A theoretical study is made of the possibilities of using an annular aperture to increase the focal depth of a photographic objective. It is shown that for a given gain in focal depth the loss in speed is the same for both annular apertures and conventional stopping down. For images of isolated point objects, the definition is improved by using an annular stop. The gain in focal depth is less for off-axis points, but it is found that, for example, a factor of 2.7 in focal depth gained by means of an annular aperture is barely affected at a field angle of 30°.
W. T. WELFORD, "Use of Annular Apertures to Increase Focal Depth," J. Opt. Soc. Am. 50, 749-752 (1960)