Another look at focus bracketing

In recent posts I've explored deep focus bracketing, for example for landscapes, where we wish to capture focus brackets from the minimum focus distance to infinity, using a simple object side hyperfocal based model:

In this post I'll shift my attention to the image side, where things get a lot simpler:

The focal length at distances less than infinity is given by (1+m).F, which is measured from the rear principal. BTW the illustration above is not to scale, it is just to show the concept of using the depth of focus, ie 2.D.

The above image side illustration showing that the lens extension is given by the magnification (m) times the focal length (F). Thus at infinity, where m is approaching zero, we see that the active focal length is simply the manufactuer's quoted focal length, ie as printed on the lens, but at the minimum focus distance (MFD) the active focal length is (1+M).F, where M is the maximum magnification, ie at the MFD.

Using the above, and similar triangles, and noting that C is very much smaller than the aperture, it is easy to show that the ‘near and far’, or front and rear, depth of focus (D), ie not the near and far depth of field which is quoted on the object side, is approximated  by (1+m).C.N, where C is the overlap circle of confusion we wish to use and N is the manufacturer's (infinity) aperture number, ie as quoted on the lens.

From the above we can see that the depth of focus, either side of the point of focus, varies according to the magnification but is independent of the focal length, and that the smallest total depth of focus, ie at infinity, is simply 2.C.N

We can therefore estimate the maximum number of equal lens rotations we need to make, to go from the MFD to infinity, by simply dividing the lens extension (M.F) by 2.C.N, which gives us a very linear appreciation of the maximum number of brackets that could get taken, ie as we have ignored changes in magnification as we focus. Or, put another way, we have introduced some 'focus overlap insurance' by not ‘worrying’ about the depth of focus varying as we adjust focus; which is not a bad assumption when doing non-macro focus bracketing, where the maximum magnification will be low.

To illustrate how we may use the above, let's assume we are using a Nikon 18mm f/2.8 lens, and we wish to manually focus bracket from the MFD to infinity.

The only thing we need to know is the magnification at the MFD, which, as this is a prime lens, we can take from the manufacturer's data sheet, or from PhotonsToPhotos or capture an image of known size, in focus, at the MFD and measure M in Photoshop. The reproduction ratio being quoted as 1:9.1, ie at the MFD, gives an M of 0.11:

We now have all the information we need to estimate the number of brackets to take at, say, an overlap circle of confusion of 20 microns and an aperture of f/10: (M.F)/(2.C.N) = (0.11*18)/(2*0.02*10), which is say 5. It is a simple matter to then use the manual focus bracketing hack that is discussed in the previous post.

To illustrate the advantage of 'going wide', let's look at another lens: an Irix 11mm lens.

Here we see the magnification at the MFD is given as 1:7.68, ie M = 0.13. 

Keeping the CoC at 20 microns and the aperture at f/10, we now arrive at (M.F)/(2.C.N) = (0.13*11)/(2*0.02*10), ie say 4.

Finally, to show why manually focus bracketing a telephoto lens is a bad idea, let’s take a Canon 200mm f/2.8, with a maximum magnification at the MFD of 0.155. In this case, the number of brackets, keeping everything else the same as before, is some 77. Well, good luck with that ;-)

Of course, looking at focus bracketing from the image side is not a new idea, for example see here for an insight into auto focus bracketing, looked at from the image side. However, the above is how I have rationalised manual focus bracketing wide angle lenses from an image side perspective.

The bottom line being: estimating the number of focus brackets, or more correctly the most you need to take, is greatly simplified by considering the image side of the lens and ignoring focus to focus changes in magnification. The final caveat being that, like looking at focus bracketing from the object side, the above image side view is just a model, but one that, hopefully, gives the reader greater appreciation of how focus bracketing works.

As usual I welcome any comments on this post or any of my posts.