Subtractive Color Mixing

Color Reproduction

Sasan Gooran May 2013

Additive color mixing

Additive color mixing, TV, Computer screen

Subtractive color mixing

Subtractive color mixing, Printers

1 COLOR PRINT

• Three primary • CYAN (C) colors • MAGENTA (M) • YELLOW (Y)

COLOR PRINT

• Three secondary • RED (R, MY) colors • GREEN (G, CY) • BLUE (B, CM)

• And Black • BLACK (K, CMY)

COLOR PRINT

Original

2 COLOR PRINT

COLOR PRINT

AM HALFTONE same angle for C, M, Y & K

3 Conventional Color Halftoning Same raster angle

Error in position can cause color shift

Conventional Color Halftoning Same raster angle

Error in raster angle can cause Moiré

AM HALFTONE different angles for C, M, Y and K 15, 75, 0 and 45 degrees

4 ROSETTE PATTERN

ROSETTE PATTERN

Conventional Color Halftoning Different raster angle, 0, 15, 75 and 45 degrees

AM different angles FM Rosette patterns

5 NUEGEBAUER’S Equations

! $ ! $ # & # & # X & # X & # i & # & # & # & # & R a R # & # & = Y a # Y & a =1 ∑ OR # &=∑ With ∑ i i # & i# i & i i # & i # & i # Z & # & # & # Z & " % # & # i & " %

R is the reflectance of the halftone print.

ai is the fractional area covered by color i with reflectance Ri

X, Y, Z are the tristimulus values for the average color of the halftone print.

ai is the fractional area covered by color i with Xi, Yi, Zi

DEMICHEL’s Equations

Aw =(1-ac)(1-am)(1-ay)

Ac =ac(1-am)(1-ay)

Am =am(1-ac)(1-ay)

Ay =ay(1-ac)(1-am)

Ar =amay(1-ac)

Ag =acay(1-am)

Ab =acam(1-ay)

Ak=acamay

Color Halftoning

• A color image is normally halftoned by halftoning its color channels (separations) independently

• Since the color perception is very much dependent on how the separations behave in relation to each other, having a good structure of dot placement in each channel doesn’t guarantee a good perception of the halftone color image, see the images in the next slide

6 Color Halftoning, FM The color channels are halftoned independently in the image to the left while being halftoned dependently in the image to the right.

Independent Dependent

IMCDP Color Halftoning

C C

M M

Y Y

IMCDP Color Halftoning

50% Cyan, 50% magenta 50% Cyan, 50% magenta

Independent Dependent

Dot-off-Dot

7 Color Halftoning

• Dot-off-dot causes color shifts. • These color shifts have to be compensated by using measurement data. • The compensation is dependent on the printing system (printer, paper etc.) used to print the colors.

Color Compensation • We look back at the example with 50% cyan, and 50% magenta. Our aim is to have the same color in both cases, i.e. independent and dependent halftoning (dot-off-dot)

• In the independent case the dots are placed independently, hence Demichel’s equations could be utilized, which meanse that in the image to the left we have 25% paper, 25% cyan, 25% magenta and 25% blue

• Knowing the tristimulus values (XYZ) for the white paper, primary and secondary colors we can find the color (XYZ values) of the image to the left, which we call the target color and denote by (Xt, Yt, Zt)

• The goal is now to find the coverage for cyan and magenta (denoted by cd and md respectively) in such a way that the image to the right has the same color as the one to the left

Color Compensation

• The following equation system should be solved to find cd and md.

⎧X t = cd X c + md X m + (1− cd − md )X p ⎪ ⎨ Yt = cdYc + mdYm + (1− cd − md )Yp ⎪ Z c Z m Z (1 c m )Z ⎩ t = d c + d m + − d − d p

Notice that it is assumed that cd+md is less than or equal to 100% (or 1). Otherwise the expression to the right hand side of the above equation system is not valid

Notice also that the above equation system has three equations and two unknowns.

8 Color Halftoning

50% Cyan, 50% magenta 50.82% Cyan, 36.51% magenta

Independent Dependent Notice! Compensation is done for Ink-Jet. For correct color reproductions the images should be printed using the same Ink-Jet.

Dependent Halftoning (dot-off-dot)

• The yellow channel can be halftoned independent of the two others (?!) • c och m denote the coverage for cyan and magenta. • c + m <= 1, dot-on-dot can be avoided • c + m > 1, Blue dots occur

Dependent Halftoning (dot-off-dot)

• c + m >1, Blue dots occur • b= c+m-1 (Coverage of blue) • c’=c-b=1-m och m’=m-b=1-c • => c’+m’<1 • Halftone c’ and m’ as before • Replace the white dots with blue

9 Dependent Halftoning vs. Independent

Independent

Dependent

10 Homogeneousness in color patterns

• The dots should be placed homogenously over the entire halftoned color image

• To use the homogeneousness measure for grayscale halftone patterns perform a logical OR (if the dots are represented by 1) or a logical AND (if the dots are represented by 0) between the color channels

• By doing that you get a black and white halftone pattern for which you can use the measure defined previously

Homogeneousness in color patterns

(Mean value, Standard deviation)

(2.69, 1.06)

(3.95, 0.37)

Example Assume in a halftone print we have two inks. The figures show the transmittance of the inks. The reflectance of the paper is denoted by Rg (Assume: Rg = 0.8)

T1 T2 1 1

λ (nm) 400 670 800 400 535 800 λ (nm)

Express the reflectance of the halftone print using T1, T2, f1, f2 and Rg if the inks are printed according to the following figure. Also plot the reflectance spectrum of the print. (The optical dot gain can be ignored) Färg T1 Ink T1 covers f1=20% and ink T2 covers f2=30% of the surface. Färg T2

Papper