scanner density-value relation

I don't know why I can't find this info on web... but people on this
list probably know a lot about this topic.

When I scan a step tablet and plot the pixel value in the raw scan
TIFF file, the relation is good for some range but then it will crap
out. With my scanner (I still use Epson Expression 1600 with TPU
because I don't print from scanned negatives) the value craps out way
below the advertised Dmax value in relation to transmission density.

Did anyone measure this relation and care to share the info here?

--
Ryuji Suzuki
"Well, believing is all right, just don't let the wrong people know
what it's all about." (Bob Dylan, Need a Woman, 1982)