Saturday, November 10, 2018

Infinity focusing in your head: The rule of 10.

For those that just want the answer, you can safety skip to the bottom of this post.

If you are a landscape photographer, you tend to have a dominant focusing need: namely getting everything from a sensible near field feature to infinity ‘in focus’.

You will also know that the ‘out of focusness’ is a blurring in your image, mainly composed of two components: the defocus that the lens creates and diffraction.

The lens defocus varies through the scene, whereas we can assume the diffraction blur remains constant.

As a landscape photographer you will also know that the lens defocus blur is only zero at the point, or plane, of focus. Falling off rapidly, and approaching infinity, in the near field; and collapsing to a value at infinity, which we call the circle of confusion (coc).

Then, of course, we have the hyperfocal distance (for example see which is where the infinity defocus blur is just acceptable for our needs.

Our needs will vary according to how we are presenting our image, for instance to judges in a print competition or online. Without regurgitating well-known things: for a full frame format, an infinity blur (coc) of, say, 30 microns, is considered OK. But for higher scrutiny, blurs lower than this should be used, recognizing that blurs below about 2 sensor pixels is likely not going to help that much more, so this is a pragmatic lower blur limit.

The above ignores the addition of diffraction blur, which most people add in through a little bit of (root mean square) math, which in this article we will be seeking to dispense with.

But, for completeness the diffraction blur is directly proportional to the aperture number, eg F/5.6 or F/16. At visual, ie not IR, frequencies the constant is about 1.3. That is the diffraction blur due to diffraction, which we assume doesn’t vary with distance, is some 1.3*N (in microns). 

If we now make use of the simplified hyperfocal equation, where we assume a simple lens arrangement and drop a few insignificant terms, we can estimate the hyperfocal distance (H), that is just due to lens defocus blur, as H = FL*FL/(N*C).

Where FL is the focal length in mm; N the aperture number; and C the circle of confusion also in mm, ie the defocus blur that meets our focus quality criterion.

Many who are reading this will have attempted to calculate the above themselves, or use one of the many Apps or look-up tables that are available, to estimate H. Some may have also fallen into the ‘trap’ of thinking that focusing a ‘third into the scene’ is a good place to go.

Whatever approach you have used to date, is mainly because the arithmetic can, at times, get non-trivial to do in your head.

So let’s make focusing trivial!

To do this all we need to do is make C (the coc in microns), our defocus blur criterion, equal to the FL (in mm) and focus at F/10. If we do this H simply becomes FL/10 in meters.

So now we have the Rule of 10 for landscape focusing.

Before you say that’s stupid. Let’s go through what we have done in order to make calculating H a trival matter of dividing the lens focal length by 10.

As we know our lens quality varies as we change aperture, with a pragmatic sweet spot often being accepted as 2 stops down from being wide open. We also know that if we stop down too much, then diffraction blur counteracts against the increase in depth of field. That is there is another, depth of field, sweet spot that most recognize as being around F/10, without complicating things with format changes, ie full frame compared with crop.

Thus, an aperture of F/10 is a good starting point for a landscape photographer seeking to achieve focus from infinity to near, and balance out lens defocus with diffraction softening

As for choosing C to be FL, really FL/1000 to account for the fact that we speak of C in microns, that is simply a way of making in-head calculations trivial.

Hence we have H, in meters, as FL*FL/(10*FL) = FL/10.

To bring this all together, without proof, we also should note that having defocus blurs, ie ignoring the diffraction component for now, of between 30 microns (OK quality) and 10 microns (high quality) is where we need to be.

So, let’s look at a few examples using the Rule of 10.

Case 1

Full frame camera at a focal length of 30mm, shooting to achieve OK defocus quality. Where should we focus?

Our rule of 10 tells us that we should focus at 3m into the scene, at which point the infinity (defocus) blur will be FL in microns, ie 30 microns, which is our OK criterion.

We also know, from the full hyperfocal equations, that the depth of field in the near field extends, from the focus point (H), back to H/2, where the defocus blur at that point is the same as at infinity, ie in this case 30 microns.

Thus the depth of field extends from 1.5m to infinity.

Well this looks too simple to be true: as we haven’t used an App or a look-up table, and have calculated things in out head. But that’s the beauty of the F/10 rule.

So, in this example, at a focal length of 30mm and at an aperture of F/10, our hyperfocal distance is at 3m, where we will realize a circle of confusion, ie an infinity blur, of 30 microns.

Case 2

Let’s extend case 1, before looking at other cases. Let’s say that a CoC, or infinity blur, needs to be higher quality, say double the quality at 15 microns.

Well our rule of 10 tells us that the blur we are using is 30 microns, ie FL in microns. So to achieve a blur of 15 microns, half of our FL (in microns), all we need to do is double the focusing distance. That is, instead of focusing at 3m, we focus at 6m into the scene.

Of course, now the depth of field, using our 15 micron criterion, extends from 6m, ie H/2, to infinity.

Case 3 – FL < 30mm

Let’s assume a focal length of, say, 16mm. What does our rule of 10 tell us?

Simply that if we focus at 1.6m (FL/10), at an aperture of F/10, we will achieve a depth of field from 0.8m (H/2 = 1.6/2) to infinity with a circle of confusion (defocus) blur of 16 microns (FL in microns).

Well a defocus blur of 16 microns is pretty good quality, ie it falls towards the high quality end of our CoC range of 10-30 microns.

But let’s assume we are ‘only’ shooting for Facebook and that we need to maximise the focus in the near field as much as possible, ie there is a feature of interest. Because we are uploading the image on line, we can tolerate shooing with an infinity blur at the low end, say, around 30 microns: in fact we could go higher than this, but for now we will assume 30ish microns.

Once again, all we need to do is note the difference between where we are, ie at 16 microns (FL in microns) and where we wish to be, ie 30ish microns: which is about a doubling. Thus, we can now refocus at half of where we are. Instead of at FL/10, ie 1.6m, we can refocus to 0.8m. Of course, now we are at 0.8m, we know that the depth of field (noting we are now using a coc of 32 microns) extends from 0.4m (H/2) to infinity.

Case 4 – FL > 30mm

Although as landscape photographers we tend to shoot wide, what if we need to shoot longer. Say at 50mm. What does our rule of 10 tells us?

Simply that, if we focus at 5m (ie FL/10 giving H = 5m) at an aperture of F/10, we will achieve a depth of field from 2.5m to infinity but (sic) with a coc of 50 microns.

As it is unlikely a CoC of 50 microns will be acceptable we need to adjust the focus. But by how much?

The F/10 rule tells us that to reduce the coc by X, we simple adjust the focus by X. That is, if we wish to achieve a coc of around 16 microns, that is about a third of 50 microns (FL in microns), then we need to refocus at 3 times from where we are using the F/10 rule, ie at 5*3, or 15m.

Which will give us a near field depth of field distance (at a coc of 50/3 microns) of 7.5m (15/2).

As the intention of this post was to just introduce the Rule of 10 for (landscape) focusing, I’ll sum up the main points:

  • Assuming you wish to achieve near to infinity focus, ie for landscapes, you should set the aperture to F/10 and focus at FL/10 in meters.
  • At this focus the circle of confusion, ie lens defocus at infinity, will be FL in microns.
  • If you wish to achieve a lower or higher coc, ie infinity defocus, all you need to do is refocus by the ratio of FL to your final coc criterion.
In future posts I’ll look further into the ‘Rule of 10’, but for now I hope you get some benefit out of the rule. At least you will now be able to leave your look up tables and Apps at home, and achieve a more informed focus than hoping 1/3 into the frame is OK. All in your head!

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