Fluorescence intensity correcting method, fluorescence intensity calculating method, and fluorescence intensity calculating apparatus
A fluorescence intensity calculating apparatus, includes: a measuring section configured to receive fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with the plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtain measured spectra by collecting detected values from the photodetectors; and a calculating section configured to approximate the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively.
1. A fluorescence intensity correcting method, comprising:
receiving fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes; and
approximating measured spectra obtained by collecting detected values from said plural photodetectors based on a linear sum of single-dyeing spectra obtained from a microparticle individually labeled with the fluorescent dyes,
wherein the approximation of the measured spectra based on the linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein a parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets a minimum value is obtained, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively:
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, and σ i represents a reciprocal number of a weight for the measured value from the i-th photodetector.
2. The fluorescence intensity correcting method according to claim 1 , wherein the parameter a k is obtained by using either a normal equation or singular value decomposition.
3. A fluorescence intensity correcting method, comprising:
receiving fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes; and
approximating measured spectra obtained by collecting detected values from said plural photodetectors based on a linear sum of single-dyeing spectra obtained from a microparticle individually labeled with the fluorescent dyes,
wherein when at least one invalid value is contained in the detected values, the at least one invalid value is excluded, and approximation of the measured spectra based on a linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein a parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets a minimum value is obtained, thereby calculating intensities of the fluorescences generated from the respective fluorescent dyes:
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single-dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, σ i represents a reciprocal number of a weight for the measured values from the i-th photodetector, an invalid detected value is taken to be y i (i=“N 1 +1” to N), and a valid detected value is taken to be y i (i=1 to N 1 ).
4. A fluorescence intensity correcting method, comprising:
receiving fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes; and
approximating measured spectra obtained by collecting detected values from said plural photodetectors based on a linear sum of single-dyeing spectra obtained from a microparticle individually labeled with the fluorescent dyes,
wherein when at least one invalid value is contained in the detected values, the at least one invalid value is excluded, and approximation of the measured spectra based on a linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein the parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets the minimum value is obtained, thereby calculating intensities of the fluorescences generated from the respective fluorescent dyes:
X
k
′
(
x
i
)
=
X
k
(
x
i
)
(
k
=
1∼M
,
i
=
1∼N
1
)
X
k
′
(
x
i
)
=
0
(
k
=
1∼M
,
i
=
N
1
+
1∼N
)
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
′
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single-dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, σ i represents a reciprocal number of a weight for the measured values from the i-th photodetector, an invalid detected value is taken to be y i (i=“N 1 +1” to N), and a valid detected value is taken to be y i (i=1 to N 1 ).
5. A fluorescence intensity calculating method, comprising:
receiving fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtaining measured spectra by collecting detected values from said photodetectors; and
approximating the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively,
wherein the approximation of the measured spectra based on the linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein a parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets a minimum value is obtained, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively:
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, and σ i represents a reciprocal number of a weight for the measured value from the i-th photodetector.
6. The fluorescence intensity calculating method according to claim 5 , wherein the parameter a k is obtained by using either a normal equation or singular value decomposition.
7. A fluorescence intensity calculating apparatus, comprising:
measuring means for receiving fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtaining measured spectra by collecting detected values from said photodetectors; and
calculating means for approximating the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively,
wherein the approximation of the measured spectra based on the linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein a parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets a minimum value is obtained, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively:
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, and σ i represents a reciprocal number of a weight for the measured value from the i-th photodetector.
8. The fluorescence intensity calculating apparatus according to claim 7 , wherein the parameter a k is obtained by using either a normal equation or singular value decomposition.
9. A fluorescence intensity calculating apparatus, comprising:
a measuring section configured to receive fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtain measured spectra by collecting detected values from said photodetectors; and
a calculating section configured to approximate the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively,
wherein the approximation of the measured spectra based on the linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein a parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets a minimum value is obtained, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively:
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, and σ i represents a reciprocal number of a weight for the measured value from the i-th photodetector.
10. The fluorescence intensity calculating apparatus according to claim 9 , wherein the parameter a k is obtained by using either a normal equation or singular value decomposition.
11. A fluorescence intensity calculating method, comprising:
receiving fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtaining measured spectra by collecting detected values from said photodetectors; and
approximating the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively,
wherein when at least one invalid value is contained in the detected values, the at least one invalid value is excluded, and approximation of the measured spectra based on a linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein a parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets a minimum value is obtained, thereby calculating intensities of the fluorescences generated from the respective fluorescent dyes:
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single-dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, σ i represents a reciprocal number of a weight for the measured values from the i-th photodetector, an invalid detected value is taken to be y i (i=“N 1 +1” to N), and a valid detected value is taken to be y i (i=1 to N 1 ).
12. A fluorescence intensity calculating apparatus, comprising:
measuring means for receiving fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtaining measured spectra by collecting detected values from said photodetectors; and
calculating means for approximating the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively,
wherein when at least one invalid value is contained in the detected values, the at least one invalid value is excluded, and approximation of the measured spectra based on a linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein a parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets a minimum value is obtained, thereby calculating intensities of the fluorescences generated from the respective fluorescent dyes:
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single-dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, σ i represents a reciprocal number of a weight for the measured values from the i-th photodetector, an invalid detected value is taken to be y i (i=“N 1 +1” to N), and a valid detected value is taken to be y i (i=1 to N 1 ).
13. A fluorescence intensity calculating apparatus, comprising:
a measuring section configured to receive fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtain measured spectra by collecting detected values from said photodetectors; and
a calculating section configured to approximate the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively,
wherein when at least one invalid value is contained in the detected values, the at least one invalid value is excluded, and approximation of the measured spectra based on a linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein a parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets a minimum value is obtained, thereby calculating intensities of the fluorescences generated from the respective fluorescent dyes:
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single-dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, σ i represents a reciprocal number of a weight for the measured values from the i-th photodetector, an invalid detected value is taken to be y i (i=“N 1 +1” to N), and a valid detected value is taken to be y i (i=1 to N 1 ).
14. A fluorescence intensity calculating method, comprising:
receiving fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtaining measured spectra by collecting detected values from said photodetectors; and
approximating the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively,
wherein when at least one invalid value is contained in the detected values, the at least one invalid value is excluded, and approximation of the measured spectra based on a linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein the parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets the minimum value is obtained, thereby calculating intensities of the fluorescences generated from the respective fluorescent dyes:
X
k
′
(
x
i
)
=
X
k
(
x
i
)
(
k
=
1∼M
,
i
=
1∼N
1
)
X
k
′
(
x
i
)
=
0
(
k
=
1∼M
,
i
=
N
1
+
1∼N
)
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
′
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single-dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, σ i represents a reciprocal number of a weight for the measured values from the i-th photodetector, an invalid detected value is taken to be y i (i=“N 1 +1” to N), and a valid detected value is taken to be y i (i=1 to N 1 ).
15. A fluorescence intensity calculating apparatus, comprising:
measuring means for receiving fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtaining measured spectra by collecting detected values from said photodetectors; and
calculating means for approximating the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively,
wherein when at least one invalid value is contained in the detected values, the at least one invalid value is excluded, and approximation of the measured spectra based on a linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein the parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets the minimum value is obtained, thereby calculating intensities of the fluorescences generated from the respective fluorescent dyes:
X
k
′
(
x
i
)
=
X
k
(
x
i
)
(
k
=
1∼M
,
i
=
1∼N
1
)
X
k
′
(
x
i
)
=
0
(
k
=
1∼M
,
i
=
N
1
+
1∼N
)
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
′
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single-dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, σ i represents a reciprocal number of a weight for the measured values from the i-th photodetector, an invalid detected value is taken to be y i (i=“N 1 +1” to N), and a valid detected value is taken to be y i (i=1 to N 1 ).
16. A fluorescence intensity calculating apparatus, comprising:
a measuring section configured to receive fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with said plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtain measured spectra by collecting detected values from said photodetectors; and
a calculating section configured to approximate the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively,
wherein when at least one invalid value is contained in the detected values, the at least one invalid value is excluded, and approximation of the measured spectra based on a linear sum of the single-dyeing spectra is carried out by using a least-squares method, and
wherein the parameter a k (k=1 to m) at which an evaluation function expressed by following Expression gets the minimum value is obtained, thereby calculating intensities of the fluorescences generated from the respective fluorescent dyes:
X
k
′
(
x
i
)
=
X
k
(
x
i
)
(
k
=
1∼M
,
i
=
1∼N
1
)
X
k
′
(
x
i
)
=
0
(
k
=
1∼M
,
i
=
N
1
+
1∼N
)
χ
2
≡
∑
i
=
1
N
[
y
i
-
∑
k
=
1
M
a
k
X
k
′
(
x
i
)
σ
i
]
2
where X k (x i ) represents a detected value from the i-th photodetector in the single-dyeing spectrum of the k-th fluorescent dye, y i represents a detected value from the i-th photodetector in the measured spectra, σ i represents a reciprocal number of a weight for the measured values from the i-th photodetector, an invalid detected value is taken to be y i (i=“N 1 +1” to N), and a valid detected value is taken to be y i (i=1 to N 1 ).