• PE, in the first graph you posted, would it be fair to say the different slit widths also illustrate the Eberhard effect?

I’d like to look a little at the math now, in the context of the acutance formula (and variations) from Higgins/Jones and Higgins/Perrin/Wolfe.

The basic formula discussed by Perrin, and used by Richard Henry in his book is the mean square gradient for the transition from high to low density. I’m assuming the basic math would be the same whether the exposure is with x-rays, visible light, through a slit, or using a knife edge test (Perrin, Henry). So, G2x. Henry then explains Higgins and Jones thought the total change in density should also be a factor so they proposed G2x * DS where DS is Dhi-Dlo. Apparently based on experimental data Higgins/Perrin/Wolfe later modified the formula to be G2x / DS , but that’s a separate issue I’m unclear on.

Here is what puzzles me. Perrin (and later Henry in his tests) says that edge effects need to be accounted for by modifying the formula, but that nobody has figured out how to do it. I don’t understand why this is so difficult. It is even more odd that as late as 1986 Henry would say it still has not been done. By introducing DS, weren’t they almost there? While Jones, Higgins, Perrin etc. Were undoubtedly a lot smarter than I am, why didn’t they just convert DS into some sort of “factor”? For example, suppose we have a given acutance experiment (either comparing two films, or the same film with different developers, or different exposures etc.), for each trace why couldn’t we multiply G2x by something like C (for Contrast) where:

Acutance = G2x * C

C = delta Dedge / delta Dexp

delta Dedge = (max Dhi – min Dlo) across the transition

delta Dexp = (Dhi – Dlo) away from the transition based on the high and low exposures given.

Thoughts?