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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 54, Iss. 3 — Mar. 1, 1964
  • pp: 406–409

Optical Measurement of Self-Radiant Line Elements by the Method of Steepest Slopes

HAROLD OSTERBERG and LUTHER W. SMITH  »View Author Affiliations

JOSA, Vol. 54, Issue 3, pp. 406-409 (1964)

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Distributions of irradiance H in the sharply focused diffraction images of self-radiant line elements are examined for objectives of Sonine type S0, S1, and S2 with the view to finding a common characteristic that can be applied to the systematic measurement of length of line elements. With respect to the distribution H(x) along the length x of the diffraction image, the only outstanding, common characteristic is the point of steepest slope, at which dH(x)/dx assumes its greatest value. The relationships between the distance xa from the center of the image to the point of steepest slope and the half-length K of the geometrical image are derived and tabulated for types S0, S1, and S2. Distances xa have a strong tendency to equal K. It is found that objectives of type S0 are more sensitive than the classical Airy type S1 for measuring the shortest measurable line elements.

HAROLD OSTERBERG and LUTHER W. SMITH, "Optical Measurement of Self-Radiant Line Elements by the Method of Steepest Slopes," J. Opt. Soc. Am. 54, 406-409 (1964)

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  1. R. W. Burnham and J. E. Jackson, Science 122, 951–953 (1955).
  2. G. N. Watson, Bessel Functions (Cambridge University Press, London, 1944), p. 373.
  3. H. Osterberg and J. E. Wilkins, Jr., J. Opt. Soc. Am. 39, 553–557 (1949).
  4. A. Gray, G. Mathews, and T. MacRobert, Bessel Functions (Macmillan and Company Ltd., London, 1931), pp. 300–302.

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