Digital BW, The Print

--- In DigitalBlackandWhiteThePrint@yahoogroups.com, "Austin 
Franklin" <darkroom@i...> wrote:

> I'm still not quite convinced of this claim, as it
> seems entirely unnecessary...when using random/stochastic
> dither algorithms, like the Epson supposedly does.
> These dither algorithms don't use fixed cell size, so
> I'm not clear of what the benefit of resizing the image is.

Random/stochastic algorithms certainly CAN use a fixed
cell size!   

Let's take an ULTRA-simplistic case of black-only printing where
some primitive printer's resolution is the same as the image
resolution, i.e., a hypothetical printer with 300x300 DPI 
resolution printing a 1" grayscale patch of 300x300 pixels.
And let's say the driver uses a fixed cell size and a stochastic
algorithm. Say the image uses 8-bit grayscale.   For each pixel
the driver will generate a random number in the range of 0-255 
and compare it to the pixel being printed.   If it's greater 
than the pixel value it deposits a drop.   As you can see, when
the pixel has a low value there is a statistically greater 
chance of a drop beng generated so it's darker where the pixels 
have low values.     

If the printer's resolution is higher, let's say, 600x600 DPI,
then it will print the same image-pixel 4 times, but because
each time it's being compared to a different random number,
it may or may not print a dot - the probability of printing
a dot depends on the value of the pixel.   That's why it's
called stochastic.

So the problem with a fixed cell size is not that you can't
use it with a stochastic algorithm; the big problem with a fixed 
cell size is that you don't get enough levels, even with a
high resolution printer.  Again, using black-only and a 300
PPI image, and let's assume we have designed our test image
so no two adjacent pixels are identical:

Suppose the printer is the Epson 2200, which has a maximum
resolution of 1440 x 2880 DPI.  One image pixel at 300x300
PPI has the area of 1/90000th of a square inch.   In a 
90000th of an inch the 2200 can place approximately 46 
dots at maximum resolution.    That's nowhere NEAR the 256
possible values that the incoming pixel could have, nor is
it near the 100 or so levels the human eye needs to see a
smooth tonal range without banding.

This dilemma clearly illustrates why dithering algorithms
are ALWAYS tradeoffs between spatial and value resolution.
The only way to extend the value range in this example is
to increase the cell size, but when you do that you overlap
the value of multiple pixels in the original image, so you
lose the ability to distinguish two adjacent pixels in the
original that we so carefully designed to be distinct.

In this thread people talk about "The Epson Driver" but my
guess, as a former inkjet driver writer, is that different
Epsons have different drivers, or at least different 
algorithms in different situations.   The tests I've run
on black-only printing on the 2200 show that source 
resolution holds up pretty well but the images are contrasty,
which suggests to me that they are using something close to
a fixed cell size and trading away tonal range to keep 
spatial resolution.   However, the cell size may have nothing
to do with incoming image resolution - the driver probably
RESAMPLES the incoming image.   If this is the case there
may be, if not an "optimal" resolution, then at least a 
maximum one.

And while we're on the subject - DPI refers to the printer
output - printers make dots.  If you're talking about the
resolution of the image it's more correct and less confusing
to refer to PPI.

BTW, the test on this lecture is worth 30% of your grade.