Gray Levels and optical densitys

Posted by James Beals on Oct 11, 2006; 8:42pm
URL: http://imagej.273.s1.nabble.com/Gray-Levels-and-optical-densitys-tp3701320.html

Can some one explain what is happening when a gray level images is inverted?

Background.
We measure the density of in situ auto radiograms.
Some folks here invert the gray level values.
So that the darker areas have higher values than the brighter areas.
black=255, white=0, and measure density like that.

If I calibrate to optical density numbers, using a Stuoffers 21 step wedge (1=0.06 to 21=3.00 OD)
and the (Rodbard) function, I get very good numbers, from different cameras and scanners.
So I know how to do it right.

But folks here have been inverting the gray levels and making measurements of that for some
time.

So, I imaged the standard and plot the values I get a prety good log curve.
If I copy and inverted gray levels, and plot them agents the original, the plots cross over at about
125, the 4th step in the standard or about 0.50 OD.
If I subtract the inverted gray levels from the gray levels, I get a very strange
curve, that starts at about 250 crosses the gray levels step 7 just bellow 100, goes into the
negative at step 4-5 and down to -255. The difference should be 0.

So i have to think that there is a difference between Inversion and difference.
any clues ??
thanks
James