I have been behind in my reading of the list so I must apologize for taking so
long to follow up on your post. I hope that this message is of some small use
to folk in explaining printers.
First we have to distinguish between addressability and spot size. Thus the
Apple LaserWriter uses a laser engine with 300 spots per inch (spi) of
addressability, but the spot size is rather larger -- closer to 150 spi. If
you think for a moment you will realize why this is done. Imagine a line
made up of a row of dots where the dot size was exactly the same as the
distance between the dot centers. It would look pretty ragged wouldn't it?
Secondly, when we talk about laser printers we have to think about whether the
engine is "write black" or "write white". That is, the laser being on writes
black or the laser being on erases black and leaves white. Most small
printers are write black, most of the big Xerox laser printers are write
white. This matters because electrostatic effects and blooming: write black
dots tend to get bigger, write white dots smaller. There are also effects
related to the process direction in the machine (leading edge, trailing edge
...) and a host of other nasty non-linearities.
Why do we care about these issues? It is because the simple calculations of
the number of grey levels for halftone size assume linear relationships
between the number of bits set to "1" and the resulting density. For many
processes this is simply not true.
Changing the subject slightly, lets consider how many bits we need. We know
the modulation transfer characteristics of the human visual system rather
accurately. I believe that it was Edward Grainger (but this is from memory
someone should correct me if I have misremembered) whose Ph.D. thesis at the
University of Rochester contained the first accurate measurements of the MTF
of the human eye. He went on to work for Eastman Kodak and there developed
the correlation between subjective quality and MTF that Pop Photo now uses to
describe the results of lens MTF testing. The MTF curves for the human eye
peak at about 100-200 spi (from memory -- if it matters you should check the
definitive sources!) when measured at normal reading distances. They roll off
rapidly for lower and higher spatial frequencies. The actual curves are in
cycles/degree but for convenience I will talk about spi at normal reading
distances. I also do not have a book with the exact numbers in front of me
right now; thus my numbers should be taken as being close but not definitive.
Basicly, a normal person will not be able to see details finer than about
500spi. In line pairs per mm this is about 20 lp/mm. In terms of MTF, the
human eye is good for between 3 and 4 bits per pixel at 400 spi. One of the
interesting things about the visual system is that thin grey lines are
perceived as even thiner black lines under the right conditions. Thus grey
fonts (fonts where each pixel can use more than two values) are more readable
than binary fonts because the eye "hallucinates" hard edges with greater
positioning accuracy than the number of spots per inch would indicate. Thus,
for the most part, ultra-high resolution is not needed if some grey is
available. [There is an exception to this statement: the eye's vernier
acuity is much greater than its spatial resolution. That is, the eye can
easily detect misalignment of two lines at resolutions 2 to 3 times higher
than the MTF curves would predict. I don't believe this is an issue for
photographs :)]
Another set of data points comes from the thermal diffusion dye tranfer
printers. A print at 200 spi with 8 bits/pixel looks damm good. Yet one more
data point is National Geographic and their use of gravure for both text and
images. I seem to recall (DON'T trust my memory if it matters) that N.G. uses
about a 150 spi gravure process at close to 8 bits. You can see the results
in the text if you look very closely, but very few folks will look that
closely.
How do we get grey? Well the notion of a halftone has been covered in other
messages. Most phototype setters run at very high resolutions so as to be
able to produce good halftones. This means that the data files are huge.
However, there are other options.
You may be interested to know that most of the current color copiers (which
are all digital due to the need to do color correction) have lasers running at
much higher resolutions than the scanners. The scanners produce information
at 400spi by 8 bits, but at the output the 400x8 is upconverted to a high
resolution format. The halftones used are carefully handcrafted to work well
with the xerographic process used in the particular engine.
Another method is one used by some of the HP ink jet printers: two different
strengths of ink, the weaker ink producing a less dense pixel. Other methods
include multiple passes. Of course, for processes such as thermal diffusion
dye transfer, the density is determined by the amount of heat (length of time)
applied to the donor roll and resulting in a transfer of dye to the receiving
substrait.
There is a possible trick which I believe would work for alternative processes
but have not had time to try (my darkroom has been packed up for some years).
It seems likely that the CMYK dyes in a printer like the Epson have very
different optical densities for the wavelengths that are of interest to us.
Thus, a set of step wedges printed by the Epson in CMYK would print very
differently. Assume that for the alternative process a pixel of black has a
density of one, yellow .95, cyan .2, and magenta .5 (these numbers are made up
for purposes of illustration!). Then by laying down combinations of CMYK on
the same pixel we can get more than two values. Assume six distinguishable
values for the purpose of discussion. Then for slightly less than 400 spi we
could use a 4x2 halftone cell (1400 x 720 original resolution) with 8 pixels,
each pixel having 6 values. This would probably work out in reality to be
about 100 values -- far more than needed. For lower spatial frequencies you
would use a larger halftone cell. Note that you would probably have to drive
the Epson in raw mode -- ie output a bit map instead of taking advantage of
any built in halftoning. Has anyone tried this?
-Bryan
pixel values from above
0 .2 .5 .7 .95 1 (plus 1.2 1.5 1.7 1.95 ???)