Tuesday, November 27, 2018

Understanding Focus: Rule of Ten

In past posts I’ve talked about focus and introduced two tools that help you make informed decisions about focusing, eg The Rule of Ten (ROT). 

In this post I’ll discuss why using the camera-agnostic ROT, is a good idea.

My reason for this tutorial is simple: some have told me they don’t understand what I’ve previously written!

Now that could be 100% down to me and how I write; or, as I prefer to believe, a bit of me and bit of a lack of knowledge in the reader about using blurs to optimise focus.

What follows in this post, ie Part 1, is a reminder on the basics of focus, which is essential to know if you are going to get the best out of the two tools mentioned above.

So what is Focus?

At its simplest focus is subjective and related to the viewing conditions. For example, one person, with a visual acuity of X, looks at a print and sees everything ‘in focus’; whereas, another person, with better eye sight, looking at the same image might see a sight softness in places. Then both look at the same image on a Facebook page and, magically, the image is in focus everywhere, for both of them.

As photographers have considered focus for over a hundred years, we now have ‘accepted standards’ when we talk of ‘sharpness’ or ‘focus’. One of the recognised ways of discussing depth of field assumes (mixing units) an enlargement to 8 x 10 inches, at a viewing distance of 10 inches, and a normal visual acuity of about 5 (black and white) line pairs per mm (lp/mm) at that viewing distance.

We then use this 5 lp/mm, or 0.2mm for 1 lp, on a print, to estimate an acceptable blur, which is often called the circle of confusion (CoC), on the sensor. A recognised estimate being:

If we now assume a full frame sensor, ie 36mm x 24mm, the above becomes:

The above resulting in the oft reported CoC of 29 microns for a full frame camera.

As we can see from the above, if the viewer was not looking at an 8 x 10 inch print at 10 inches, then the CoC would change. For example, viewing a large bill board at 20 feet away vs viewing a Facebook image on a phone screen.

This leads to the first guidance on focusing that I would offer, namely, unless you really know the final viewing size and conditions, stick with the standard CoC guidance. For shear convivence, I personally use 30 microns on a full frame and 20 microns on a crop sensor, as my base CoCs: that is acceptable focus quality; as they are also easy numbers to remember.

Rather than keep saying CoC , I find it more convenient to call the CoC a blur; and recognise that the total blur is made of two main components: the lens defocus blur and the diffraction blur; and without proof, it is usual to discuss these three blurs in the following way:

Lenses, of course, are complex mechanisms and far too complex to handle without a great deal of mathematics and computer modelling. Thus, for convenience, photographers resort to making use of a simple, thin lens model of the lens, that allows us to estimate the focus field in front of and behind the point of focus. These simple equations are really only suited for non-macro photography, eg landscape photography.

Before looking at a little more maths, let’s look at a what a typical lens defocus field looks like, ie ignoring diffraction. The horizontal axis is the distance from the lens (ie approximately the camera) and the vertical axis measures the defocus blur, with the defocus blur criterion, in this plot, being set at 30 microns.

Here we see the classical shape of the defocus blur. The in-focus portion is where the blur is less than our 30 microns. These two distances, near and far, are thus our near and far depths of field.

We also begin to see that, the focus in front of the point of focus, does not equal the focus behind the point of focus. The two extremes being:

· As the point of focus approaches the lens minimum, ie macro shooting, the focus in front and behind collapses towards being the same, ie symmetric around the point of focus.

· There is a distance where the far depth of field is at infinity and the same as our criterion (30 microns here) and, at this point, the near depth of field is half of the focus. This point is called the hyperfocal distance or H.

Once again, for pragmatic reasons, and assuming we are not doing macro photography, we can make further simplifying assumptions that lead to the hyperfocal distance being estimated from the following:

Where f is the focal length and N the aperture number; and where the defocus blur can be found from:

Now the diffraction blur, in microns, can be estimated from:

Where k is 1.34, for normal visible, ie not IR, photography: thus, at an aperture of F/10, the diffraction blur may be estimated at just over 13 microns.

BTW, F/8-F/11 is recognised a sweet spot for a lens in general, ie overall image capture quality.

The above simple equations now give us everything we need to estimate H and account for diffraction; and if we focus at H we get the following result, with an infinity blur of the defocus criterion:

As an example, let’s take our 30mm lens at F/10 and work out H to meet a total (sic) blur of 30 microns. First, the diffraction blur we know is 13.4 microns. Plugging this into the above gives the following:

Which equals 26.8 microns, which we now plug into the equation for H, converting 26.8 microns into mm, to get:

Which gives a diffraction informed hyperfocal distance of 3.35m, which may be compared to the hyperfocal if we did not account for diffraction, which would have been 3m, ie:

Using the ROT to make it simple

The above, although a simplification, is still not that easy to calculate in your head, which is why most revert to Apps or look-up tables, or guess the hyperfocal.

We can, however, greatly simply things by using the Rule of 10, which simply says set the defocus blur to the focal length (f) in microns, ie:

And if we set N to F/10, we have a very simple way of estimating H, in meters, in our heads, ie HROT = f/10.

Thus, in our example above, ie a 30mm lens used at F/10, using the ROT we note that this will be at a defocus blur of 30 microns, ie focal length in microns, H will be 3m.

But let’s say we wish to achieve a higher quality print with a defocus blur, say, of 15 microns; then, using our ROT all we need to do is factor the ROT H by a factor of 2, ie 30/15. Thus, if we focus at 6m, this becomes our new H, but with a defocus blur criterion now of 15 microns.

But what if we weren’t using a 30mm lens? Once again, the ROT approach allows us to quickly calculate where we should focus. As an example, let’s choose a 15mm lens set at F/10 and seek out H at a defocus blur criterion of 30 microns.

Using the ROT methodology, we would focus at 15/10 = 1.5m, but of course this means our defocus blur is the focal length in microns, ie 15 microns, whereas we are seeking H at 30 microns, which is twice the ROT number. So all we need do is focus at half of H, or 0.75m.

Once you get the ROT approach in your head, it is a very simple matter to estimate defocus based hyperfocal distance, H.

As a recap, here is the ROT:

But why are blurs and H so important?

Knowing your defocus blur, and thus H, means you are in full control of focusing information. Also, by being sensible with aperture, ie setting it to 10 or there about, means you are not letting diffraction beat you. Thus, pragmatically, at F/10, you can ignore diffraction and simply use the ROT-informed H. As shown above, if we ignore diffraction the total blur is only made up of the defocus blur, say, at 30 microns, and if we include F/10 based diffraction, the defocus blur only reduces to about 27 microns.

Thus we can safety use the ROT approach without worrying about diffraction, as long as we focus a little beyond H. Certainly 2*H, ie a defocus blur of 15 microns for a 30mm lens using the ROT approach, is well beyond a ‘little beyond H’.

In general, H based focusing looks like this:

Here we see if you focus as H, your near depth of field will be H/2; and if that is not sufficient, all you need to do is refocus at the odd fractions of H, ie H/3, H/5 etc until you have covered your required depth of field needs. Your near and far depths of field at these new points of focus simply become the even fractions either side of the odd fraction. Thus if you focus at H/9, the near and far depths of field will be at H/10 and H/8. Let’s call this the Odds and Evens rule. 

In addition, as you focus towards infinity and away from H, you can simply dial in the infinity blur that you wish to use. Thus at 2H, the infinity blur will be half of that at H.

BTW the above also shows us that the often repeated advice that focus is one third in front and two thirds behind the point of focus, is only true when the focus is H/3.

Pragmatically, five focus brackets is most probably a sensible lower limit, which we now know will extend your near depth of field from H/2, that a single image gives you, to H/10. 

In future posts I’ll discuss how easy it is to use the above to focus bracket by thinking from the lens perspective and not from your eye’s perspective, That is, to focus bracket all we need to do is to rotate the lens, ie refocus, by a fixed amount each time. 

Bottom line

In this post we have reminded ourselves that focus is really the ‘zone of acceptable out of focusness’, based on reasonable assumptions about viewing distance and eyesight. We also recognise that the total blurriness in an image is made up of the lens out of focus and a contribution from diffraction.

In order for diffraction not to become an issue, and to maximise image quality, on a full frame camera,  F/10 is a good place to be capturing images, as we can also make use of a very simple rule (Rule of 10) to find the hyperfocal distance, H. That is H, in meters, is the focal length in mm divided by 10 (or in general N), generating an infinity defocus blur of the focal length in microns.

Finally, knowing this focal length informed H, we can estimate any near and far depth of field; and undertake focus bracketing using the odds and evens rule, ie by focusing at the odd fractional parts of H.

In the next post, now that we know all about blurs and the power of knowing the hyperfocal, I’ll discuss how to make use of the Depth of Field Bar that runs under Magic Lantern.

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