Digital BW, The Print

Hi Peter

This is much simpler than anything on Bruce's site.

I do know that in its simplified form:

Luminance = (normalised pixel value)^gamma

And that:

Density = -log10(luminance)

So if gamma =2.2

Density = -log10(normalised pixel value^2.2)

Which means:

(Normalised pixel value)^2.2 = 10^(-Density)

And here is where my knowledge of algebra leaves me wanting.  [if my gamma
were simply 2 then I know I could take the square root of both sides and be
done]

If I know a density value, eg 1.65, then

(normalised pixel value)^2.2 = 10^-1.65 = 0.02239

I am having trouble with the very last step in this simple algebra.

By the very unsatisfactory method of interpolation I know the answer is
normalised pixel value is approx 0.1775.  In other words, a density of 1.65
- about the max we can get from EEM - is roughly equivalent to a 82.25%
black in a 2.2 gamma space.  Any black darker than this can not be
reproduced on the printer.  So if you were to look at your nicely stretched
image's histogram in PS, you would know that the left-most 17.75% (or you
prefer to think in an 8 bit 0-255 range... all values from 0 to 45) could
never be printed as you are looking at it!  All those pixel values are
simply outside the tonal range of the printer.  A similar calculation can be
done for the highlights.

Cheers

Steve


> From: Peter <spamme2001@...>
> Reply-To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Date: Thu, 02 Dec 2004 02:10:58 -0000
> To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Subject: Re: [Digital BW] Tonal range and linearization
> 
> 
> 
> --- In DigitalBlackandWhiteThePrint@yahoogroups.com, Steve Kale
> <stevekale@b...> wrote:
> 
>> So I would be grateful if someone could help me with my maths
> problem and
>> also for input on the printer gamma point.
>> 
>> Cheers
>> 
> 
> 
> Hi Steve,
> 
> If you haven't done so already, check out Bruce Lindbloom's site
> (http://www.brucelindbloom.com). He has many helpful conversion
> calculators, equations, and information about color and perception
> theory.
> 
> Regards,
> Peter.
>