Distributions of irradiance <i>H</i> in the sharply focused diffraction images of self-radiant line elements are examined for objectives of Sonine type <i>S</i><sub>0</sub>, <i>S</i><sub>1</sub>, and S<sub>2</sub> 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 <i>H</i>(<i>x</i>) along the length <i>x</i> of the diffraction image, the only outstanding, common characteristic is the point of steepest slope, at which <i>dH</i>(<i>x</i>)/<i>dx</i> assumes its greatest value. The relationships between the distance <i>x</i><sub><i>a</i></sub> from the center of the image to the point of steepest slope and the half-length <i>K</i> of the geometrical image are derived and tabulated for types <i>S</i><sub>0</sub>, <i>S</i><sub>1</sub>, and <i>S</i><sub>2</sub>. Distances <i>x</i><sub><i>a</i></sub> have a strong tendency to equal <i>K</i>. It is found that objectives of type <i>S</i><sub>0</sub> are more sensitive than the classical Airy type <i>S</i><sub>1</sub> 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)