The f-number - new technical article

Some of you like to see pictures of baby birds, and some would like to know more about the f-number. We try to cater to both.

I have recently completed (after years of its being stalled) a technical article giving the background of the f-number, that parameter we use to tell us the photometric performance of a lens. It is entitled "The f-number". I have not yet indexed it on The Pumpkin, but it is directly available here :

http://pumpkin.annex.home.att.net/articles/f-number.pdf

A warning: this article is heavily based on mathematics (there are 47 equations!), although there are many intuitive insights woven in. The mathematics is all algebra - no higher mathematics is involved.

A second warning: One of my anniversary gifts to Carla (ten years on 2009.06.12) was not to ask her to copy edit this article. Thus, there is a greater than normal chance that it will have editorial or typographic errors. I will hope to clean these out in time for its full "publication". Please don't hesitate to help me out there!

The article takes advantages of the insights gained during recent discussions of the matter in various threads in this form. Thanks to my various colleagues for contributing to my understanding and to the most clear and usable identification of the technical factors involved.

Doug_Kerr said:

Some of you like to see pictures of baby birds, and some would like to know more about the f-number. We try to cater to both.

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Both are appreciated, one albeit dry but the other emotive.

Doug_Kerr said:

The article takes advantages of the insights gained during recent discussions of the matter in various threads in this forum.

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I appreciate that you acknowledge the back and forth discussion. especially the contributions by Olaf Ulrich here!

Asher

Hi, Asher,

Asher Kelman said:

I appreciate that you acknowledge the back and forth discussion. especially the contributions by Olaf Ulrich.

We are fortunate to have Olaf join us. I appreciate both his technical background and his awareness of semantic issues.

Best regards,

Doug

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I wish I had time to worry about little things like that, lol

Hi, Daniel,

Daniel Buck said:

I wish I had time to worry about little things like that, lol

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Oh, I don't advocate people worry about anything. Especially little things.

Doug

Hi Doug,

I very interesting article, it answered a question I've often wondered about.

I do feel though that for an article on the f-number, it would be interesting to emphasize that the f-number gives up an exposure notation that's independant of the focal length. For me the f-number's great achievement is that it gives an exposure value that's correct for any focal length (macro aside, as noted) even though the phyical diameter of the aperture changes.

f/2 on a 200mm donates a 100mm diameter, whereas f/2 on a 50mm lens donates a 25mm diameter, and yet the exposure is the same. Cunning stuff I've always felt.

Tim

Hi, Tim,

Tim Armes said:

For me the f-number's great achievement is that it gives an exposure value that's correct for any focal length (macro aside, as noted) even though the phyical diameter of the aperture changes.

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Indeed, that is the f-number's basic attraction - its "claim to fame".

And, through the concept of "effective f-number", we can preserve that benefit into the regime of larger magnifications.

A subtlety that is sometimes not recognized is that the "aperture" of interest here is not the the actual physical aperture stop but rather the entrance pupil, which we could cynically call an "just an optical illusion". (If we put the aperture stop in front of all the lens elements, as in many "box cameras", there is no difference, but for most cases of interest to us, the distinction is significant.)

Best regards,

Doug