Abstract

Resolution of shape of self-radiant line elements by objectives of Sonine types <i>S</i><sub><i>v</i></sub> is stated quantitatively as the ratio <i>R</i><sub><i>s</i></sub> of length to width of a uniquely chosen contour of constant irradiance in the diffraction image. This contour passes through the point <i>x</i><sub><i>s</i></sub> of steepest slope of the irradiance <i>H</i> (<i>x</i>) along the length <i>x</i> of the geometrical image. Computations are included of the resolution factor <i>R</i><sub><i>s</i></sub> as a function of the halflength <i>K</i> (in Airy units) of line elements imaged by objectives of types <i>S</i><sub>0</sub>, <i>S</i><sub>1</sub>, and <i>S</i><sub>2</sub>. Type <i>S</i><sub>0</sub> excels type <i>S</i><sub>1</sub> (identical with the Airy type) for resolving shape. In turn, the apodized type <i>S</i><sub>2</sub> is inferior to type <i>S</i><sub>1</sub>.

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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.

Burnham, R. W.

R. W. Burnham and J. E. Jackson, Science 122, 951–953 (1955).

Jackson, J. E.

R. W. Burnham and J. E. Jackson, Science 122, 951–953 (1955).

Osterberg, H.

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 406 (1964).

Rowe, L. F.

L. F. Rowe developed the numerical method on a basis of finite differences and used an IBM 7070 computer.

Smith, L. W.

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 406 (1964).

Watson, G. N.

G. N. Watson, Bessel Functions (Cambridge University Press, London, 1944), p. 147.

Other (8)

Objects that scatter radiation into the objective can be considered self-radiant.

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 406 (1964).

R. W. Burnham and J. E. Jackson, Science 122, 951–953 (1955).

L. F. Rowe developed the numerical method on a basis of finite differences and used an IBM 7070 computer.

G. N. Watson, Bessel Functions (Cambridge University Press, London, 1944), p. 147.

See Ref. 2.

See Eqs. (8) and (10) and Ref. 5, p. 417.

See Ref. 5, pp. 666–697.

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