Digital BW, The Print

>  I am still not conceptually getting
>what is happening when, with monochrome checked, a channel is set to greater
>than 100% or at a negative value...

I think you're making it more complicated than it really is. The 
Channel Mixer just does addition.

Remember that each of R, G, B for each pixel is just a number, 0 to 
255 (in 8-bit mode). Channel Mixer in monochrome mode just takes each 
number, multiplies it by the percentage set, and adds them all up to 
get the luminance number for the result. If the sum is more than 255, 
it gets clipped to 255; if it's less than 0, it gets clipped to 0.

Each channel contributes to the sum according to the percentages, in 
proportion to the brightness of that channel. Where the R channel is 
bright, it contributes a lot to the sum. Where the R channel is dark, 
it contributes little or nothing to the sum, so the end result comes 
mainly or entirely from the G and B channels. And so on.

Where all the channels are dark, the result will be dark regardless 
of the percentages.

Increasing the percentage of R means that R values will contribute 
more to the sum. So areas that are bright in Red will be brighter in 
the result.

If you set R to a negative value, that reverses the contribution of 
the R channel. So areas that are bright in Red will become *darker* 
in the result. This is exactly as if you inverted the R channel and 
then added it in at the same positive percentage.

There's nothing magic about 100% per channel. The magic combination 
is 30% red, 59% green, and 11% blue. That mixture is what Photoshop 
uses when you just use Desaturate, and it corresponds to some notion 
of "normal" luminance perception. If you want red tones to be lighter 
than "normal", use more than 30% for the R channel (and don't worry 
if it goes over 100). If you want them to be darker than "normal", 
use less than 30% (and don't worry if it goes below 0).

This is like using colored filters. They reduce the effect of certain 
colors of light on the result. With colored filters, you have to 
compensate for the lost light by increasing the exposure. That allows 
more of the colors that aren't filtered out to get to the film. Same 
thing here. If you reduce the percentage of one channel, you will 
probably want to increase the percentage of the other channels to 
compensate for the overall loss of brightness. Making them add up to 
100 is like using the filter factor out of the book: it gets you into 
the right ballpark. Your creative vision may require a different sum. 
Keep the histogram palette open and check it for clipping while you 
adjust the percentages.

There ought to be a button that says "scale my percentages to add up 
to 100", but there isn't. So you have to do it manually.

   -Paul (another one)