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This question is related to this one; I am asking a very similar one because I didn't see in the answers how to arrive to a numeric answer in practice.

Suppose I'm going to shoot a portrait and have most other parameters figured out:

Sensor size: full frame; focal distance: 100 mm; subject distance: 1.5 meters; desired DoF: something like "would like the face to be sharp and the rest look blurred on 8x10 prints".

Now I want to compute the aperture that would help me take that shot. I need to clarify two things for that:

First, I need to make make the notions of "sharp" and "blurred on 8x10 prints" numeric; that is, I have to decide what's the size of the circle of confusion on a full frame that separates "sharp" from "blurred".

Second, I need to assign a numeric value to the depth of focus that would make the face sharp and the the wall behind the subject blurred.

Thus the questions:

  1. What numeric values for the circle of confusion correspond to the above scenario?

  2. What DoF values are appropriate for portrait shots?

  • The size of the circle of confusion is just a made-up number. You choose what you want it to be. If you want sharper, you choose a smaller number. If you're more tolerant, you choose a larger number. (I leave it to someone else to write an detailed account of how to pick a specific number.) – xiota Jan 21 at 23:57
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    Your second question is simply: all of them. There are more common focal lengths and more common apertures...but at the end of the day...they’re all “appropriate”. – Hueco Jan 22 at 1:40
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Cribbing liberally from Wikipedia's Circle of confusion article, then with the information you provided, you can calculate what the CoC should be.

In the following equation,

  • ƒ is the lens's focal length;
  • N is the f-number (aperture) of the lens;
  • S₁ is the distance to the in-focus subject;
  • S₂ is the distance beyond which you determine to be not in acceptable focus.

Then the formula for your CoC is (remember to be consistent with units):

equation for circle of confusion

So for your 100 mm lens (I'm going to assume ƒ/2.8), focusing on the tip of the person's nose at 1.5 m away, and giving a far depth of field of 2 cm (0.02 m), then the CoC is calculated as (0.02/1.52) * (0.1²/(2.8 * 1.4)) = 0.033 mm. This is somewhat close to the 0.03 mm cited by WayneF in his answer. Note that it sounds close, but that 10% difference in CoC size actually translates to a (relatively) huge difference in depth of field.

For 8" × 10" prints viewed at about 10" away, typical visual acuity results in a CoC of 0.029 – 0.030 mm.

  • How is S2 determined? Does OP have to take and print test shots until he finds the DOF that he is happy with, and then measure the distance to the out of focus subject? Thats sounds like a pretty expensive and time consuming way to do it. – Orbit Jan 23 at 9:39
  • @Orbit S2 is chosen. It's the arbitrary distance that you decide that anything closer to S1 is "acceptably in focus". Unless you were using some precise test targets that allowed you to measure the blur (resolution) at S2, it's not really measurable. But that's just part-and-parcel of the whole DoF thing: the DoF is a soft quality that is easy to mathematically define, but not really quantifiably measurable in photos — its presence and degree are characterized by its quality (especially relative to another photo w/ different DoF). – scottbb Jan 23 at 13:27
  • But if you then use the CoC value that you get in a DOF calculator, and you keep aperture and subject distance the same, it will just give back the DOF that you have arbitrarily chosen (S2). The DOF calculators use exactly the same formula, so you would just go around in circles. – Orbit Jan 23 at 17:26
  • @Orbit. Yes. Again, that's the nature of DoF calculation. If you are trying to quantitatively determine CoC given S1, S2, N, and ƒ, that's what you get. People want to approach DoF as an engineering or RPG player min-max thing. Sure, the math will show you a bunch of theoretical stuff. But it's all based on calculations from the thin-lens equation, which is just 1st-order approximation for marginal rays close to the optical axis. In the end, DoF limits are arbitrary boundaries based on arbitrary decisions (lp/mm resolution, or "sufficiently in/out of focus" focal distances, etc.). – scottbb Jan 23 at 21:58
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With full frame, use f/8 with appropriate lens (maybe 100 to 120 mm) to allow 8 or 10 foot subject distance, and focus on the near eye, and you'd do fine (with the subject sharpness). That is perhaps 7+ inches of total DOF span, with subject in the middle.

Lenses are "sharp" at only the one focused distance, and become progressively less sharp with distance away from focus.

Full Frame CoC is typically used as 0.03 mm, which in practice has seemed mostly reasonable. CoC only provides a limiting guide for calculating DOF numbers for an 8x10 inch print (meaning, at the DOF extreme near or far range, CoC WILL BE 0.03mm diameter blur there of a point source. The 0.03 mm on the full frame sensor is historically judged to Not be very detectable by the human eye on an 8x10 inch print (viewed at about 10 inches). When CoC grows to 0.03 mm with distance, DOF calculations announce that is the DOF limit distance). Whether that result pleases you or not is your own decision. If it does, then DOF calculations can tell you if your focal length, distance and aperture will provide that range. Deciding a different CoC does not affect the image sharpness in any way. It simply produces different DOF numbers which you may find more appropriate (or not), but it does not change the image in any way. The lens does what it does. DOF tries to compute what it does, based entirely on the decided CoC guideline that you find acceptable.

  • Maybe adding a formula for calculating the COC would be useful. COC=(acceptable blur in print)/(enlargement factor). – Orbit Jan 22 at 16:21
  • Thanks. I am a little surprised though with f/8 for portraits: I thought most photographers prefer f/2.8, and some even invest into 85 mm f/1.4. – Michael Jan 22 at 16:39
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    @Orbit, IMO it's more usual to use the standard CoC, and then DOF computes that range. Standard CoC was selected by history to be slightly better than the human eye can detect any problem in an 8x10 inch print. However, larger prints may of course need it better. But technically, any notion of selecting a better CoC without considering viewing enlargement and human eye capabilities is missing all the facts. – WayneF Jan 22 at 22:17
  • @Michael, I meant f/8 in the studio. Some do imagine they need very wide aperture to blur the background outdoors, but then all they get is all the wide aperture can do. IMO, professionals who hope to sell the result would never use f/1.4 or f/1.8 without extreme need first, and certainly never in the studio. Even outdoors, they instead know the better plan is to use a longer lens and stand back more, for greater background blur results, and for a selectively small background area, and certainly better sharpness at the subject too. My site has info at scantips.com/lights/dof.html – WayneF Jan 22 at 22:18
  • @WayneF "But technically, any notion of selecting a better CoC without considering viewing enlargement and human eye capabilities is missing all the facts" Thats exactly why I suggested basing the CoC on those two factors. I agree that using the default is most convenient, but some people have special wishes. Then it could make sense to deviate from the default. I think an answer that gives both options is more complete. – Orbit Jan 23 at 9:02
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Since "Standard Viewing Conditions" assumed by the vast majority of depth of field (DoF) calculators that don't offer the option of inputting specific viewing sizes and distances are based on an 8x10 inch image viewed at 10-12 inches by a person with 20/20 vision, the default circles of confusion (CoC) of 0.03 mm for full frame cameras and 0.02 mm or 0.019 mm for 1.5X and 1.6X APS-C cameras, respectively, can be used for your intended purpose.

On the other hand, if you decide you want the same depth of field with a 16x20 image, also viewed at 12 inches by a person with 20/20 vision, you would need to halve the CoC (because you doubled the display size) and use a CoC of 0.015 mm for a FF camera. Likewise, if you only want to view at a 4x5 inch display size, you can double the CoC (because you halved the display size) to 0.06 mm.

If you decide to use the more stringent standard that assumes the viewer has 20/15 vision, as Zeiss does with their lens specifications, then for an 8x10 inch image viewed at 10-12 inches you need to use a CoC of 0.025 mm for FF cameras and 0.017 mm or 0.016 mm for 1.5X and 1.6X APS-C cameras, respectively.

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