Digital BW, The Print

BTW you can see from the formula below why people say L* is roughly the cube
root of luminance.  Luminance, XYZ_Y, can range from 0 to 1 and so for most
L*:

L* = XYZ_Y^(1/3) x 116 - 16

And you get very close with just L*=XYZ_Y^(1/3)


> From: Steve Kale <stevekale@...>
> Reply-To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Date: Sun, 30 Oct 2005 14:30:58 +0000
> To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Conversation: [Digital BW] Black Density measurement
> Subject: Re: [Digital BW] Black Density measurement
> 
> Tony
> 
> It's worth understanding this in two steps.  Density is a log function of
> luminance.  Log functions are simply nice because they turn curves into
> straight lines.  In 1931 the Commission Internationale de l'Eclairage
> standards body developed the CIE XYZ colour space is their best attempt to
> represent the eye's reaction to light and the Y component/axis models the
> average luminance function of the eye's cones.
> 
> The formulae you have been presented with do two things in one step.  They
> convert CIELab's L* (the Lab colour space is a perceptually uniform colour
> space) to CIE YYZ's Y.  From there you get to density by taking the log of
> XYX_Y (ie the log of luminance).  The last thing is to multiply by -1
> because it is reflective rather than emmissive.
> 
> So first you need to get from L* to XYZ_Y:
> 
> If L*>7.9996248 (or >8) then:
> 
> XYZ_Y = ((L*+16)/116)^3
> 
> Else
> 
> XYZ_Y = L* x 27/24389
> 
> And once you have XYZ_Y then
> 
> Density = -LOG(XYZ_Y)
> 
> Of course your EyeOne also gives you the XYZ_Y directly depending on the
> manner in which it is used.
> 
> Unless I am mistaken, John needs to check the second part of the equation he
> gave you.
> 
> Cheers
> 
> Steve
>