, J. Opt. Soc. Am. 57, 610 (1967).
    [Crossref]
  14. M. H. Horman, Appl. Opt. 6, 2011 (1967). There appears to be an error in this paper concerning the “Gabor phase zone plate”: The fluxes for that device are given correctly in Ref. 15.
    [Crossref] [PubMed]
  15. H. Dammann, Optik 31, 95 (1970).
  16. H. H. M. Chau, Appl. Opt. 8, 1209 (1969).
    [Crossref] [PubMed]
  17. E. Champagne, Appl. Opt. 7, 381 (1968).
    [Crossref] [PubMed]
  18. G. S. Waldman, J. Opt. Soc. Am. 56, 215 (1966).
    [Crossref]
  19. M. H. Horman and H. H. M. Chau, Appl. Opt. 6, 317 (1967); Appl. Opt. 6, 1415 (1967).
    [Crossref] [PubMed]
  20. F. A. Markus, Opt. Spektrosk. 32, 1216 (1972) [Opt. Spectrosc. 32, 661 (1972)].
  21. L. F. Collins, Appl. Opt. 7, 1236 (1968); A. R. Jones, J. Phys. D 2, 1789 (1969).
    [Crossref] [PubMed]
  22. B. L. Bracewell and W. J. Veigele, in Developments in Applied Spectroscopy, Vol. 9, edited by E. L. Grove and A. J. Perkins (Plenum, New York, 1971), p. 357.
    [Crossref]
  23. B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Rept. 14 (3–4), 112 (1967).
  24. J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967), Ch. 6; W. R. Hunter, D. W. Angel, and R. Tousey, Appl. Opt. 4, 891 (1965); O. M. Sorokin and V. A. Blank, Opt. Spektrosk. 28, 1178 (1970) [Opt. Spectrosc. 28,634 (1970)]; R. Haensel, C. Kunz, T. Sasaki, and B. Sonntag, Appl. Opt. 7, 301 (1968).
    [Crossref] [PubMed]
  25. T. Sasaki and M. Inokuti, in Proceedings of the Third International Conference on Vacuum Ultraviolet Radiation Physics, edited by Y. Nakai (Phys. Soc. Jap., Tokyo, 1971); R. W. Ditchburn and G. H. C. Freeman, Proc. R. Soc. A 294, 20 (1966); A. Daude, A. Savary, G. Jezequel, and S. Robin, C. R. Acad. Sci. B 269, 901 (1969); W. R. Hunter, J. Opt. Soc. Am. 54, 208 (1964); and J. Phys. (Paris) 25, 154 (1964); V. A. Fomichev and A. P. Lukirskii, Opt. Spektrosk. 22, 796 (1967) [Opt. Spectrosc. 22,432 (1967)]; R. Haensel, B. Sonntag, C. Kunz, and T. Sasaki, J. Appl. Phys. 40, 3046 (1969).
    [Crossref]
  26. A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Yu. F. Shepelev, Opt. Spektrosk. 16, 310 (1964) [Opt. Spectrosc. 16,168 (1964)]; Q. A. Ershov, I. A. Brytov, and A. P. Lukirskii, Opt. Spektrosk. 22, 127 (1967) [Opt. Spectrosc. 22,66 (1967)]; E. P. Savinov, I. I. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, Opt. Spektrosk. 27, 342 (1969) [Opt. Spectrosc. 27,179 (1969)].
  27. O. A. Ershov, Opt. Spektrosk. 22, 468 (1967) [Opt. Spectrosc. 22, 252 (1967)].
  28. Buckbee–Mears Co., 245 E. 6th St., Saint Paul, Minn. More-recent designs are available from Dr. Johannes Heidenhain Co., 8228 Traunreut, W. Germany.
  29. K. H. v. Grote, G. Möllenstedt, and R. Speidel, Optik 22, 252 (1965).
  30. B. E. Bol Raap, J. B. Le Poole, J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Small Rocket Instrumentation Techniques, edited by K. I. Maeda (North–Holland, Amsterdam, 1969), p. 203.
  31. G. G. Sliusarev, Dokl. Akad. Nauk SSSR 113, 780 (1956) [Sov. Phys.-Dokl. 2, 161 (1957)].
  32. K. Miyamoto, J. Opt. Soc. Am. 51, 17 (1961).
    [Crossref]
  33. J. A. Jordan, P. M. Hirsch, L. B. Lesem, and D. L. Van Rooy, Appl. Opt. 9, 1888 (1970).
  34. H. Gursky and T. Zehnpfennig, Appl. Opt. 5, 875 (1966).
    [PubMed]

1973 (1)

1972 (3)

1971 (1)

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

1970 (3)

H. Dammann, Optik 31, 95 (1970).

G. Elwert and J. V. Feitzinger, Optik 31, 600 (1970); H. H. Fink, Optik 31, 150 (1970).

J. A. Jordan, P. M. Hirsch, L. B. Lesem, and D. L. Van Rooy, Appl. Opt. 9, 1888 (1970).

1969 (2)

H. H. M. Chau, Appl. Opt. 8, 1209 (1969).
[Crossref] [PubMed]

G. Schmahl and D. Rudolph, Optik 29, 577 (1969). There appears to be a typographic error in Eq. (2) of this paper. The second term in the numerator should be n2λH2(3ξη+ξ2+η2)/4.

1968 (2)

1967 (5)

1966 (2)

1965 (1)

K. H. v. Grote, G. Möllenstedt, and R. Speidel, Optik 22, 252 (1965).

1964 (1)

A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Yu. F. Shepelev, Opt. Spektrosk. 16, 310 (1964) [Opt. Spectrosc. 16,168 (1964)]; Q. A. Ershov, I. A. Brytov, and A. P. Lukirskii, Opt. Spektrosk. 22, 127 (1967) [Opt. Spectrosc. 22,66 (1967)]; E. P. Savinov, I. I. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, Opt. Spektrosk. 27, 342 (1969) [Opt. Spectrosc. 27,179 (1969)].

1961 (1)

1956 (1)

G. G. Sliusarev, Dokl. Akad. Nauk SSSR 113, 780 (1956) [Sov. Phys.-Dokl. 2, 161 (1957)].

1952 (1)

1951 (1)

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

1898 (1)

R. W. Wood, Philos. Mag. 45, 511 (1898).

1875 (1)

J. L. Soret, Arch. Sci. Phys. Nat. 52, 320 (1875). According to Wood, the first Fresnel zone plate was made by Lord Rayleigh in 1871, but this work was never published [see R. W. Wood, Physical Optics, 3rd ed. (Macmillan, New York, 1934), p. 37].

Baez, A. V.

Bol Raap, B. E.

B. E. Bol Raap, J. B. Le Poole, J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Small Rocket Instrumentation Techniques, edited by K. I. Maeda (North–Holland, Amsterdam, 1969), p. 203.

Bracewell, B. L.

B. L. Bracewell and W. J. Veigele, in Developments in Applied Spectroscopy, Vol. 9, edited by E. L. Grove and A. J. Perkins (Plenum, New York, 1971), p. 357.
[Crossref]

Bräuninger, H.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

Champagne, E.

Chau, H. H. M.

Collins, L. F.

Dammann, H.

H. Dammann, Optik 31, 95 (1970).

de Graaf, W.

B. E. Bol Raap, J. B. Le Poole, J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Small Rocket Instrumentation Techniques, edited by K. I. Maeda (North–Holland, Amsterdam, 1969), p. 203.

Dijkstra, J. H.

B. E. Bol Raap, J. B. Le Poole, J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Small Rocket Instrumentation Techniques, edited by K. I. Maeda (North–Holland, Amsterdam, 1969), p. 203.

Einighammer, H. J.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

Elgin, R. L.

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Rept. 14 (3–4), 112 (1967).

Elwert, G.

G. Elwert and J. V. Feitzinger, Optik 31, 600 (1970); H. H. Fink, Optik 31, 150 (1970).

Ershov, O. A.

O. A. Ershov, Opt. Spektrosk. 22, 468 (1967) [Opt. Spectrosc. 22, 252 (1967)].

A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Yu. F. Shepelev, Opt. Spektrosk. 16, 310 (1964) [Opt. Spectrosc. 16,168 (1964)]; Q. A. Ershov, I. A. Brytov, and A. P. Lukirskii, Opt. Spektrosk. 22, 127 (1967) [Opt. Spectrosc. 22,66 (1967)]; E. P. Savinov, I. I. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, Opt. Spektrosk. 27, 342 (1969) [Opt. Spectrosc. 27,179 (1969)].

Feitzinger, J. V.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

G. Elwert and J. V. Feitzinger, Optik 31, 600 (1970); H. H. Fink, Optik 31, 150 (1970).

Ferris, L. D.

Fink, H. H.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

Grote, K. H. v.

K. H. v. Grote, G. Möllenstedt, and R. Speidel, Optik 22, 252 (1965).

Gursky, H.

Henke, B. L.

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Rept. 14 (3–4), 112 (1967).

Hirsch, P. M.

Höhn, D. H.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

Horman, M. H.

Inokuti, M.

T. Sasaki and M. Inokuti, in Proceedings of the Third International Conference on Vacuum Ultraviolet Radiation Physics, edited by Y. Nakai (Phys. Soc. Jap., Tokyo, 1971); R. W. Ditchburn and G. H. C. Freeman, Proc. R. Soc. A 294, 20 (1966); A. Daude, A. Savary, G. Jezequel, and S. Robin, C. R. Acad. Sci. B 269, 901 (1969); W. R. Hunter, J. Opt. Soc. Am. 54, 208 (1964); and J. Phys. (Paris) 25, 154 (1964); V. A. Fomichev and A. P. Lukirskii, Opt. Spektrosk. 22, 796 (1967) [Opt. Spectrosc. 22,432 (1967)]; R. Haensel, B. Sonntag, C. Kunz, and T. Sasaki, J. Appl. Phys. 40, 3046 (1969).
[Crossref]

Jordan, J. A.

Keating, P. N.

Koops, H.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

Krämer, G.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

Lantwaard, L. J.

B. E. Bol Raap, J. B. Le Poole, J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Small Rocket Instrumentation Techniques, edited by K. I. Maeda (North–Holland, Amsterdam, 1969), p. 203.

Le Poole, J. B.

B. E. Bol Raap, J. B. Le Poole, J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Small Rocket Instrumentation Techniques, edited by K. I. Maeda (North–Holland, Amsterdam, 1969), p. 203.

Ledingham, R. B.

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Rept. 14 (3–4), 112 (1967).

Lent, R. E.

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Rept. 14 (3–4), 112 (1967).

Lesem, L. B.

Lukirskii, A. P.

A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Yu. F. Shepelev, Opt. Spektrosk. 16, 310 (1964) [Opt. Spectrosc. 16,168 (1964)]; Q. A. Ershov, I. A. Brytov, and A. P. Lukirskii, Opt. Spektrosk. 22, 127 (1967) [Opt. Spectrosc. 22,66 (1967)]; E. P. Savinov, I. I. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, Opt. Spektrosk. 27, 342 (1969) [Opt. Spectrosc. 27,179 (1969)].

Markus, F. A.

F. A. Markus, Opt. Spektrosk. 32, 1216 (1972) [Opt. Spectrosc. 32, 661 (1972)].

Mayer, U.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

Mittra, R.

Miyamoto, K.

Möllenstedt, G.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

K. H. v. Grote, G. Möllenstedt, and R. Speidel, Optik 22, 252 (1965).

Mozer, M.

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

Mueller, R. K.

Myers, Ora E.

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

Pfeifer, D. C.

Rayleigh,

Rayleigh, Wave Theory, in Encyclopedia Britannica, 9th ed., Vol. 24, 429 (1888).

Rudolph, D.

G. Schmahl and D. Rudolph, Optik 29, 577 (1969). There appears to be a typographic error in Eq. (2) of this paper. The second term in the numerator should be n2λH2(3ξη+ξ2+η2)/4.

(a)D. Rudolph and G. Schmahl, in Symposium on New Techniques in Space Astronomy, edited by F. Labuhn and R. Lust, International Astronomical Union Symposium (Reidel, Dordrecht, Netherland, 1971), Vol. 41, p. 205; (b)J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Ref. 8 (a), p. 207.

Samson, J. A. R.

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967), Ch. 6; W. R. Hunter, D. W. Angel, and R. Tousey, Appl. Opt. 4, 891 (1965); O. M. Sorokin and V. A. Blank, Opt. Spektrosk. 28, 1178 (1970) [Opt. Spectrosc. 28,634 (1970)]; R. Haensel, C. Kunz, T. Sasaki, and B. Sonntag, Appl. Opt. 7, 301 (1968).
[Crossref] [PubMed]

Sasaki, T.

T. Sasaki and M. Inokuti, in Proceedings of the Third International Conference on Vacuum Ultraviolet Radiation Physics, edited by Y. Nakai (Phys. Soc. Jap., Tokyo, 1971); R. W. Ditchburn and G. H. C. Freeman, Proc. R. Soc. A 294, 20 (1966); A. Daude, A. Savary, G. Jezequel, and S. Robin, C. R. Acad. Sci. B 269, 901 (1969); W. R. Hunter, J. Opt. Soc. Am. 54, 208 (1964); and J. Phys. (Paris) 25, 154 (1964); V. A. Fomichev and A. P. Lukirskii, Opt. Spektrosk. 22, 796 (1967) [Opt. Spectrosc. 22,432 (1967)]; R. Haensel, B. Sonntag, C. Kunz, and T. Sasaki, J. Appl. Phys. 40, 3046 (1969).
[Crossref]

Savinov, E. P.

A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Yu. F. Shepelev, Opt. Spektrosk. 16, 310 (1964) [Opt. Spectrosc. 16,168 (1964)]; Q. A. Ershov, I. A. Brytov, and A. P. Lukirskii, Opt. Spektrosk. 22, 127 (1967) [Opt. Spectrosc. 22,66 (1967)]; E. P. Savinov, I. I. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, Opt. Spektrosk. 27, 342 (1969) [Opt. Spectrosc. 27,179 (1969)].

Sawatari, T.

Schmahl, G.

G. Schmahl and D. Rudolph, Optik 29, 577 (1969). There appears to be a typographic error in Eq. (2) of this paper. The second term in the numerator should be n2λH2(3ξη+ξ2+η2)/4.

(a)D. Rudolph and G. Schmahl, in Symposium on New Techniques in Space Astronomy, edited by F. Labuhn and R. Lust, International Astronomical Union Symposium (Reidel, Dordrecht, Netherland, 1971), Vol. 41, p. 205; (b)J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Ref. 8 (a), p. 207.

Semonin, R. G.

Shepelev, Yu. F.

A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Yu. F. Shepelev, Opt. Spektrosk. 16, 310 (1964) [Opt. Spectrosc. 16,168 (1964)]; Q. A. Ershov, I. A. Brytov, and A. P. Lukirskii, Opt. Spektrosk. 22, 127 (1967) [Opt. Spectrosc. 22,66 (1967)]; E. P. Savinov, I. I. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, Opt. Spektrosk. 27, 342 (1969) [Opt. Spectrosc. 27,179 (1969)].

Sliusarev, G. G.

G. G. Sliusarev, Dokl. Akad. Nauk SSSR 113, 780 (1956) [Sov. Phys.-Dokl. 2, 161 (1957)].

Soret, J. L.

J. L. Soret, Arch. Sci. Phys. Nat. 52, 320 (1875). According to Wood, the first Fresnel zone plate was made by Lord Rayleigh in 1871, but this work was never published [see R. W. Wood, Physical Optics, 3rd ed. (Macmillan, New York, 1934), p. 37].

Speidel, R.

K. H. v. Grote, G. Möllenstedt, and R. Speidel, Optik 22, 252 (1965).

Stigliani, D. J.

Van Rooy, D. L.

Veigele, W. J.

B. L. Bracewell and W. J. Veigele, in Developments in Applied Spectroscopy, Vol. 9, edited by E. L. Grove and A. J. Perkins (Plenum, New York, 1971), p. 357.
[Crossref]

Waldman, G. S.

Wood, R. W.

R. W. Wood, Philos. Mag. 45, 511 (1898).

Yen, W. M.

Young, M.

Zehnpfennig, T.

Am. J. Phys. (1)

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

Appl. Opt. (7)

Arch. Sci. Phys. Nat. (1)

J. L. Soret, Arch. Sci. Phys. Nat. 52, 320 (1875). According to Wood, the first Fresnel zone plate was made by Lord Rayleigh in 1871, but this work was never published [see R. W. Wood, Physical Optics, 3rd ed. (Macmillan, New York, 1934), p. 37].

Dokl. Akad. Nauk SSSR (1)

G. G. Sliusarev, Dokl. Akad. Nauk SSSR 113, 780 (1956) [Sov. Phys.-Dokl. 2, 161 (1957)].

J. Opt. Soc. Am. (7)

Norelco Rept. (1)

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Rept. 14 (3–4), 112 (1967).

Opt. Spektrosk. (3)

A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Yu. F. Shepelev, Opt. Spektrosk. 16, 310 (1964) [Opt. Spectrosc. 16,168 (1964)]; Q. A. Ershov, I. A. Brytov, and A. P. Lukirskii, Opt. Spektrosk. 22, 127 (1967) [Opt. Spectrosc. 22,66 (1967)]; E. P. Savinov, I. I. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, Opt. Spektrosk. 27, 342 (1969) [Opt. Spectrosc. 27,179 (1969)].

O. A. Ershov, Opt. Spektrosk. 22, 468 (1967) [Opt. Spectrosc. 22, 252 (1967)].

F. A. Markus, Opt. Spektrosk. 32, 1216 (1972) [Opt. Spectrosc. 32, 661 (1972)].

Optik (4)

H. Dammann, Optik 31, 95 (1970).

G. Elwert and J. V. Feitzinger, Optik 31, 600 (1970); H. H. Fink, Optik 31, 150 (1970).

G. Schmahl and D. Rudolph, Optik 29, 577 (1969). There appears to be a typographic error in Eq. (2) of this paper. The second term in the numerator should be n2λH2(3ξη+ξ2+η2)/4.

K. H. v. Grote, G. Möllenstedt, and R. Speidel, Optik 22, 252 (1965).

Philos. Mag. (1)

R. W. Wood, Philos. Mag. 45, 511 (1898).

Sol. Phys. (1)

H. Bräuninger, H. J. Einighammer, J. V. Feitzinger, H. H. Fink, D. H. Höhn, H. Koops, G. Krämer, U. Mayer, G. Möllenstedt, and M. Mozer, Sol. Phys. 20, 81 (1971).
[Crossref]

Other (7)

(a)D. Rudolph and G. Schmahl, in Symposium on New Techniques in Space Astronomy, edited by F. Labuhn and R. Lust, International Astronomical Union Symposium (Reidel, Dordrecht, Netherland, 1971), Vol. 41, p. 205; (b)J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Ref. 8 (a), p. 207.

Rayleigh, Wave Theory, in Encyclopedia Britannica, 9th ed., Vol. 24, 429 (1888).

B. E. Bol Raap, J. B. Le Poole, J. H. Dijkstra, W. de Graaf, and L. J. Lantwaard, in Small Rocket Instrumentation Techniques, edited by K. I. Maeda (North–Holland, Amsterdam, 1969), p. 203.

Buckbee–Mears Co., 245 E. 6th St., Saint Paul, Minn. More-recent designs are available from Dr. Johannes Heidenhain Co., 8228 Traunreut, W. Germany.

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967), Ch. 6; W. R. Hunter, D. W. Angel, and R. Tousey, Appl. Opt. 4, 891 (1965); O. M. Sorokin and V. A. Blank, Opt. Spektrosk. 28, 1178 (1970) [Opt. Spectrosc. 28,634 (1970)]; R. Haensel, C. Kunz, T. Sasaki, and B. Sonntag, Appl. Opt. 7, 301 (1968).
[Crossref] [PubMed]

T. Sasaki and M. Inokuti, in Proceedings of the Third International Conference on Vacuum Ultraviolet Radiation Physics, edited by Y. Nakai (Phys. Soc. Jap., Tokyo, 1971); R. W. Ditchburn and G. H. C. Freeman, Proc. R. Soc. A 294, 20 (1966); A. Daude, A. Savary, G. Jezequel, and S. Robin, C. R. Acad. Sci. B 269, 901 (1969); W. R. Hunter, J. Opt. Soc. Am. 54, 208 (1964); and J. Phys. (Paris) 25, 154 (1964); V. A. Fomichev and A. P. Lukirskii, Opt. Spektrosk. 22, 796 (1967) [Opt. Spectrosc. 22,432 (1967)]; R. Haensel, B. Sonntag, C. Kunz, and T. Sasaki, J. Appl. Phys. 40, 3046 (1969).
[Crossref]

B. L. Bracewell and W. J. Veigele, in Developments in Applied Spectroscopy, Vol. 9, edited by E. L. Grove and A. J. Perkins (Plenum, New York, 1971), p. 357.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1

Graphical method for finding amplitude in primary image from one pair of zones, using wavelets. Ap is the amplitude from the open zone, As from the-zone with shifter, introducing phase shift ϕ.

Fig. 2
Fig. 2

The phase shift ϕopt, which provides maximum image flux as a function of η.

Fig. 3
Fig. 3

Optical performance of zone plate as a function of η with phase shifter set for maximum image flux (Fig. 2). The fraction of incident flux in the primary image (solid curve) and in the undiffracted zero-order background (dashed curve) are shown, as well as the fraction absorbed by the zone-plate material. The points η = ∞ correspond to conventional Fresnel zone plate with opaque zones. The Rayleigh–Wood zone plate has η = 0.

Fig. 4
Fig. 4

Zone profiles. The thickness is shown in terms of the phase shift ϕ. (a) Rectangular profile. θ1 = π corresponds to conventional zone plate with equal open and shifting zone areas. (b) Distorted profile with sloping transition regions II and IV between open (I) and shifting (III) areas.

Fig. 5
Fig. 5

Optical performance of zone plate with rectangular profile as a function of the boundary position θ1 between open and shifting areas (see inset). Fraction of incident flux in primary image (a), in undiffracted background (b), and in zone-plate absorption (c) are shown for ϕ = ϕopt. The curves marked η = ∞ refer to Fresnel zone plates with opaque zones, η = 0 refers to Rayleigh–Wood design.

Fig. 6
Fig. 6

Optical performance of zone plate with rectangular profile as a function of the thickness of the shifting layer in units of ϕopt (see inset). Fraction of incident flux in primary image (a), in undiffracted background (b), and in zone-plate absorption (c) are shown for equal open and phase-shifted areas (θ1 = π). The curves marked η = ∞ refer to the Fresnel zone plates with opaque zones, η = 0 refers to Rayleigh–Wood design.

Fig. 7
Fig. 7

Characteristics of zone plate with rectangular profile, designed to eliminate zero-order undiffracted background, as a function of η. The curves represent the position of the zone boundary (θ1), the fraction of the incident flux in the primary image (imaged) and in zone plate absorption (absorbed). For this design, ϕ0 = π.

Fig. 8
Fig. 8

Phase thickness ϕ0, giving maximum flux in primary image of zone plate with sloping transition regions (see inset). The profile is rectangular for α = 0, and triangular for α = π. The fully open, and fully shifted regions are of the same width (θ1 + α = π).

Fig. 9
Fig. 9

Fraction of the incident flux in the primary image (solid curves), in the undiffracted background (dashed curves), and in zone-plate absorption (dotted curves) for various values of η for zone plates with sloping profiles. Profile shape and phase thickness are shown in Fig. 8. (Absorption is 0 for η = 0.)

Tables (3)

Tables Icon

Table I Distribution of the flux incident on zone plates.

Tables Icon

Table II Optical properties of materials for zone-plate construction.a

Tables Icon

Table III Transmittance of substrate materials.a

Equations (25)

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r n 2 = n f λ + n 2 λ 2 4 ,
r n ( n f λ ) 1 2 .
1 p + 1 q = 1 f ,
r n 2 = q n λ 2 ( n λ ( q - f ) + 4 f q n λ ( q - f ) + 2 q 2 ) + n 2 λ 2 16 ( n λ ( q - f ) + 4 f q n λ ( q - f ) + 2 q 2 ) 2 .
r n 2 = n f λ + n 2 λ 2 4 ( 1 - 3 f ( q - f ) q 2 ) + 0 ( n 3 λ 3 q ) .
r n 2 = n f λ + n 2 λ 2 16 .
n = 1 - δ - i k ,
η = k δ .
A p = C 2 π 0 π e i θ d θ = i C π ,
A s = C 2 π e - 2 π k t / λ π 2 π e i ( θ - ϕ ) d θ = - i C π e - 2 π k t / λ e - i ϕ .
I 1 = A p + A s 2 = C 2 π 2 ( 1 + e - 4 π k t / λ - 2 e - 2 π k t / λ cos ϕ ) .
2 π k t / λ = η ϕ
I 1 = C 2 π 2 ( 1 + e - 2 η ϕ - 2 e - η ϕ cos ϕ ) .
I m = { C 2 m 2 π 2 ( 1 + e - 2 η ϕ - 2 e - η ϕ cos ϕ ) , m = ± 1 , ± 3 , ± 5 , 0 , m = ± 2 , ± 4 , ± 6 , .
I 1 ϕ = C 2 π 2 ( - 2 η e - 2 η ϕ + 2 η e - η ϕ cos ϕ + 2 e - η ϕ sin ϕ ) = 0.
I abs = C 2 2 ( 1 - e - 2 η ϕ ) ,
I 0 = | C 2 π [ 0 π d θ + e - η ϕ π 2 π e - i ϕ d θ ] | 2 = C 2 4 ( 1 + e - 2 η ϕ + 2 e - η ϕ cos ϕ ) .
δ = N e r e 2 π λ 2
n max f λ 4 ( Δ r ) 2 .
A 1 = C 2 π 0 2 π e - η ϕ ( θ ) e i [ θ - ϕ ( θ ) ] d θ .
A 1 = C π e i ( θ 1 / 2 ) { ( 1 - α 2 α 2 + ϕ 0 ( η + i ) 2 ) × [ sin θ 1 2 - e - ϕ 0 ( η + i ) sin ( α + θ 1 2 ) ] + α ϕ 0 ( η + i ) α 2 + ϕ 0 2 ( η + i ) 2 [ cos θ 1 2 - e - ϕ 0 ( η + i ) cos ( α + θ 1 2 ) ] } .
A 0 = C 2 π 0 2 π e - η ϕ ( θ ) e - i ϕ ( θ ) d θ = C 2 π { ( 1 - e - ϕ 0 ( η + i ) ) ( θ 1 + 2 α ϕ 0 ( η + i ) ) + 2 ( π - α ) e - ϕ 0 ( η + i ) } .
I abs = C 2 2 π 0 2 π ( 1 - e - 2 η ϕ ( θ ) ) d θ = C 2 { ( 1 - θ 1 2 π ) ( 1 - e - 2 η ϕ 0 ) - α π [ 1 2 η ϕ 0 - e - 2 η ϕ 0 ( 1 + 1 2 η ϕ 0 ) ] } .
I 1 = A 1 2 + C 2 π 2 sin 2 θ 1 2 ( 1 + e - 2 η ϕ 0 - 2 e - η ϕ 0 cos ϕ 0 ) .
θ 1 π = 2 e - η π 1 + e - η π .