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.
© 1964 Optical Society of America
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