Digital BW, The Print

I've been doing some more experiments with black only and I've run 
into another technical issue.   (When I get back from my vacation 
I'll put this on my webpage with some sample images but here's a 
summary).

As I mentioned before I've been user-testing Black Only.  I tried it 
on my wife's musician friends with mixed results - some people could 
see the dots and found them annoying; most people couldn't see the 
dots and those people liked the prints.

So today I took some sample images to work where I showed them to my 
fellow engineers.  (My company makes systems used for high-end image 
display used in medicine and scientific research.)   And they 
complained about something the musicians hadn't noticed - mach 
banding, especially in the wedges.

The problem is this.  These were printed with the output resolution 
set at 300 Pixels Per Inch in Photoshop, which is a pretty common 
number to use when printing photographs.  300 PPI corresponds to 
90,000 pixels/square inch of printed output.   The 2200 is capable of 
2880x1440 DPI, i.e., 4147200 dots/square inch. So the printer driver 
has 47 distinct values (i.e., 0 dots of black to 46 dots of black)  
to use for each pixel in the supplied image.   But that pixel could 
be 0 to 255!  And, anyway, 46 is not NEARLY enough to avoid mach 
banding!  The human eye needs a minimum of closer to 100 distinct 
levels to see smooth transitions.

But the mach banding is not as bad as what you would get with 46 
levels, so I'm assuming the driver is trying to be smart and 
integrate over adjacent pixels in the image.  (most modern drivers do 
not just operate one pixel at a time)  This is fine as long as we 
remember that ALL dithering algorithms are a tradeoff between spatial 
resolution and value or color resolution.  You gain one ONLY at the 
expense of the other.   If the driver is integrating over two pixels 
it could be cutting the resolution in half.  Based on the banding I 
see, it looks like the Epson driver is trying to compromise between 
these two cases.

A test for this would be to print adjacent black lines, 1 pixel of 
white dividing them at 300 pixels per inch.  The printer SHOULD be 
able to print them as two distinct lines given its 2880x1440 DPI 
resolution.  Now try two gray lines, or two black lines with gray in 
between them.  I'll do all this when I get back and post the results 
on my website.

This may explain why some people say that Black Only seems too 
contrasty.   It just doesn't have enough levels to play with to make 
subtle gradations.   If my math is right, using black ink plus light 
black ink (pretending for a moment that light black ink isn't brown)  
assuming that light black has roughly half the pigment as black, 
would yield 93 values, above, where we had 46.   Obviously all these 
numbers would be much worse with lower resolution printers.

This also raises the interesting prospect that we can manipulate the 
number of gray levels the printer uses by varying the Pixel Per Inch 
setting in Photoshop.  However, depending on what they do internally, 
it's hard to predict WHICH numbers would give us the best results.  
Also it would almost certainly vary from one printer model to 
another, because the drivers would be different.