RE: filmscanners: Magnification of light - AND brief density math lesson...

["Austin Franklin" <darkroom@ix.netcom.com>]

> But yes, as I understand it (scanner-wise), DMax is the maximum amount of
> density a CCD will recognize and record from a piece of film as "Black."
> DMin is the maximum amount of light (non-density) a CCD will recognize as
> "White."  The Density Range is what lies between.

All correct, but that's not the math involved.  Here's a brief density math
lesson...

1) Density is relative:

Let's call density values, such as DMax, "D" values.  Density is described
as a ratio value...ie, relative to something else.

As a note, the "D" values are in Bels, like deci-bels, a decibel is 1/10th
of a Bel...so a DMax of 3.4 is actually 34dB...  Bels are used to describe a
logarithmic relative power value, and since that is what we are
measuring...the power of the light, it is fitting.  As far as relating this
to audio dB, sound is different than light, so it's not quite the same...

2) Relative to what:

Say you assign the brightest measurement you sense a ratio value of 1:1.
Simply, the brightest spot is equal to how bright it is.  Something that is
half as bright is a 2:1 ratio, something that is 1/10th as bright is a 10:1
ratio...

3) Converting D values to actual ratio values:

A D value of 0 is 10 to the 0th power, which is 1, so the ratio value for a
D value of 0 is 1:1.  A D value of 1 is 10**1 or a ratio value of 10:1, D
value of 2 is 10**2 or 100:1, D value of 3 is 10**3 or 1000:1.  A D value of
3.4 is 10**3.4 or a ratio value of ~2,512:1...etc.

A DMax of 3.4, with a DMin of 0, means the scanner can detect a range of
light intensities from 0, to a value that is 1/2,512th as bright...

4) How does this get related to the numbers of bits my scanner is:

The integer ratio values are what your scanner gives you.  14 bits means you
can represent an integer number from 0 to 16,383.  This means if your
scanner can record integer density ratio values from 1:1 (0) to 16,384:1
(16,383).  16,384:1 is a D value of 4.2 (log 16,384 = 4.2).  That is why
scanners that have 14 bit A/Ds claim to have a DMax of 4.2...all that means
is they can support integer density ratio values of 1:1 to 16384:1, but that
does not mean the scanner CCD and analog circuitry can provide that!  That's
another topic of discussion...


That's the simple math behind "D" values and "density ratios".  I'll stop
there and see if that makes sense...