Linearising Fine-Art Monochrome Prints

From SarahWiki

For some time now, I've been using an Epson R2400 to produce fine-art monochrome prints, with results ranging from sadly lacking to outstanding. The problem has been consistency -- though in colour mode, I've had good results using the standard profiles, in advanced Monochrome mode, the closed loop between what's shown on the screen and what ends up on paper is broken. Generally speaking, my prints always ended up way too dark, so I'd end up creating gamma curves manually in Photoshop, looking something like this:

Simple adjustment curve -- not really good enough

With a few manual tweaks and iterations, I could generally manage to get a decent print, but it was a frustrating and annoying process. It was particularly disheartening to get something that really sings on the screen and just never quite manage to translate it into a print.

This is something that has been bothering me for quite some time now, though until now I've not really been able to come up with an adequate solution.

The problem

Put simply, the problem is that the curve that maps image information to the brightness of pixels on the monitor isn't sufficiently similar to the curve that maps that same information to ink on the paper. I knew I wasn't going to be able to attack this conventionally and still be able to use the Epson's Advanced B&W mode, so I decided to come up with an engineer's hack.

The conventional way to address this is to have a monitor profile that maps from the image's colour space to the monitor's colour space, and a printer profile that does the same thing in the printer world. A bit of maths, and you end up with a glued-together transform inside Photoshop that results in the correct colours on the page. My hack is basically to leave all of that machinery alone, let it do its thing, then come up with a way to map the errors in such a way that this could be used to fix the problem.

My first thought was to write some fancy software, and maybe even to build my own screen/print densitometer from scratch, but happily I figured out an easier, if slightly laborious, way to do it.
( The solution... )