DD231866A1 - METHOD FOR CORRECTING THE COLOR INPUT SIGNAL IN MULTICOLOR PRINTING - Google Patents

Abstract

The invention relates to a method for correcting the color input signal in multi-color printing as a function of the spectral aberration of the printing inks. The aim of the invention is to achieve a better reproduction quality in reproduction processes. It is the task to be solved, to find a method that determines the maximum possible possible account for the spectral errors of the printing inks the printing parameters, which provide a predetermined print result during printing. The solution according to the invention consists in calculating, after a single determination of the remission proportions of the body colors used in the spectral blue, green and red regions, the necessary color measurements for the respective body colors with mutual consideration of the spectral color errors according to a given equation system and then performing a result selection. Fig. 11

Description

Title of the invention

Method for correcting the color input signal in multicolor printing 5

Field of application of the invention

The invention relates to a method for correcting the color input signal in multi-color printing in dependence on the spectral error of the printing inks.

Characteristic of the known technical solutions .

A correction of an incoming color signal can be carried out with various methods and means and with very different objectives. The methods used in practice emanate in the majority of analog signals for the blue color, the green color and the red color, which can be used as a video signal for a color monitor. A collection of these signals can be done in various ways, for example by a color image camera or the scanning of a multicolor template by a scanner, in which the three signals are obtained via appropriate filters. A color correction goal may be to correct the errors that occurred when taking the image in accordance with the

-7 8.84-0190251

were able to compensate for error characteristics; Another goal would be to correct for expected playback errors by the reproduction device known in their behavior. If there is a non-linear transmission behavior, then the color signals can be influenced simply by passing the signals through circuit circuits which nonlinearly change this signal as a function of the signal strength. Examples have become known from DE-AS 1 772 234, DE-AS 1 522 488 and DE-PS 2 313 195, which apply a constant correction function (power function, logarithmic function, linear function). Similar simple corrections are achieved by additions and subtractions between the three color signals. DE-PS 1 900 266, DE-AS 1 447 945, DE-AS 2 600 901, DE-OS 1 622 768 and DE-OS 2 360 720 use such measures in different order, also in pairs, etc. A suitable Correction of a spectral misconduct of printing inks for reproduction, however, can be achieved only very incompletely.

There are also known devices and methods which, starting from existing color separation signals change them in dependence on the special known properties of the reproduction process so that after conversion into video signals the expected print result is displayed on a color monitor. A manual adjustment of correction parameters by the operator then takes place in such a way that, according to the view, the display is optimized. The now read adjustment values are used to define the Druok parameters. Examples of this method can be found in DE-OS 2,949,102, DE-OS 3,049,349 and DE-PS 2,054,099. These methods can predict the result of the previously known pressure parameters, but not the necessary pressure parameters computationally unique determine if a pressure target result is specified.

A series of notices describes a color correction tool which consists of a memory indexed by the color input values and containing the corrected color signals. In some other cases, correction values are stored which are somehow processed with the color input values and thus result in the corrected signal. Such so-called "look-up tables" determine the necessary gradation of signal sizes with their storage capacity. In some cases, an interpolation is performed. Examples of a correction value storage arrangement are described in DE-OS 30 15 337, DE-OS 26 37 055 and DE-AS 26 21 008 and in other applications. However, a substantial deficiency is inherent in all of these methods: no methodology for generating the correction values is described and used, which fully takes into account all the spectral errors of the primary colors used and the resulting mixed colors. One tries here only to approach a desired state with simple means.

Object of the invention

The aim of the present invention is to avoid the existing shortcomings of the above-described methods and devices, and thus to achieve a better reproduction quality in reproduction processes.

Explanation of the essence of the invention

, - The technical problem which is solved by the invention

The invention has for its object to find a method that determines the full or maximum possible consideration of the spectral error of the printing inks, the printing parameters, which provide a predetermined pressure 'result in printing.

- 4 - Features of the invention

The object is achieved by the method steps listed in the characterizing part of item 1 of claim. Further developments are specified in the sub-items of the claim.

embodiment

The invention will be explained below using an exemplary embodiment

 In the accompanying drawing show:

Fig. 1: the ideal spectral behavior of the primary primary colors

2 shows an example of the real spectral behavior of body colors

3: an example of the real spectral behavior of the tertiary color "black"

4 shows a graphical representation of the error correction regions 25

Fig. 5 to

10 shows a diagram of the color mixing behavior for producing spectrally pure primary colors (yellow, magenta, red, blue, cyan, green) 30

11 is a diagram of a signal flow in a device incorporating the invention.

In multicolor printing, the color nuances of the printed image are achieved by subtractive color mixing of body colors. Either the color density of the printed primary colors in the .Picture point is varied or the raster tonal value is changed. The latter means that the proportion of solid printed surfaces of a pixel area is changed. The invention relates to the last case. It is to be reckoned with the printing with body colors with falsifications of the color results. A spectral purity does not exist in body colors. There are used as dyes in the printing inks a whole series of chemical compounds that can fulfill the spectral requirements of the pressure only for a specific part.

If the requirements for the spectral behavior of the primary primary colors cyan, magenta and yellow are assumed, then the image shown in FIG. 1 would have to result

 Practically, however, the body colors have side absorptions and side remissions in the spectrum. The resulting error due to the secondary absorptions is higher than the error caused by the secondary emissions. Especially the primary base color cyan is affected. Pure is the basic color yellow achievable

 The side remissions cause a whitening of the color, while the secondary absorptions bring a black component in the print result. Since these spectral errors increase in the subtractive mixing of real body colors, an even greater error is found in the secondary mixed colors. The uncoloured part (black and white) is still increasing during the color mixing. For example, the following average real spectral RemisT onsgrade are to be used for common body colors (the abbreviations are: C = cyan, Y = yellow, M = magenta):

Remission Degree In the body colors spectral ranges GYM

ideal

10 ^real

blue 1 , 6 0 15 4 5 green 1 Λ 1 9 0 2 red 0 15 1 95 1 9 blue 0 O, O, green 0 O, O, red 0 O, O,

However, the remittance data can only be used as a

1 5

serve. They are to be replaced by the actually measured values of the printing inks used in an error compensation calculation. The average for the reflectance grades in each of the spectral ranges (blue, green, red) is a useful concession

20

Simplified accounting in the error correction calculation allows. With this average, the real spectral behavior of the body colors, for example, as shown in Fig. 2 represents.

25

Determination of the printing result taking into account the color errors

When the remission of the three printed primary colors (cyan, yellow, magenta) in the blue, green and red regions of the spectrum is known, for example

35

cyan: ^R CB = o, 6 Magenta: ^R MB " O, 5 Yellow: ^R YB ⁼ 0 15 ^R CG = o, 4 ^R MG ⁼ O, 2 ^R YG ⁼ O , 9 ^R CR = o, 15 ^R MR ⁼ O, 9 ^R YR ⁼ 0 , 95,

  - 7 -

then one can calculate the remissions of the mixed colors (B = blue, G = green, R = red, S = black) from these three values. The following applies:

^R mixed ~ ^R 1 * ^R 2

(D

(R., Rp - remissions of the primary colors to be mixed)

10 15 20

This results in:

Red: / R R R

RB \

RG

RR /

Green: / R R R

GB GG

GR,

Blue: / R R R

BB BG

BR

Black: / R R R

R.

= IR. R

25

SB '

SG I = SG

TBYG

YR /

YR /

^r mb \

^R MG ^? MR /

MB MG MR

/ R

MB MG

\ ^K MR

^r yb \ / ^1l gb

^R YG * ^R CG

In screen printing, in which the ratio of the area printed on the full color area of the pixel total area to the pixel total area determines the achieved integral color, arise in the subtractive color mixing in this pixel surface sections,

- which contain the achromatic white (A _w ),

- contain the primary colors (A _n , A _M , A _v ),

- contain the colorful secondary mixed colors (A ₁ - ,, A _n , A _n "

- which contain the achromatic tertiary mixed color black (Ag).

These eight colors determine, according to their printed area A, the integral color mixing result perceived by the human eye. Of course, one or more colors of this series may not be included in the biopoint at all.

The area shares of the 8 colors are always complementary to 1:

+ A _B + A _G + A _R +

(2)

For the remission of the pixel in the spectral ranges blue, green and red, it is assumed on the assumption that the recording medium has an ideal white:

= A _£

+ A

CB CG

\ ^R CR

YB YG YR

'R

YB

./R

-YB

^R YG

\ ^R YR,

CB CG CR

+ A

MB \

^R YG I ⁺ 1M · I ^R MG I ⁺ 1C

MR /

^r cb \

^R cGr

^R CR /

CB CG CR

(3)

Thus, a system of equations consisting of three equations arises here, which can be read as follows after the onset of the remission values of the primary colors in the three spectral ranges:

^R B =

^R R =

0.045 × Ag + 0.300. A _B + 0.090. A _Q + 0.075

+ 0.150. Α _γ + 0.500. A _M + 0.600. A _Q + A ^.

0.072. Ag + 0.080.,. A _B + 0.360. A _Q + 0.180

+ 0.900. Α _γ + 0.200. A ₁ + 0.400. A _Q + A ^

0.128. Ag + 0.135. _Aβ + 0.143. A _Q + 0.855

+ 0.950. Α _γ + 0.900. A ₁ + 0.150 ·. A ₀ + A _w

A _R (6)

Rg = O, 045 ^R G = O, 072 ^R R ' O, 128

By inserting the area to be printed for the eight basic and mixed colors into Equations (4), (5) and (6). one can calculate the print result taking into account the spectral error behavior.

The tertiary color black becomes very strongly falsified when the three subtractive primary colors yellow, magenta and cyan overlay to full proportions. It is here:

since all other summands of the equation system to zero

become

, c This print result does not correspond in any way to an ideal black, which is to result from the additive mixture of blue = 0, green = 0 and red = 0. Fig. 3 illustrates the practically achievable "black".

The three-color print provides a very insufficient black. 2Q The result is a mixture of dark gray and red orange.

A correction option does not exist.

However, if black is used as the fourth printing ink to print, then the conditions improve considerably. It is then in the equations (4), (5) and (6) to change the coefficients for A ~ according to the remission behavior of this black ink in the blue, green and red range. An "ideal black" would null those coefficients.

Inventive determination of flawless color mixture 30

If no corrective measures are taken, then one must live with the resulting error, which results from the secondary absorption and emission of the printing inks. The print result will be more or less satisfactory. An optimum of

Reproduction is not achieved.

Possible corrective measures include interdependence of these side absorptions and remissions

Color design to take into account. Of course, this can only be done if z. For example, a "too much green" for the magenta print may be considered as a "less green" for the yellow print in that blend. Of course, this only works in full if the proportion of "green" in the "yellow" to be printed is sufficient for this compensation. The solution of the equation system (4), (5) and (.6) is therefore necessary, inter alia, for error compensation. It is specified and prompted for the surface portions Ag, A _33, A ^, A _R, A _v, A ^, A ^ and A ^ is the result to be achieved as Rg, _R and R _R. As you can see, this is an inhomogeneous system of linear equations consisting of three equations and eight unknowns. It is unsolvable in this form and has certainly not least led to the abortion of the "attempt of an analytical determination of the error correction values in many places.

However, there are a number of limiting conditions whose knowledge enables the computational solution of the problem. Thus, one has to keep in mind the effects of a purely subtractive mixture of the three primary primary colors cyan, magenta and yellow in one pixel. It applies here:

1. Only one of the primary colors (cyan, yellow or magenta) can be present in the mixture because two primary colors mix to form a secondary color area fraction, which is supplemented by a primary color area fraction if the primary color areas were of different sizes.

2. Only one of the secondary colors (blue, red or green) can be present in the mixture, as two secondary colors require surface proportions of all three primary colors. This common three-color component is black in the mix.

3 · There are no complementary color surface components in the mixture. Thus there is no simultaneous presence of yellow and blue, cyan and red, as well as magenta and green, because a subtractive mixture of complementary colors in equal proportions gives black.

- ΊΊ -

4. Black and white parts can be present in every mix.

Applying these rules, a total of only six different base mixtures are possible, with only a maximum of four different color surfaces forming the pixel surface next to one another in the mixtures. These are the mixtures:

1. Black - Red - Yellow - White 2. Black - Green - Yellow - White.

3. Black - Red - Magenta - White

4. Black - Blue - Magenta -White

5. Black - Green - Cyan - White

6. Black - Blue - Cyan - White 15

In all six basic mixture variants, up to three of the components can become zero. For example, you would have to classify the mixture black-blue-magenta into the 4th variant. Including equation (2) in the equation system, this now consists of four equations. If the principle color composition of the pixel surface is known - and it must correspond to one of the six variants according to the above, then one can solve the inhomogeneous linear system of equations. For the 1st basic mixture variant then stand

z. B .:

^R B * O, 045 • ^A s ^H , 075, 150 , Α _γ + 1 • ^A w (7) ^R G ⁼ O, 072 • ^A s ^H , 180, 900 , Α _γ + 1 (8th) ^R R - O, 128 • ^A s ^H , 855, 950 A-f · Ί * ^A w (9) 1 = 1 , Α _σ H 1 , 1 , A + 1 (10) h 0 ' ^A R ^H h 0 , A _R H I · 0 ' ^A R ' f- • ^A R ^H - 0 - 0 - 0

(Rt ₃ , Rp) Rr, are the default values, while A ₀ , A _n , A _v and

JD U * it O JLL I

Ar, the real roots of the system of equations.) The system of equations can be solved, for example, with the help of determinant calculation. One determines the coefficient end determinants D and the determinants D ₀ , D _n , D _v and D _T , with

ü Yes X W

ο, 045 0 075 0 15 1 1 ' ^D S 0 = ^R B O, 0,075 0 0 J 15 1 1 D = ο, 072 0 18 0 fs 1 1 0 ^R G O, 0.18 0 0 9 .1 1 ο, 128 ο, 855 0 95 1 1 0 ^R R O, 0.855 0 0 1 95 1 1 1 1 1 1 1 1 1 1 1 1 1 9 1 1 ο, 045 ^R B 0 15 D ₁ = 075 . 5 ^D R = ο, 072 ^R G 0 9 18 ο, 128 ^R R O, 95 855 95 1 1 1 , 045 , 072 128

0.045 0.075 0.15

0.072 0.18 0.0

0.128 0.855 0.95

1 1

^R CR

The general solution of a determinant of the present form

D =

^r 2 ^l 2

^E 3 G ₃

is:

D =

2 ^R 3 ^R 4 1 1 1

³ 2 '

1 1

^R 1 ^R 2 ^R 4 1 1

-B

G ₁ G ₂ G ₃

1 1

then D:

D = B ₁ - (G ₃ -R ₃ + G ₃ -R ₄ + G ₄ .

(G ₁ .R ₃ + G ₃₁ R ₄ +

+ B

₃ ..

+ G ₂ . R ₄ + + G ₂ .R ₃ +

- ^G 2 ' ^R 4 ~ ^G 3' ^R 2

- G ₁ -R ₄ - G ₃ -R ₁

PR PP

- G ₁ -R ₄ - G ₂ -R ₁

(11)

If the coefficient determinant D of the system is not equal to zero (and this is always the case here), then such a system of equations has one and only one solution. The

Roots A _g , A _R , Ay and A ^ result according to the Kramer rule according to the formulas:

D _q D _n D _v D _T7

λ _ -2. λ _ -JL λ _ _1 a - - (12 ~) H 3 ") Γ14") ί15) S ~ DR ~ DY "D ¥" D ^ ^J '^ ^ ^} ' ^{κ J} '^ ^;

If the error caused by the side absorptions and side remissions can be fully compensated, then all 4 roots of the equation system are positive. Are positive

,, -, but in any case the roots for the chromatic color components (in this example for A _R and Ay).

In the event that any of the area fractions is less than zero, then this means that something of this color would have to be subtracted out of the pixel, which of course would be subtracted out of the pixel.

, C- lent practically impossible. At best, this area can be set to zero here. The shortfall has an irreproducible error. The same applies if the solution of the system of equations results in a value greater than 1 for an area fraction.

p _n More than the total area can not be printed; the non-printable area remainder acts as a non-compensable error.

But how can one now recognize which of the six basic mixture variants for the solution of the color optimization problem

pt- is to be used? It turns out that, if one solves all six systems of equations, only one solution exists within the six possible solutions, in which the area proportions for the two bright colors are positive. This solution should then be used as a sought-after solution. So nothing else remains

ο «res, than to solve all 6 systems of equations and then to select the solution sought according to the criterion written above

 There can be three different solutions:

1. All area shares are positive. The spectral errors caused by side absorptions and remissions have been fully compensated, i. the print result fully corresponds to the specification.

2. The two areas for the uncoloured colors (black and white) are negative. The spectral color errors are not fully compensated. A subsequent optimization calculation after the minimum error is necessary. The print result contains a maximum of 3 colors.

3 · One of the areas of the uncoloured colors is smaller than zero. The print result consists of a maximum of 3 different color areas. The spectral errors are not fully compensated. The error minimum can be calculated by a subsequent optimization.

For example, the calculation produces the following variants:

Guideline: Blue: R _ß = 0.7

Green: R _& D = 0.7 (cyan with 30 % black and white)

Red: 'R _R = 0.3 30 % white content

1 . ^A S = O, 911 ^A R = -0,673 Ay = 0.061 ^A w - 0,700 Second ^A S = -0, 684 ^A G = 1.544 ^A Y = -0.531 - ^A w = 0.672 Third ^A S = o, 907 ^A R = -0.552 ^A M = -0.112 0,756 4th ^A S = o, 008 ^A B = 0.875 ^A M = -0.641 ^A w - 0.758 5th ^A S = -0, 699 ^A G = 0.693 ¹ C = 0.842 0.164 6th ^A S = o, 620 ^A B = -1.254 ^A C = 1.463 ^A W ⁼ 0,170

pt- In this example, it would have been necessary to execute the calculation up to variant 5 to determine that

- the mixture can not be produced flawlessly (there is no variant without neg. A) *

- the optimum mixture of area proportions of the components o _n black, green, cyan and white exists (where components of

this mixture can also be zero)

- a calculation of the calculation of these area proportions must be made.

Tc The following describes the calculation of color mixing with the minimum error.

Determination of the error criterion

In cases where color compensation is practically no longer possible, ie where the solution of the linear G-system requires a negative black and / or white area, optimization calculations have to be carried out. The result is a color mixture that shows the smallest possible error compared to the default.

Using the absolute deviation as an error criterion does not make sense for this problem. The solution is to minimize the variance or standard deviation when comparing the preset with the color mix result. For this purpose, the respective absolute error is first determined by subtraction.

The standard deviation is then at these three. Difference values:

(R ₁₃ -r ') ² + (R _n -R *) ² + (R _D -r') j (16)

Where R ", R _fi and R _{1 are} the remission values of the color specification; Rn, Rp and Rp describe the remissions of the print result in the three spectral ranges.

The optimal mixture according to the specification is.

reached when there is no other solution that has a lower standard deviation.

In the case of the need for optimization (Ag <0 and / or A-TT <0), it is not clear in advance whether the optimal mixture of three or two components or even only out

a component must exist (only a flawless mixture has a maximum of 4 different colored area proportions). A total of 14 different cases are possible:

Cases 1 to 4: (only one color involved) 35

1 . 4 = 1 Second A ₁ = 1 Third A ₃ = 1 4th A ₂ = 1

A ο ^ ^Α 4 = 1 ά = 1

Cases 5 to 10: (2 colors involved)

5. A ₂ + A ₃ = 1

.6. A ₁ + A ₃ = 1

7. A ₁ + A ₂ = 1

8. A ₁ + A ₄ = 1

9. A ₂ + A ₄ - 1

10. A ₃ + A ₄ = 1

Cases 11 to 14: · (3 colors involved)

11 A + A + A =

12. A ₁ + A ₂ + A ₄ =

13. A ₁

14. A ₂

If one adjusts the optimization for these 3 basically different variants (with a total of 14 cases), then a solution with the smallest error results.

Optimization of the 1-color problem 20

This is the simplest case, because the relationships

^R B - ^R nB · ^A n

^R G ^{= R} n G ' ^A n

R "= R _D .AR nR η

result in the print result for the 4 possible cases with η = to 4. The index η denotes the respective possible color (S, B, G, R, Y, M, C, W). For B _n , - G _n and R _n , the remissions belonging to the respective color of the areas A in the respective spectral ranges are to be selected. After (16), the standard deviation is determined. ·

Optimization of the 2-color problem

Mean here

A ₁ , A ₂ - Planned shares of the 2 par-

ben

I II

Rg, Rn, Rp - print result achieved (remissions in the three spectral ranges)

Rg, Ro, Gp - default to which the print result should approximate

Bp, Gp, Rp - remissions of the two colors in the

spectral

It applies according to equations (2) and (3):

(17) (18)

R _D = R,. A, + R ₀ . A ₀ . (19)

(20)

Substituting equation (20) into equations (17), (18) and (19) provides:

R _B = B ₁ - (B ₁ -B ₂ ). A ₂ .

^R B - B ₁ ' ^A 1 + ^B 2 , A ₂ I = ^G 1 • ^A 1 + ^G 2 * O ^R R = ^R 1 • ^A 1 + H ₂ A ₁ = 1 -A ₂

R p = R ₁ - (R ₁ - R ₂ ). A ₂

Error minimization can be performed by attempting to run the mean square deviation of the result values Rg, Rn and Rp from the default values Rg, Ro and Rp towards a minimum. For this bill

it is also possible to minimize the sum of the squares of the deviations.

With this criterion applies:

= (R _B -

(R _ß -

(R _R -

(21)

(A X should run against a minimum)

After inserting the values:

A X = ((Rg - B ₁ ) + (B ₁ - B ₂ ). A + ((R _G - G ₁ ) + (G ₁ - G ₂ ). A

+ ((R _R - R ₁ ) + (R ₁ - R ₂ ). A

Substituting _Rβ -

then stands for

= B

G ^ ₁ R _R -

^R 1 * ^R 2 ^{= R} E '

= f

2. (B _D.

+ G _E ² +

(22)

The minimum for ^ X can be determined by taking the 1st derivative of ^ i X after Ap and then setting it equal to zero.

becomes:

f '(A ₂ ) = 2. (B _D .B _E + G _D .G _E + R _D .R _E ) + 2.

(23)

So it is with f (A ₂ ) = 0:

C.

^G E ^{+ R} E

The corresponding A, is then to be determined according to equation (20), -j- Thus, the area proportions A ₁ and A _{2 of} the two colors are determined, in which the mean square deviation of the result values from the default values has the minimum.

Optimization of the 3-color problem

Here comes to the treating sizes nor the area A ^ added, which stands for a further color component of a third color.

According to (2) and (3) applies here:

Rg = B ₁ . A ₁ + B ₂ . A ₂ + B ₃ . A ₃ (25)

, R ^ = G ₁ . A ₁ + G ₂ . , A ₂ + G ₃ . A ₃ (26)

R ^ = R ₁ . A ₁ + R ₂ . A ₂ + R ₃ . A ₃ (27)

A ₁ = 1 - A ₂ - A ₃ (28)

If the quantity A becomes equations (25) according to equation (28),

(26) and (27), it then appears that:

R ₅ = B ₁ + (B ₂ -B ₁ ). A ₂₊ (B ₃ -B ₁ ). A ₃

R ^ = G ₁ + (G ₂ -G ₁ ). A ₂₊ (G ₃ -G ₁ ). A ₃ on '

R _R = R ₁ + (R ₂ - R ₁ ). A ₂₊ (R ₃ - R ₁ ). A ₃

Substituting here Bp-B, = B ^ ₁ Gp - G. = G ₁ -., Rp - R ^ = R ₁ -.,

B ₃ -B ₁ = B _E , G 25

^B 3 " ^B 1 ^{= B} E ' ^G 3" ^G 1 ^{= G} E' ^R 3 " ^R 1 ^{= R} E '

then the above equation is read as follows:

1 Rg = B 1 ^{+ B} D • ^A 2 ^y , A ^ j ^R G = ^G 1 ^{+ G} D. • ^A 2 ^A 3 R _R = R 1 ^{+ R} D , A ₂ - • ^A 3 ^ ⁵ E ^{h G} E ^{h R} E

After inserting B, G and R into the equation (21) where the sum of the squares of the deviations is formed,

you find: 35

f D "D" D Λ "D Λ Λ

- (R - G - G .A - G-n. A)

- (Rp - R, - R _71, A - R -, A ") (29)

it I JJ 'C. ΣΛ J

Within "brackets it is possible to replace:

^R B " ^B 1 ^{= B} F ' ^R G ~ ^G 1 ^{= G} F' ^R R" ^R 1 ^{= R} F

Now stands for the sum of the squares of the deviations

after inserting and changing: 10

£ X = B _p "+ G _F ² + R _p ²

+ (Β / + G _D ² + .R ^). A ₂

- 2. (Bj ₁ - B _D ² + G _p G _D + R _F R _D ). A ₂

+ 2. (B _D B _B G _D , G _E + R _D R _E ). A ₃ . , A ₃ - 2. (B _p - B _E + G _F G _E + R _p R _E ). A ₃

⁽³⁰⁾

So it is ^ U = f (A ₂ , A ₃ ).

To determine the functional minimum, proceed as in the calculation of the sink of a curved surface. First, the 1st derivative of the function is formed after the 1st variable and set equal to zero, and then the 1st derivative of the function is formed after the 2nd variable and set to zero. The result is a system of equations whose roots represent the points Ap, A- of the minimum of the function.

f _A2 (A ₂ , A ₃ ) = 2. (B _D + G _D + R _D ). A ₂

- 2. (B _p B _p + G _p G _D + R _p R _D )

+ 2. (B _D, B _E + G _D, G _E + R _D, R _E ) .A ₃

f _A3 (A ₂ , A ₃ ) = 2. (B _E + G _E + R _E ). A ₃

- 2. (Bp B _E + G _p G _D + Rp R _D ) (32)

, + 2. (B _D B _E + G _D G _E + R _D R _E ) A ₂

Α2 P '3 ~ \ J'j)

^f A3 ^(A 2'V ⁼ °. ⁽³⁴⁾

.5 Setting B ^ + G _D + R ^ = H.

^B D ' ^B E ^{+ G} D' ^G E ^{+ R} D ' ^R E ^{= H} 3

B "Q, Γτ Ρ ι" D "D XJ

tt - * - VTt-, IT -4- Π · ™ Γι. -τ-, ij. ι

IjI * "^^ lil ^" Nl * TjI JjI * LjI "" ^ / j

2 2 2

υ Δ Ü O

then stands for (31) and (32) with (33) and (34)

, A ₂ - H ₄ + H '. A ₃ = 0

According to the 2nd equation is-

λ _ ^ 3 λ, fi '(35)

3H ₅ 2H ₅

Substituting A_ into the 1st equation yields:

H,

 or 1.

₉ - ^H 2 + H ₃ . (- ^. 5 Λ J _- ilp T ^H 5 ) = 0 Oh ^A 2 results: Λ H 2 × ^H 5 H ₃ . H ₄ A ₃ H 1 · ^H 5 " R ² H ₃

a (36)

3 ~ 2

H ^. H ^ - H ₃

Thus, (36), (35) and (28) have been used to calculate the color area proportions of the three colors involved, for which the mean square deviation of the print result from the preset values is minimal. The comparison of the standard deviations of the total of 14 solutions provides the optimum of the mixing result to be achieved.

Explanation of the optimization results of the method according to the invention

By the method of the present invention, it is possible to minimize the mixing error caused by the spectral errors of the body colors. In many areas, the error is fully compensated. There are 4 qualitatively delimited areas in the solution of the equation system which has been selected from the 6 possible equation systems. These 4 areas are shown graphically in FIG.

The horizontal hatched area is that in which the spectral errors can be fully compensated. If the working point is on the color line, then only black and white is required. If he is on the baseline, then no black is required. If it is on the right vertical border, then no white part is required. The dashed line divides the working triangle into two parts. In these parts, other color component parts respectively form the color portion (e.g., black, blue, magenta, and white at the top and black, red, magenta, and white at the bottom). An operating point on the dotted line describes a mixture in which the transition components of the chromatic colors are zero (in the example: area of blue area = 0, area of red area = 0, the mixture contains only black, white and magenta). In the area of the working triangle several such color transition are possible. FIGS. 5 to 10 show, in the diagram representation described, the color mixing behavior for producing spectrally pure primary colors red, blue, green, yellow, magenta and cyan, in which example the printing inks having the characteristic shown in FIG. 2 are used. The hatched area here is the area in which the spectral errors of body colors can be compensated. It can be seen that also for the formation of pure primary colors

a secondary color must be added to the spectral. To achieve purity. For example, pure yellow with a

To obtain certain uncoloured portion (black and white), body color yellow is always mixed with body color cyan as a second colorful color, forming a green area portion. The mixture of pure red can be magenta as well as cyan and yellow. Here are 3 color transitions to observe. The largest areas of complete correctability are red and yellow. In the other colors, it is only possible to print the spectrally pure color at high uncoloured content. As can be seen from the diagrams, the point of maximum chroma of the print result of a spectrally pure primary color lies with the following color area proportions:

colour red spectrally pure Black- White yellow Chromatic colors share proportion of proportion of magenta 68 % 13 % 19 % cyanogen 66 % 20 % 14 % blue 25 % 64 % 11 % green 24 % 61 % 15 % 22 % 64 % 14 % 22 % 64% 14%

It can be seen that the amount of correction by which one or more body color components must be changed to obtain the best possible printing result is between 0% and about 20 % . With the method, the correction of any input signals on the computing path is possible or else the signals are discretely stepped, in the second case, the number of different signals to be processed is limited. Assuming that the applied printing method, the variation of the surface portions of the used for subtractive mixing 3 primary colors in discrete stages and you in this specific case,

if the result of the correction procedure requires an amount lying between two stages, then it has to decide on one of the two levels, then a correction in a rough grading is limited.

If the correction method is to be used sensibly, then the step distance for the area proportions of the printing inks in the pixel must not be greater than the maximum expected correction value. It follows from this consideration that the method of error correction can be usefully applied to printing processes which can form the color surface portions in more than 5 discrete steps. At a sufficiently high processing speed of the device using the inventive device, the correction of the input signals can be carried out directly and the corrected output signals can be supplied to the reproduction device.

With a limited number of achievable color combinations, there is also the possibility of prior determination of the color value assignments of the exposure values to the print. values and then storing the results in a semiconductor memory. In such a "look-up-tab-Ie", the direct corrected assignment of the print data can be requested after reading the color signals into the printer.

If, for example, every primary color is printed in 16 steps, the result is 4096 color combinations. The memory required for the look-up table is limited

 The correction method described here was developed for the correction of the color input signals for an ink jet matrix printer. The signals come z. B. from the image memory of a multi-color monitor. The remission or absorption behavior of the printing inks used in the printer is to be determined by a single spectral measurement. The amount of ink applied to the recording medium per drop is very constant. A color density gradation is given by the number of side by side in

An ink droplet deposited in a sector-divided pixel of constant size.

However, the method is not limited to this technique, it is transferable to all other methods of printing and recording technology in which the color errors of the colorant used falsify the mixture.

On the basis of the schematasehen representation corresponding to FIG. 11 is finally again the method of the invention in its environment will be explained. As input signals, for example, analog video signals Rg (t), Rp (t) and Rp (t) can serve, as they are fed to the color monitor., For the processing of the signals in digital computers, an analog / digital conversion is required. Subsequently, in the correction computer, the signal processing according to the inventive method, in the result for the currently to be printed pixel of fixed size to be printed surface Unbuntflächenanteile (A "- Schwarzflächenanteil, A ^ r - ~ white area) and * the Buntflächenanteile (A. Primaryfarbflächenanteil, A ~ - Secondary color area fraction) are present. However, since in a three-color printer, the secondary colors and the black areas are formed by superimposing the three primary colors, a further simple color conversion must take place, the result of which can then be used directly for the control of the reproduction device. For example, here is the conversion:

1 area unit red = 1 area unit magenta above

1 area unit printed in yellow

^ q The signals Rq _B > rrv Rp _R ... R _W rj flowing into the correction computer are the constants determined once for the printing inks used.

Claims (3)

claim 1. Method for correcting the color input signal in multicolor printing as a function of the spectral error behavior of the printing inks used, characterized by the following method steps: a) one-time determination of the remission proportions of the body colors used in the spectral blue, green and red areas (Primary colors: Rq ₅ , ^R yb ' ^R MB' ^R CG ' ^R YG' ^R MG
^R CR ' ^R YR' ^R MR) b) one-time determination of the resulting remissions for the mixed colors, which result from the subtractive color mixing c) Determination of the reflectance specification in the three spectral ranges (blue, green and red) for the result to be achieved in the respective pixel area (R-njRpjRr,) d) Calculation of the real roots (A "; A; A"; Ay) of the inhomogeneous system of linear equations R = R A-4-R A + R A + A B SB * S 1B "1 2B * 2 W R-R A -I-R Aj-R A-I-A u oli ο Ί (i 1 dSsi d W T? - R A-t-R A-t-R Δ-4-Α R ~ SR ' ^Ä S 1R * ^Ä 1 ⁺ 2R' 2 ¥ Ί = Δ 4-Δ - * - Δ 4-Δ O IC. ti one after the other for the six cases
Case R _1B R _1G R _{1 R} A ^ R ₃ where the color area proportion of black with Ag, of White with A ", indicated by red with A _R , etc., up to the case where tLie solution of the equation system for both the Buntflächehanteil A, as well as for the chromatic surface area Ap gives a positive value, e) in this case "both - A ₁ -, = 0 and A _w = 0, there is error-free solution and corrected color input signal, but if A ^ <0 and / or A _T7 <Ό a ο w or more of the remaining area shares as long be changed until the sum of these area ratios is 1 and the area ratio J with the negative value is O; f) conversion of the corrected color input signals into speaking Farbzumessungeii for each involved Body colors. 2. Method according to item 1, characterized in that cie Determining the reflectance of the body colors used by forming the remissions for each of the body colors used according to the formula JhU) 4λ for each of the three areas (blue, green, red), where X _{1 represents} the beginning and Xp the end of the respective spectral range. 3 · Method according to point 1, characterized in that for the case Ag <0 and / or A "<0 an optimization calculation for minimizing the error is to be carried out with the optimization criterion of the quadratic error Δx = (R _B - R _g ) + (R _G - R q) + (R _R - _R β) I t where Rn, Rp and R _{R represent} the remissions of the optimization result and Ax is to run against a minimum A ₁ - 4. The method according to item 3, characterized in that separate optimization calculations are performed for. the 14 cases that and that the results are compared with respect to the optimization criterion shown in point 3 of the claim and the optimum solution is used for printing. For this 6 pages drawings.