Abstract

A new type of Fresnel zone plate has been constructed which can focus ultraviolet radiation of any wavelength down to the soft x-ray region. It consists of a set of thin circular gold bands made self supporting by radial struts, leaving the transparent zones empty. Experimental tests at 6700, 4358, and 2537 A showed that the theoretical minimum angular resolution obeys the Rayleigh criterion, sinθmin=1.22λ/D. The diameter of the zone plate is D=0.26 cm and contains 19 opaque zones, the narrowest of which measured about 20 μ across. The zone plate was better than the optimum pinhole in resolution by a factor of about 6 and in speed by a factor of 40. The zone plate produced pictures that compared favorably with those made with a lens of similar focal length and aperture. The lens was about 20 times faster than the zone plate at 4358 A, but at 1000 A the zone plate would have been far faster than the lens. Focusing tests are contemplated at 1000 A and at 100 A where lenses and mirrors, the conventional image-forming devices, may fail. The angular resolution at 2537 A was close to the theoretical value of 1.2×10−4 rad and held over a field of at least 1.75×10−2 rad, which is 2.0 times the angle subtended by the sun’s disk at the earth. A zone plate telescope, operating in the soft x-ray or extreme ultraviolet region, far above the earth’s atmosphere in an orbiting satellite, now seems possible.

© 1961 Optical Society of America

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References

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  1. Symposium on X-Ray Microscopy and Microradiography, Cambridge, England, August 16–21, 1956. The proceedings of this conference were published in the following work: V. E. Cosslett, A. Engstrom, and H. H. Pattee, X-ray Microscopy and Microradiography (Academic Press, Inc., New York, 1957).
  2. Second International Symposium on X-Ray Microscopy and X-Ray Microanalysis, Stockholm, Sweden, June 15–17, 1959.
  3. R. Jastrow, J. Geophys. Research 64, 1647 (1959).
    [Crossref]
  4. L. R. Koller, Ultraviolet Radiation (John Wiley & Sons, Inc., New York, 1952), Chap. 5, p. 146.
  5. F. L. Whipple and R. J. Davis, Astron. J. 65, 285 (1960).
    [Crossref]
  6. W. C. Walker, O. P. Rustgi, and G. L. Weissler, J. Opt. Soc. Am. 49, 471 (1959).
    [Crossref]
  7. G. Hass and R. Tousey, J. Opt. Soc. Am. 49, 593 (1959).
    [Crossref]
  8. G. R. Sabine, Phys. Rev. 55, 1064 (1939).
    [Crossref]
  9. P. H. Berning, G. Hass, and R. P. Madden, J. Opt. Soc. Am. 50, 586, (1960).
    [Crossref]
  10. L. M. Rieser, J. Opt. Soc. Am. 47, 987 (1957).
    [Crossref]
  11. A. H. Compton and S. K. Allison, X-Rays in Theory and Experiment (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1935), 2nd ed., Chap. IV, p. 305et seq.
  12. P. Kirkpatrick and A. V. Baez, J. Opt. Soc. Am. 38, 766 (1948).
    [Crossref] [PubMed]
  13. P. Kirkpatrick and H. H. Pattee, “X-ray microscopy,” Handbuch der Physik edited by S. Flugge (Springer-Verlag, Berlin, 1957), Vol. XXX.
    [Crossref]
  14. V. E. Cosslett, A. Engstrom, and H. H. Pattee, X-ray Microscopy and Microradiography (Academic Press, Inc., New York, 1957).
  15. A. V. Baez, J. Opt. Soc. Am. 42, 756 (1952).
    [Crossref]
  16. D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).
  17. O. E. Myers, Am. J. Phys. 19, 359 (1951).
    [Crossref]
  18. J. Strong, Concepts of Classical Optics (W. H. Freeman & Company, San Francisco, California, 1958).
  19. B. L. Henke, Proceedings Seventh Annual Conference on Industrial Applications of X-Ray Analysis, University of Denver, Denver, Colorado, 1958.
  20. C. DeJager, Ann. Geophys. II, 1 (1955).
  21. J. E. Mack and M. J. Martin, The Photographic Process (McGraw-Hill Book Company, Inc., New York, 1939).
  22. D. S. Kirby, Publs. Astron. Soc. Pacific 71, No. 334 (1959).
    [Crossref]
  23. R. Giacconi and B. Rossi, J. Geophys. Research 65, 773 (1960).
    [Crossref]

1960 (3)

F. L. Whipple and R. J. Davis, Astron. J. 65, 285 (1960).
[Crossref]

R. Giacconi and B. Rossi, J. Geophys. Research 65, 773 (1960).
[Crossref]

P. H. Berning, G. Hass, and R. P. Madden, J. Opt. Soc. Am. 50, 586, (1960).
[Crossref]

1959 (4)

1957 (1)

1955 (1)

C. DeJager, Ann. Geophys. II, 1 (1955).

1952 (1)

1951 (1)

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

1949 (1)

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).

1948 (1)

1939 (1)

G. R. Sabine, Phys. Rev. 55, 1064 (1939).
[Crossref]

Allison, S. K.

A. H. Compton and S. K. Allison, X-Rays in Theory and Experiment (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1935), 2nd ed., Chap. IV, p. 305et seq.

Baez, A. V.

Berning, P. H.

Compton, A. H.

A. H. Compton and S. K. Allison, X-Rays in Theory and Experiment (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1935), 2nd ed., Chap. IV, p. 305et seq.

Cosslett, V. E.

V. E. Cosslett, A. Engstrom, and H. H. Pattee, X-ray Microscopy and Microradiography (Academic Press, Inc., New York, 1957).

Davis, R. J.

F. L. Whipple and R. J. Davis, Astron. J. 65, 285 (1960).
[Crossref]

DeJager, C.

C. DeJager, Ann. Geophys. II, 1 (1955).

Engstrom, A.

V. E. Cosslett, A. Engstrom, and H. H. Pattee, X-ray Microscopy and Microradiography (Academic Press, Inc., New York, 1957).

Gabor, D.

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).

Giacconi, R.

R. Giacconi and B. Rossi, J. Geophys. Research 65, 773 (1960).
[Crossref]

Hass, G.

Henke, B. L.

B. L. Henke, Proceedings Seventh Annual Conference on Industrial Applications of X-Ray Analysis, University of Denver, Denver, Colorado, 1958.

Jastrow, R.

R. Jastrow, J. Geophys. Research 64, 1647 (1959).
[Crossref]

Kirby, D. S.

D. S. Kirby, Publs. Astron. Soc. Pacific 71, No. 334 (1959).
[Crossref]

Kirkpatrick, P.

P. Kirkpatrick and A. V. Baez, J. Opt. Soc. Am. 38, 766 (1948).
[Crossref] [PubMed]

P. Kirkpatrick and H. H. Pattee, “X-ray microscopy,” Handbuch der Physik edited by S. Flugge (Springer-Verlag, Berlin, 1957), Vol. XXX.
[Crossref]

Koller, L. R.

L. R. Koller, Ultraviolet Radiation (John Wiley & Sons, Inc., New York, 1952), Chap. 5, p. 146.

Mack, J. E.

J. E. Mack and M. J. Martin, The Photographic Process (McGraw-Hill Book Company, Inc., New York, 1939).

Madden, R. P.

Martin, M. J.

J. E. Mack and M. J. Martin, The Photographic Process (McGraw-Hill Book Company, Inc., New York, 1939).

Myers, O. E.

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

Pattee, H. H.

P. Kirkpatrick and H. H. Pattee, “X-ray microscopy,” Handbuch der Physik edited by S. Flugge (Springer-Verlag, Berlin, 1957), Vol. XXX.
[Crossref]

V. E. Cosslett, A. Engstrom, and H. H. Pattee, X-ray Microscopy and Microradiography (Academic Press, Inc., New York, 1957).

Rieser, L. M.

Rossi, B.

R. Giacconi and B. Rossi, J. Geophys. Research 65, 773 (1960).
[Crossref]

Rustgi, O. P.

Sabine, G. R.

G. R. Sabine, Phys. Rev. 55, 1064 (1939).
[Crossref]

Strong, J.

J. Strong, Concepts of Classical Optics (W. H. Freeman & Company, San Francisco, California, 1958).

Tousey, R.

Walker, W. C.

Weissler, G. L.

Whipple, F. L.

F. L. Whipple and R. J. Davis, Astron. J. 65, 285 (1960).
[Crossref]

Am. J. Phys. (1)

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

Ann. Geophys. (1)

C. DeJager, Ann. Geophys. II, 1 (1955).

Astron. J. (1)

F. L. Whipple and R. J. Davis, Astron. J. 65, 285 (1960).
[Crossref]

J. Geophys. Research (2)

R. Jastrow, J. Geophys. Research 64, 1647 (1959).
[Crossref]

R. Giacconi and B. Rossi, J. Geophys. Research 65, 773 (1960).
[Crossref]

J. Opt. Soc. Am. (6)

Phys. Rev. (1)

G. R. Sabine, Phys. Rev. 55, 1064 (1939).
[Crossref]

Proc. Roy. Soc. (London) (1)

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).

Publs. Astron. Soc. Pacific (1)

D. S. Kirby, Publs. Astron. Soc. Pacific 71, No. 334 (1959).
[Crossref]

Other (9)

J. E. Mack and M. J. Martin, The Photographic Process (McGraw-Hill Book Company, Inc., New York, 1939).

J. Strong, Concepts of Classical Optics (W. H. Freeman & Company, San Francisco, California, 1958).

B. L. Henke, Proceedings Seventh Annual Conference on Industrial Applications of X-Ray Analysis, University of Denver, Denver, Colorado, 1958.

P. Kirkpatrick and H. H. Pattee, “X-ray microscopy,” Handbuch der Physik edited by S. Flugge (Springer-Verlag, Berlin, 1957), Vol. XXX.
[Crossref]

V. E. Cosslett, A. Engstrom, and H. H. Pattee, X-ray Microscopy and Microradiography (Academic Press, Inc., New York, 1957).

A. H. Compton and S. K. Allison, X-Rays in Theory and Experiment (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1935), 2nd ed., Chap. IV, p. 305et seq.

L. R. Koller, Ultraviolet Radiation (John Wiley & Sons, Inc., New York, 1952), Chap. 5, p. 146.

Symposium on X-Ray Microscopy and Microradiography, Cambridge, England, August 16–21, 1956. The proceedings of this conference were published in the following work: V. E. Cosslett, A. Engstrom, and H. H. Pattee, X-ray Microscopy and Microradiography (Academic Press, Inc., New York, 1957).

Second International Symposium on X-Ray Microscopy and X-Ray Microanalysis, Stockholm, Sweden, June 15–17, 1959.

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Figures (10)

Fig. 1
Fig. 1

The transmissivity of several materials in the ultraviolet. The crystalline materials that might serve for lenses cease to show any appreciable transmission below 1000 A. The thin metal films could serve as filters.

Fig. 2
Fig. 2

Normal incidence reflectivities of various materials in the ultraviolet. Aluminum overcoated with magnesium fluoride gives useful reflectivity even below 1000 A. Below 400 A there is a dearth of experimental information on reflectivity.

Fig. 3
Fig. 3

An enlarged photograph of the self-supported gold zone plate used in these experiments. The diameter of the outer circle is 0.2596±0.0002 cm. The central circle has a diameter of 0.0426±0.0002 cm. The thickness of the gold is estimated as 10 μ. The white bands representing the transparent regions are completely open and hence will transmit electromagnetic radiation of all wavelengths.

Fig. 4
Fig. 4

The layout of the apparatus on the optical bench. The light source consisted of a tungsten filament lamp and a condensing lens system. For the experiments at 2537 A the source was a 4-w General Electric germicidal lamp, No. GT4/1. The filters are described in the text. The zone plate was mounted at the open end of a bellows extension. The camera was an Exakta VX IIa. Eastman Kodak Microfile Contrast Copy film was used throughout, processed in D 19. Object and image distances are labeled p and q, respectively.

Fig. 5
Fig. 5

Pictures of a mesh with four lines per mm taken with the zone plate at three different wavelengths. Working out from the center we see pictures taken at 6700, 4358, and 2537 A, in sizes proportional to the original image sizes obtained with a fixed object-to-zone plate distance of 47 cm. The shorter wavelength results not only in a longer focal length and hence a larger image size but also in improved resolution. See also Fig. 6.

Fig. 6
Fig. 6

The pictures of Fig. 5 are here enlarged to produce equal image sizes. From left to right, they were made at 6700, 4358, and 2537 A. The angles subtended at the zone plate by two adjacent midpoints of the open area of the object mesh were 1.68 θmin, 2.59 θmin, and 4.44 θmin, where θmin is the theoretical minimum angle of resolution computed at the respective wavelengths. The improvement in resolution with shorter wavelength is apparent.

Fig. 7
Fig. 7

An object consisting of a coarse grid, one rectangle of which measures 1.43 mm by 1.72 mm within which there is a fine mesh with four lines per mm, photographed through a pinhole whose aperture was chosen to produce the optimum resolution for the wavelength and distances involved. Only the coarse grid is resolved. Compare this with Fig. 8.

Fig. 8
Fig. 8

The object of Fig. 7 photographed through a zone plate, with all other factors fixed except the exposure. The exposure time required for the pinhole picture was about 40 times greater than that used for the zone plate picture. This time the fine meshed screen is clearly resolved.

Fig. 9
Fig. 9

Comparison of a lens and a zone plate as image forming devices near the limit of resolution. On the left is a picture of a fine mesh screen taken with a zone plate. On the right is a picture of the same screen taken with a plano-convex lens of similar aperture and focal length. All other factors were kept the same except exposure which was 20 times greater for the zone plate. The wavelength used was 4358 A. If the exposure comparison had been made at 1000 A the results would have been much more favorable for the zone plate.

Fig. 10
Fig. 10

The vector AB represents the resultant of the infinitesimal vectors contributed by the subzones of one open Fresnel zone in a zone plate. The length of the arc ABC represents the amplitude of the contributions due to two successive Fresnel zones in a lens. The continuously changing thickness of a lens causes the infinitesimal vectors to line up since they all have the same phase. The ratio of the length of the arc ABC to the length AB is approximately π.

Equations (7)

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r n = r 1 n 1 2 ;             n = 1 , 2 , 3 .
f λ = r 1 2 ,
s n = [ ( n + 1 ) 1 2 - n 1 2 ] r 1 ,
s n = r 1 / 2 n 1 2 .
r n = ( f n λ ) 1 2 [ 1 + ( n λ / 4 f ) ] 1 2 .
sin θ min = 1.22 ( λ / D ) .
d = 2 [ 0.9 p q λ / ( p + q ) ] 1 2 .