Digital BW, The Print

Austin & Keith,

I have copied two postings from another list on this subject. Since they are
fairly detailed I'll put them in separate postings:-

Posting 1

"I ran some tests soon after buying my 1270 printer, over 18 months ago,
which were similar to those which Bob mentions, except that I also
printed swatches of different tones as well, just in case there was a
difference in the resampling due to the ink density.

Although I did find resampling occurring, I found no evidence of it
changing as a function of ink density, which also indicated that the
dithering was very random.

The resampling pitch I found was 720ppi in both horizontal and vertical
axes - which is quite surprising given that the printer is capable of
1440ppi in one direction and the horizontal lines were more clearly
defined than the vertical lines.

The proof of this was quite simple really.  Proceed as Bob outlined
above with a line pattern of vertical and horizontal lines one pixel
wide, increasing the dpi of the test image at each run (resampling
switched off in Photoshop so that only a size change occurs).

Eventually, distortion will begin to appear due to aliasing.  Initially
this is quite subtle, since only the harmonics of the pixels are being
aliased by the resampling process.   However, eventually, the aliased
component becomes the dominant part of the image as the fundamental
increases beyond half of the resampling rate and higher ppi input simply
results in coarser line patterns.

In my tests, which I still have copies of, this "reflection" occurred at
exactly 720ppi, or a fundamental frequency for the line patterns of
360cycles per inch.  So the print at 750ppi produced identical line
pitches as the print at 690ppi and a print at 1080ppi produced identical
pitches to the print at 360ppi.  Clearly the "quality" of the lines
differed, depending on where the harmonics of the fundamental were
aliased to and what phase they occurred at, but it is the fundamental
which is easiest to see and use to identify the resampling rate.

So the maximum spatial frequency which the printer can reproduce without
aliasing is 360cycles per inch and, by Nyquist's Theorem, the resampling
rate is simply double this maximum spatial frequency - 720ppi.

I suspect that the main effect that Bob is seeing at lower resolution
tests is aliasing of the harmonics of his line patterns.  A square wave,
such as the line pattern, has harmonics at odd multiples (3x, 5x, 7x,
etc.) of the fundamental.  Hence at 180ppi the finest lines are 90lppi,
which have harmonics at 270, 450, 630cy/in.  Clearly, however, the 5th
harmonic exceeds the resolution of the printer and aliasing results -
reflecting exactly onto the 3rd harmonic and reinforcing it.  Whilst
this does not affect the line pitch and size, it does affect the
"quality" and uniformity of the lines.

However it is important to remember that these harmonics are not part of
the actual image, but a characteristic of the low pixel density - the
highest spatial frequency of the image that 180ppi can reproduce is
90cy/in.  The harmonics are a consequence of pixelation and generally
the intention is to minimise pixelation.  So I would argue that the
MINIMUM pixel density to print for photorealism is where the third
harmonic is well beyond the resolution limit of the printer.  For the
x70 series this occurs at 240ppi.  The maximum is clearly at 720ppi,
since the printer will downsample to that pixel density anyway.

Typically I print at 360ppi (where, coincidentally, the first harmonic
aliases back onto the fundamental) but occasionally go up to 480ppi
(where the first harmonic aliases back to 0cy/in) for some images with a
lot of fine detail in them.  Usually however I don't make any effort to
print at an exact ppi rating if it falls between these densities and
rely on the stochastic dither to do its work.
--
Kennedy"


Bob Frost