Systems and methods for sensing marking substrate area coverage using a spectrophotometer
View Patent ↗A multiple-LED sensor is used to detect area coverage of marked patches on a marking substrate. The same sensor may also be used for color calibration. The marking substrate area coverage sensor obtains reflectance measurements from marked patches of a marking substrate. For example, the marked patches may be patches of a marking substance such as toner, ink or paint, or patches marked by etching or the like. A Neugebauer model may be used to obtain the reflectance measurements. A batch least squares algorithm may be used to estimate the appropriate parameters of the Neugebauer model. For improved accuracy, a recursive least squares algorithm may be used. The recursive least squares algorithm allows the marking substrate area coverage sensor to calibrate itself to changes in the sensing environment.
1. A method of obtaining marking substrate area coverage information, comprising:
obtaining a base reflectance of an unmarked portion of a marking substrate;
obtaining a reference reflectance of a reference marked patch of the marking substrate at substantially complete coverage;
obtaining a target reflectance of a target marked patch of the marking substrate; and
obtaining an estimated marking substrate area coverage ĉ of the target marked patch by a least squares algorithm, based on the base reflectance, the reference reflectance and the target reflectance, using a Neugebauer model of the form
y=Ac
where
y
_
=
[
r
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
and
A
_
=
[
r
2
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
2
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
2
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
,
and c is the actual marking substrate area coverage, where λ 1 , λ 2 , . . . λ N represent the wavelengths at which reflectance values are measured, r 1 (λ) is the spectral reflectance of the base color of the marking substrate, r 2 (λ) is the spectral reflectance of a marked patch of substantially 100% area coverage, r(λ) is a predicted spectral reflectance corresponding to a marked patch under analysis, n is a Yule-Nielsen correction factor, and N is a number of measured wavelengths of visible light, and
wherein the least squares equation is defined by
ĉ=[A T A] −1 A T y
where T indicates a matrix transpose.
2. The method of claim 1 , wherein the marked patch comprises a marking substance.
3. The method of claim 2 , wherein the marking substance is one of ink, toner and paint.
4. The method of claim 1 , wherein the least squares algorithm minimizes the square of errors between the reference reflectance and the target reflectance.
5. A computer-readable storage medium on which is recorded a program for implementing the method of claim 1 .
6. A marking system parameter control system, comprising a controller that:
obtains a base reflectance of an unmarked portion of a marking substrate using information output by the sensor;
obtains a reference reflectance of a reference marked patch of the marking substrate at substantially complete coverage;
obtains a target reflectance of a target marked patch of the marking substrate; and
obtains an estimated marking substrate area coverage ĉ of the target marked patch by a least squares algorithm, based on the base reflectance, the reference reflectance and the target reflectance, using a Neugebauer model of the form
y=Ac
where
y
_
=
[
r
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
and
A
_
=
[
r
2
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
2
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
2
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
,
and c is the actual marking substrate area coverage, where λ 1 , λ 2 , . . . λ N represent the wavelengths at which reflectance values are measured, r 1 (λ) is the spectral reflectance of the base color of the marking substrate, r 2 (λ) is the spectral reflectance of a marked patch of substantially 100% area coverage, r(λ) is a predicted spectral reflectance corresponding to a marked patch under analysis, n is a Yule-Nielsen correction factor, and N is a number of measured wavelengths of visible light, and
wherein the least squares equation is defined by
ĉ=[A T A] −1 A T y
where T indicates a matrix transpose.
7. A method of obtaining marking substrate area coverage information, comprising:
obtaining a base reflectance of an unmarked portion of a marking substrate;
obtaining a reference reflectance of a reference marked patch of the marking substrate at substantially complete coverage;
obtaining an initial estimated marking substrate area coverage ĉ of a target marked patch of the marking substrate;
obtaining a target reflectance of the target marked patch;
obtaining a first improved estimated marking substrate area coverage ĉ by an adaptive equation, based on the initial estimated marking substrate area coverage ĉ, the base reflectance, the reference reflectance and the target reflectance using a Neugebauer model of the form
y=Ac
where
y
_
=
[
r
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
and
A
_
=
[
r
2
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
2
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
2
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
,
and c is the actual marking substrate area coverage, where λ 1 , λ 2 , . . . λ N represent the wavelengths at which reflectance values are measured, r 1 (λ) is the spectral reflectance of the base color of the marking substrate, r 2 (λ) is the spectral reflectance of a marked patch of substantially 100% area coverage, r(λ) is a predicted spectral reflectance corresponding to a marked patch under analysis, n is a Yule-Nielsen correction factor, and N is a number of measured wavelengths of visible light, and
wherein the adaptive equation is defined by
ĉ k+1 =ĉ k +αP k+1 A T ( y k+1 −Aĉ k )
where P k+1 is an intermediate gain value obtained using
P
k
+
1
=
P
k
-
P
k
A
_
T
A
_
P
k
1
+
A
_
T
P
k
A
_
where an initial estimate of scalar quantity P k is obtained using
P k =A T A
and α is a positive constant and T indicates a matrix transpose.
8. The method of claim 7 , further comprising:
repeating the obtaining a target reflectance of the target marked patch; and
repeating the obtaining a second improved estimated marking substrate area coverage ĉ, using the first improved estimated marking substrate area coverage ĉ as the initial estimated marking substrate area coverage ĉ, the second improved estimated marking substrate area coverage ĉ being closer than the first improved estimated marking substrate area coverage ĉ to actual marking substrate area coverage c.
9. The method of claim 7 , wherein the marked patch comprises a marking substance.
10. The method of claim 9 , wherein the marking substance is one of ink, toner and paint.
11. The method of claim 7 , wherein the obtaining the initial estimated marking substrate area coverage ĉ comprises using a Neugebauer model of the form
y=Ac
where
y
_
=
[
r
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
and
A
_
=
[
r
2
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
2
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
2
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
,
and c is the actual marking substrate area coverage, where λ 1 , λ 2 , . . . λ N represent the wavelengths at which reflectance values are measured, r 1 (λ) is the spectral reflectance of the base color of the marking substrate, r 2 (λ) is the spectral reflectance of a marked patch of substantially 100% area coverage, r(λ) is a predicted spectral reflectance corresponding to a marked patch under analysis, n is a Yule-Nielsen correction factor, and N is a number of measured wavelengths of visible light.
12. A computer-readable storage medium on which is recorded a program for implementing the method of claim 7 .
13. A marking system parameter control system, comprising a controller that:
obtains a base reflectance of an unmarked portion of a marking substrate;
obtains a reference reflectance of a reference marked patch of the marking substrate at substantially complete coverage;
obtains an initial estimated marking substrate area coverage ĉ of a target marked patch of the marking substrate;
obtains a target reflectance of a target marked patch;
obtains a first improved estimated marking substrate area coverage ĉ by an adaptive equation, based on the initial estimated marking substrate area coverage ĉ, the base reflectance, the reference reflectance and the target reflectance using a Neugebauer model of the form
y=Ac
where
y
_
=
[
r
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
and
A
_
=
[
r
2
1
/
n
(
λ
1
)
-
r
1
1
/
n
(
λ
1
)
r
2
1
/
n
(
λ
2
)
-
r
1
1
/
n
(
λ
2
)
⋮
r
2
1
/
n
(
λ
N
)
-
r
1
1
/
n
(
λ
N
)
]
,
and c is the actual marking substrate area coverage, where λ 1 , λ 2 , . . . λ N represent the wavelengths at which reflectance values are measured, r 1 (λ) is the spectral reflectance of the base color of the marking substrate, r 2 (λ) is the spectral reflectance of a marked patch of substantially 100% area coverage, r(λ) is a predicted spectral reflectance corresponding to a marked patch under analysis, n is a Yule-Nielsen correction factor, and N is a number of measured wavelengths of visible light, and
wherein the adaptive equation is defined by
ĉ k+1 =ĉ k +αP k+1 A T ( y k+1 −Aĉ k )
where P k+1 is an intermediate gain value obtained using
P
k
+
1
=
P
k
-
P
k
A
_
T
A
_
P
k
1
+
A
_
T
P
k
A
_
where an initial estimate of scalar quantity P k is obtained using
P k =A T A
and α is a positive constant and T indicates a matrix transpose.