In the last post I introduced a hyperfocal-based model to 'calibrate' in-camera focus bracketing, to be able to set the manufacturers’ step size, from 1 to 10, according to the overlap blur we wish to use.

Using the model we can also __estimate__ the number of brackets that will
be captured for a given deep focus, ie near to
infinity.

In this post we will extend the model to cover the macro use case, eg using a magnification of 1; where, unlike in non-macro photography, we need to account for a few other things, such as the (object) magnification and the pupil magnification.

The advantage of having a model to __estimate__ the number of brackets to take is that the alternative is to guess a number and hope you have set enough to cover the required focus range, or simply set the number to a very large number, and then, in post processing, throw away all the images you don’t need.

As in the last post we will start with the simplified hyperfocal bracketing model, but adjust it to bracket between a near point in focus (x) and a far point (y), which is less than the hyperfocal:

From the above all we need to do, to estimate the number of brackets (B), is to solve the following:

Where n is the number of hyperfocal brackets at the nearest point of focus, and m the number at the furthest point of interest. Giving us:

Where H is the short form of the hyperfocal distance, giving us, after simplification:

Which in turn we can write as:

Finally, as we are now covering large magnification, we should recognise N, the aperture number, in its non-infinity form, ie respecting magnification and the pupil magnification. Giving us, via the bellows factor, our final estimate for the number of macro brackets:

Where f is the focal length, N is the infinity aperture number, ie as quoted on the lens, m is the magnification, ie reproduction ratio, p the pupil magnification, and C the overlap blur we wish to use.

To illustrate how to use the above, let’s look at a Canon EF-M 28mm f/3.5 Macro IS STM lens on my Canon M6 Mk II.

Using the last post, and wishing to use an overlap blur (C) of 10 microns, I’ll select a step size of 4.

I’ll select an (infinity) N of f/8.

From the PhotonsToPhotos optical bench the lens details at a magnification of 1 are as follows:

From the above we can find x, the nearest focus we can achieve after focusing at a magnification 1, ie at the minimum focus distance. Unlike in the previous post, where we could get away with using a common zero at the entrance pupil, in macro photography we need to be slightly more selective; remembering that focus distance is measured from the front principal, blue H (which is not the hyperfocal H) in the above diagram, which gives us a minimum focus distance (x) of 36mm, ie the distance between O and H in the diagram.

The P2P lens information also tells us the pupil magnification (p), at this focus, is 1.9.

The final piece of data is to decide what y to use, once again measured from the front principal, which we will do by adding a delta distance to x, in this example 20mm, as the flower in this test image is small. We will also assume the same magnification and pupil magnification at x and y.

Plugging all the above in the equation for B gives us the following:

That is, we need to set the number of images to capture to at least 31.

It is then a simple matter to switch the macro lens to its minimum focus, switch on the inbuilt lens light, set the focus bracketing to on, the image count to 35 (adding a few images for insurance) and the step size to 4. Then move the camera so that the nearest part of the subject was in focus, set exposure, and press the shutter.

After ingesting 35 images into Lightroom, using LR’s denoise feature (although I did shoot at ISO 100), and a round trip to a focus stacking app and a little bit of LR tweaking, I ended up with the following test image:

As you can see, I missed placing the nearest focus, but, overall, I think the above model, the overall process and the experiment was worth it; as I now have a way of estimating the number of macro images to set.

Using the above equation we can also explore other lenses, for instance I have an EF 100mm f/2.8L IS USM macro. Keeping the aperture the same as above, but using the 100mm details from P2P, results in the required number of brackets to cover the same 20mm flower being 11, which can be compared to the 31 required with the 28mm macro at the same unity magnification. The model allowing us to see the advantages of using a telephoto 100mm lens, ie pupil magnification of 0.28, rather than a retrofocus 28mm lens with a pupil magnification of 1.9; and exploiting the larger working distance of the 100mm.

Bringing this post to a conclusion, I hope the above has been helpful to others trying to get the best out of their in-camera macro focus bracketing.

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