## Tuesday, November 13, 2018

### Further examples on using the Rule of 10

In the last couple of posts I introduced and illustrated, what I call, the Rule of 10 (ROT) approach to focusing. Namely, achieving focus solutions in your head, without any Apps or look-up tables.

In this post I’ll continue with a few more examples. All assuming a full frame, 35mm camera system, ie infinity blurs (Circle of Confusions, CoCs) between 30 microns and 10 microns.

Although the ROT can be used for long lenses, I believe it is best suited for short to wide angle lenses.

For example, with a 200mm lens, the initial (ie before adjustments) ROT focus, at F/10 and with a CoC (infinity blur) of 200 microns (FL in microns), will be 20m (FL/10 = 200/10).

Clearly, an infinity blur of 200 microns needs adjusting, say, to 20 microns (to make the numbers easy), giving a final ROT (at 20 microns CoC, ie 1/10 of 200 microns) of 200m (20 * 10). Thus giving a depth of field (at 20 microns) of 100m (ROT/2) to infinity.

Whereas at, say, a focal length of 16mm, the initial (and final) F/10 ROT = 1.6m (16/10) at a CoC of 16 microns. Giving a depth of field of 0.8m (1.6/2) to infinity.

And at a focal length of 50mm, the initial F/10 ROT = 5m (50/10) at a CoC of 50 microns. Leading to an adjusted ROT (to achieve 25 (50/2) microns, say) of 10m. Giving a depth of field of 5m (10/2) to infinity.

In other words, my guidance is to restrict the ROT approach to lenses shorter than, say, 50mm. Also, for lenses shorter than 28mm, your ROT CoC (FL in microns) will automatically fall into the 10-30 micron range: 30 microns being OK quality and 10 microns being high quality.

As for focus stacking, the approach here should be to decide the maximum blur you wish to see through the scene and make this the infinity blur (CoC).

As an example, let’s use a 20mm lens and look at seeing what three focus brackets does for us, at, say, a maximum blur of 10 microns.

First the ROT at F/10 is simply 2m, ie 20/10, but with an infinity blur of 20 microns, ie the FL in microns. As we need to realise a 10 micron blur, ie half of the initial figure of 20 microns, all we need to double the initial ROT, ie to 4m.

We then use our simple stacking rule, ie focus at the odd numbers, to work out the focus points, namely:
• ROT/1 = 4m - contributing a depth of field of ROT/0 to ROT/2
• ROT/3 = 1.3m - contributing a depth of field of ROT/2 to ROT/4
• ROT/5 = 0.8m - contributing a depth of field of ROT/4 to ROT/6
The final near depth of field being ROT/6 = 4/6 = 0.66m; giving a final depth of field, over three images, of 0.66m to infinity, at a maximum blur of 10 microns, ie a high-quality focus bracket capture.

As usual with ROT-based focusing, the above examples were all done in my head: no paper; no apps; no look-up tables.

Well, as we know, diffraction blurring will occur through the scene and can be estimated from k*N, where k is around 1.3 for a visible band camera, ie not an IR one, and N is simply the aperture number. The usual practice being to combine the lens defocus blur with the diffraction blur, in quadrature. That is the total-blur^2 = Lens-blur^2 + diffraction-blur^2.

This allows us to calculate the lens ROT-based CoC, ie infinity blur, requirement from required-ROT-blur = SQRT(total-blur^2 - diffraction-blur^2).

Thus, if we are shooting at F/10 our diffraction blur can be estimated at 13 microns (1.3*10). If we now need to find an infinity blur (total) solution at, say, 30 microns, then we can calculate the lens component, ie our final ROT blur, at SQRT(30^2 -13^2), ie just over 27 microns.

But what if the total blur requirement was 15 microns at F/10? Well this would result in a final ROT blur of SQRT(15^2 - 13^2), ie some 7 microns.

As we can see, accounting for diffraction complicates our simple ROT method. Thus, my recommendation is that you seek out defocus solutions (on a full frame) between 10 and 20-25 micron.

That is, if you wish to account for diffraction, don’t push the lens defocus blur beyond 20-25 microns, and keep it down around 10 microns for the highest quality. Also don't push the aperture much beyond F/10, unless you are only uploading to Facebook, or you really need to cover the near field and you can't focus bracket.