Why is 45 degrees the traditional single-plate angle?

Because the eye is far better at detecting horizontal and vertical lines than diagonal ones. A screen at 0 degrees puts its dots in obvious rows and columns and the pattern announces itself; the identical screen at 45 puts them on diagonals and the same pattern becomes much harder to see as a pattern. There is no optical difference in what the dots reproduce — only in how readily you notice them doing it.

What is a rosette, exactly?

The small flower of overlapping dots that four correctly-angled plates produce where they meet. Because the four grids are rotated relative to one another, no two of them ever line up for long, and the local arrangement of cyan, magenta, yellow and black repeats on a much larger scale than any individual screen. You can see it with a loupe on any magazine page. It is not a defect; it is the intended result of choosing angles that refuse to agree.

My halftone has a second, much coarser pattern in it. Where is that from?

From your screen grid beating against the pixel grid of the picture. When the cell size gets close to a small whole number of pixels, the rounding of every cell centre falls into a repeating cycle, and that cycle is visible as a large, slow-moving pattern that is not in the photograph at all. Raising the cell size above about four pixels usually clears it; so does changing the angle away from 0, 45 and 90, where the interference is strongest.

How many pixels does one dot need before it prints properly?

A useful rule is a dozen across at the resolution the file is going out at. A dot described by four or five pixels of diameter has a visibly stepped edge that a printer will reproduce faithfully, steps and all; the same dot described by twelve or more reads as round. That is what the render scale in the export step is for — at 2× the same halftone arrives with four times as many pixels per dot without the dots changing size relative to the picture.

Why halftone dots have angles

Lay two regular grids over each other and you get a third pattern that neither of them contains. Everything printers know about screen angles is a response to that one fact.

The problem angles exist to solve

Take two sheets of fine mesh and hold one over the other. Where the holes almost line up you see light; where they almost do not, you see dark. Because “almost” drifts slowly across the sheet, the light and dark regions are enormous compared with the mesh itself — a pattern perhaps a hundred times coarser than either grid, made entirely out of the relationship between them.

That is interference, and it is the central difficulty of colour printing. Four separate screens have to be laid over one another on the same sheet of paper. Give any two of them the same angle and you get the mesh problem: a coarse, swimming pattern across the whole picture that is in neither plate and cannot be removed by improving either one.

Rotating the screens apart does not eliminate the interference — nothing does — but it pushes the resulting pattern up in frequency until it is finer than the screens themselves, at which point the eye stops seeing it as a pattern and starts seeing it as texture. Thirty degrees turns out to be the spacing that pushes it furthest.

Why those four numbers

Screens repeat every ninety degrees, because a square grid rotated by ninety degrees is the same grid. So there are ninety degrees of genuinely different angles to share between four plates, and the widest even spacing that gives is thirty degrees between three of them — which is exactly what cyan, magenta and black get.

The standard separation, and what each plate is doing there
Plate	Angle	Reasoning
Yellow	0°	Palest ink, least visible pattern, takes the worst angle
Cyan	15°	Thirty from magenta, thirty from black
Black	45°	Strongest plate takes the least noticeable angle
Magenta	75°	The far side of the same thirty-degree spacing

The fourth plate has to go somewhere, and yellow gets the leftover because yellow on white paper is the lowest-contrast ink of the four. Its screen is closest to the two orientations the eye reads most easily, and it still disappears, because there is barely enough contrast between yellow and paper for a pattern to register at all.

What happens when you rotate all four together

The angle control on this site’s halftone page does exactly that in four-plate mode: it adds your number to all four press angles at once. The relationships between the plates are preserved, so the rosette stays intact and no two screens ever approach each other — what changes is the orientation of the whole rosette relative to the picture.

That is worth having because a rosette that lines up with a strong horizontal in the photograph — a horizon, a table edge, the top of a building — can pick up a visible interaction with it. Rotating the whole set by ten or fifteen degrees moves the rosette off that line without disturbing the separation the four angles exist to maintain.

The other interference: your screen against the pixels

A digital halftone has a second grid that a press never had to worry about — the pixel grid of the source picture. When the cell size approaches a small whole number of pixels, the rounding that decides where each cell centre falls starts repeating on a cycle, and that cycle is a pattern in its own right, typically far coarser than the screen.

This is why the cell size control on the halftone page carries a warning under four pixels rather than simply allowing it. It is not that small cells are forbidden — they are useful on very large source files — but at small cells on a modest photograph the interference dominates, and someone seeing it for the first time reasonably concludes the tool is broken. It is not; it is a real consequence of two regular grids, and it is the same phenomenon the press angles were invented for.

Three things move it: a coarser cell, an angle away from 0, 45 and 90, or a larger source picture, which changes the ratio between the two grids.

Resolution, and what a dot needs to survive

A halftone drawn for a screen and one drawn for paper are different files. On a display, a dot six pixels across reads perfectly well as a dot. Sent to a printer at 300 dots per inch, those six pixels become about half a millimetre of visibly stepped edge, and the press reproduces the steps as faithfully as it reproduces the dot.

The practical figure is around twelve pixels across the widest mark at output resolution. That means a halftone with eight-pixel cells, which looks right on screen, wants to go out at two or three times the dimensions it was tuned at. The render scale does this without changing the design: every length is multiplied alongside the output size, so the dots keep the same size relative to the picture and simply arrive described by four or nine times as many pixels.

Then save it as PNG. A halftone is two colours with hard boundaries — the shape a lossless format compresses best and a lossy one damages most.

Questions about the screen

Why is 45 degrees the traditional single-plate angle?: Because the eye is far better at detecting horizontal and vertical lines than diagonal ones. A screen at 0 degrees puts its dots in obvious rows and columns and the pattern announces itself; the identical screen at 45 puts them on diagonals and the same pattern becomes much harder to see as a pattern. There is no optical difference in what the dots reproduce — only in how readily you notice them doing it.
What is a rosette, exactly?: The small flower of overlapping dots that four correctly-angled plates produce where they meet. Because the four grids are rotated relative to one another, no two of them ever line up for long, and the local arrangement of cyan, magenta, yellow and black repeats on a much larger scale than any individual screen. You can see it with a loupe on any magazine page. It is not a defect; it is the intended result of choosing angles that refuse to agree.
My halftone has a second, much coarser pattern in it. Where is that from?: From your screen grid beating against the pixel grid of the picture. When the cell size gets close to a small whole number of pixels, the rounding of every cell centre falls into a repeating cycle, and that cycle is visible as a large, slow-moving pattern that is not in the photograph at all. Raising the cell size above about four pixels usually clears it; so does changing the angle away from 0, 45 and 90, where the interference is strongest.
How many pixels does one dot need before it prints properly?: A useful rule is a dozen across at the resolution the file is going out at. A dot described by four or five pixels of diameter has a visibly stepped edge that a printer will reproduce faithfully, steps and all; the same dot described by twelve or more reads as round. That is what the render scale in the export step is for — at 2× the same halftone arrives with four times as many pixels per dot without the dots changing size relative to the picture.

Back to the lab

Rendered on your computer, not on a server.