# How do XMP files encode aperture?

When I open a Lightroom XMP file, I read this odd line (the photo has been taken at f/8.0, all tools agree with that)

``````   exif:ApertureValue="6/1"
``````

Apparently, `6/1` means `f/8.0`, but where is this correspondance defined? Is it Lightroom specific? defined by XMP?

Note: It's not only for science's sake, I am currently trying to recover for a hard disk crash where I lost all filenames

The Exif:ApertureValue is stored as an APEX value as mandated by various EXIF standards.

The APEX system is a way to calculate exposure and works using base-2 logarithms. The use of base-2 means a rise of one in the value equates to a doubling, which we know as `1 stop`; which makes it pretty handy for photographers if they're good with logarithms (which we don't use much nowadays). Do note, however, that 1 stop in aperture means doubling of the square of the F-number -- for example, going from f/2.8 to f/4 is 1 stop because 42 = 2 * 2.82 (approximately).

To convert from APEX to F-numbers, use the following equation:

ApertureValue (Av) = log2 (F-number)2 = 2 log2 (F-number)
⇒ F-number = 2Av / 2

To convert `f/8.0` to it's APEX value `6/1`...

`Log2(8) = 3`
`3 * 2 = 6` (or `6/1` as a fraction)

To convert the `6/1` APEX value back to f/8...

`6/2 = 3`
`2^3 = 8` giving us back f/8.0