CMYK halftone: screen angles, frequency and moiré
How four halftone screens print full colour: the angles for cyan, magenta, yellow and black, why they sit 30° apart, and what causes moiré between them.
Published
A colour photograph is printed as four halftones laid over each other, one each in cyan, magenta, yellow and black ink. Each is a grid of dots whose sizes follow how much of that ink the picture needs. The four grids are turned to different angles: in the arrangement the printing standards give, cyan, magenta and black are 30° apart, with the dominant colour at 45°, and yellow sits 15° from one of the others. The angles are chosen to keep moiré, the interference between regular patterns, too small to notice. What is a halftone? covers a single screen.
Y 0°, C 15°, K 45°, M 75°
Even texture of small rings
All four at 45°
The dots stack into one
C 45°, K 50°
Broad bands of moiré
Why the screens are turned
A halftone screen is a regular grid. Put two regular grids on top of each other and they interfere. ISO 12647-1, the part of the print process control standard that sets out its terms and measurement methods, defines a moiré pattern (in the text adopted as IS 15963 (Part 1)) as an “unwanted periodic structure produced by interference between two or more two-dimensional periodic structures”.
There are two ways to get it wrong.
All at the same angle. If the four screens match exactly, the dots land on top of each other, as in the middle square. That only holds while the sheets are in perfect register. Stephen Horgan described the result in his 1913 manual: three impressions from one halftone, printed exactly over each other, “would appear like a single impression in black ink. Should these printings be repeated and the impressions be out of register, as they are most likely to be, then varying color effects, called moire, will appear in the proofs” (Horgan’s Half-tone and Photomechanical Processes).
At nearly the same angle. Two grids a few degrees apart drift in and out of step, and a new, much larger pattern appears, as in the right-hand square.
The size of that pattern can be worked out. For two grids of the same spacing, crossed at an angle A, the interference repeats at the dot spacing divided by twice the sine of half A.
| Angle between two screens | The pattern repeats every |
|---|---|
| 2° | 28.6 dots |
| 5° | 11.5 dots |
| 15° | 3.8 dots |
| 30° | 1.9 dots |
| 45° | 1.3 dots |
At 5° the pattern repeats every eleven or twelve dots, and shows as the broad bands of the right-hand square. At 30° it repeats in less than two dots, about the size of the dots themselves.
The rule for the angles
A grid of round or square dots looks the same after a quarter turn, so there are only 90° to share out. Three screens fit at 30° apart. The fourth has no slot left, so it goes halfway between two of the others, and the ink given that place is yellow.
The offset printing standard states it as a rule. ISO 12647-2 (2004 edition): “For half-tone dots without a principal axis, the nominal difference between the screen angles for cyan, magenta, and black shall be 30°, with the screen angle of yellow separated at 15° from another colour. The screen angle of the dominant colour should be 45°.” The text is public as IS 15963 (Part 2), the Indian standard that adopts it word for word.
One set of angles that satisfies it:
| Ink | Angle | Why |
|---|---|---|
| Black | 45° | Taken here as the dominant colour, which the standard puts at 45° |
| Cyan | 15° | 30° from black |
| Magenta | 75° | 30° from black on the other side |
| Yellow | 0° | 15° from cyan |
Other sets are the same pattern turned. For screen printing, ISO 12647-5 (2001, adopted as IS 15963 (Part 5)) turns the set by 7.5° so that no screen lines up with the mesh, and its example shows black at 37.5°, magenta at 67.5° and yellow at 82.5°.
The rule is old. Horgan gave it in 1913 for four-colour blocks: “it has been found best to retain the angles of the stronger color”, which he lists as black or grey, blue and red, “at thirty degrees separation, and introduce the yellow at fifteen degrees between any two”.
Elliptical dots
An elliptical dot has a long axis, so its grid only looks the same after a half turn, and there are 180° to share. The standard doubles the spacing: “the nominal difference between screen angles for cyan, magenta and black shall be 60°, with the screen angle of yellow separated by 15° from another colour. The screen angle of the dominant colour should be 45° or 135°.”
What the right angles look like
With the angles of the table, the dots fall into small rings that repeat evenly across the tint, as in the left-hand square. It is the same interference as moiré, at the scale of a couple of dots: the 1.9 dots of the table above.
Frequency
The four screens normally share one frequency, the number of lines of dots per inch or centimetre. ISO 12647-2 gives 45 to 80 lines per centimetre for four-colour offset work, which is 114 to 203 lines per inch, and prefers 45 to 70 per centimetre for web-offset periodicals and 60 and higher for commercial printing.
Two refinements appear in its notes. With computer-made screens the frequency “is often varied slightly from one process colour to another in order to minimize moire patterns”, by 3 or 4 lines per centimetre. And the black or yellow screen is sometimes much finer than the rest, “for example, 84 cm⁻¹ versus 60 cm⁻¹”.
Screen printing uses coarser screens. ISO 12647-5 sets the range at 20 to 40 lines per centimetre, 51 to 102 lines per inch.
Who sets the angles
For real printing, usually not you. The screens are made when the separations are output, by the printing software or the print shop’s raster image processor.
CorelDRAW 2019’s help on printing separations is blunt about it: “we recommend that you use the default settings; otherwise, screens can be improperly set and result in undesirable moiré patterns and poor color reproduction.” It adds: “Before customizing a halftone screen, consult the print service provider to determine the correct setting.”
Spot colours also get screen angles. The same help page gives the example of a fill made of two spot colours, where “you can set one to print at 45 degrees and the other at 90 degrees”. For two inks, 45° apart is the widest separation a square grid allows.
Making a CMYK halftone as an effect
The dots can also be the point: a picture that looks like enlarged print. This is an effect on an image, not a separation.
CorelDRAW 2019: Effects > Color transform > Halftone, with a slider for the largest dot and four that, in the help’s words, “specify the angles of the cyan, magenta, yellow, and black color screens”.
GIMP 2.10: choose Filters > Distorts > Newsprint, set the colour model to CMYK, turn off Lock angles and give each channel its own angle. The manual is frank about what the filter is for: “Newsprint is not a filter for generating half-tone screens for print, but for simulating the appearance of printing with them” (GIMP manual).
Plotcaster does not make four-colour halftones. Its halftone patterns are single-colour vector dots, and multi-colour pen plotting covers splitting a picture into separate inks for a plotter. For screen printing in particular, see halftones for screen printing.
Questions
Why is black at 45°? The standard gives 45° to the dominant colour, and the reason for that angle is an old one. Horgan wrote that the 45° alignment of halftone dots “is selected because it was found at that angle they were least objectionable. Were they arranged, for instance, horizontally and vertically, they would be most obvious”.
Do all printers use these angles? No. ISO 12647-1 has a term for the alternative: a non-periodic half-tone screen, one “without a regular half-tone dot pattern”. For such screens, it says, “no screen angles need to be stated”.