Help me calculate/understand the physics of aperture, DOF and BG blur -

Started 7 months ago | Discussions thread
Darren James New Member • Posts: 12
Re: Help me calculate/understand the physics of aperture, DOF and BG blur -

Hi Bill,

I did my own review in the meantime and it still conflicts with your original comments. I am not sure what I am to make of the depth of field calculator from PhotoPills which only mentions exit pupil once in reference to pupil magnification for macro work (great app btw!) and an archived web page by an independent author. I was hoping for something a bit more.. official? Excerpt from a textbook on the subject, course outline from an optical engineering course, something like that.

Here is what I know of the subject, which I admit may not be correct, but is similarly reflected on Wikipedia and thus has the benefit of being crowd-sourced by some of the most dedicated, and dare I (lovingly) say, analretentive, people on the planet. I have recreated it here along with citations.

Depth of Field calculation:

for a given circle of confusion (c), focal length (f), f-number (N), and distance to subject (u)

Elizabeth Allen; Sophie Triantaphillidou (2011). The Manual of Photography. Taylor & Francis. pp. 111ā€“. ISBN 978-0-240-52037-7.

"Depth of field".

F-number calculation:

where f is the focal length and D is the diameter of the entrance pupil (effective aperture)


Smith, Warren Modern Optical Engineering, 4th Ed., 2007 McGraw-Hill Professional, p. 183.

As we can see, Entrance Pupil is the term that factors into the final DOF calculation, at least according to Modern Optical Engineering, 4th Edition, published by McGraw-Hill Professional.

So I'm going to go with the textbook on this one, at least until it can be credibly shown to be incorrect. Although, at the end of the day I'm not sure it matters in practice: because aperture open, shallower DOF, aperture closed, deeper DOF.

Edit: If anything, I don’t dispute that an equation exists that includes exit pupil (you could replace D with Exit Pupil/Pupil Mag) but rather I dispute your assertion that Entrance Pupil is not a factor, as there clearly seem to be proofs for DOF that use Entrance Pupil.

bclaff wrote:

Darren James wrote:

Hi Bill,

Indeed, the entrance and exit pupils have different virtual diameters, which is easy to experience by looking at both ends of a lens.

Every source I have read references the entrance pupil and distance to the exact external plane in focus (I simplified this as referencing distance to subject). This seems to be a possible knowledge gap for me, as I am taking these sources at their face value which may be a mistake.

In that same spirit: Can you provide me an independent source that is not your own website for your correction about exit pupil being the important factor for depth of field as opposed to entrance pupil? I don’t mean to cause offence, but as I don’t know you or your website in any great detail I don’t have any cause to prioritize your information over any other source. I hope you understand.

Indeed I miss-used depth of focus. Even as a film shooter I have trouble keeping those terms straight.

I know there are others but here are a couple things to ponder:

Derivation of the DOF equations (via "wayback machine")This great site on optics is no longer online and although I have a mirror copy the author has not given me permission to share it with the world.

Macro Depth of Field (Dof) CalculatorThis calculator provides for Pupil magnification which is most relevant in close-up work.

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