**Introduction**

Camera movement and vibration, subject movement, lens aberrations, defocus, and diffraction can all contribute to blur in photographic images. The subject of this paper is defocus and diffraction, and their combined effects. Defocus blur *decreases* with smaller apertures. On the other hand, diffraction blur *increases* with smaller apertures. Because defocus and diffraction blurs respond in opposite directions to changes in aperture, there can be an optimal setting that minimizes their combined effect. The purpose of this paper is to develop the concept of optimal aperture in photographic applications, and to provide formulas for its determination. This treatment is an expansion of the work of Peterson and Hansma; and the immediate inspiration for the present analysis was provided by several iOS apps developed by George Douvos. In particular, my goal has been to make the mathematics behind optimal aperture calculations explicit, and to extend the analysis to consideration of camera format (sensor size).

**1. Blur**

**1.1 Total Blur**

Peterson and Hansma suggest that the combined effects of defocus and diffraction can be calculated by the following formula:

*Key words: defocus blur, diffraction blur, total blur, optimal aperture, hyperfocal distance, depth of field, camera equivalence, Stephen Peterson, Paul Hansma, George Douvos*