Focus Bracketing: An Integrated Perspective

In previous posts I've discussed focus bracketing models from both the object and image side of the lens. In this post I'll bring together both perspectives and show they are essentially the same.

Before going into the details, I have to admit an error crept into my first post in this series, about focus bracketing, that I've now corrected.

Also, up until now I've constructed my object side model by assuming focus bracketing takes place from the hyperfocal, thus requiring an additional bracket to be added to account for a focus bracket at infinity. In this post, I'll assume the object side focus, hyperfocal bracketing model, starts at infinity:

In the above we see that the first focus bracket is at H/0, ie infinity, and the last bracket, ie the nearest to the camera, is placed at H/(2(n-1)). Thus if the last bracket was, say, the 5th, that bracket would be taken at H/8. Noting that x, the nearest focus distance, is measured from the front principal which, in this model, is also the entrance pupil, as we are ignoring pupil magnification.

To estimate the number of brackets, all we need to do is solve x = H/(2(n-1)), for n.

We thus end up with the simple insight that the number of brackets, ie images to be taken, can be estimated from (H/(2x) + 1).

If we now substitute the approximation for H, (f*f)/(N*C), ie dropping the single focal length term, we end up with the number of brackets (n) being given by:

To appreciate the image and objective side perspectives, we can now layout the two models, side by side:

As previously discussed, from the image side perspective, the number of brackets can be estimated by dividing the total depth of focus at infinity (2NC) into the lens extension at the nearest focus of interest and adding one, to account for the fact we are starting at infinity or at the minimum focus distance (MFD). If we take the extreme focus to be the MFD, the lens extension is simply the focal length (f) times the magnification (M) at the MFD. Which gives us an estimate of the maximum number of brackets, from the image side perspective, of:

These two models are virtually the same for lenses, when the focal length is small relative to the focus distance, where we can approximate magnification as f/x, rather than use f/(x-f). 

Clearly, the simplest model to use to explore auto focus bracketing, is that from the image side, eg the overlap circle of confusion being estimated from:

As an example, let's say we wish to estimate the circle of confusion (C) for an auto bracketing step size of 4. All we need to do is set the camera to the focal length of interest (if it is a zoom), set the aperture, and either measure or accept the manufacturer's stated magnification at the MFD; and then focus at the MFD and take a bracket set, even with the lens cap on.

Let's say the focal length was 22mm, the aperture was set to f/11, that the magnification at the MFD was 0.3 and that 16 images were captured.

Plugging these numbers into (f.M)/(2.N.(n-1)) gives us an estimated overlap circle of confusion of 20 microns.

It’s as simple as that.

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