Abstract

The most severe problems in the recording of x-ray holograms have been overcome and the investigation of Fraunhofer holograms extended to the x-ray region. An in-line Fraunhofer hologram was made of a 5.9-μ-diam. glass fiber using beryllium x rays (114 Å) produced in a scanning electron-probe microanalyzer. A magnified real image of the fiber was reconstructed from the negative hologram using He–Ne laser light. A lateral magnification of approximately 9X was obtained in the two-step imaging process. An analysis of the x-ray source, recorded hologram, and reconstructed real image is presented.

© 1969 Optical Society of America

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  1. A. V. Baez and H. M. A. El-Sum, in X-Ray Microscopy and Microradiography, V. E. Cosslett, A. Engström, and H. H. Pattee, Eds. (Academic Press Inc., New York, 1957), pp. 347–366.
  2. J. T. Winthrop, Doctoral Dissertation, University of Michigan (1966).
  3. D. Gabor, Nature 161, 777 (1948).
    [Crossref]
  4. D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).
  5. D. Gabor, Proc. Phys. Soc. (London) B64, 449 (1951).
  6. B. J. Thompson, Japan J. Appl. Phys. Suppl. I 4, 302 (1965).
  7. J. B. DeVelis and G. O. Reynolds, Theory and Applications of Holography (Addison–Wesley Publ. Co., Reading, Mass., 1967), pp. 43–48, 73.
  8. B. J. Thompson, J. Opt. Soc. Am. 53, 1350 (1963).
  9. J. B. DeVelis, J. Opt. Soc. Am. 54, 1407 (1964).
  10. G. B. Parrent and B. J. Thompson, Opt. Acta 11, 183 (1964).
    [Crossref]
  11. J. B. DeVelis, G. B. Parrent, and B. J. Thompson, J. Opt. Soc. Am. 56, 424 (1966).
    [Crossref]
  12. H. M. A. El-Sum, doctoral dissertation, Stanford University (1952).
  13. A. V. Baez, J. Opt. Soc. Am. 42, 756 (1952).
    [Crossref]
  14. G. Kellström, Nova Acta Soc. Sci. Upsal. 8, 60 (1932).
  15. H. M. A. El-Sum and A. V. Baez, Phys. Rev 99, 624 (1955).
  16. H. M. El-Sum and P. Kirkpatrick, Phys. Rev. 85, 763 (1952).
  17. P. Kirkpatrick and H. H. Pattee, in Handbuch der Physik, Vol. 30, S. Flügge, Ed. (Springer-Verlag, Berlin, 1957), p. 320.
  18. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), 3rd ed., p. 384.
  19. S. Silver, in Microwave Antenna Theory and Design, S. Silver, Ed. (McGraw–Hill Book Co., New York, 1949), p. 199.
  20. A. Sommerfeld, Optics, Lectures on Theoretical Physics, Vol. IV (Academic Press Inc., New York, 1954), p. 195.
  21. V. E. Cosslett, Modern Microscopy (Cornell University Press, Ithaca, New York, 1966), pp. 139–156.
  22. P. Duncumb, in The Encyclopedia of Spectroscopy, G. L. Clark, Ed. (Reinhold Publ. Corp., New York, 1960), pp. 768–776; in The Encyclopedia of X Rays and Gamma Rays, G. L. Clark, Ed. (Reinhold Publ. Corp., New York, 1963), pp. 818–824; Brit. J. Appl. Phys. 11, 169 (1960).
  23. J. W. Giles, J. Opt. Soc. Am. 59, 778 (1969).
    [Crossref]
  24. B. L. Henke, in Advances in X-Ray Analysis, G. R. Mallett, M. Fay, and W. M. Mueller, Eds. (Plenum Press, Inc., New York, 1966), Vol. 9, pp. 430–439.
    [Crossref]
  25. J. A. Bearden, Rev. Mod. Phys. 39, 48 (1967).
  26. R. Theisen, Quantitative Electron Microprobe Analysis (Springer-Verlag, Inc., New York, 1965), p. 9.
  27. P. Duncumb and P. K. Shields, in The Electron Microprobe, T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, Eds. (John Wiley & Sons, Inc., New York, 1966), p. 284.
  28. Reference 26, p. 15.
  29. H. M. O’Bryan and H. W. B. Skinner, Phys. Rev. 44, 602 (1933); Phys. Rev. 45, 371 (1934).
    [Crossref]
  30. H. W. B. Skinner, Phil. Trans. Roy. Soc. (London), Ser. A 239, 95 (1940).
    [Crossref]
  31. D. H. Tomboulian, in Handbuch der Physik, Vol. 30, S. Flügge, Ed. (Springer–Verlag, Berlin, 1957), p. 273.
  32. S. T. Stephenson and F. D. Mason, Phys. Rev. 75, 1711 (1949).
    [Crossref]
  33. B. D. Cullity, Elements of X-Ray Diffraction (Addison–Wesley Publ. Co., Reading, Mass., 1956), p. 6.
  34. A. J. Campbell, Proc. Roy. Soc. (London), Ser. A 274, 319 (1963).
    [Crossref]
  35. L. L. Birks, Electron Probe Microanalysis (Wiley–Interscience, Inc., New York, 1963), p. 133.
  36. N. Swanson and K. Codling, J. Opt. Soc. Am. 58, 1192 (1968).
    [Crossref]
  37. G. L. Clark, Applied X Rays (McGraw–Hill Book Co., New York, 1955), 4th ed., p. 115.
  38. H. P. Klug and L. E. Alexander, X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials (John Wiley& Sons, Inc., New York, 1954), pp. 87–88.
  39. R. Witty and P. Wood, Nature 163, 323 (1949).
    [Crossref]
  40. R. D. Evans, The Atomic Nucleus (McGraw–Hill Book Co., New York, 1955), p. 565; E. H. S. Burhop, The Auger Effect and Other Radiationless Transitions (Cambridge University Press, Cambridge, 1952).
  41. See Ref. 18, p. 319; M. Françon, Diffraction (Pergamon Press, Inc., New York, 1966), p. 60; Optical Interferometry (Academic Press Inc., New York, 1966), p. 10.
  42. Reference 7, pp. 123–124.
  43. A. V. Baez, Nature 169, 963 (1952).
    [Crossref]
  44. M. E. Haine and T. Mulvey, Nature 170, 202 (1952).
    [Crossref] [PubMed]
  45. G. W. Stroke and D. G. Falconer, Phys. Letters 13, 306 (1964).
    [Crossref]
  46. E. N. Leith, J. Upatnieks, and K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).
    [Crossref]
  47. C. C. Eaglesfield, Electronics Letters 1, 181 (1965).
    [Crossref]
  48. J. A. Armstrong, IBM J. Res. Develop. 9, 171 (1965).
    [Crossref]
  49. G. W. Stroke, An Introduction to Coherent Optics and Holograpy (Academic Press Inc., New York, 1966), pp. 114–116.
  50. F. I. Diamond, J. Opt. Soc. Am. 57, 503 (1967).
    [Crossref]
  51. Reference 12, p. 78.
  52. B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Reporter 14, 112 (1967).
  53. For a discussion of total reflection of x rays see, V. E. Cosslett and W. C. Nixon, X-Ray Microscopy (Cambridge University Press, Cambridge, England, 1960), pp. 87–91.
  54. See, A. Messiah, Quantum Mechanics, Vol. II, (North–Holland Publ. Co., Amsterdam, 1962), p. 1015.
  55. Reference 31, p. 265.
  56. G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955).
    [Crossref]
  57. G. L. Johnson and R. F. Wuerker, in X-Ray Optics and X-Ray Microanalysis, H. H. Pattee, V. E. Cosslett, and A. Engström, Eds. (Academic Press Inc., New York, 1963), pp. 229–239.
  58. G. L. Johnson, doctoral dissertation, Stanford University (1962).
  59. F. Zernike, Proc. Phys. Soc. (London) 61, 147 (1948).
    [Crossref]
  60. Reference 7, p. 71.
  61. Reference 35, pp. 134–135.
  62. A. Franks, Nature 201, 913 (1964).
    [Crossref]
  63. A. V. Baez, J. Opt. Soc. Am. 51, 405 (1961).
    [Crossref]
  64. G. Möllenstedt, K. H. von Grote, and C. Jönsson, in Ref. 57, pp. 73–79.
  65. G. W. Stroke, D. Brumm, A. Funkhouser, and R. Restrick, J. Opt. Soc. Am. 55, 1566A (1965).
  66. G. W. Stroke, Appl. Phys. Letters 6, 201 (1965).
    [Crossref]
  67. J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 56, 1362 (1966).
    [Crossref]
  68. J. T. Winthrop and C. R. Worthington, Phys. Letters 15, 124 (1965).
    [Crossref]
  69. G. W. Stroke, D. Brumm, and A. Funkhouser, J. Opt. Soc. Am. 55, 1327 (1965).
    [Crossref]
  70. J. T. Winthrop and C. R. Worthington, Phys. Letters 21, 413 (1966).
    [Crossref]

1969 (1)

1968 (1)

1967 (3)

F. I. Diamond, J. Opt. Soc. Am. 57, 503 (1967).
[Crossref]

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Reporter 14, 112 (1967).

J. A. Bearden, Rev. Mod. Phys. 39, 48 (1967).

1966 (3)

J. B. DeVelis, G. B. Parrent, and B. J. Thompson, J. Opt. Soc. Am. 56, 424 (1966).
[Crossref]

J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 56, 1362 (1966).
[Crossref]

J. T. Winthrop and C. R. Worthington, Phys. Letters 21, 413 (1966).
[Crossref]

1965 (8)

J. T. Winthrop and C. R. Worthington, Phys. Letters 15, 124 (1965).
[Crossref]

G. W. Stroke, D. Brumm, and A. Funkhouser, J. Opt. Soc. Am. 55, 1327 (1965).
[Crossref]

G. W. Stroke, D. Brumm, A. Funkhouser, and R. Restrick, J. Opt. Soc. Am. 55, 1566A (1965).

G. W. Stroke, Appl. Phys. Letters 6, 201 (1965).
[Crossref]

E. N. Leith, J. Upatnieks, and K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).
[Crossref]

C. C. Eaglesfield, Electronics Letters 1, 181 (1965).
[Crossref]

J. A. Armstrong, IBM J. Res. Develop. 9, 171 (1965).
[Crossref]

B. J. Thompson, Japan J. Appl. Phys. Suppl. I 4, 302 (1965).

1964 (4)

J. B. DeVelis, J. Opt. Soc. Am. 54, 1407 (1964).

G. B. Parrent and B. J. Thompson, Opt. Acta 11, 183 (1964).
[Crossref]

A. Franks, Nature 201, 913 (1964).
[Crossref]

G. W. Stroke and D. G. Falconer, Phys. Letters 13, 306 (1964).
[Crossref]

1963 (2)

B. J. Thompson, J. Opt. Soc. Am. 53, 1350 (1963).

A. J. Campbell, Proc. Roy. Soc. (London), Ser. A 274, 319 (1963).
[Crossref]

1961 (1)

1955 (2)

G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955).
[Crossref]

H. M. A. El-Sum and A. V. Baez, Phys. Rev 99, 624 (1955).

1952 (4)

H. M. El-Sum and P. Kirkpatrick, Phys. Rev. 85, 763 (1952).

A. V. Baez, J. Opt. Soc. Am. 42, 756 (1952).
[Crossref]

A. V. Baez, Nature 169, 963 (1952).
[Crossref]

M. E. Haine and T. Mulvey, Nature 170, 202 (1952).
[Crossref] [PubMed]

1951 (1)

D. Gabor, Proc. Phys. Soc. (London) B64, 449 (1951).

1949 (3)

S. T. Stephenson and F. D. Mason, Phys. Rev. 75, 1711 (1949).
[Crossref]

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

R. Witty and P. Wood, Nature 163, 323 (1949).
[Crossref]

1948 (2)

F. Zernike, Proc. Phys. Soc. (London) 61, 147 (1948).
[Crossref]

D. Gabor, Nature 161, 777 (1948).
[Crossref]

1940 (1)

H. W. B. Skinner, Phil. Trans. Roy. Soc. (London), Ser. A 239, 95 (1940).
[Crossref]

1933 (1)

H. M. O’Bryan and H. W. B. Skinner, Phys. Rev. 44, 602 (1933); Phys. Rev. 45, 371 (1934).
[Crossref]

1932 (1)

G. Kellström, Nova Acta Soc. Sci. Upsal. 8, 60 (1932).

Alexander, L. E.

H. P. Klug and L. E. Alexander, X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials (John Wiley& Sons, Inc., New York, 1954), pp. 87–88.

Armstrong, J. A.

J. A. Armstrong, IBM J. Res. Develop. 9, 171 (1965).
[Crossref]

Baez, A. V.

A. V. Baez, J. Opt. Soc. Am. 51, 405 (1961).
[Crossref]

H. M. A. El-Sum and A. V. Baez, Phys. Rev 99, 624 (1955).

A. V. Baez, Nature 169, 963 (1952).
[Crossref]

A. V. Baez, J. Opt. Soc. Am. 42, 756 (1952).
[Crossref]

A. V. Baez and H. M. A. El-Sum, in X-Ray Microscopy and Microradiography, V. E. Cosslett, A. Engström, and H. H. Pattee, Eds. (Academic Press Inc., New York, 1957), pp. 347–366.

Bearden, J. A.

J. A. Bearden, Rev. Mod. Phys. 39, 48 (1967).

Bedo, D. E.

Birks, L. L.

L. L. Birks, Electron Probe Microanalysis (Wiley–Interscience, Inc., New York, 1963), p. 133.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), 3rd ed., p. 384.

Brumm, D.

G. W. Stroke, D. Brumm, A. Funkhouser, and R. Restrick, J. Opt. Soc. Am. 55, 1566A (1965).

G. W. Stroke, D. Brumm, and A. Funkhouser, J. Opt. Soc. Am. 55, 1327 (1965).
[Crossref]

Campbell, A. J.

A. J. Campbell, Proc. Roy. Soc. (London), Ser. A 274, 319 (1963).
[Crossref]

Clark, G. L.

G. L. Clark, Applied X Rays (McGraw–Hill Book Co., New York, 1955), 4th ed., p. 115.

Codling, K.

Cosslett, V. E.

V. E. Cosslett, Modern Microscopy (Cornell University Press, Ithaca, New York, 1966), pp. 139–156.

For a discussion of total reflection of x rays see, V. E. Cosslett and W. C. Nixon, X-Ray Microscopy (Cambridge University Press, Cambridge, England, 1960), pp. 87–91.

Cullity, B. D.

B. D. Cullity, Elements of X-Ray Diffraction (Addison–Wesley Publ. Co., Reading, Mass., 1956), p. 6.

DeVelis, J. B.

J. B. DeVelis, G. B. Parrent, and B. J. Thompson, J. Opt. Soc. Am. 56, 424 (1966).
[Crossref]

J. B. DeVelis, J. Opt. Soc. Am. 54, 1407 (1964).

J. B. DeVelis and G. O. Reynolds, Theory and Applications of Holography (Addison–Wesley Publ. Co., Reading, Mass., 1967), pp. 43–48, 73.

Diamond, F. I.

Duncumb, P.

P. Duncumb and P. K. Shields, in The Electron Microprobe, T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, Eds. (John Wiley & Sons, Inc., New York, 1966), p. 284.

P. Duncumb, in The Encyclopedia of Spectroscopy, G. L. Clark, Ed. (Reinhold Publ. Corp., New York, 1960), pp. 768–776; in The Encyclopedia of X Rays and Gamma Rays, G. L. Clark, Ed. (Reinhold Publ. Corp., New York, 1963), pp. 818–824; Brit. J. Appl. Phys. 11, 169 (1960).

Eaglesfield, C. C.

C. C. Eaglesfield, Electronics Letters 1, 181 (1965).
[Crossref]

Elgin, R. L.

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Reporter 14, 112 (1967).

El-Sum, H. M.

H. M. El-Sum and P. Kirkpatrick, Phys. Rev. 85, 763 (1952).

El-Sum, H. M. A.

H. M. A. El-Sum and A. V. Baez, Phys. Rev 99, 624 (1955).

A. V. Baez and H. M. A. El-Sum, in X-Ray Microscopy and Microradiography, V. E. Cosslett, A. Engström, and H. H. Pattee, Eds. (Academic Press Inc., New York, 1957), pp. 347–366.

H. M. A. El-Sum, doctoral dissertation, Stanford University (1952).

Evans, R. D.

R. D. Evans, The Atomic Nucleus (McGraw–Hill Book Co., New York, 1955), p. 565; E. H. S. Burhop, The Auger Effect and Other Radiationless Transitions (Cambridge University Press, Cambridge, 1952).

Falconer, D. G.

G. W. Stroke and D. G. Falconer, Phys. Letters 13, 306 (1964).
[Crossref]

Franks, A.

A. Franks, Nature 201, 913 (1964).
[Crossref]

Funkhouser, A.

G. W. Stroke, D. Brumm, A. Funkhouser, and R. Restrick, J. Opt. Soc. Am. 55, 1566A (1965).

G. W. Stroke, D. Brumm, and A. Funkhouser, J. Opt. Soc. Am. 55, 1327 (1965).
[Crossref]

Gabor, D.

D. Gabor, Proc. Phys. Soc. (London) B64, 449 (1951).

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

D. Gabor, Nature 161, 777 (1948).
[Crossref]

Giles, J. W.

Haine, M. E.

M. E. Haine and T. Mulvey, Nature 170, 202 (1952).
[Crossref] [PubMed]

Haines, K. A.

Henke, B. L.

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Reporter 14, 112 (1967).

B. L. Henke, in Advances in X-Ray Analysis, G. R. Mallett, M. Fay, and W. M. Mueller, Eds. (Plenum Press, Inc., New York, 1966), Vol. 9, pp. 430–439.
[Crossref]

Johnson, G. L.

G. L. Johnson, doctoral dissertation, Stanford University (1962).

G. L. Johnson and R. F. Wuerker, in X-Ray Optics and X-Ray Microanalysis, H. H. Pattee, V. E. Cosslett, and A. Engström, Eds. (Academic Press Inc., New York, 1963), pp. 229–239.

Jönsson, C.

G. Möllenstedt, K. H. von Grote, and C. Jönsson, in Ref. 57, pp. 73–79.

Kellström, G.

G. Kellström, Nova Acta Soc. Sci. Upsal. 8, 60 (1932).

Kirkpatrick, P.

H. M. El-Sum and P. Kirkpatrick, Phys. Rev. 85, 763 (1952).

P. Kirkpatrick and H. H. Pattee, in Handbuch der Physik, Vol. 30, S. Flügge, Ed. (Springer-Verlag, Berlin, 1957), p. 320.

Klug, H. P.

H. P. Klug and L. E. Alexander, X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials (John Wiley& Sons, Inc., New York, 1954), pp. 87–88.

Ledingham, R. B.

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Reporter 14, 112 (1967).

Leith, E. N.

Lent, R. E.

B. L. Henke, R. L. Elgin, R. E. Lent, and R. B. Ledingham, Norelco Reporter 14, 112 (1967).

Mason, F. D.

S. T. Stephenson and F. D. Mason, Phys. Rev. 75, 1711 (1949).
[Crossref]

Messiah, A.

See, A. Messiah, Quantum Mechanics, Vol. II, (North–Holland Publ. Co., Amsterdam, 1962), p. 1015.

Möllenstedt, G.

G. Möllenstedt, K. H. von Grote, and C. Jönsson, in Ref. 57, pp. 73–79.

Mulvey, T.

M. E. Haine and T. Mulvey, Nature 170, 202 (1952).
[Crossref] [PubMed]

Nixon, W. C.

For a discussion of total reflection of x rays see, V. E. Cosslett and W. C. Nixon, X-Ray Microscopy (Cambridge University Press, Cambridge, England, 1960), pp. 87–91.

O’Bryan, H. M.

H. M. O’Bryan and H. W. B. Skinner, Phys. Rev. 44, 602 (1933); Phys. Rev. 45, 371 (1934).
[Crossref]

Parrent, G. B.

J. B. DeVelis, G. B. Parrent, and B. J. Thompson, J. Opt. Soc. Am. 56, 424 (1966).
[Crossref]

G. B. Parrent and B. J. Thompson, Opt. Acta 11, 183 (1964).
[Crossref]

Pattee, H. H.

P. Kirkpatrick and H. H. Pattee, in Handbuch der Physik, Vol. 30, S. Flügge, Ed. (Springer-Verlag, Berlin, 1957), p. 320.

Restrick, R.

G. W. Stroke, D. Brumm, A. Funkhouser, and R. Restrick, J. Opt. Soc. Am. 55, 1566A (1965).

Reynolds, G. O.

J. B. DeVelis and G. O. Reynolds, Theory and Applications of Holography (Addison–Wesley Publ. Co., Reading, Mass., 1967), pp. 43–48, 73.

Shields, P. K.

P. Duncumb and P. K. Shields, in The Electron Microprobe, T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, Eds. (John Wiley & Sons, Inc., New York, 1966), p. 284.

Silver, S.

S. Silver, in Microwave Antenna Theory and Design, S. Silver, Ed. (McGraw–Hill Book Co., New York, 1949), p. 199.

Skinner, H. W. B.

H. W. B. Skinner, Phil. Trans. Roy. Soc. (London), Ser. A 239, 95 (1940).
[Crossref]

H. M. O’Bryan and H. W. B. Skinner, Phys. Rev. 44, 602 (1933); Phys. Rev. 45, 371 (1934).
[Crossref]

Sommerfeld, A.

A. Sommerfeld, Optics, Lectures on Theoretical Physics, Vol. IV (Academic Press Inc., New York, 1954), p. 195.

Sprague, G.

Stephenson, S. T.

S. T. Stephenson and F. D. Mason, Phys. Rev. 75, 1711 (1949).
[Crossref]

Stroke, G. W.

G. W. Stroke, Appl. Phys. Letters 6, 201 (1965).
[Crossref]

G. W. Stroke, D. Brumm, A. Funkhouser, and R. Restrick, J. Opt. Soc. Am. 55, 1566A (1965).

G. W. Stroke, D. Brumm, and A. Funkhouser, J. Opt. Soc. Am. 55, 1327 (1965).
[Crossref]

G. W. Stroke and D. G. Falconer, Phys. Letters 13, 306 (1964).
[Crossref]

G. W. Stroke, An Introduction to Coherent Optics and Holograpy (Academic Press Inc., New York, 1966), pp. 114–116.

Swanson, N.

Theisen, R.

R. Theisen, Quantitative Electron Microprobe Analysis (Springer-Verlag, Inc., New York, 1965), p. 9.

Thompson, B. J.

J. B. DeVelis, G. B. Parrent, and B. J. Thompson, J. Opt. Soc. Am. 56, 424 (1966).
[Crossref]

B. J. Thompson, Japan J. Appl. Phys. Suppl. I 4, 302 (1965).

G. B. Parrent and B. J. Thompson, Opt. Acta 11, 183 (1964).
[Crossref]

B. J. Thompson, J. Opt. Soc. Am. 53, 1350 (1963).

Tomboulian, D. H.

G. Sprague, D. H. Tomboulian, and D. E. Bedo, J. Opt. Soc. Am. 45, 756 (1955).
[Crossref]

D. H. Tomboulian, in Handbuch der Physik, Vol. 30, S. Flügge, Ed. (Springer–Verlag, Berlin, 1957), p. 273.

Upatnieks, J.

von Grote, K. H.

G. Möllenstedt, K. H. von Grote, and C. Jönsson, in Ref. 57, pp. 73–79.

Winthrop, J. T.

J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 56, 1362 (1966).
[Crossref]

J. T. Winthrop and C. R. Worthington, Phys. Letters 21, 413 (1966).
[Crossref]

J. T. Winthrop and C. R. Worthington, Phys. Letters 15, 124 (1965).
[Crossref]

J. T. Winthrop, Doctoral Dissertation, University of Michigan (1966).

Witty, R.

R. Witty and P. Wood, Nature 163, 323 (1949).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), 3rd ed., p. 384.

Wood, P.

R. Witty and P. Wood, Nature 163, 323 (1949).
[Crossref]

Worthington, C. R.

J. T. Winthrop and C. R. Worthington, Phys. Letters 21, 413 (1966).
[Crossref]

J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 56, 1362 (1966).
[Crossref]

J. T. Winthrop and C. R. Worthington, Phys. Letters 15, 124 (1965).
[Crossref]

Wuerker, R. F.

G. L. Johnson and R. F. Wuerker, in X-Ray Optics and X-Ray Microanalysis, H. H. Pattee, V. E. Cosslett, and A. Engström, Eds. (Academic Press Inc., New York, 1963), pp. 229–239.

Zernike, F.

F. Zernike, Proc. Phys. Soc. (London) 61, 147 (1948).
[Crossref]

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[Crossref]

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[Crossref]

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For a discussion of total reflection of x rays see, V. E. Cosslett and W. C. Nixon, X-Ray Microscopy (Cambridge University Press, Cambridge, England, 1960), pp. 87–91.

See, A. Messiah, Quantum Mechanics, Vol. II, (North–Holland Publ. Co., Amsterdam, 1962), p. 1015.

Reference 31, p. 265.

Reference 12, p. 78.

G. W. Stroke, An Introduction to Coherent Optics and Holograpy (Academic Press Inc., New York, 1966), pp. 114–116.

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Figures (8)

Fig. 1
Fig. 1

Parameters used in discussion of recording of x-ray hologram of glass fiber.

Fig. 2
Fig. 2

Diffraction-pattern irradiance vs position for Rayleigh–Sommerfeld method.

Fig. 3
Fig. 3

Diffraction-pattern irradiance vs position for Huygens–Fresnel method.

Fig. 4
Fig. 4

Schematic diagram of modified electron microprobe used in this experiment.

Fig. 5
Fig. 5

Parameters used in discussion of glass fiber as black diffracting screen.

Fig. 6
Fig. 6

Enlarged negative hologram of 5.9-μ glass fiber obtained with 114-Å x rays.

Fig. 7
Fig. 7

Densitometer trace of negative of hologram shown in Fig. 6.

Fig. 8
Fig. 8

Photographically enlarged positive print of reconstructed real image (between upper and lower arrows) from x-ray hologram with visible light.

Tables (1)

Tables Icon

Table I Positions of experimentally and theoretically determined interference maxima and minima for 5.9-μ glass fiber.

Equations (43)

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Z 0 ( ζ 2 + η 2 ) max / λ 1 ;             Z 1 ( ζ 2 + η 2 ) max / λ 1 ,
Z 0 ( 2 a ) 2 / λ 1 ;             Z 1 ( 2 a ) 2 / λ 1 .
( 2 b ) 2 / λ 1 Z 1 ;
Z 0 = 4.67 cm , Z 1 = 7.85 cm , λ 1 = 114 Å , b = 0.508 cm , 2 a = 5.9 × 10 - 4 cm ,
u ( x ) = - 1 4 π σ u ( ξ ) G u ( ξ , x ) d σ .
( 2 + k 1 2 ) G ( ξ , x ) = δ ( ξ - x ) ,
k 1 = 2 π / λ 1             and             G = 0 on σ .
I ( x ) = 1 - 2 k 1 a 2 Z 1 sin k 1 x 2 2 Z 1 sinc ( k 1 a x Z 1 ) + k 1 2 a 4 Z 1 2 [ sinc ( k 1 a x Z 1 ) ] 2 ,
I = ( 1 2 ) [ M 2 + N 2 ] I 0 ,
M = - - p + q cos π v 2 2 d v + p + q + cos π v 2 2 d v , N = - - p + q sin π v 2 2 d v + p + q + sin π v 2 2 d v ,
p = a [ 2 λ 1 ( 1 Z 0 + 1 Z 1 ) ] 1 2             q = x [ 2 Z 0 λ 1 Z 1 ( Z 0 + Z 1 ) ] 1 2 ,
M = - 0 cos π v 2 2 d v - - p + q 0 cos π v 2 2 d v + 0 cos π v 2 2 d v - 0 p + q cos π v 2 2 d v , N = - 0 sin π v 2 2 d ν - - p + q 0 sin π v 2 2 d v + 0 sin π v 2 2 d v - 0 p + q sin π v 2 2 d v ,
C ( W ) = 0 W cos π v 2 2 d v , S ( W ) = 0 W sin π v 2 2 d v ,
C ( - W ) = - C ( W ) ,             S ( - W ) = - S ( W ) , C ( ) = - C ( - ) = 1 2 ,
S ( ) = - S ( - ) = 1 2 ,
I / I 0 = ( 1 2 ) ( M 2 + N 2 ) = ( 1 2 ) { [ 1 - C ( p + q ) - C ( p - q ) ] 2 + [ 1 - S ( p + q ) - S ( p - q ) ] 2 } .
d = 4 × 10 - 6 V 2 A / Z 2 / ρ ,
A / Z 2 = 0.558 ρ = 1.82 g / cm 3 V = 8 keV
d = 0.785 μ .
λ SWL ( Å ) = 12 400 / V ,
I const . spectrum = A i Z V m ,
and             I = Bi ( V - V K ) 2             V K < V < 3 V K I = Bi ( V - V K )             V > 3 V K ,
d a = 0.5 λ 1 / N . A . = 0.5 λ 1 / sin α ,
Δ l = ( λ ¯ 1 ) 2 Δ λ 1 ,
X max ( 2 Z 1 Δ l ) 1 2 .
L λ 1 > d / ( 2 N k n 2 )
k n 2 = 1 / [ 8 ( n + 1 ) ]             for             n 5 ,
δ = ( 1.22 ) Z 1 ( λ 1 / c ) ,
( 2 N ) - 1 ,
Si 112 000 , O 2 55 000 , Mg 127 000 , Na 115 000 , B 11 500 ,
Al 109 000 cm 2 / gram .
n = 1 - δ λ 2 ,
δ = ρ 2 π e 2 m c 2 ,
sin σ c = [ 2 ( 1 - n ) ] 1 2 = ( 2 δ ) 1 2 λ c ,
I = I u e - μ ρ Z ,
I / I u = e - 33.4 .
tan ψ = 0.508 cm / 7.85 cm
ψ = 3.7 ° .
I 1 I 0 = 3.9 × 10 - 7 cm 0.5 cm 10 - 6
k 2 / R 2 - k 1 R 1 / [ Z 1 ( R 1 + Z 1 ) ] + k 2 / Z 2 = 0 ,
1 / R 2 + 1 / Z 2 = 1 / f ;
m = ( λ 2 / λ 1 ) ( Z 2 / Z 1 ) .
λ 1 = 114 Å , λ 2 = 6328 Å , Z 2 = 1.27 cm , Z 1 = 7.85 cm ,