
258 OPTICS FOR ENGINEERS
81%. We should be careful not to “mix and match,” however. It is common, and incorrect, to
use the 81% Wadsworth criterion for the valley depth and the 0.61λ/NA Rayleigh criterion for
the spacing of the points.
In 1916, Sparrow, recognizing [149] that the 81% (or 73%) valley depth is arbitrary,
suggested dening the resolution that just minimally produces a valley, so that the second
derivative of irradiance with respect to transverse distance is zero. Wider spacing results in
a valley (rst derivative positive) and narrower spacing leads to a single peak (rst derivative
negative). Sparrow’s idea is sound theory, but in practice, ...