# US 2022/0276152 A1 · Method and system for matching and adjusting pigmentation of a sample coating to a target coating

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- Number: US 2022/0276152 A1
- Document ID: US20220276152A1
- Status: Published application
- Kind: A1
- Application number: 17/632,591
- Filed: 2020-08-01
- Published: 2022-09-01
- Earliest claimed: 2019-08-06
- Assignees: BASF Coatings GmbH
- Applicants: BASF Coatings GmbH
- Inventors: Guido Bischoff; Florian Steufmehl
- Web page: https://patentgrep.com/patent/US20220276152A1

## CPC

- G01J 3/463: {Colour matching}
- G01N 21/251: {Colorimeters; Construction thereof}
- G01N 21/31: Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry {(G01N21/72 takes precedence)}
- H04N 1/60: Colour correction or control {(H04N1/54 takes precedence)}
- G01J: MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY (light sources F21, H01J, H01K, H05B; investigating properties of materials by optical means G01N)
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)
- H04N: PICTORIAL COMMUNICATION, e.g. TELEVISION

## Abstract

Described herein is a computer-implemented method for matching and adjusting pigmentation of a target coating, the method including at least the steps of: retrieving from a formulation database which includes formulas for coating compositions with different pigmentations, one preliminary matching formula; providing a match metric; and by using one or more processors: calculating a match metric value for the preliminary matching formula; and deciding, based on a magnitude of the match metric value, whether the pigmentation is significantly improvable; in the case that the pigmentation is significantly improvable: defining a selection of at least one additional tinting base which might be eligible for further adjusting the preliminary matching formula to the target coating; calculating, for each of the at least one additional tinting base, a match metric value; and issuing, via an output device, a list of eligible additional tinting bases of the at least one additional tinting base.

## Claims

### Claim 1

A computer-implemented method for matching and adjusting pigmentation of a target coating, the method comprising at least the steps of:
a) retrieving from a formulation database which comprises formulas for coating compositions with different pigmentations, one preliminary matching formula;
b) providing a match metric that describes a color difference and a spectral similarity between a remission curve given for the target coating and a remission curve determined for the preliminary matching formula; and
by using one or more processors:
c) calculating a match metric value for the preliminary matching formula based on the remission curve given for the target coating and the remission curve determined for the preliminary matching formula;
d) adjusting the preliminary matching formula with respect to concentrations of included pigments in the way that the match metric is minimal;
e) evaluating the match metric value of the adjusted preliminary formula; and
f) deciding, based on a magnitude of the match metric value of the adjusted preliminary formula, whether the pigmentation of the adjusted preliminary matching formula is significantly improvable;
in the case that the pigmentation of the adjusted preliminary matching formula is significantly improvable:
g) defining a selection of at least one additional tinting base which might be eligible for further adjusting the adjusted preliminary matching formula to the target coating, each additional tinting base being associated with a respective modified preliminary matching formula consisting of the adjusted pigmentation of the adjusted preliminary formula and the respective tinting base;
h) calculating, for each of the at least one additional tinting base, a match metric value for the respective modified preliminary matching formula;
i) adjusting the modified preliminary matching formula with respect to concentrations of the included pigments in the way that the match metric value is minimal;
j) assigning each of the at least one additional tinting base to the respective one match metric value which has been calculated for the respective adjusted modified preliminary matching formula, respectively; and
k) issuing, via an output device, a list of at least those additional tinting bases of the at least one additional tinting base whose associated adjusted modified preliminary matching formula has a remission curve that is more similar to the remission curve of the target coating than the remission curve of the adjusted preliminary matching formula with respect to the match metric, respectively.

### Claim 2 (depends on 1)

The method according to claim 1, wherein step f) comprises:
f1) comparing the match metric value for the adjusted preliminary matching formula with a first threshold value wherein
the adjusted preliminary matching formula is decided to be acceptable in the case that the match metric value is smaller or equal to the first threshold value, otherwise the matching and adjusting procedure is continued with step g).

### Claim 3 (depends on 1)

The method according to claim 1, further comprising the step of:
l) sorting the list with respect to a magnitude of the match metric values, respectively.

### Claim 4 (depends on 1)

The method according to claim 1, wherein step k) further comprises:
k1) comparing for each adjusted modified preliminary formula a difference between the respective match metric value and the match metric value of the adjusted preliminary matching formula; and
k2) listing only those additional tinting bases whose difference between both match metric values is smaller than a second threshold value and whose assigned match metric values are smaller or equal to a definite ratio of the match metric value of the adjusted preliminary matching formula.

### Claim 5 (depends on 3)

The method according to claim 3, wherein the adjusted modified preliminary matching formula which is associated with said at least one additional tinting base with the smallest assigned match metric value is selected as starting formula with an optimal pigmentation for further processing.

### Claim 6 (depends on 5)

The method according to claim 5, further comprising the step of:
m) issuing at least one tinting base encompassed by the adjusted preliminary matching formula that is redundant and, thus, to be reduced in amount or completely excluded.

### Claim 7 (depends on 1)

The method according to claim 1, wherein the match metric is chosen as:
dShape
=
k
2
·
31
n
·
∑
i
=
0
n
-
2
θ
λ
i
wherein n is an integer and k2 is a linear scaling factor with, for example,
k2=0.65, θλi is calculated by:
θ
λ
i
=
cos
-
1
(
u
λ
i
·
v
λ
i
❘
"\[LeftBracketingBar]"
u
λ
i
❘
"\[RightBracketingBar]"
·
❘
"\[LeftBracketingBar]"
v
λ
i
❘
"\[RightBracketingBar]"
)
wherein
u
λ
i
=
(
k
1
·
Δλ
i
Δ
⁢
R
ref
,
λ
i
norm
)
v
λ
i
=
(
k
1
·
Δλ
i
Δ
⁢
R
smp
,
λ
i
norm
)
with
R
ref
,
λ
i
norm
=
Δ
⁢
R
ref
,
λ
i
+
Δλ
i
norm
-
Δ
⁢
R
ref
,
λ
i
norm
,
and
Δ
⁢
R
smp
,
λ
i
norm
=
Δ
⁢
R
smp
,
λ
i
+
Δλ
i
norm
-
Δ
⁢
R
smp
,
λ
i
norm
,
and
Δλ
i
=
λ
i
+
1
-
λ
i
,
wherein Rref,λinorm indicates a normalized reflectance value of the target coating at the wavelength value, λi, Rref,λi+Δλinorm indicates a normalized reflectance value of the target coating at the wavelength value, λi+1, Rsmp,λinorm indicates a normalized reflectance value of the sample coating at the wavelength value, λi, Rsmp,λi+1norm indicates a normalized reflectance value of the sample coating at the wavelength, value λi+1, k1 is a non-linear damping parameter with, for example, k1=0.005, and θλi indicates the angle between the two normalized vectors uλi and vλi, the vector uλi indicating a normalized gradient of the reflectance curve of the target coating at λi and the vector vλi indicating a normalized gradient of the reflectance curve of the sample coating at λi.

### Claim 8 (depends on 1)

The method according to claim 1, wherein the match metric is chosen as follows:
dShape
*
=
k
2
*
·
3
⁢
1
n
·
∑
i
=
0
n
-
2
❘
"\[LeftBracketingBar]"
Δ
⁢
R
smp
,
λ
i
norm
-
Δ
⁢
R
ref
,
λ
i
norm
❘
"\[RightBracketingBar]"
k
1
·
Δλ
i
wherein n is an integer and k2* is a linear scaling factor with, for example,
k2*=100,
ΔRref,λinorm=Rref,λi+Δλinorm−Rref,λinorm, and
ΔRref,λinorm=Rref,λi+Δλinorm−Rref,λinorm, and
Δλi=λi+1−λi,
wherein Rref,λinorm indicates a normalized reflectance value of the target coating at the wavelength value, λi, Rref,λi+Δλinorm indicates a normalized reflectance value of the target coating at the wavelength value, λi+1, Rsmp,λinorm indicates a normalized reflectance value of the sample coating at the wavelength value, λi, Rsmp,λi+1norm indicates a normalized reflectance value of the sample coating at the wavelength value, and λi+1, k1 is a non-linear damping parameter with, for example, k1=0.005.

### Claim 9 (depends on 7)

The method according to claim 7, wherein the reflectance values are normalized by a scaling function which is chosen as a non-linear scaling function ƒ as follows:
f
ref
/
smp
=
1
Norm
R
ref
/
smp
with
Norm
R
ref
/
smp
=
116
·
x
r
⁢
e
⁢
f
/
s
⁢
m
⁢
p
-
1
⁢
6
1
⁢
0
⁢
0
with
x
r
⁢
e
⁢
f
/
s
⁢
m
⁢
p
=
{
R
ref
/
smp
,
center
3
,
R
ref
/
smp
,
c
⁢
e
⁢
n
⁢
t
⁢
e
⁢
r
>
2
⁢
1
⁢
6
2
⁢
4
⁢
3
⁢
8
⁢
9
2
⁢
4
⁢
3
⁢
8
⁢
9
2
⁢
7
⁢
R
ref
/
smp
,
c
⁢
e
⁢
n
⁢
t
⁢
e
⁢
r
+
1
⁢
6
1
⁢
1
⁢
6
,
otherwise
wherein Rref/smp,center is given by:
R
ref
/
smp
,
center
=
R
ref
/
smp
,
m
⁢
i
⁢
n
+
R
ref
/
smp
,
m
⁢
ax
-
R
ref
/
smp
,
m
⁢
i
⁢
n
2
,
with
R
ref
/
smp
,
m
⁢
ax
=
Max
⁡
(
R
ref
/
smp
,
λ
i
)
⁢
and
⁢
R
ref
/
smp
,
m
⁢
i
⁢
n
=
Min
⁡
(
R
ref
/
smp
,
λ
i
)
.

### Claim 10

A system for providing a match metric for matching and adjusting pigmentation of a target coating and at least one specimen coating, the system comprising:
A) a computing device; and
B) a computer program product, the computer program product comprises computer executable codes stored on a computer readable storage medium functionally coupled to the computing device and causes the computing device to perform a computing process when in operation, the computing process comprises the steps of:
B1) retrieving from a formulation database which comprises formulas for coating compositions with different pigmentations, one preliminary matching formula;
B2) providing a match metric that describes a color difference and a spectral similarity between a remission curve given for the target coating and a remission curve determined for the preliminary matching formula; and
by using one or more processors:
B3) calculating a match metric value for the preliminary matching formula based on the remission curve given for the target coating and the remission curve determined for the preliminary matching formula;
B4) adjusting the preliminary matching formula with respect to concentrations of included pigments in the way that the match metric is minimal;
B5) evaluating the match metric value of the adjusted preliminary formula; and
B6) deciding, based on a magnitude of the match metric value of the adjusted preliminary formula, whether the pigmentation of the adjusted preliminary matching formula is significantly improvable;
in the case that the pigmentation of the adjusted preliminary matching formula is significantly improvable:
B7) defining a selection of at least one additional tinting base which might be eligible for further adjusting the adjusted preliminary matching formula to the target coating, each additional tinting base being associated with a respective modified preliminary matching formula consisting of the adjusted pigmentation of the adjusted preliminary formula and the respective tinting base;
B8) calculating, for each of the at least one additional tinting base, a match metric value for the respective modified preliminary matching formula;
B9) adjusting the modified preliminary matching formula with respect to concentrations of the included pigments in the way that the match metric value is minimal;
B10) assigning each of the at least one additional tinting base to the respective one match metric value which has been calculated for the respective adjusted modified preliminary matching formula; and
B11) issuing, via an output device, a list of at least those additional tinting bases of the at least one additional tinting base whose associated adjusted modified preliminary matching formula has a remission curve that is more similar to the remission curve of the target coating than the remission curve of the adjusted preliminary matching formula with respect to the match metric, respectively.

### Claim 11 (depends on 10)

The system according to claim 10, further comprising:
C) a color measuring device; and
D) the formulation database;
wherein the computing device is functionally coupled to the color measuring device and the formulation database.

### Claim 12 (depends on 10)

The system according to claim 10, wherein the computing process further comprises the step of:
B12) sorting the list with respect to a magnitude of the match metric values, respectively.

### Claim 13 (depends on 10)

The system according to claim 10, wherein step B11) further comprises:
B11-1) comparing the match metric value for the adjusted preliminary matching formula with a first threshold value, wherein
the adjusted preliminary matching formula is decided to be acceptable in the case that the match metric value is smaller or equal to the first threshold value, otherwise the matching and adjusting procedure is continued with step B7).

### Claim 14

A computer readable storage medium functionally coupled to a computing device storing a computer program product which comprises computer executable codes and causes the computing device to perform a computing process when in operation, the computing process comprising the steps of:
B1) retrieving from a formulation database which comprises formulas for coating compositions with different pigmentations, one preliminary matching formula;
B2) providing a match metric that describes a color difference and a spectral similarity between a remission curve given for the target coating and a remission curve determined for the preliminary matching formula;
B3) calculating a match metric value for the preliminary matching formula based on the remission curve given for the target coating and a remission curve determined for the preliminary matching formula;
B4) adjusting the preliminary matching formula with respect to concentrations of included pigments in the way that the match metric is minimal;
B5) evaluating the match metric value of the adjusted preliminary formula; and
B6) deciding, based on a magnitude of the match metric value of the adjusted preliminary formula, whether the pigmentation of the adjusted preliminary matching formula is significantly improvable;
in the case that the pigmentation of the adjusted preliminary matching formula is significantly improvable
B7) defining a selection of at least one additional tinting base which might be eligible for further adjusting the adjusted preliminary matching formula to the target coating, each additional tinting base being associated with a respective modified preliminary matching formula consisting of the adjusted pigmentation of the adjusted preliminary formula and the respective tinting base;
B8) calculating, for each of the at least one additional tinting base, a match metric value for the respective modified preliminary matching formula;
B9) adjusting the modified preliminary matching formula with respect to concentrations of the included pigments in the way that the match metric value is minimal;
B10) assigning each of the at least one additional tinting base to the respective one match metric value which has been calculated for the respective adjusted modified preliminary matching formula; and
B11) issuing, via an output device, a list of at least those additional tinting bases of the at least one additional tinting base whose associated adjusted modified preliminary matching formula has a remission curve that is more similar to the remission curve of the target coating than the remission curve of the adjusted preliminary matching formula with respect to the match metric, respectively.

### Claim 15 (depends on 14)

The computer readable storage medium according to claim 14, wherein the computing process further comprises the step of:
B12) sorting the list with respect to the magnitude of the match metric values, respectively.