John, any updates on this?
Hi nerologic. Yes, I made some progress. I created a custom negative characteristic curve for my printer. It is specific to my printer (Epson P400), ink (Ultrachrome), printer settings (suggested by Naranjan), and transparency material (Pictorico Ultra). How I did it: Using Photoshop, I printed a 101-step grayscale step table on Pictorico Ultra. I measured the UV transmission density of each step with an XRite 361T. Plotting transmission density vs K% gives the digital negative characteristic curve. It is analogous to an analog film curve, with K% (gray image tone) playing the role of exposure (logH). From a single master curve I can derive a family of curves having density ranges lower than the master curve.
As I mentioned earlier in this thread, I am using this curve in simulations of the tone reproduction cycle. A simulation requires two inputs
(1) the characteristic curve of the process that you wish to study. Get this by printing a target with a Stouffer step wedge and measuring Lab L* values for each of 21 or 31 steps. The plot of L* vs logH is the characteristic curve of the process. But since logH is the inverse of transmission density, you can also look at the curve as a plot of L* vs. transmission density, which is how it is used in the simulation.
(2) the characteristic curve of the digital negative. Get this as described above.
With (1) and (2) you have the ability to map L* to K%, from which you can derive an image adjustment curve.
The above simulation is for a negative whose density range is perfectly matched to the process exposure scale. I can simulate the effect of negative density range errors (negative too dense or too thin) and exposure errors (overexposure, underexposure). It's interesting to observe how these errors affect the image adjustment curve.
The first question anyone is likely to ask is: Do your simulations produce usable adjustment curves? The simulator can generate a LUT which can be used as a Photoshop image adjustment curve, but I have purposely avoided darkroom testing until I'm confident that the simulation is mathematically sound. Once I start testing, I'll be glad if the results are even somewhat encouraging. After all, my goal was to develop an educational tool, not a tool for automating digital negative calibration.