metadata - 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

Answer

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 = 2^{Av / 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

See also:

• 
  

  Wikipedia: APEX System.

  
  


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  ExifTool: Exif Tags

  
  
  


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  APEX—The Additive System of Photographic Exposure (PDF) – Contains tables and equations, but no calculation examples.

  
  


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  JEITA CP-3451 Exif 2.2 (PDF) – Contains conversion equations.