Digital BW, The Print

Hi Steve, I approximated 27/24389 as 1/903.3.  That and using 8 rather than 7.9996248 gives errors around the 5th decimal place.
I had cobbled that function together some time ago.  Yours, and the function Tom Moore coded in VBA are much elegant, and what I would use for new work.
 
Best regards,
John Moody
 
-----Original Message-----
From: DigitalBlackandWhiteThePrint@yahoogroups.com [mailto:DigitalBlackandWhiteThePrint@...m]On Behalf Of Steve Kale
Sent: Sunday, October 30, 2005 9:31 AM
To: DigitalBlackandWhiteThePrint@yahoogroups.com
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




> From: John Moody <moodymz3@...>
> Reply-To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Date: Sun, 30 Oct 2005 08:59:02 -0500
> To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Subject: RE: [Digital BW] Black Density measurement
> 
> Well, LAB_L is a cell name; you can read about names in the user guide if
> you wish.
> 
> Try this, paste the following into cell B1.
> =IF(A1>=8,LOG(((A1+16)/116)^3)*-1,LOG(A1/903.3)*-1)
> 
> Now if you put 14 in A1, you should see 1.762 show up in B1.
> 
> John
> 


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