Error Diffusion

A photographic halftone screen makes grey by varying how BIG each dot is, on a fixed grid. That works because an emulsion will give you any dot size you ask for. A laser printer and an inkjet will not: they have one dot, the smallest they can make, and it is either there or it is not. So the arrangement has to be turned round. Keep the dot size fixed and vary HOW MANY, and now the question is which pixels get one. Simply rounding each pixel to black or white throws away up to half a level every time and the picture collapses into two tones. Robert Floyd and Louis Steinberg published the fix in 1976, and it is four lines long. Round the pixel. Subtract what you actually printed from what was asked for. Hand that difference forward to the four neighbours you have not decided yet, in the proportions seven, three, five and one sixteenths. The error is never discarded, only moved somewhere the eye will average it away - so a region that has been printing slightly too dark accumulates a debt that forces the next pixel white. The cost is one row of buffer and four additions per pixel, which is why it went straight into printer firmware and stayed there. The signature is worms: at middle greys the dots chain into short drifting diagonals, because the debt travels the same way every time. A halftone screen fails by beating against another screen; error diffusion fails by growing worms, and no screen angle can fix that.