f/optimum

Optimal Aperture in Photography. 3. Testing the Theory — The Diffraction Blur Coefficient

Summary:  A previous experiment indicated that the effective size of the diffraction blur circle is substantially smaller than customarily assumed.  Smaller size can be accounted for in optimal aperture calculations by incorporating a diffraction blur coefficient, α.  The present paper describes a simple procedure to estimate α.  Although simple in concept, the described experiment can be difficult in practice because results are sensitive to focus accuracy.  The value of the diffraction blur coefficient was determined to be α ≈ 0.70.  That is slightly larger than the value 0.60 from the previous experiment.  Additionally, N_min(Blur) was shown to be an optimal aperture under experimental conditions.

 

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Key words: optimal aperture, diffraction blur coefficient, defocus blur, blur equivalence, Sigma DP3 Merrill, Iridient Developer

 

Optimal Aperture in Photography. 2. Testing the Theory — Blur Equivalence

 

Summary:  The fundamental requirement of optimal aperture calculations is that diffraction and defocus blurs be interchangeable — that they make equivalent contributions to total blur.  Examples are shown in which images that contain exclusively diffraction blur are indistinguishable from images that contain mostly defocus blur.  However, the conditions under which equivalence is obtained imply that the formulas previously used for blur calculation are approximate.  Experimental determination of equivalence suggests that the effective diffraction blur circle may be as little as 60% of the size customarily assumed.  Smaller diffraction blur means smaller optimal aperture, in some cases more by than one f-stop.  That results in a corresponding increase in depth of field at optimal aperture.  If the goal of optimal aperture calculation is to minimize blur of an object at a known distance from the plane of focus, the effect of this correction may be minor — the decreased defocus blur obtained by having a smaller optimal aperture is partially offset by the attendant increase in diffraction blur.  However, if the goal is to maximize depth of field, or to determine hyperfocal distance, while controlling total blur to a specific value, the effect of the diffraction blur correction may be important.

 

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Key words: optimal aperture, diffraction blur coefficient, blur equivalence, Sigma DP3 Merrill, Iridient Developer, Photoshop, defocus blur, Airy disk, Leica Disto D5, depth of field, hyperfocal distance 

Optimal Aperture in Photography. 1. Theory

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:

 

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