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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 54, Iss. 5 — May. 1, 1964
  • pp: 599–605

Resolution of Shape of Self-Radiant Line Elements

HAROLD OSTERBERG and LUTHER W. SMITH  »View Author Affiliations

JOSA, Vol. 54, Issue 5, pp. 599-605 (1964)

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Resolution of shape of self-radiant line elements by objectives of Sonine types Sv is stated quantitatively as the ratio Rs of length to width of a uniquely chosen contour of constant irradiance in the diffraction image. This contour passes through the point xs of steepest slope of the irradiance H (x) along the length x of the geometrical image. Computations are included of the resolution factor Rs as a function of the halflength K (in Airy units) of line elements imaged by objectives of types S0, S1, and S2. Type S0 excels type S1 (identical with the Airy type) for resolving shape. In turn, the apodized type S2 is inferior to type S1.

HAROLD OSTERBERG and LUTHER W. SMITH, "Resolution of Shape of Self-Radiant Line Elements," J. Opt. Soc. Am. 54, 599-605 (1964)

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  1. Objects that scatter radiation into the objective can be considered self-radiant.
  2. H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 406 (1964).
  3. R. W. Burnham and J. E. Jackson, Science 122, 951–953 (1955).
  4. L. F. Rowe developed the numerical method on a basis of finite differences and used an IBM 7070 computer.
  5. G. N. Watson, Bessel Functions (Cambridge University Press, London, 1944), p. 147.
  6. See Ref. 2.
  7. See Eqs. (8) and (10) and Ref. 5, p. 417.
  8. See Ref. 5, pp. 666–697.

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