Editing Depth of field (section)

==DOF formulae==
This section covers some additional formula for evaluating depth of field; however they are all subject to significant simplifying assumptions: for example, they assume the [[paraxial approximation]]  of [[Gaussian optics]]. They are suitable for practical photography, lens designers would use significantly more complex ones.

===Focus and f-number from DOF limits===
For given near and far {{abbr|DOF|depth of field}} limits {{math|''D''{{sub|N}}}} and {{math|''D''{{sub|F}}}}, the required [[f-number]] is smallest when focus is set to

<math display="block">s = \frac{2 D_{\mathrm N} D_{\mathrm F}}{D_{\mathrm N} +  D_{\mathrm F}},</math>

the [[harmonic mean]] of the near and far distances. In practice, this is equivalent to the [[arithmetic mean]] for shallow depths of field.<ref>{{Cite web |last=Conrad |first=Jeff |title=Depth of Field in Depth |url=https://www.largeformatphotography.info/articles/DoFinDepth.pdf |access-date=10 February 2023 |website=Large Format Photography Info}}</ref>  Sometimes, view camera users refer to the difference {{math|''v''{{sub|N}} &minus; ''v''{{sub|F}}}} as the ''focus spread''.{{sfn|Hansma|1996| p=55}}

===Foreground and background blur===
If a subject is at distance {{mvar|s}} and the foreground or background is at distance {{mvar|D}}, let the distance between the subject and the foreground or background be indicated by

<math display="block">x_{\mathrm d} = |D - s|.</math>

The blur disk diameter {{mvar|b}} of a detail at distance {{math|''x''{{sub|d}}}} from the subject can be expressed as a function of the subject magnification {{math|''m''{{sub|s}}}}, focal length {{mvar|f}}, [[f-number]] {{mvar|N}}, or alternatively the [[aperture]] {{mvar|d}}, according to

<math display="block">b = \frac{fm_\mathrm s}{N} \frac{x_\mathrm{d}}{s \pm x_\mathrm{d}} = dm_\mathrm{s} \frac{x_\mathrm{d}}{D}.</math>

The minus sign applies to a foreground object, and the plus sign applies to a background object.

The blur increases with the distance from the subject; when {{mvar|b}} is less than the circle of confusion, the detail is within the depth of field.