Let's assume a thin lens and an object O in focus at a distance of dO from the lens. Further, let's assume there's a large out-of-focus background object B at a distance of dB. Now, we know intuitively, and can easily derive from the thin lens formula, that as dB tends to infinity, the image of B on the projection surface asymptotically approaches some finite amount of "blurriness" -- the focused image of B is formed at some finite distance from the projection surface, and by straightforward geometry, points of B are projected as blur circles whose diameter is proportional to that distance.

However, as dB grows, the "amount" of background visible in the image grows proportionally to it. When striving to achieve a minimally distracting background, we often seek to minimize the amount of background visible while maximizing the blur. My question is: Is there a rule of thumb for figuring out an "optimal" dB as a function of dO that does just that? Obviously the focal length and aperture size of the lens matter greatly here, but let's assume that these are fixed andwe can only change dB.

  • For that you would need to formulate something to make the "distractingness" of the background measurable. How distracting the background is at different distances depends on what the background looks like, and in what way that would be distracting. – Guffa Aug 1 '14 at 11:32
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    There will be no mathematical optimal distance or even a rule of thumb, as the tradeoff between including more of the background and having the background more blurred depends entirely on the content of the background! – Matt Grum Aug 1 '14 at 11:44

I think the only possible answer to your question is "no such rule of thumb exists". The problem is just too complicated - as Matt indicates in a comment, how "distracting" the background is depends immensely on the content of the background, so you're first of all going to have to capture that. And if you can do that, you're pretty close to having reduced "art" to "science", and at that point I suspect you're going to be able to make a lot more money from your algorithm than by telling some photographers how far away to put their background.

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  • Yeah, I suppose this was more of an exercise in thinking aloud (and not quite thinking through) than a "proper" question from my part. Still, the answer and comments were helpful, thank you, and sorry about the delay in accepting! – JohannesD Aug 12 '14 at 14:53

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