Method and apparatus enabling color or black/white bi-level or
multi-level halftone images to be displayed or printed on various raster output
devices, in particular on display devices (cathode ray tubes, plasma displays,
liquid crystal displays) or on printing devices (printers, telefaxes). The
originality of the present invention is found in the dither matrix
*R^*^{c*n} which is obtained by applying on a
*c*-fold replication of a well-dispersed threshold matrix
*D^*^{n} a one-to-one discrete rotation of
Pythagorean angle *alpha = arctan(b/a)* or *beta = arctan(a/b)*
around an arbitrary point, where *{a,b,c}* are Pythagorean triplets
satisfying Diophantine equation
*a^*^{2}+b^^{2}=c^^{2}
and *n* is an integer. The images produced using the disclosed method are
visually pleasing due to the absence of visible artifacts and to the small
typical structure size. In addition, this method offers very smooth intensity
gradations throughout the dynamic range.
The disclosed method can be applied to different one-to-one discrete rotations
of a *c*-fold replication of a well-dispersed threshold matrix
*D^*^{n} but it has proved especially effective in
the case where a 5-fold replication of well-dispersed threshold matrix
*D^*^{n} is rotated by angle *alpha =
arctan(3/4)* or *beta = arctan(4/3)*. The most interesting cases are
those where *n= 8, 16*, and where the dither matrices can faithfully
reproduce respectively 65 and 257 distinct intensity levels.

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