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Recovery of Specimen Information for Strongly Scattering Objects

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Computer Processing of Electron Microscope Images

Part of the book series: Topics in Current Physics ((TCPHY,volume 13))

Abstract

The previous chapter described the highly satisfactory theory of image formation and processing that results when the specimen is sufficiently thin and light to be treated in projection, and produces no more than slight attenuation and phase shifting of the incident electron beam. This limit is an increasingly close approximation as accelerating voltage and resolution increase; it is an approximation at best, however, and is sometimes simply untenable. Accordingly, this chapter is devoted to the much more difficult problem of image correction for stronger objects, when the imaging process is nonlinear. Although more laborious than the analyses applicable to weak objects, the methods reviewed here are still useful if applied to specimens which are too thick or heavy to be weak, but not too much so to be treated in projection still.

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References

References

  1. P.W. Hawkes: Electron Optics and Electron Microscopy ( Taylor and Francis, London 1972 )

    Google Scholar 

  2. D.L. Mi sell: J. Phys. D9 9 1849–1866 (1976)

    ADS  Google Scholar 

  3. D.L. Mi sei 1: In Advances in Optical and Electron Microscopy, ed. by V.E. Coss- lett, R.E. Barer, Vol. 7 ( Academic, London 1979 ) pp. 185–279

    Google Scholar 

  4. D.F. Lynch, A.F. Moodie, M.A. O’Keefe: Acta Cryst. AZI 9 300 - 307 (1975)

    Article  Google Scholar 

  5. P. Goodman, A.F. Moodie: Acta Cryst. A30 9 280 - 290 (1974)

    Google Scholar 

  6. WlO. Saxton: Computer Techniques for Image Processing in Electron Microscopy, Advances in Electronics and Electron Physics Supp. Vol. 10, ed. by L. Marton ( Academic, New York 1978 )

    Google Scholar 

  7. D.L. Mise!1, R.E. Bürge, A.H. Greenaway: J. Phys. D7, L27–30 (1974); an almost identical paper appears in Nature 247, 401–402 (1974)

    Google Scholar 

  8. D.L. Mi sei 1, A.H. Greenaway: J. Phys. D7, 832–855, 1660–1669 (1974)

    Google Scholar 

  9. A. Lannes: In Proc. 4th Int. Cong. High Voltage Electron Microscopy Toulouse 1975, ed. by B. Jouffrey, P. Favard ( SFME, Paris 1976 ) pp. 155–158

    Google Scholar 

  10. A. Lannes: J. Phys. D9 9 2533–2544 (1976)

    ADS  Google Scholar 

  11. P. van Toorn, A.M.J. Huiser, H.A. Ferwerda: Optik 51, 309–326 (1978)

    Google Scholar 

  12. A.M. MacLeod, J.N. Chapman: J. Phys. E10, 37–42 (1977)

    ADS  Google Scholar 

  13. R.W. Gerchberg, W.O. Saxton: Optik 35, 237–246 (1972)

    Google Scholar 

  14. R.W. Gerchberg, W.O. Saxton: In Image Processing and Computer-Aided Design in Electron Optics, ed. by P.W. Hawkes ( Academic, London 1973 ) pp. 66–81

    Google Scholar 

  15. D.L. Mi sell: J. Phys. D6 9 L6–9 (1973)

    ADS  Google Scholar 

  16. D.L. Mise!1: J. Phys. D6 9 2200–2216, 2217–2225 (1973)

    Google Scholar 

  17. R.W. Gerchberg, W.O. Saxton: J. Phys. D6 9 L31 (1973)

    ADS  Google Scholar 

  18. R.W. Gerchberg: Nature 2409 404–406 (1972)

    Article  ADS  Google Scholar 

  19. J.N. Chapman: Philos. Mag. 527–540, 541–552 (1975)

    Article  ADS  Google Scholar 

  20. N. Toms, J.N. Chapman, R.P. Ferrier: Manchester (1972), pp. 422–423

    Google Scholar 

  21. A.M.J. Huiser, A.J.J. Drenth, H.A. Ferwerda: Optik 45, 303–316 (1976); A.M.J. Huiser, H.A. Ferwerda: Optik 4,407–420 (1976); A.M.J. Huiser, P. van Toorn, H.A. Ferwerda: Optik 47, 1–8 (1977); P. van Toorn, H.A. Ferwerda: Optik 47, 123–134 (1977)

    Google Scholar 

  22. J.A. Venables (ed.): Developments in Electron Microscopy and Analysis ( Academic, London 1976 )

    Google Scholar 

  23. M. Horner: In Ref. 2.22, pp. 209–212

    Google Scholar 

  24. P. Schiske: Optik 40, 261–275 (1974)

    Google Scholar 

  25. H. Lipson, W. Cochran: The Determination of Crystal Structures (Bell, London 1966 )

    Google Scholar 

  26. E.N. Fowle: IEEE Trans. IT-10, 61–67 (1964)

    Google Scholar 

  27. P. Schiske: J. Phys. D8, 1372–1386 (1975)

    ADS  Google Scholar 

  28. A.J.J. Drenth, A.M.J. Huiser, H.A. Ferwerda: Opt. Acta 22, 615–628 (1975); B.J. Hoenders, H.A. Ferwerda: Opt. Acta 23, 445–456 (1976); P. van Toorn, H.A. Ferwerda: Opt. Acta 23, 457–468, 469–481 (1976)

    Google Scholar 

  29. S.R. Robinson: J. Opt. Soc. Am. £5, 87–92 (1978)

    Google Scholar 

  30. E.M. Hofstetter: IEEE Trans. U-10, 119–127 (1964)

    Google Scholar 

  31. H.B. Voelcker: Proc. IEEE 54, 340–353, 735–755 (1966)

    Google Scholar 

  32. J. Gassmann: Optik 48, 347–356 (1977)

    Google Scholar 

  33. J. Gassmann: Acta Cryst. A33, 474–479 (1977)

    Article  Google Scholar 

  34. W.J. Dallas: Optik 44, 45–49 (1975)

    Google Scholar 

  35. R.H.T. Bates: Optik 51, 161–170, 223–234 (1978)

    Google Scholar 

  36. W.J. Dallas: Opt. Commun. 18, 317–320 (1976)

    Article  ADS  Google Scholar 

  37. H.A. Ferwerda: Jerusalem (1976), Vol. 1, pp. 1–3

    Google Scholar 

  38. R.A. Gonsalves: J. Opt. Soc. Am. 66, 961–964 (1976)

    Article  ADS  Google Scholar 

  39. J. Frank: Biophys. J. 12, 484–511 (1972)

    Article  Google Scholar 

  40. W.O. Saxton, A. Howie, A. Mistry, A. Pitt: In Developments in Electron Microscopy and Analysis 1977, ed. by D.L. Mi sei 1, Institute of Physics Conference Series 36 ( Institute of Physics, London 1977 )

    Google Scholar 

  41. H.A. Ferwerda, B.J. Hoenders, A.M.J. Huiser, P. van Toorn: Photogr. Sei. Eng. 21, 282–289 (1977)

    Google Scholar 

  42. H.A. Ferwerda: “The Phase Reconstruction Problem for Wave Amplitudes and Coherence Functions”, in Inverse Source Problems in Optics, ed. by H.P. Baltes, Topics in Current Physics, Vol. 9 ( Springer, Berlin, Heidelberg, New York 1978 ) pp. 13–39

    Google Scholar 

  43. B.J. Hoenders: “The Uniqueness of Inverse Problems” in Inverse Source Problems in Optics, ed. by H.P. Baltes, Topics in Current Physics, Vol. 9 ( Springer, Berlin, Heidelberg, New York 1978 ) pp. 41–82

    Google Scholar 

  44. W.O. Saxton: J. Phys. D7, L63–64 (1974)

    ADS  Google Scholar 

  45. J.C.H. Spence: Opt. Acta 10, 835–837 (1974)

    Article  ADS  Google Scholar 

  46. W. Hoppe, R. Langer, F. Thon: Optik 30, 538–545 (1969)

    Google Scholar 

  47. D.L. Mi sei 1: J. Phys. D7, L69–71 (1974)

    ADS  Google Scholar 

  48. K.H. Downing, B.M. Siegel: Optik 42, 155–175 (1975)

    Google Scholar 

  49. W.O. Saxton: “The Theory of Image Formation and Processing” in Ref. 2.22, pp. 191–196

    Google Scholar 

  50. R.E. Bürge, M.A. Fiddy, A.H. Greenaway, G. Ross: J. Phys. D7, L65–68 (1974)

    Article  Google Scholar 

  51. R.E. Bürge: In Principles and Techniques of Electron Microscopy: Biological Applications, ed. by M.A. Hayat, Vol. 6 ( Van Nostrand-Reinhold, New York 1976 ) pp. 85–116

    Google Scholar 

  52. W. Hoppe: Z. Naturforsch. 1 155–1 168 (1971)

    Google Scholar 

  53. A.H. Greenaway: “Determination of the Image Wavefunction with Particular Reference to Electron Microscopy”; Thesis, Queen Elizabeth College, Univ. London (1976)

    Google Scholar 

  54. A. Walther: Opt. Acta 10, 41–49 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  55. B.J. Hoenders: J. Math. Phys. 16, 1719–1725 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  56. R.H.T. Bates: Mon. Not. R. Astron. Soc. 142, 413–428 (1969)

    ADS  Google Scholar 

  57. R.H.T. Bates, P.J. Napier: Mon. Not. R. Astron. Soc. 158, 405–424 (1972)

    ADS  Google Scholar 

  58. R.H.T. Bates, P.J. Napier, A.E. McKinnon, M.J. McDonnell: Optik 44, 183–201 (1976) A.E. McKinnon, M.J. McDonnell, P.J. Napier, R.H.T. Bates: Optik 44, 253–272 (1976)

    Google Scholar 

  59. R.E. Bürge, M.A. Fiddy, A.H. Greenaway, G. Ross: Proc. R. Soc. Lond. A 350, 191–212 (1976)

    Article  ADS  Google Scholar 

  60. J.S. Toll: Phys. Rev. 104, 1760–1770 (1956)

    Article  ADS  MathSciNet  Google Scholar 

  61. G. Ross, M.A. Fiddy, M. Nieto-Vesperinas, M.W.L. Wheeler: Proc. R. Soc. Lond. A 360, 25–45 (1978); a shorter account is given in Optik 49, 71–80 (1977)

    Google Scholar 

  62. M.A. Fiddy: Personal communication

    Google Scholar 

  63. P.J. Napier, R.H.T. Bates: Astron. Astrophys. Suppl. 15, 427–430 (1974)

    ADS  Google Scholar 

  64. H. Wahl: Optik 39, 585–588 (1974)

    Google Scholar 

  65. J. Munch: Optik 43, 79–99 (1975)

    Google Scholar 

  66. R.H.T. Bates, R.M. Lewitt: Optik 44, 1–16 (1975)

    Google Scholar 

  67. R.H. Wade, W.K. Jenkins: Optik 50, 1–17 (1978)

    Google Scholar 

  68. J.E. Baldwin, P.J. Warner: Mon. Not. R. Astron. Soc. 175, 345–353 (1976)

    ADS  Google Scholar 

  69. A.H. Greenaway: Opt. Lett. 1, 10–12 (1977)

    Article  ADS  Google Scholar 

  70. T. Hidaka: J. Opt. Soc. Am. 66, 147–150 (1976)

    Article  ADS  Google Scholar 

  71. A.H. Greenaway, A.M.J. Huiser: Optik 45, 295–300 (1976)

    Google Scholar 

  72. J. Frank: Optik 38, 582–584 (1973)

    Google Scholar 

  73. A.W. Lohmann: Optik 41, 1–9 (1974)

    Google Scholar 

  74. W. Hoppe: Acta Cryst. A25, 495–501 (1969); W. Hoppe, G. Strube: Acta Cryst. A25, 502–507 (1969); W. Hoppe: Acta Cryst. A25, 508–514 (1969)

    Google Scholar 

  75. W. Hoppe, G. Strube: Acta Cryst. A25, 502–507 (1969);

    Google Scholar 

  76. W. Hoppe: Acta Cryst. A25, 508–514 (1969)

    Google Scholar 

  77. R. Hegerl, W. Hoppe: Manchester (1972), pp. 628–629

    Google Scholar 

  78. J.C.H. Spence: Optik 49, 117–120 (1977)

    Google Scholar 

  79. H. Berndt, R. Doli: Optik 46, 309–332 (1976); 51, 93–96 (1978)

    Google Scholar 

  80. J.U. Madsen, R.M.J. Cotterill: Acta Cryst. A34, 378–384 (1978)

    Google Scholar 

  81. W. Krakow, D.C. Ast, W. Goldfarb, B.M. Siegel: Philos. Mag. 985–1014 (1976)

    Google Scholar 

  82. K.H. Downing, B.M. Siegel: Optik 35, 21–28 (1973)

    Google Scholar 

  83. W.K. Jenkins: “Contrast Transfer in Bright-Field Electron Microscopy of Amorphous Objects”; Thesis, Univ. Cambridge (1979)

    Google Scholar 

  84. A. McPherson, Jr.: In Principles and Techniques of Electron Microscopy: Biological Applications, ed. by M.A. Hayat, Vol. 6 ( Van Nostrand-Reinhold, New York 1976 ) pp. 117–240

    Google Scholar 

  85. D.L. Dorset, H.A. Hauptman: U1tramicroscopy 1, 195–201 (1976)

    Article  Google Scholar 

  86. A. Lannes: Opt. Commun. 20, 356–359 (1977)

    Article  ADS  Google Scholar 

  87. A.N. Barrett, D.L. Misell: In Ref. 2.22, pp. 213–216

    Google Scholar 

  88. N.H. Dekkers, H. de Lang: Optik 41, 452–456 (1974); Philips Tech. Rev. 37, 1–9 (1977)

    Google Scholar 

  89. J.N. Chapman, P.E. Batson, E.M. Waddell, R.P. Ferrier: U1tramicroscopy 3, 203–214 (1978)

    Article  Google Scholar 

  90. P.W. Hawkes: J. Opt. (Paris) 9, 235–241 (1978)

    ADS  Google Scholar 

  91. W. Gale, E. Guth, G.T. Trammel 1: Phys. Rev. 165, 1434–1436 (1968)

    Article  ADS  Google Scholar 

  92. F.A. Grünbaum: Proc. Nat. Acad. Sei. USA 72, 1699–1761 (1975)

    Article  ADS  Google Scholar 

  93. B.R. Frieden: “Image Enhancement and Restoration”, in Picture Processing and Digital Filtering, ed. by T.S. Huang, Topics in Applied Physics, Vol. 6 ( Springer, Berlin, Heidelberg, New York 1975 ) pp. 177–248

    Google Scholar 

  94. S.J. Wernecke, L.R. d’Addario: IEEE Trans. C–26, 351–364 (1977)

    Google Scholar 

  95. S.F. Gull, G.J. Daniell: Nature 272, 686–690 (1978)

    Article  ADS  Google Scholar 

  96. J.G. Abies: Astron. Astrophys. Suppl. 15, 383–393 (1974)

    ADS  Google Scholar 

Additional References

  • R.E. Burge, M.A. Fiddy: Object reconstruction in electron microscopy from the real part of the scattered wave, Optik 54, 21–26 (1979). (This area has, however, already been covered more fully elsewhere, cf. Sects.2.2 and 2. 4 )

    Google Scholar 

  • N.H. Dekkers: Object wave reconstruction in STEM. Optik 53, 131–142 (1979)

    Google Scholar 

  • M.A. Fiddy, A.H. Greenaway: Object reconstruction from intensity data. Nature 276, 421 (1978)

    Article  ADS  Google Scholar 

  • W.O. Saxton: “SEMPER-a Portable Image-Processing System Applied to Electron Microscopy”, in Machine-aided Image Analysis 1978, ed. by W.E. Gardner ( Institute of Physics, Bristol 1979 ) pp. 78–87

    Google Scholar 

  • W.O. Saxton, A.J. Pitt, M. Horner: Digital image processing: The SEMPER system. Ultramicroscopy 4, 343–354 (1979)

    Article  Google Scholar 

  • J.C.H. Spence: Practical phase determination of inner dynamical reflections in STEM. Scanning Electron Microscopy/1978, Vol.1 ( SEM, AMF O’Hare, 1978 ) pp. 61–68

    Google Scholar 

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Authors
  1. W. O. Saxton
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Editors and Affiliations

  1. Laboratoire d’Optique Electronique du CNRS, Toulouse Cedex, B. P. 4347, F-31055, France

    Peter W. Hawkes M. A., Ph. D.

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Saxton, W.O. (1980). Recovery of Specimen Information for Strongly Scattering Objects. In: Hawkes, P.W. (eds) Computer Processing of Electron Microscope Images. Topics in Current Physics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81381-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-81381-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81383-2

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