Entrance pupil and background blur

A mathematical question regarding optics:

 

After some reading on photo.net and elsewhere, I have come to the understanding

that the actual physical size of the aperture of a lens is directly proportional

to the amount of background blur (circle of confusion) at infinity (the absolute

blur of an object at infinity, given a constant subject magnification). However,

this doesn't hold true for less distant backgrounds. Furthermore, my

understanding is that the entrance pupil (ie, focal length divided by f-stop) is

directly proportional to format size for a given angle of view and f-stop.

 

Put another way, if you were to scale the format size, focal length, and

entrance pupil of a system proportionally, (thus retaining the same f-stop and

angle of view), you would also scale the amount of blur. So, for example, a

Ricoh GR-D (28mm equivalent) f/2.4 would not render the same amount of

background blur as a 28/2.4 lens on a 35 mm camera.

 

Sorry if this explanation is confusing. I'm shaky on the math and physics. Can

anyone confirm or correct me on this?

I am trying to find the question in there?

There is a good explanation and set of equations for depth of field at http://www.bobatkins.com.

<cite>

Can anyone confirm or correct me on this?</cite>

<p>

You're correct. That's a source of the notion that small formats have greater depth of field. When you scale the entire camera system down, you shrink the entrance pupil, and thereby reduce background blur, among other things.

<p>

There are a whole bunch of interrelated variables related to blur. Among them are, the format size, the focal length, the degree of enlargement, the entrance pupil size, the f stop, the reproduction ratio, the focused distance, the angle of view, the circle of confusion size, the depth of field, the image size of a point source at infinity, and probably a few dozen more. They're all interrelated, so when comparing two situations, you've got to decide which factors you want to hold constant and which you allow to vary.

<p>

Different people will hold different things constant and vary others, so will come to different conclusions, such as "Background blur depends only on physical aperture size", or "Depth of field depends only on reproduction ratio and f stop", or "Small and large formats have the same depth of field; it's only the focal length, f stop, and focused distance that matters", or "Small formats have more depth of field than larger formats". Each of these can be defended in its own way. No wonder the subject is confusing.

Paul van Walree explains the intricacies here:

 

http://www.pinnipedia.org/optics/dofderivation.html

 

if you look at his eq4. you will see that your assumptions aren't quite correct:

 

http://www.pinnipedia.org/optics/dofderivation.html#eq4

 

and that in particular the approximate relationship breaks down at close focus. His DoF discussion is also worth reading:

 

http://www.pinnipedia.org/optics/dof.html

 

However, if you use his DoF calculator, you can see how it all plays out - including the corrections for the pupil magnification ratio

Thanks, everyone. The Bob Atkins page is a good summary, and the van Walree site is the best on optics I have seen so far. I'm trying to put together some rules of thumb for different lenses on different formats. I hadn't considered the effect of pupil magnification or lens asymmetry. I guess I'll have to wade through all those equations...

Let me state the obvious: lens mechanics aside, even a cheap P&S digital can shoot beautiful ``Bokeh`` if (the qualifier)<br>1. <i>there is nothing behind your subject to <b>be</b> in focus</i>.<br>2. The further behind your subject, the better the ``Bokeh``. <p>i.e.: careful selection of the/your background can increase or compliment your shots: <br>background detrius = visual distraction.