Aperture values

One thing I don't understand when looking at the exif details of a digital photograph, the difference between the "aperture value" and the "F-Stop".

If you look they are completely different, e.g.

F-Stop: f/11
Aperture Value: f/6.9 .

Shouldn't they be the same?

I have always assumed that aperture value meant the maximum aperture available at that particular zoom setting (most zooms have variable apertures) and that f stop was the stop actually set by the user. It would be easy enough to test out this theory and I may do so when I get a moment.

It won't refer to transmission values (T stops) because a variation such as that indicated would be very excessive indeed and rather unlikely given modern multi-coating techniques.

Explained here

It is explained there, althoug it seems a bit over-convoluted to me as explanations go. One day I'll look into it.

Clear as mud, can it be explained in "words of one syllable"?

There is no discrepancy.

Take as an example an F-stop of f13. The corresponding "aperture value" will read 7.4.

Why? Av is formally defined as 2 x log(base2) of the aperture. So 2 x ln(13)/ln(2) is ~7.40.

Why log(base2)? Because each whole number increase represents a doubling, i.e. one stop.

Why multiply by 2? Because the amount of light let in by a given f-stop is proportional to the aperture's area rather than its diameter, so the aperture squared is the key variable.

A fuller explanation is here:

http://en.wikipedia.org/wiki/APEX_system