US2016161390A1PendingUtilityA1
Method for identifying and quantifying of emitting particles in systems
Est. expiryJul 8, 2033(~7 yrs left)· nominal 20-yr term from priority
Inventors:Benjamin Greiner
G01N 15/14G01N 2015/1402G01N 2015/1486G01N 2021/6417G01N 21/64G01N 21/6408
44
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Claims
Abstract
The invention relates to a method for quantifying emitting particles and for characterizing the time-dependent behavior of the particles. The number n of emissions of the particles in the measuring period that have been detected in a time interval having a predetermined interval width within the measuring period is ascertained, wherein the evaluation is performed particularly for a plurality of time intervals having the same interval width, with a distribution function p(n) for the number n of detected emissions being determined. For the interval width different bin times τ are stipulated, and, for each bin time τ, the evaluation is performed and a distribution function p τ (n) is ascertained, wherein, for each bin time τ, moments m i,τ Mess for the distribution function p τ (n) are ascertained, from which bin time dependent moment functions m i Mess (τ) are presented. Comparison with a theoretical signal function comprising moments m i sig (τ) for the theoretical signal distribution ascertains constants that characterize the particles in the system.
Claims
exact text as granted — not AI-modified1 . Method for quantification of particles emitting specific emittends and for characterizing the time-dependent performance of the particles in a system, the system comprising particles of at least one species j, in particular different species, wherein emissions of the particles are detected within a measurement during a measuring period and the number n of the emissions, which have been detected within one time interval within the measuring period having a predetermined interval width is determined in an evaluation and is stored, wherein the evaluation is carried out particularly for several time intervals having the same interval width, wherein a distribution function p(n) of the number n of the emissions detected is determined,
characterized in that a) different bin times τ are stipulated for the interval width and the evaluation is performed for each bin time τ and a distribution function p τ (n) is ascertained, and wherein moments m i,τ Mess of the distribution function p τ (n) are ascertained for each bin time τ and bin time dependent moment functions m i Mess are prepared therefrom, b) constants characterizing the particles in the system are ascertained by a numerical fit of a theoretical signal function comprising moments m i sig (τ) of a theoretical signal distribution P sig (n,τ), which indicates an expected signal distribution determined by means of theoretical functions, to a measurement value function comprising the moment functions m i Mess (τ).
2 . Method according to claim 1 , characterized in that the theoretical signal function is being based upon a definition of the theoretical signal distribution P sig (n,τ) which goes back to the assumption of a specific local detection rate μ j ({right arrow over (r)})=μ 0,j ƒ({right arrow over (r)}) for a particle of species j, wherein μ j ({right arrow over (r)})=μ 0,j ƒ({right arrow over (r)}) represents a characteristic detection brightness of a particle, to the assumption of a specific local probability distribution and a specific local emission probability of the particles of species j and to the assumption of a specific measurement volume V in which the particles have to reside so that emissions of the particles can be detected, wherein P sig (n,τ) comprises the local detection rate μ j ({right arrow over (r)}), a partial concentration c j and a decay time ν j of the particle species j as well as the noise performance of the measuring apparatus as parameters independent on bin time and wherein the constants relate at least to the parameters μ 0,j , ν j , and particularly c j .
3 . Method according to claim 1 , characterized in that a theoretical species signal distribution P sig j (n,τ) is stipulated for each particle species when applying the method to a system having s different particle species, wherein the theoretical signal distribution P sig (n,τ) of the system is determined by an s+1-fold convolution of the s different signal distributions P sig j (n,τ) of the s different species and a noise signal distribution P noise (n,τ).
4 . Method according to claim 1 , characterized in that the measurement volume V used in the definition of P sig (n,τ) is defined by means of a bin time dependent, fictitiously introduced effective volume V eff,j (τ), wherein by definition at least one emission from each particle of species j residing in the volume τV eff,j (τ) is detected during the bin time τ and the particle does not leave τV eff,j (τ) during the bin time τ, wherein by definition the mean number of particles of species j in V eff,j (τ) is determined by a mean occupation number ω j (τ) with ω j (τ)=c j V eff,j (τ)τ.
5 . Method according to claim 4 , characterized in that a Poisson distribution is assumed as distribution of the occupation number.
6 . Method according to claim 1 , characterized in that it is assumed in determining the theoretical signal distribution P sig (n,τ) that the local emission probability of the particles is distributed according to a Poisson distribution.
7 . Method according to claim 1 , characterized in that for each bin time τ the bin time dependent mean value n (τ) and the bin time dependent variance σ 2 (τ) are determined from the distribution functions p τ (n) and that the measurement value function comprises n (τ) and σ 2 (τ).
8 . Method according to claim 7 , characterized in that
Q
(
τ
)
=
σ
(
τ
)
2
-
n
_
(
τ
)
n
_
(
τ
)
is stipulated as the measurement value function, wherein the numerical fit is carried out by means of
the relation
Q
(
τ
)
=
σ
(
τ
)
2
-
n
_
(
τ
)
n
_
(
τ
)
=
m
2
sig
(
τ
)
-
[
m
1
sig
(
τ
)
]
2
-
m
1
sig
(
τ
)
m
1
sig
(
τ
)
,
wherein m 1 sig (τ) represents the first moment and m 2 sig (τ) represents the second moment of P sig (n,τ).
9 . Method according to claim 1 , characterized in that the theoretical signal function is being defined as time-dependent, wherein several measurements are performed at a respective specific point in time assigned to the respective measurement, wherein a bin time dependent measurement value function assigned to the respective specific point in time is determined for each of the measurements, wherein each measurement value function is approximated by an approximation graph, wherein a limit value of the respective measurement value function which is adopted by the measurement value function for
lim
τ
->
0
is determined from the approximation graph of each measurement value function, wherein limit values of the theoretical signal function are ascertained at the specific points in time for
lim
τ
->
0
by means of a limit consideration
lim
τ
->
0
or the theoretical signal function, wherein the numerical fit is carried out by fitting the limit value of one of the measurement value functions to the limit value of the theoretical signal function at the specific point in time assigned to this measurement value function.
10 . Method according to claim 1 , characterized in that a mean local detection rate μ 1,j of the species j is being stipulated by means of the integral
μ
_
1
,
j
=
∫
R
3
r
μ
j
(
r
->
)
over a space R, particularly an unlimited space, and being introduced as a parameter independent on bin time into the theoretical signal distribution P sig (n,τ).
11 . Method according to claim 1 , characterized in that a mean detected emission number of a single particle of species j is established to
φ
1
,
j
(
τ
)
=
∫
0
τ
t
∫
R
3
r
0
(
∫
R
3
r
μ
j
(
r
->
)
ψ
j
(
r
->
,
t
r
->
0
)
)
2
∫
R
3
μ
j
(
r
->
)
for applying the method to a stochastic transport of the particles and to
φ
1
,
j
(
τ
)
=
∫
R
3
r
0
(
∫
0
τ
t
∫
R
3
r
μ
j
(
r
->
)
ψ
j
(
r
->
,
t
r
->
0
)
)
2
∫
R
3
r
μ
j
(
r
->
)
for applying the method to a deterministic transport of the particles, wherein R is in particular an unlimited space.
12 . Method according to claim 3 , characterized in that the measurement value function is assumed as
Q
(
τ
)
=
σ
2
(
τ
)
-
n
_
(
τ
)
n
_
(
τ
)
and the numerical fit is carried out by means of the relation
∑
j
=
1
s
μ
_
1
,
j
c
j
φ
1
,
j
(
τ
)
λ
+
∑
j
=
1
s
μ
_
1
,
j
c
j
,
wherein s different particle species are assumed in the system and λ represents a noise constant.
13 . Method according to claim 12 , characterized in that the numerical fit is carried out by means of the relation Q(τ)=φ 1,j (τ) when applying the method to a system having only one particle species j as the only species emitting the emittends.
14 . Method according to claim 1 , characterized in that a Gaussian function
μ
j
(
r
->
)
=
μ
0
,
j
exp
(
-
2
a
x
y
2
(
x
2
+
y
2
)
)
exp
(
-
2
a
z
2
z
2
)
with constants a x,y and a z is assumed as the local detection rate μ j ( r ).
15 . Method according to claim 1 , characterized in that a mean detected emission number of one single particle of species j is established to
φ
1
,
j
(
τ
)
=
π
2
2
μ
0
,
j
2
a
ϑ
j
2
τ
∫
-
∞
∞
z
0
(
e
r
f
[
1
ϑ
j
(
z
0
v
+
τ
)
]
-
e
r
f
[
z
0
v
ϑ
j
]
)
2
for defining the theoretical signal distribution P sig (n,τ) when applying the method to a fluidic transport of the particles with transport velocity v.
16 . Method according to claim 1 , characterized in that a mean detected emission number of one single particle of species j is established to
φ
1
,
j
(
τ
)
=
μ
0
,
j
2
ϑ
j
(
1
-
1
1
+
τ
ϑ
j
)
for defining the theoretical signal distribution P sig (n,τ) when applying the method to a diffusion transport of the particles with spherical measurement symmetry.
17 . Method according to claim 1 , characterized in that a mean detected emission number of one single particle of species j is established to
φ
1
,
j
(
τ
)
=
μ
0
,
j
2
3
2
∫
0
τ
t
(
1
+
t
ϑ
j
,
x
y
)
1
+
t
ϑ
j
,
z
,
with decay times ν j,xy and ν j,z for particles of species j, for defining the theoretical signal distribution P sig (n,τ) when applying the method to a diffusion transport of the particles with rotation ellipsoidal measurement symmetry.Join the waitlist — get patent alerts
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