A few things:
No, the size of the plate dot does not have relevance. Note also that the densitometer that is used to measure dot gain does not "see" the dots. It can only measure reflectance values so it cannot be a geometric measure of the dots. You tell it that you are measuring a given % dot (tone area) and the formula then derives a dot area tone value based on the relationship between the measured paper reflectance, the measured solid relfectance, and the measured reflectance of the patch that you've told it is, for example, a 50% patch. The dot area can then be compared with the original tone request (i.e. measured 50% on the film or requested 50% in the authoring application in the case of CtP) and a simple subtraction provides the dot gain value. I.e. I requested 50% in the file but in the presswork the dot area tone value measures 64%. 64-50=14% dot gain.
For the purposes of dot gain measurement it does not matter what the actual dot % value on the plate is, nor the size, shape or frequency of the halftone dots are. It also does not matter whether the plates/film are linear or not.
The Murray-Davis equation inherently assumes (like its predecessor the Demichael and Neugebauer equations) that the amount of reflection is linearly dependent on the relative amounts of ink and paper over the surface and that the halftones dots are well defined and that only direct reflection in the surface occurs, which in reality is far from true.
The issue of dot gain measurement is very complex, with a long history of attempts (did I mention the two-flux approximation and Kubelka-Munk theory?).
The best resource on the topic - if you want to hurt your brain is "Dot Gain in Colour Halftones" by Stefan Gustavson (ISBN 91-7871-981-X) - it's hard to find but for dot heads worth the search.
best, gordo
All I can picture is the old school superman standing with hands on hips and red cape blowing just slightly to the left. "Dun-dah-dah-DUN! Gordo to the rescue!"
That is one of the clearest explanations I've seen yet on dot gain and color scanning.
Am I understanding this right? to calculate dot gain...
1. The scanner reads the paper and gets a reflective value it pegs as "Point A" on the color gamut and calls it "0%".
2. The scanner reads the 100% patch you give it and gets a reflective value it pegs as "Point C" on the color gamut and calls it 100%
3. The scanner reads say the 50% patch you give it and gets a reflective value it pegs as "Point B" on the gamut.
4. Then, it compares the "distance" from "Point A" to "Point B" and "Point C" to "Point B", and on a scale returns the value of "Point B" based on that comparison.
Now, to get that reflective value, it essentially "blurs" it's vision so it sees a "solid" color based off the paper/ink combination that is in front of it? Kind of like stepping back so that you can no longer see the dot, but only the illusion of solid color?
If that is right, then really, it doesn't even "see" the dot or care on the dot shape/size? Or have I completely jumped the train off the track and off the bridge on this one? If I did, just say so, and I'll edit this out so I don't confuse anyone else.