Digital BW, The Print

I did a little more playing around with this and the following might provide
some food for thought for RIP designers as they think about their
"linearize" functions.

I was interested in what value for gamma would produce the least total error
in print reflectance (XYZ_Y) vs that proposed by the CIELab model of
vision's L*.  Someone with better stats skills could find a better measure
of "fit" I am sure but this is a useful first observation.  I simply
calculated the XYZ_Y value for each 8 bit value (and measured the difference
between that and the XYZ_Y value that Lab would generate).

I assumed an average matte paper had a dynamic range of L*=16 to L*=96 and
an average photo paper had a dynamic range of L*=3.3 to L*=96.  (The
reference, Lab, of course goes from 0 to 100.)

For matte paper, if the RIP linearizes printed L* values from ink black to
paper white (as they do today) the shape of the print reflection function
(as measured by XYZ_Y) is best approximated (by this measure of fit) by a
gamma of 2.05.  For photo paper this number is 2.38.  So these are the sorts
of gamma implicit in the way we do things today.

I then asked what gamma would be the BEST fit to the benchmark, Lab, given
the particular black and white points of the two papers.  This produced
gammas of 2.38 for matte paper and 2.27 for photo paper, ie quite different
from those produced by linearising L*.

All this of course assumes that getting as close to CIELab is the goal, ie
that that model best represents the way we see.

Food for thought....

Steve