Thursday, April 8, 2021

M3 Brackets: Pupil Magnification Update

Assuming you have read the last post, you will know what this post is all about: namely adding pupil magnification to the M3 Bracketing script.

Rather than explicitly modelling pupil magnification, I've decided to 'exploit' pupil magnification as overlap focus insurance.

Without proof, the expression (in u space, ie from the front principal) for the next focus position is:

Where f is the focal length, p the pupil magnification and h is (f*f)/(Nc).

Following from the last post, M3 Brackets now includes a new menu item called

Assumed Pupil Mag

The thinking behind the new menu item is that it is easy to know if the lens you are using is of a retrofocus or telephoto design, by simply looking at the exit and entrance pupils (see the last post). Plus you can eyeball things to estimate the pupil magnification, ie without measuring anything.

As most deep focus bracketing will be undertaken with a retrofocus lens (telephoto focus bracketing will likely result in there being too many brackets), this post will only discuss that use case in detail. If your lens is telephoto and you still wish to use M3 Brackets to auto focus bracket, then set "Assumed Pupil Mag" to 1, where you are guaranteed to underestimate telephoto DoFs, ie achieve positive focus bracketing overlaps.

In the case of a retrofocus lens, we know that if we ignore the pupil magnification (p), we will over estimate the depth of field; which could result in focus gaps. 

As a reminder the following chart shows the amount we will over estimate if we ignore pupil magnification. Each contour is at 10% value, varying from 0 to 100% over/under estimate. The top part of the curve applies to retrofocus lenses (where we overestimate DoF by assuming a symmetric lens), the bottom to telephoto ones (where we underestimate DoF by assuming a symmetric lens). The chart also graphically shows a retrofocus lens is rather insensitive to pupil magnification at low image magnifications.

Let's now consider a real example, using the EF-M 11-22mm lens at 11mm.

If we 'eyeball' the lens the exit and entrance pupils are small! But the pupil mag looks to be about 4, ie the exit pupil diameter looks to be about four times the size of the entrance pupil. That is it’s a retrofocus lens.

To be sure, let's use an M3 Brackets value of 5 and enter this as our assumed pupil magnification. 

If we just look at pupil magnifications greater than 1, as we have a retrofocus lens, our plot now looks like this:

 Let's zoom in a bit:

The above tells us that, as the maximum magnification of the lens is 0.3, by assuming a pupil magnification of 5, if the actual p was 5, we would model the DoF correctly: obviously!

If, on the other hand, at the maximum object magnification the pupil magnification was only, say, 2, ie we were way off guesstimating p, we would be underestimating the DoF by just under 10%. Which is good when you are focus bracketing, where you are trying to not create focus gaps against your blur criterion. Nor do you wish to create large overlaps, which will increase the number of brackets you need to take.

As I don't wish to bore readers with more of the gory details, let's cut to the bottom line. When using M3 Brackets:

  • Check if your lens, at the focal length of interest, is of a retrofocus or telephoto design;
  • Estimate the pupil magnification by eye, eg 2 or 4 or 0.5;
  • If your estimate is less than 1, ie you are using a telephoto lens, then set M3 Brackets Assumed Pupil Mag to 1;
  • If your estimate is greater than 1, ie you are using a retrofocus lens, then set M3 Brackets Assumed Pupil Mag to slightly larger than what you think the pupil magnification is;
  • Set the overlap blur to a sensible number, eg 20 um;
  • Set the infinity blur value to, say, 3, ie we will take a final image at three times the hyperfocal, giving an infinity blur of 20/3, ie about 7 um.

Finally, as I've said before, M3 Brackets is ideally suited for wide angle lenses, eg the EF-M 11-22mm. Having said that, I've now added my other EF-M lenses to the pre-registered list, as you can use M3 Brackets outside of Alt mode to set focus on any registered lens:

  • EF-M11-22mm f/4-5.6 IS STM
  • EF-M28mm f/3.5 MACRO IS STM
  • EF-M55-200mm f/4.5-6.3 IS STM
  • EF-M18-55mm f/3.5-5.6 IS STM

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

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