[Openexr-devel] f-stops and steps. How are they related?

[Yves Poissant]

Hi there,

I'm reading the OpenEXR File Format document and the post by Florian Kainz
on 26 feb 2004 and I'm trying to understand what the numbers mean. If 
anybody can correct some (or all?) of my assumptions, I would appreciate. 
BTW, Sorry for the format, I'm just trying to write down my reasoning in a 
readable way.

First, I understand what an f-stop means and Mr. Kainz explanation fits in
very well.

In the OpenEXR File Format, in the "Features of OpenEXR" under "high dynamic 
range", I read "With 16-bits, the representable dynamic range is ... 10^9 or 
30 f-stop without loss of precision"

1: - That is because the 5-bit exponent = 30 something mantissa shifts.
2: - Thus each f-stop corresponds to 1 mantissa shift or said another way, 
one divide by 2 or one multiply by 2. That makes perfect sense.

Then a little bit further, I read "Most 8-bit file formats have around 7 to 
10 f-stops"

3: - Lets say a given file have a range of 8 f-stops. That would mean each 
f-stop is represented by 32 of the 256 steps. It is as if the mantissa had 5 
bits precision and the exponent 3 bits.
4: - Since 1 f-stop means double intensity, that also means that the data 
stored in this file represent a range of intensity going from 1i to 256i. Or 
the intensity of the brightest pixel represent an intensity which is 256 
brighter than the intensity of the darkest pixel. This is intuitive since we 
can shift 8 times an 8-bit value or divide (or multiply) 8 times by 2..

Then in the next paragraph, under "good color resolution", I read: 
"somewhere around 20 to 80 steps per f-stop for most 8-bit file formats"

5: - The actual values stored in an 8 bit buffer may be scaled down or up 
with a contrast operator of some sort.
6: - My 32 steps per f-stop as computed above fits confortably in this 
range. So we're talking about the same thing here.


In the same sentense, I read: "With 16-bit ... color resolution is 1024 
steps per f-stop"

7: - 1024 steps because of the 10-bit mantissa.
8: - "1024 steps per f-stop" means that step 1024 represents only double the 
intensity as step 1.

Then later, under "What's in the number", I read "By storing linear data in 
the file (double the number, double the light)"

9: - This is consistent with the above reasoning.

Everything seems to fall in place. Did I missed anything or misinterpret 
anything?

Yves Poissant
Hash Inc.