Digital BW, The Print

--- In DigitalBlackandWhiteThePrint@yahoogroups.com, Jeff Medkeff <medkeff@g...> 
wrote:
....

> 
> Think of it this way. If you are sampling a brightness ratio of ten, and 
> you have 4096 ADUs to do it with, the difference between two adjacent 
> ADUs is a ratio of 1.0024. In other words, a part of the scene producing 
> an ADU of 100 is 1.002 times brighter than a part of the scene producing 
> an ADU of 101. Let's consider this a "small" difference. You can take a 
> picture full of subtle tonal differences, and really define a texture 
> (like an egg, say) with such a camera.
> 
> If, however, you are sampling a brightness ratio of 100 with 4096 ADUs, 
> then the step ratio is (predictably) 1.024. In this new situation there 
> is a big real-world brightness difference between a pixel value of 100 
> and a pixel value of 101. This leads to posterization; you aren't 
> recording enough brightness differences to define a surface. Therefore, 
> (most) makers of sensors that have a big dynamic range (usually) provide 
> more ADUs in output. Photographers tend to reduce this to the formula 
> that the more bits a camera outputs, the more dynamic range it has. 
> Unfortunately, using that formula to choose a camera can burn you badly, 
> because there are a number of exceptions to the rule. Some cameras 
> merely sample a poor dynamic range with excessive precision.
...
> 
> --
> Jeff Medkeff
> Eagle River, Alaska

Jeff,

I'm curious about this last couple of paragraphs.  You've referred to
the ADU's as producing output that is spaced in equal ratio -- i.e.

> the difference between two adjacent 
> ADUs is a ratio of 1.0024. In other words, a part of the scene producing 
> an ADU of 100 is 1.002 times brighter than a part of the scene producing 
> an ADU of 101. 

Seems to me this would imply an exponential relationship between the
light energy input and the digital values from the A/D.   But I thought there
was a linear relationship from the photon energy to the voltage out to the
raw A/D values.  -- We later apply a gamma (expontial function) to the raw data
in order get that exponential relationship that we really want.

Roy