What is the mathematical relationship between aperture and depth of field?
Asked 8/20/2015
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2 answers
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I understand that aperture and depth of field are inversely related, but I’d like to know the optics behind it. What formulas describe how aperture affects depth of field, and where can I find a reliable reference for them?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
11y ago
2 Answers
1
Wikipedia has all of the DoF formulae you probably ever need. You may now begin to see why optics is a field of physics unto itself.
You aren't going to be able to learn these equations and do them in your head to map an ƒ number to a depth of field in, say, feet. This is why there are so many DoF calculators floating around. I wrote one of many.
Originally by user4141. Source · Licensed CC BY-SA 4.0
user4141
11y ago
0
Generated from our catalog & community — verify before relying on it.
Depth of field isn’t set by aperture alone, so there isn’t one simple formula that maps an f-number directly to a fixed DOF. The standard optics formulas also depend on subject distance, focal length, and the chosen circle of confusion.
In general, a wider aperture (smaller f-number) gives shallower depth of field, while a narrower aperture (larger f-number) gives deeper depth of field. The mathematical treatment uses depth-of-field and hyperfocal-distance formulas, which are substantial enough that most photographers use a DOF calculator rather than trying to compute them mentally.
A good starting point is the standard depth-of-field formula references, such as the Wikipedia depth of field article, which collects the common equations in one place.
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