Method and device for determining the color appearance of color overprints

A method for determining respective sets of np parameters that spectrally characterize one or more colorants in order to predict the color of an overprint of the colorants printed in an order of printing at a set of respective coverage percentages on a substrate of a substrate type using a printing technique, each of the colorants defined by a respective recipe of one or more basic colorants, the method comprising, for any particular colorant of the colorants:

• (a) for each basic colorant of the respective recipe defining the particular colorant:
• (a)(i) making a selected number of sets of prints of the basic colorant on a selected number of respective substrates of the same substrate type, a set of prints comprising prints of the basic colorant on the respective substrate at a range of coverage percentages of interest, the selected number of prints at any particular coverage percentage being on backgrounds of said selected number of different background colors,
• (a)(ii) measuring the spectra of the prints of the selected number of sets of prints and the spectra of each of the different background colors, and
• (a)(iii) if the selected number of sets of measured spectra is not sufficient to determine the set of np colorant parameters of the basic colorant as a function of wavelength and the coverage percentage of the basic colorant, overprinting one or more of the sets of prints of the basic colorant one a more times with at least one overprinting colorant, and measuring the spectra of the overprinted prints in the overprinted set of prints until a sufficient number of different measured spectra is obtained for determining the set of np colorant parameters of the basic colorant;
• and
• (b) determining from the recipe and from the measured spectra, the set of np colorant parameters of the particular colorant as a function of the coverage percentage and of wavelength.

A method of accurately predicting the color of an overprint of a set of colorants on a substrate at a respective set of coverage percentages, the method comprising:

• (a) characterizing each colorant with a set of colorant parameters determined at the coverage percentage of the colorant in the overprint;
• and
• (b) calculating the color of the overprint using the colorant parameters and the color of the substrate,
• said characterizing not requiring measurement of colors of overprints of the colorants,
• wherein said characterizing step (a) includes determining a sets of np parameters for each of the colorants, the set of parameters spectrally characterize the colorant, each of the colorants defined by a respective recipe of one or more basic colorants, said characterizing step (a) further comprising, for any particular colorant of the colorants:
• (a)(i) for each basic colorant of the respective recipe defining the particular colorant:
• making a selected number of sets of prints of the basic colorant on said selected number of respective substrates of the same substrate type, a set of prints comprising prints of the basic colorant on the respective substrate at a range of coverage percentages of interest, the selected number of prints at any particular coverage percentage being on backgrounds of said selected number of different background colors, and
• measuring the spectra of the prints of the selected number of sets of prints and the spectra of each of the different background colors;
• if the selected number of sets of measured spectra is not sufficient to determine the set of np colorant parameters of the basic colorant as a function of wavelength and the coverage percentage of the basic colorant, overprinting one or more of the sets of prints of the basic colorant one a more times with at least one overprinting colorant, and measuring the spectra of the overprinted prints in the overprinted set of prints until a sufficient number of different measured spectra is obtained for determining the set of np colorant parameters of the basic colorant;
• and
• (a)(ii) determining from the recipe and from the measured spectra, the set of np colorant parameters of the particular colorant as a function of the coverage percentage and of wavelength.

A method of accurately predicting the color of an overprint of a set of colorants on a substrate at a respective set of coverage percentages, the method comprising:

• (a) characterizing each colorant with a set of colorant parameters determined at the coverage percentage of the colorant in the overprint;
• and
• (b) calculating the color of the overprint using the colorant parameters and the color of the substrate,
• said characterizing not requiring measurement of colors of overprints of the colorants,
• wherein said step (b) of calculating comprises:
• determining the color spectrum of the overprint of the colorants printed at the set of respective percentages, including, for each colorant, in the order of the overprinting, recursively calculating the spectrum of the overprint on a selected base substrate using the parameters of said each colorant and the spectrum of the selected base substrate, the selected base substrate for the first printed colorant being the substrate, and the selected base substrate for each successive overprint being the overprint of all the previously printed colorants on the substrate, such selected base substrate for each successive overprint having the spectrum calculated in the previous recursion.

A method of accurately predicting the color of an overprint of a set of colorants on a substrate at a respective set of coverage percentages, the method comprising:

• (a) characterizing each colorant with a set of colorant parameters determined at the coverage percentage of the colorant in the overprint;
• and
• (b) calculating the color of the overprint using the colorant parameters and the color of the substrate,
• said characterizing not requiring measurement of colors of overprints of the colorants,
• wherein the effective coverage of at least one particular colorant in the overprint is affected by at least one of the other colorants laid over or under the particular colorant in the overprint of the colorants, and wherein the set of colorant parameters of the particular colorant substantially incorporates the effect of the other colorants laid over or under the colorant in the overprint, the method further comprising:
• determining a set of effective parameters for any colorant whose effective coverage percentage is affected by at least one of the colorant parameters, said set of effective parameters determined by the respective coverage percentages of any other colorants laid over or under the particular colorant,
• determining the color spectrum of the overprint of the colorants printed at the set of respective percentages, including, for each colorant, in the order of the overprinting, recursively calculating the spectrum of the overprint on a selected base substrate using the effective parameters of said each colorant and the spectrum of the selected base substrate, the selected base substrate for the first printed colorant being the substrate, and the selected base substrate for each successive overprint being the overprint of all the previously printed colorants on the substrate, such selected base substrate for each successive overprint having the spectrum calculated in the previous recursion, the effective parameters of any colorant whose effective coverage percentage is unaffected by the coverage percentages of any of the other colorants being the parameter of the colorant.

A method of accurately predicting the color of an overprint of a set of colorants on a substrate at a respective set of coverage percentages, the method comprising:

• (a) characterizing each colorant with a set of colorant parameters determined at the coverage percentage of the colorant in the overprint;
• and
• (b) calculating the color of the overprint using the colorant parameters and the color of the substrate,
• said characterizing not requiring measurement of colors of overprints of the colorants,
• wherein the overprint is of a pixel of an image and wherein predicting the color of the overprint is repeated for all pixels in the image.

An apparatus for determining the color of an overprint of one or more colorants each colorant printed in an order at a respective coverage percentage on a substrate of a substrate type, each colorant defined by a set of np colorant parameters for the coverage percentage the colorant is printed on for the substrate type the colorant is printed on, np being at least 2 for a non-scattering colorant and at least 3 for a scattering colorant, the set of colorant parameters defined by a relationship relating the spectrum of a print of a selected colorant at a selected coverage percentage on a base substrate to the spectrum of the base substrate and the set of colorant parameters of the selected colorant at the selected coverage percentage, the apparatus comprising:

• (a) a first memory for storing a spectrum, said first memory initially storing the spectrum of the substrate;
• (b) a logic unit, the logic unit including a set of one or more inputs, the inputs coupled to signals specifying a coverage percentage, a second memory for storing the values of the colorant parameters of at least one of the colorants at a selected set of coverage percentages, a set of one or more multidimensional outputs, each multidimensional output generating the values of the colorant parameters at the coverage percentage of a respective input of the set of inputs,
• (c) a combiner unit having a first input coupled to the first memory, the combiner unit coupled to said set of outputs of the logic unit for determining as an output the spectrum of an overprint essentially according to the relationship.