Method and apparatus for reproducing blended colorants on an electronic display

Claim 1

A process for measuring XYZ values of colorant blends of a sample with an image digitizer and converting to RGB values for reproduction on an electronic display comprising the steps of: (a) measuring XYZ values of said sample in an uncolored condition with said image digitizer; (b) measuring XYZ values of said sample having a single colorant denoted as i thereon at a plurality of concentrations of said colorant with said image digitizer; (c) measuring XYZ values of said sample having a pair of colorants denoted as i and j thereon at said plurality of concentration of said colorants i and j with said image digitizer; (d) computing K o of said sample in uncolored condition by the following formula: K=Light absorbing coefficient for said sample S=Light scattering coefficient for said sample K o =Light absorbing coefficient for said sample in uncolored condition R o =Said XYZ values of said sample in an uncolored condition with scaled values less than 1 Subscript o =Zero colorant concentration (K/S) o =K o =(1-R o ) 2 /2R o ; (e) computing K i and S i for each single colorant denoted as i by the following formulas: (K/S) i =(1-R i ) 2 /2R i R i =Said XYZ values of said sample having said single colorant i thereon at said plurality of concentrations of said colorant i with scaled values less than 1 y=(K/S) i -K o y=Dependent variable x 1 =C i C i =Concentration of said colorant i x 1 =First independent variable x 2 =(K/S) i C i x 2 =Second independent variable w=(R i /(R o -R i ) 2 ) 2 w=Least squares weight that forces relative errors to be uniform q=Different color concentrations P=Total number of different color concentrations ##EQU13## K i =Light absorption coefficient for said colorant i ##EQU14## S i =Light scattering coefficient for said colorant i; (f) computing K ij for each said pair of colorants denoted as i and j by the following formulas: (K/S) ij =(1-R ij ) 2 /2R ij R ij =Said XYZ values of said sample having said pair of colorants i and j thereon at said plurality of concentrations of said colorants i and j with scaled values less than 1 y=(1+S i C i +S j C j )(K/S) ij -(K o +K i C i +K j C j ) C j =Concentration of said colorant j x=C i C j W=(R ij /(R o -R ij ) 2 ) 2 ##EQU15## K ij =Light absorption coefficient for said colorants i and j Index q refers to different colorant concentrations with a letter P designating the total thereof; (g) utilizing computed K o , K i , S i , and K ij values to compute XYZ tristimulus color values from the following formulas with a letter N designating the total number of colorants: ##EQU16## R ij =(1+(K/S) ij )-[(1+(K/S) ij ) 2 -1] 1/2 ; (h) converting said computed XYZ tristimulus color values to RGB values; (i) storing said RGB values on a computer; and (j) reproducing said RGB values on an electronic display.

Claim 37

A system for measuring XYZ values of colorant blends of a sample with an image digitizer and converting to RGB values for reproduction on an electronic display comprising the steps of: (a) means for measuring XYZ values of said sample in an uncolored condition with said image digitizer; (b) means for measuring XYZ values of said sample having a single colorant denoted as i thereon at a plurality of concentrations of said colorant with said image digitizer; (c) means for measuring XYZ values of said sample having a pair of colorants denoted as i and j thereon at said plurality of concentrations of said colorants i and j with said image digitizer; (d) means for computing K o said sample in uncolored condition by the following formula: K=Light absorbing coefficient for said sample S=Light scattering coefficient for said sample K o =Light absorbing coefficient for said sample in uncolored condition R o =Said XYZ values of said sample in an uncolored condition with scaled values less than 1 Subscript o =Zero colorant concentration (K/S) o =K o =(1-R o ) 2 /2R o ; (e) means for computing K i and S i for each single colorant denoted as i by the following formulas: (K/S) i =(1-R i ) 2 /2R i R i =Said XYZ values of said sample having said single colorant i thereon at said plurality of concentrations of said colorant i with scaled values less than 1 y=(K/S) i -K o y=Dependent variable x 1 =C i C i =Concentration of said colorant i x 1 =First independent variable x 2 =(K/S) i C i x 2 =Second independent variable w=(R i /(R o -R i ) 2 ) 2 w=Least squares weight that forces relative errors to be uniform q=Different color concentrations P=Total number of different color concentrations ##EQU29## K i =Light absorption coefficient for said colorant i ##EQU30## S i =Light scattering coefficient for said colorant i; (f) means for computing K ij for each pair of colorants denoted as i and j by the following formulas: (K/S) ij =(1-R ij ) 2 /2R ij R ij =Said XYZ values of said sample having said pair of colorants i and j thereon at said plurality of concentrations of said colorants i and j with scaled values less than 1 y=(1+S i C i +S j C j )(K/S) ij -(K o +K i C i +K j C j ) C j =Concentration of said colorant j x=C i C j w=(R ij /(R o -R ij ) 2 ) 2 ##EQU31## K ij =Light absorption coefficient for said colorants i and j Index q refers to different colorant concentrations with a letter P designating the total thereof; (g) means for utilizing computed K o , K i , S i , and K ij values to compute XYZ tristimulus color values from the following formulas with a letter N designating the total number of colorants: ##EQU32## R ij =(1+(K/S) ij )-[(1+(K/S) ij ) 2 -1] 1/2 ; (h) means for converting said computed XYZ tristimulus color values to RGB values; (i) means for storing said RGB values on a computer; and (j) means for reproducing said RGB values on an electronic display.

Claim 38

A system for measuring XYZ values of colorant blends of a sample with an image digitizer and converting to RGB values for reproduction on an electronic display comprising the steps of: (a) means for measuring XYZ values of said sample in an uncolored condition with said image digitizer; (b) means for measuring XYZ values of said sample having a single colorant denoted as i thereon at a plurality of concentrations of said colorant with said image digitizer; (c) means for measuring XYZ values of said sample having a pair of colorants denoted as i and j thereon at said plurality of concentrations of said colorants i and j with said image digitizer; (d) means for computing K o said sample in uncolored condition by the following formula: K=Light absorbing coefficient for said sample S=Light scattering coefficient for said sample K o =Light absorbing coefficient for said sample in uncolored condition R o =Said XYZ values of said sample in an uncolored condition with scaled values less than 1 Subscript o =Zero colorant concentration (K/S) o =K o =(1-R o ) 2 /2R o ; (e) means for computing K i and S i for each single colorant denoted as i by the following formulas: (K/S) i =(1-R i ) 2 /2R i R i =Said XYZ values of said sample having said single colorant i thereon at said plurality of concentrations of said colorant i with scaled values less than 1 y=(K/S) i -K o y=Dependent variable x 1 =C i C i =Concentration of said colorant i x 1 =First independent variable x 2 =(K/S) i C i x 2 =Second independent variable w=(R i /(R o -R i ) 2 ) 2 w=Least squares weight that forces relative errors to be uniform q=Different color concentrations P=Total number of different color concentrations ##EQU29## K i =Light absorption coefficient for said colorant i ##EQU30## S i =Light scattering coefficient for said colorant i; (f) means for computing K ij for each pair of colorants denoted as i and j by the following formulas: (K/S) ij =(1-R ij ) 2 /2R ij R ij =Said XYZ values of said sample having said pair of colorants i and j thereon at said plurality of concentrations of said colorants i and j with scaled values less than 1 y=(1+S i C i +S j C j )(K/S) ij -(K o +K i C i +K j C j ) C j =Concentration of said colorant j x=C i C j w=(R ij /(R o -R ij ) 2 ) 2 ##EQU31## K ij =Light absorption coefficient for said colorants i and j Index q refers to different colorant concentrations with a letter P designating the total thereof; (g) means for utilizing computed K o , K i , S i , and K ij values to compute XYZ tristimulus color values from the following formulas with a letter N designating the total number of colorants: ##EQU32## R ij =(1+(K/S) ij )-[(1+(K/S) ij ) 2 -1] 1/2 ; (h) means for converting said computed XYZ tristimulus color values to RGB values; (i) means for storing said RGB values on a computer; and (j) means for reproducing said RGB values on an electronic display.

Claim 46

A system for measuring XYZ values of colorant blends of a sample with a colorimeter and converting to RGB values for reproduction on an electronic display comprising the steps of: (a) means for measuring XYZ values of said sample in an uncolored condition with said colorimeter; (b) means for measuring XYZ values of said sample having a single colorant denoted as i thereon at a plurality of concentrations of said colorant i with said colorimeter; (c) means for measuring XYZ values of said sample having a pair of colorants denoted as i and j thereon at said plurality of concentrations of said colorants i and j with said colorimeter; (d) means for computing K o of said sample in uncolored condition by the following formula: K=Light absorbing coefficient for said sample S=Light scattering coefficient for said sample K o =Light absorbing coefficient for said sample in uncolored condition R o =Said XYZ values of said sample in an uncolored condition with scaled values less than 1 Subscript o =Zero colorant concentration (K/S) o =K o =(1-R o ) 2 /2R o ; (e) means for computing K i and S i for each single colorant denoted as i by the following formulas: (K/S) i =(1-R i ) 2 /2R i R i =Said XYZ values of said sample having said single colorant i thereon at said plurality of concentrations of said colorant i with scaled values less than 1 y=(K/S) i -K o y=Dependent variable x 1 =C i C i =Concentration of said colorant i x 1 =First independent variable x 2 =(K/S) i C i x 2 =Second independent variable w=(R i /(R o -R i ) 2 ) 2 w=Least squares weight that forces relative errors to be uniform q=Different color concentrations P=Total number of difference color concentrations ##EQU33## K i =Light absorption coefficient for said colorant i ##EQU34## S i =Light scattering coefficient for said colorant i; (f) means for computing K ij for each said pair of colorants denoted as i and j by the following formulas: (K/S) ij =(1-R ij ) 2 /2R ij R ij =Said XYZ values of said sample having said pair of colorants i and j thereon at said plurality of concentrations of said colorants i and j with scaled values less than 1 y=(1+S i C i +S j C j )(K/S) ij -(K o +K i C i +K j C j ) C j =Concentration of said colorant j x=C i C j w=(R ij /(R o -R ij ) 2 ) 2 ##EQU35## K ij =Light absorption coefficient for said colorants i and j Index q refers to different colorant concentrations with a letter P designating the total thereof; (g) means for utilizing computed K o , K i , S i , and K ij values to compute XYZ tristimulus color values from the following formulas with a letter N designating the total number of colorants: ##EQU36## R ij =(1+(K/S) ij )-[(1+(K/S) ij ) 2 -1] 1/2 ; (h) means for converting said computed XYZ tristimulus color values to RGB values; (i) means for storing said RGB values on a computer; and (j) means for reproducing said RGB values on an electronic display.

Claim 47

A system for measuring XYZ values of colorant blends of a sample with a colorimeter and converting to RGB values for reproduction on an electronic display comprising the steps of: (a) means for measuring XYZ values of said sample in an uncolored condition with said colorimeter; (b) means for measuring XYZ values of said sample having a single colorant denoted as i thereon at a plurality of concentrations of said colorant i with said colorimeter; (c) means for measuring XYZ values of said sample having a pair of colorants denoted as i and j thereon at said plurality of concentrations of said colorants i and j with said colorimeter; (d) means for computing K o of said sample in uncolored condition by the following formula: K=Light absorbing coefficient for said sample S=Light scattering coefficient for said sample K o =Light absorbing coefficient for said sample in uncolored condition R o =Said XYZ values of said sample in an uncolored condition with scaled values less than 1 Subscript o =Zero colorant concentration (K/S) o =K o =(1-R o ) 2 /2R o ; (e) means for computing K i and S i for each single colorant denoted as i by the following formulas: (K/S) i =(1-R i ) 2 /2R i R i =Said XYZ values of said sample having said single colorant i thereon at said plurality of concentrations of said colorant i with scaled values less than 1 y=(K/S) i -K o y=Dependent variable x 1 =C i C i =Concentration of said colorant i x 1 =First independent variable x 2 =(K/S) i C i x 2 =Second independent variable w=(R i /(R o -R i ) 2 ) 2 w=Least squares weight that forces relative errors to be uniform q=Different color concentrations P=Total number of difference color concentrations ##EQU33## K i =Light absorption coefficient for said colorant i ##EQU34## S i =Light scattering coefficient for said colorant i; (f) means for computing K ij for each said pair of colorants denoted as i and j by the following formulas: (K/S) ij =(1-R ij ) 2 /2R ij R ij =Said XYZ values of said sample having said pair of colorants i and j thereon at said plurality of concentrations of said colorants i and j with scaled values less than 1 y=(1+S i C i +S j C j )(K/S) ij -(K o +K i C i +K j C j ) C j =Concentration of said colorant j x=C i C j w=(R ij /(R o -R ij ) 2 ) 2 ##EQU35## K ij =Light absorption coefficient for said colorants i and j Index q refers to different colorant concentrations with a letter P designating the total thereof; (g) means for utilizing computed K o , K i , S i , and K ij values to compute XYZ tristimulus color values from the following formulas with a letter N designating the total number of colorants: ##EQU36## R ij =(1+(K/S) ij )-[(1+(K/S) ij ) 2 -1] 1/2 ; (h) means for converting said computed XYZ tristimulus color values to RGB values; (i) means for storing said RGB values on a computer; and (j) means for reproducing said RGB values on an electronic display.

Claim 55

A system for measuring XYZ values of colorant blends of a sample with a chroma meter and converting to RGB values for reproduction on an electronic display comprising the steps of: (a) means for measuring XYZ values of said sample in an uncolored condition with said chroma meter; (b) means for measuring XYZ values of said sample having a single colorant denoted as i thereon at a plurality of concentrations of said colorant i with said chroma meter; (c) means for measuring XYZ values of said sample having a pair of colorants denoted as i and j thereon at said plurality of concentrations of said colorants i and j with said chroma meter; (d) means for computing K o of said sample in uncolored condition by the following formula: K=Light absorbing coefficient for said sample S=Light scattering coefficient for said sample K o =Light absorbing coefficient for said sample in uncolored condition R o =Said XYZ values of said sample in an uncolored condition with scaled values less than 1 Subscript o =Zero colorant concentration (K/S) o =K o =(1-R o ) 2 /2R o ; (e) means for computing K i and S i for each single colorant denoted as i by the following formulas: (K/S) i =(1-R i ) 2 /2R i R i =Said XYZ values of said sample having said single colorant i thereon at said plurality of concentrations of said colorant i with scaled values less than 1 y=(K/S) i -K o y=Dependent variable x 1 =C i C i =Concentration of said colorant i X 1 =First independent variable x 2 =(K/S) i C i X 2 =Second independent variable w=(R i /(R o -R i ) 2 ) 2 w=Least squares weight that forces relative errors to be uniform q=Different color concentrations P=Total number of different color concentrations ##EQU37## K i =Light absorption coefficient for said colorant i ##EQU38## S i =Light scattering coefficient for said colorant i; (f) means for computing K ij for each said pair of colorants denoted as i and j by the following formulas: (K/S) ij =(1-R ij ) 2 /2R ij R ij =Said XYZ values of said sample having said pair of colorants i and j thereon at said plurality of concentrations of said colorants i and j with scaled values less than 1 y=(1+S i C i +S j C j )(K/S) ij -(K o +K i C i +K j C j ) C j =Concentration of said colorant j x=C i C j w=(R ij (R o -R ij ) 2 ) 2 ##EQU39## K ij =Light absorption coefficient for said colorants i and j Index q refers to different colorant concentrations with a letter P designating the total thereof; (g) means for utilizing computed K o , K i , S i , and K ij values to compute XYZ tristimulus color values from the following formulas with a letter N designating the total number of colorants: ##EQU40## R ij =(1+(K/S) ij )-[(1+(K/S) ij ) 2 -1] 1/2 ; (h) means for converting said computed XYZ tristimulus color values to RGB values; (i) means for storing said RGB values on a computer; and (j) means for reproducing said RGB values on an electronic display.

Claim 56

A system for measuring XYZ values of colorant blends of a sample with a chroma meter and converting to RGB values for reproduction on an electronic display comprising the steps of: (a) means for measuring XYZ values of said sample in an uncolored condition with said chroma meter; (b) means for measuring XYZ values of said sample having a single colorant denoted as i thereon at a plurality of concentrations of said colorant i with said chroma meter; (c) means for measuring XYZ values of said sample having a pair of colorants denoted as i and j thereon at said plurality of concentrations of said colorants i and j with said chroma meter; (d) means for computing K o of said sample in uncolored condition by the following formula: K=Light absorbing coefficient for said sample S=Light scattering coefficient for said sample K o =Light absorbing coefficient for said sample in uncolored condition R o =Said XYZ values of said sample in an uncolored condition with scaled values less than 1 Subscript o =Zero colorant concentration (K/S) o =K o =(1-R o ) 2 /2R o ; (e) means for computing K i and S i for each single colorant denoted as i by the following formulas: (K/S) i =(1-R i ) 2 /2R i R i =Said XYZ values of said sample having said single colorant i thereon at said plurality of concentrations of said colorant i with scaled values less than 1 y=(K/S) i -K o y=Dependent variable x 1 =C i C i =Concentration of said colorant i X 1 =First independent variable x 2 =(K/S) i C i X 2 =Second independent variable w=(R i /(R o -R i ) 2 ) 2 w=Least squares weight that forces relative errors to be uniform q=Different color concentrations P=Total number of different color concentrations ##EQU37## K i =Light absorption coefficient for said colorant i ##EQU38## S i =Light scattering coefficient for said colorant i; (f) means for computing K ij for each said pair of colorants denoted as i and j by the following formulas: (K/S) ij =(1-R ij ) 2 /2R ij R ij =Said XYZ values of said sample having said pair of colorants i and j thereon at said plurality of concentrations of said colorants i and j with scaled values less than 1 y=(1+S i C i +S j C j )(K/S) ij -(K o +K i C i +K j C j ) C j =Concentration of said colorant j x=C i C j w=(R ij (R o -R ij ) 2 ) 2 ##EQU39## K ij =Light absorption coefficient for said colorants i and j Index q refers to different colorant concentrations with a letter P designating the total thereof; (g) means for utilizing computed K o , K i , S i , and K ij values to compute XYZ tristimulus color values from the following formulas with a letter N designating the total number of colorants: ##EQU40## R ij =(1+(K/S) ij )-[(1+(K/S) ij ) 2 -1] 1/2 ; (h) means for converting said computed XYZ tristimulus color values to RGB values; (i) means for storing said RGB values on a computer; and (j) means for reproducing said RGB values on an electronic display.

Claim 64

A system for measuring XYZ values of colorant blends of a sample with a spectrophotometer and converting to RGB values for reproduction on an electronic display comprising the steps of: (a) means for measuring XYZ values of said sample in an uncolored condition with said spectrophotometer; (b) means for measuring XYZ values of said sample having a single colorant denoted as i thereon at a plurality of concentrations of said colorant i with said spectrophotometer; (c) means of measuring XYZ values of said sample having a pair of colorants denoted as i and j thereon at said plurality of concentrations of said colorants i and j with said spectrophotometer; (d) means for computing K o of said sample in uncolored condition by the following formula: K=Light absorbing coefficient for said sample S=Light scattering coefficient for said sample K o =Light absorbing coefficient for said sample in uncolored condition R o =Said XYZ values of said sample in an uncolored condition with scaled values less than 1 Subscript o =Zero colorant concentration (K/S) o =K o =(1-R o ) 2 /2R o ; (e) means for computing K i and S i for each single colorant denoted as i by the following formulas: (K/S) i =(1-R i ) 2 /2R i R i =Said XYZ values of said sample having said single colorant i thereon at said plurality of concentrations of said colorant i with scaled values less than 1 y=(K/S) i -K o y=Dependent variable x 1 =C i C i =Concentration of said colorant i x 1 =First independent variable x 2 =(K/S) i C i x 2 =Second independent variable w=(R i /(R o -R i ) 2 ) 2 w=Least squares weight that forces relative errors to be uniform q=Different color concentrations P=Total number of different color concentrations ##EQU41## K i =Light absorption coefficient for said colorant i ##EQU42## S i =Light scattering coefficient for said colorant i; (f) means for computing K ij for each said pair of colorants denoted as i and j by the following formulas: (K/S) ij =(1-R ij ) 2 /2R ij R ij =Said XYZ values of said sample having said pair of colorants i and j thereon at said plurality of concentrations of said colorants i and j with scaled values less than 1 y=(1+S i C i +S j C j )(K/S) ij -(K o +K i C i +K j C j ) C j =Concentration of said colorant j x=c i C j w=(R ij /(R o -R ij ) 2 ) 2 ##EQU43## K ij =Light absorption coefficient for said colorants i and j Index q refers to different colorant concentrations with a letter P designating the total thereof; (g) means for utilizing computed K o , K i , S i , and K ij values to compute XYZ tristimulus color values from the following formulas with a letter N designating the total number of colorants: ##EQU44## R ij =(1+(K/S) ij )-[(1+(K/S) ij ) 2 -1] 1/2 ; (h) means for converting said computed XYZ tristimulus color values to RGB values; (i) means for storing said RGB values on a computer; and (j) means for reproducing said RGB values on an electronic display.

Claim 65

A system for measuring XYZ values of colorant blends of a sample with a spectrophotometer and converting to RGB values for reproduction on an electronic display comprising the steps of: (a) means for measuring XYZ values of said sample in an uncolored condition with said spectrophotometer; (b) means for measuring XYZ values of said sample having a single colorant denoted as i thereon at a plurality of concentrations of said colorant i with said spectrophotometer; (c) means of measuring XYZ values of said sample having a pair of colorants denoted as i and j thereon at said plurality of concentrations of said colorants i and j with said spectrophotometer; (d) means for computing K o of said sample in uncolored condition by the following formula: K=Light absorbing coefficient for said sample S=Light scattering coefficient for said sample K o =Light absorbing coefficient for said sample in uncolored condition R o =Said XYZ values of said sample in an uncolored condition with scaled values less than 1 Subscript o =Zero colorant concentration (K/S) o =K o =(1-R o ) 2 /2R o ; (e) means for computing K i and S i for each single colorant denoted as i by the following formulas: (K/S) i =(1-R i ) 2 /2R i R i =Said XYZ values of said sample having said single colorant i thereon at said plurality of concentrations of said colorant i with scaled values less than 1 y=(K/S) i -K o y=Dependent variable x 1 =C i C i =Concentration of said colorant i x 1 =First independent variable x 2 =(K/S) i C i x 2 =Second independent variable w=(R i /(R o -R i ) 2 ) 2 w=Least squares weight that forces relative errors to be uniform q=Different color concentrations P=Total number of different color concentrations ##EQU41## K i =Light absorption coefficient for said colorant i ##EQU42## S i =Light scattering coefficient for said colorant i; (f) means for computing K ij for each said pair of colorants denoted as i and j by the following formulas: (K/S) ij =(1-R ij ) 2 /2R ij R ij =Said XYZ values of said sample having said pair of colorants i and j thereon at said plurality of concentrations of said colorants i and j with scaled values less than 1 y=(1+S i C i +S j C j )(K/S) ij -(K o +K i C i +K j C j ) C j =Concentration of said colorant j x=c i C j w=(R ij /(R o -R ij ) 2 ) 2 ##EQU43## K ij =Light absorption coefficient for said colorants i and j Index q refers to different colorant concentrations with a letter P designating the total thereof; (g) means for utilizing computed K o , K i , S i , and K ij values to compute XYZ tristimulus color values from the following formulas with a letter N designating the total number of colorants: ##EQU44## R ij =(1+(K/S) ij )-[(1+(K/S) ij ) 2 -1] 1/2 ; (h) means for converting said computed XYZ tristimulus color values to RGB values; (i) means for storing said RGB values on a computer; and (j) means for reproducing said RGB values on an electronic display.