Unified Analysis of Depths of Field and Focus

The depths of field and of focus contribute independently to the size of the circle of confusion in the viewing plane. An integrated analysis permits treating both a three-dimensional object space and a film surface that does not conform to the curvature of the image field, or is not smooth. The investigation is restricted to a symmetric lens in order to avoid complications concerning the size and location of entrance and exit pupils. In a design problem the following quantities are assumed to be specified: (1) the depths of field and of focus, as defined by the nature of the object surface and tolerances in the film plane; (2) the overall magnification between the object and the ultimate image for viewing purposes, as well as the acceptable size of the circle of confusion in the final viewing plane; and (3) the aperture setting, as indicated by the conditions of exposure. For these conditions the camera magnification is uniquely determined — provided that the f/number exceeds a value of m(Do + dp‘)/2c“. In this equation m is the overall magnification, Do is the depth of the object field, dp’ is the accuracy of the lens setting, and c” is the size of the circle of confusion in the viewing plane. In the development, it is assumed that all effects are additive in enlarging the circle of confusion, and also occur at their maximum magnitudes. As a consequence, the worst possible case is analyzed, so that the design is handled conservatively.

Print ISSN

0361-4573

Published

1959-12

Content type

Original Research

DOI

10.5594/J10985