CN101627298A - Determine to contain the method for characteristic properties of the sample of particle - Google Patents

Abstract

The invention provides a kind of method of characteristic properties of sample of the particle of determining to contain at least one species, described particle is the particle of the species of emission in predetermined observation capacity, scattering and/or refraction photon, and this method comprises the steps: 1) will be in observing time Continuous time interval Δ t _i=[t _I-1, t _i) (i=1,2,3 ...) and in the number n of photo-event of registration _i(counting rate) registered and counted, 2) determine the distribution function p (n) and 3 of the photo-event number n in the interval of delta t at the fixed time) the single particle distribution function P of the distribution function p (n) that uses in expectation, concentration c, the photo-event number n that in each photo-event just is derived from the gedanken experiment of single particle interval of delta t at the fixed time, expects ₁(n) and useful capacity V _Eff=＜m 〉/ theory relation between the c (wherein＜m〉be the average to the effective particle of each counting rate) determines P ₁(n), V _Eff, concentration c and/or further feature character, wherein＜m be average to the effective particle of each counting rate, it can carry out match by the p (n) with these character and measurement and determine.

Description

Determine to contain the method for characteristic properties of the sample of particle

Technical field

The present invention relates to a kind of method of characteristic properties of sample of the particle of determining to contain at least one species, the emission in the observation capacity in the fixing continuous time interval of this particle, scattering and/or refraction photon.In addition, the present invention also extends to the characteristic properties of being determined to contain the sample of particle the different time intervals.

Background technology

Said method is according to fluorescence fluctuation spectrum method (Fluorescence FluctuationSpectroscopy, FFS) [referring to L.Mandel:Fluctuations of photon beamsand their correlations, Proc.Phys.Soc.72, pages 1037-1048, (1958)], it is set up as in application fields, particularly in the standard method of biophysics and biochemical field.The theory and the realization that are developed to be applied in high-pressure process screening (High-throughputScreening) and on-line analysis aspect are from WO 98/16814 and PeetKask, Kaupo Palo, Dirk Ullmann, and Karsten Gall:Fluorescence-intensity distribution analysis and its application inbiomolecular detection technology, Proc.Natl.Acad.Sci.USA 96, pages 13765-13761, (1999) and the fluorescence intensity distributional analysis (FIDA) known.

In the individual molecule experiment, situation is as follows: the photon of the molecular emission from little observation capacity V hits photon detector.Discrete time point t _i(i=0,1,2 ...) will be divided into the equidistant time interval Δ t observing time _i=[t _I-1, t _i) (i=1,2,3 ... N).At time interval Δ t _iThe number of the photon of middle counting is ordered series of numbers { n ₁, n ₂, n ₃....Once complete measurement provides a limited number of counting rate n ₁, n ₂..., n _NThere is the number in the time interval (#k) that n photon be counted to provide photon counting distribution (#k (n)) therein.

With the sum of each element among the sequence #k (n) divided by the interval $N=\underset{n=0}{\overset{\∞}{\text{\Σ}}}\#k\left(n\right)$ Provided a real number

$p_N\left(n\right)=\frac{\#k\left(n\right)}{N},$

It can be interpreted as measuring the probability of n photon at least in time interval Δ t under the situation of the limit in the time interval that " in a large number " measures.Corresponding physics probability distribution by

$p\left(n\right)=\underset{N\→\∞}{\lim }{p}_N\left(n\right)$

Definition.

For the sake of simplicity, we suppose that all photons all are to ignore the ground unrest that is for example produced by detector hardware or scattered light by the molecule (s) of interest generation.The ground unrest that merges is directly, and its influence to p (n) will come into question later.

The method of determining the characteristic properties of sample in FFS comprises two basic steps:

1) will be in observing time $T=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\Δ}{t}_i$ Continuous time interval Δ t _i=[t _I-1, t _i) (i=1,2,3 ... N) the number n of the photo-event of registration in _i(counting rate) registered and counted,

2) determine the photo-event number n in the interval of delta t at the fixed time distribution function p (n) and

3) determine interested one or several character by this way, given in the method theoretical model meets (hereinafter becoming " match ") with optimum measurement result p (n) is described.

Can comprise from the typical character that p (n) extracts:

1. the concentration of the molecule in pure solution

2. the concentration of the molecule in potpourri

3. the dynamics of intermolecular cohesive process

4. the kinetic rate of intermolecular dissociation process

5. the kinetic rate that conformal changes in the molecule

6. the diffusivity of molecule

7. molecule brightness

8. the spatial brightness function of optics assembling (set up is set)

9. the distinctive singlet current of molecule

10. the afterpulse of detecting device (after-pulse) rate

In FIDA, theoretical photon counting distribution p (n) is passed through generating function $G\left(\mathrm{\ξ}\right)=\underset{n=0}{\overset{\∞}{\mathrm{\Σ}}}p\left(n\right){\mathrm{\ξ}}^n$ Calculate.G (ξ) is expressed as depending on so-called spatial brightness function

The index of space integral of function.The spatial brightness function is the long-pending of the excitating light strength of optical device and fluorescence transmission coefficient, as standardization (normalization, normalized) function of the coordinate of the particle in sample.Use

Naive model come the characterization optical device, determine by the experiment of single species

The adjustment parameter.Unknown sample parameter, concentration c and particular luminance value q is by the nonlinear fitting method or bring definite by the regularization inversion.The shortcoming of FIDA is:

1. the method for generating function makes theoretical model very not directly perceived, and method is extended in the more complicated application is difficult.

2. model is being highly nonlinear aspect unknown parameter c and the q, determines that these parameters are complicated.

3. to be represented as all species all be the long-pending of common spatial brightness function and the certain luminance that each species is had an eigenwert in the brightness of each molecule.Because very big, so in all measurements, violated this hypothesis to a certain extent to different plant species triplet population difference.

4. the coordinate of hypothesis molecule is constant during gate time interval (interval width, bin width).Even to the very short time interval in the scope of several microseconds, this also is rough being similar to.And (dependence dependence) has the useful information that can not extract from model to p (n) to the dependence of the diffusion motion of molecule.

By in FIDA, introducing the semiempirical correction factor, set up the many distributional analysiss of so-called fluorescence intensity (FIMDA) come to determine simultaneously diffusion time and molecule brightness [referring to Kaopo Palo, Mets, Stefan

Peet Kask, and Karsten Gall:Fluorescenceintensity multiple distribution analysis:Concurrent determination ofdiffusion times and molecular brightness, Biophysical J.79, pages2858-2866, (2000)].Compare with FIDA, directly calculate the photon counting distribution by master equation and demonstrate significantly improved match quality.Yet this numerical simulation is very slow, and be not suitable for high productivity use [referring to Kaopo Palo,

Mets, Vello Loorits, and Peet Kask:Calculation of photon count number distributions viamaster equatons, Biophysical J.90, pages 2179-2191, (2006)].

The method that substitutes FIDA and succession thereof is based on the interval PCH algorithm of photon counting [referring to Yan Cheng, D.M ü ller Joachi, Peter T.C.So, and Enrico Gratton:The photon counting histogram in fluorescence fluctuationspectroscopie, Biophysical J.77, pages 553-557, (1999), Yan Cheng:Analysis and applications of fluorescence fluctuation spectroscopy. PhD dissertation, University of Illinois at Urbana-Champain, Urbana, Illinois, (1999), can Http:// www.lfd.uiuc.edu/staff/grattonObtain, Thomas D.Perroud, Bo Huang, and Richard N.Zare:Effect on bintime on the photon counting histogram for one-photon excitation, ChemPhysChem 6, and pages 905,912, (2005), Y.Cheng, M.Tekmen, L.Hillesheim, J.Skinner, B.Wu, and J.M ü ller:Dual-color photoncounting histogram, Biophysical is J.88, pages 2177-2192, (2005)].These methods only are different from FIDA on ins and outs, and are the different shape of space laser Luminance Distribution hypothesis.The PCH method is used commerce and is played a secondary role.The detection capacity must quite at random be selected in the PCH method.Character as the photon probability distribution of the average number of the molecule that works and individual molecule becomes abstract character, and without any physical significance.

The object of the present invention is to provide improved theoretical platform to come priori prediction photon counting interval.Another object of the present invention is to provides more deep physics clairvoyance and the PCH method is extended in the complicated experimental duties intuitively to FFS.

Embodiment

Above-mentioned purpose of the present invention is solved by the method for the feature with claim 1.

Useful capacity V _EffBe not easy to describe, also depend on the character of the particle species that will consider by the optics assembling.And if only if when particle works to counting rate, and particle just is defined in during a certain specified time interval at capacity " interior ".To being positioned at the particle of any locus, non-vanishing to the probability that counting rate works.Therefore, useful capacity V _EffCan not determine by the physical space border.In any case, the process of " entering " and " leaving " this capacity is a stochastic process, is similar to the diffusion process of a little physical capacity of turnover.Can notice, picture stimulated emission loss (STED) is [referring to Lars Kastrup, Hans Blom, Christian Eggeling, andStefan W.Hell:Fluorescence fluctuation spectroscopy insubdiffraction focal volume, Phys.Rev.Lett.94, (2005)] technology can significantly reduce useful capacity.

According to definition, " single particle " in the useful capacity can not produce any zero count rate.Therefore, " single particle " in the term useful capacity with have " single particle " to be very different at any spatial content conceptive.By only considering the non-zero counting rate, can in gedanken experiment (Gedankenexperiment), measure probability distribution P physically ₁(n).At time interval Δ t _iAll during this time photo-events only are derived from a single particle.The stack that is derived from the signal of several particles must be out in the cold be fallen.

According to the present invention, to given experiment assembling, with two amount: useful capacity V _EffWith single particle distribution P ₁(n) with for example particle species characterization of molecular species.As discussed above, these two amounts have clear physical meaning.Can utilize its unique Property P ₁(n=0)=0 P distributes single particle ₁(n) with FIDA method and PCH method in single particle of the same name distribute and make a distinction.

Can utilize V _EffAnd P ₁(n) knowledge determines fast and steadily to comprise the molecular conecentration in the sample of molecule of one or several species (potpourri).It is steadily and surely jamproof that this method interference effect such as excites to restriction such as for example afterpulse, molecular diffusion or the singlet of all existing methods such as FIDA, FIMDA or PCH algorithm.The method according to this invention is not limited only to the short interval width as FIDA or PCH algorithm.It is applicable to appoints what environment, for example stream, microstructure, cell, capsule, latex or gel (not experimental verification as yet till now) of molecule.

The method according to this invention is simpler than all existing methods.Say technically, it can with the standard fit method combination of for example nonlinear fitting, generating function or square method (square metering method, method ofmoment).Realize that according to technology this is a method very fast that is suitable for inline diagnosis.

In FIDA, a kind of molecule specific molecular brightnessization of giving by real number value.According to the present invention, a kind of molecule is by V _EffAnd P ₁(n) characterization fully.

Comprise on the meaning as all information relevant of diffusivity or singlet excitation probability with regard to them and to say character V with experiment assembling _EffAnd P ₁(n) enrich.In principle, can be to all information of the particle characteristicsization of for example molecule from V _EffAnd P ₁(n) extract.But, obtain this information, must use concrete theoretical model.

Not say character V to the nature and characteristicization of single particle, in any experiment with regard to them because of several particles act on the meaning that has averaging process simultaneously _EffAnd P ₁(n) be simple.

In a preferred embodiment of the invention, based on the single particle distribution function P of Markovian process theory ₁(n) by

$P_1\left(n\right)=1/V_{\mathrm{eff}}\underset{R^3}{\∫}\mathrm{Poi}(n,\mathrm{\μ}\left(\stackrel{\→}{r}\right))\mathrm{dV},$

Provide, wherein P ₁(n=0) :=0, wherein

The luminance function of expression particle, it is by in the position

The mean value of photo-event of single particle and Poisson distribution Poi (n, μ)=exp (μ) μ ⁿ/ n! Definition.

Because the photon of different laser intensity and optics assembling is collected character on the space, so, width Delta t between the given area _iPhoton count rate n _iDepend on the position of all molecules strongly with respect to laser spot.Near laser spot molecule produces big effect to photon count rate, and produces effect little or zero away from the molecule of laser spot.The effect of individual molecule can be by being fixed on the surface (as glass surface) or the appointed positions in the matrix (as gel)

Measure.The photon counting n that this assembling is write down _iSequence provided probability distribution p (n).The mean value of the photon counting of Ce Lianging like this $\⟨n\⟩=\underset{n}{\mathrm{\Σ}}\mathrm{np}\left(n\right)$ Be called as in the position

Molecule brightness μ.Molecule brightness

Measurement can be to any position Carry out,

Functional form can repeat this process by each position to molecule, for example by to all positions on the equidistant space lattice

Measure μ and between net point interpolation, measure.Because molecule luminance function

The time-consuming costliness of measurement, so normally use based on the model of molecular fluorescence spectral theory and the given model approximation of space laser intensity of illumination.Under this background, the brightness of molecule

Depend on interval width Δ t for example, space distribution and at the fluorescence quantum yield of the molecule of quantum efficiency, xsect (σ) and the given type of the collection efficiency function of the light intensity of excitation wavelength (λ), optics assembling, detecting device (q)

Parameter.Also be proved to be such as the parameter of the afterpulse of triplet excitation and detecting device and brought into play vital role.

Any prognostic experiment photon counting that starts anew is distributed, to molecule brightness

Understanding be inevitable.In FIDA and PCH, used Theoretical model.Free parameter in these models is determined by test on single species.

If putative molecule luminance function

Be approximate and known by direct measurement or theoretical model, so, the classical formulas of Mandel (Mandel) has been described the probability P of measuring n photon from individual molecule ₁(n) [referring to L.Mandel:Fluctuations of photon beamsand their correlations, Proc.Phys.Soc.72, pages 1037-1048, (1958)]:

$P_1\left(n\right)=\underset{V}{\∫}\mathrm{Poi}(n,\mathrm{\μ}\left(\stackrel{\→}{r}\right))p\left(\stackrel{\→}{r}\right)\mathrm{dV}$

Poisson distribution Poi in the formula (n, μ)=exp (μ) μ ⁿ/ n! The all possible position of molecule is asked average. $p\left(\stackrel{\→}{r}\right)=1/V$ Spatial point is found in expression The constant probability of place's particle.Unfortunately, above-mentioned equation $P_1\left(n\right)=\underset{V}{\∫}\mathrm{Poi}(n,\mathrm{\μ}\left(\stackrel{\→}{r}\right))p\left(\stackrel{\→}{r}\right)\mathrm{dV}$ Under the limit of infinitely great integration capacity V, produced and simply separated P ₁(n)=δ _0n, this reflects a physics fact, promptly the individual molecule in infinitely great capacity can not produce any photon counting incident corresponding to zero-dose at all.A kind of general way is to evade this shortcoming by introducing big and limited capacity, referring to for example at Yan Cheng, Joachim D.M ü ller, Peter T.C.So, and Enrico Gratton:The photoncounting histogram in fluorescence fluctuation spectroscopie, Biophysical J.77, pages 553-557, the discussion in (1999).

According to the present invention, by with useful capacity V _EffIn the definition of " individual molecule " be applied to the Mandel formula, the problems referred to above of PCH algorithm are avoidable, the Mandel formula becomes so.

$P_1\left(n\right)=1/V_{\mathrm{eff}}\underset{R^3}{\∫}\mathrm{Poi}(n,\mathrm{\μ}\left(\stackrel{\→}{r}\right))\mathrm{dV},$

P wherein ₁(n=0) :=0.

This formula has been set up at P ₁(n), V _EffWith

Between relation, this can be used for determining in these characteristic properties one or other.

In addition, cause being used for＜m based on the Poisson of Markovian process theory is approximate and V _EffFollowing formula.

Consider the non-zero concentration c under real physical conditions, the average number＜m of the molecule that each counting rate is worked〉by

$\⟨m\⟩=\underset{R^3}{\∫}[1-\mathrm{Poi}(n=0,\mathrm{\μ}\left(\stackrel{\→}{r}\right))]\mathrm{cdV},$

Provide, wherein cdV is illustrated in the molecule number among the dV of capacity unit, the factor $[1-\mathrm{Poi}(n=0,\mathrm{\μ}\left(\stackrel{\→}{r}\right))]$ Each molecule among the expression dV produces the probability of at least one photon counting incident.

By relational expression V _EffThe m of :=＜〉/c, obtain

$V_{\mathrm{eff}}=\underset{R^3}{\∫}[1-\mathrm{Poi}(n=0,\mathrm{\μ}\left(\stackrel{\→}{r}\right))]\mathrm{dV}.$

Above-mentioned formula has been set up respectively at＜m 〉,

And between the c and at V _EffWith Between theory relation, this can be used for determining in these characteristic properties one or other.

In the application of most of FFS, the particle of same species (molecule) fluoresces or is fluorescently-labeled, and uses laser beam to come excited particles.

Luminance function

Maximal value determine by the first moment (first moment) of distribution function:

${\mathrm{\&mu;}}_{\max }=\frac{v_2\left(p\right)-{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="A2007800510310034H1.png,A2007800510310034H2.png"\; state="\{\{state\}\}">v</figure-callout>}}_1^2\left(p\right)-v_1\left(p\right)}{v_1\left(p\right)}.$

Importance as this square method of the alternative Process of nonlinear fitting process will be further considered below.

If consider noise contributions＜n 〉 _Noise, luminance function

Maximal value just by having parameter a _jWith different luminance functions

(j=1,2 ..., the stack of different luminance function K) $\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right)=\underset{j}{\mathrm{\&Sigma;}}{a}_j{\mathrm{\&mu;}}_j\left(\stackrel{\&RightArrow;}{r}\right)$ Come modeling.

Replacedly, luminance function

(j=1,2 ..., K) can be by having parameter a _jWith different luminance functions

(j=1,2 ..., the stack of different luminance function K) $\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right)=\underset{j}{\mathrm{\&Sigma;}}{a}_j{\mathrm{\&mu;}}_j\left(\stackrel{\&RightArrow;}{r}\right)$ Come modeling.

Each luminance function

(j=1,2 ..., K) by M characteristic parameter μ of given number _Jk(k=1,2 ..., M) determine.

A kind of common model that is used for luminance function is the space Gaussian distribution:

$\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right):={\mathrm{\&mu;}}_{\max }\exp (-2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A2007800510310035H2.png"\; state="\{\{state\}\}">r</figure-callout>}}^2/a^2),$

μ wherein _MaxBe in the heart the brightness of molecule in the laser spot, a represents the waist parameter of laser beam.Several groups have showed with this limitation that quite complicated three dimensions luminance function is described of slightly approaching, referring to Bo Huang, Zhomas D.Perroud, and Richard N.Zare, Photon counting histogram:One-photon excitation, ChemPhysChem 5, pages 1323-1331, (2004) and document wherein.Being fit to do several places illustrates and confirms this selection of the example of property as an illustration.At first, our method of the present invention goes for any spatial brightness function.Secondly, approximate being easy to usually of Gaussian function handled, verified, contracing of Gaussian function converges to any spatial function that amasss [referring to BrunoKlahn and Werner A.Bingel:The convergence of the Raleigh-RitzMethod in Quantum Chemistry, Theoret.Chim.Acta 44, pages 9-43, (1977)].This is one of their reasons of being widely used in modern quantum Chemical Study decades.

Respectively Gaussian distribution is inserted the definition and the individual molecule function of useful capacity, the conversion of coordinate r → μ and the rotation integration that deserves to be called is obtained

$V_{\mathrm{eff}}=\frac{{\mathrm{\&pi;a}}^3}{\sqrt{2}}F\left({\mathrm{\&mu;}}_{\max }\right),$

With

$P_1\left(n\right)=\frac{1}{n!F\left({\mathrm{\&mu;}}_{\max }\right)}Q(n,{\mathrm{\&mu;}}_{\max })$

Wherein,

$F\left({\mathrm{\&mu;}}_{\max }\right):=\underset{{\mathrm{\&mu;}}_{\max }}{\overset{0}{\&Integral;}}\frac{1-e^{-\mathrm{\&mu;}}}{\mathrm{\&mu;}}\sqrt{1n(\mathrm{\&mu;}/{\mathrm{\&mu;}}_{\max })\mathrm{d\&mu;}},$

With

$Q(n,{\mathrm{\&mu;}}_{\max }):=\underset{{\mathrm{\&mu;}}^{\max }}{\overset{0}{\&Integral;}}{e}^{-\mathrm{\&mu;}}{\mathrm{\&mu;}}^{n-1}\sqrt{1n(\mathrm{\&mu;}/{\mathrm{\&mu;}}_{\max }}\mathrm{d\&mu;}.$

Numerical value Romberg integration be can use and computing function F and Q come.What illustrate is that Q is only to n 〉=1st, and is limited, and n=0 is dispersed.To Gaussian

Useful capacity V _EffBecome identical, right with relevant detection capacity among the FCS $F\left({\mathrm{\&mu;}}_{\max }\right)=\sqrt{2\mathrm{\&pi;}},$ $V_{\mathrm{fcs}}={\mathrm{\&pi;}}^{\frac{3}{2}}{a}^3$ , that is, and to μ _MaxSome values, P ₁(n) can be with for μ _MaxNumerical stability and fast mode calculate and have definite physical significance.

A more accurate luminance function

Modeling by having parameter μ _J1And μ _J2(j=1,2 ..., the stack of Gaussian distribution K) is carried out:

$\mathrm{\&mu;}\left(\stackrel{\&OverBar;}{r}\right)=\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="A2007800510310034H1.png,A2007800510310034H2.png"\; state="\{\{state\}\}">j</figure-callout>}1}\exp (-2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A2007800510310035H2.png"\; state="\{\{state\}\}">r</figure-callout>}}^2/{\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A2007800510310035H2.png"\; state="\{\{state\}\}">j</figure-callout>}2}^2).$

Characteristic parameter μ _Jk(j=1,2 ..., K; K=1,2 ..., M) determine by the standard method of deconvoluting.

Characteristic parameter μ _Jk(j=1,2 ..., K; K=1,2 ..., M) also can-Lucy (Richardson-Lucy) deconvolution algorithm gloomy determine by the iteration Richard.

Above-mentioned individual molecule function P ₁(n) and V _EffK-theoretic operation K be based on classical Mandel formula.But this formula has certain limitation.The distribution of photon count rate may depart from Poisson distribution

Because the productive rate of photon (production rate) may change during time interval Δ T.Some influences may cause the change of the productive rate of this photon.T is in the position at time point

Individual molecule may move, this molecule may be visited other place during time interval Δ t.Because space laser intensity changes, so diffusion process for example may cause the invalid of great revocable photon productive rate and Mandel formula.In these cases, the Poisson distribution in the Mandel formula must replace with widely and distribute

To n＞0,

$P_1\left(n\right)=1/V_{\mathrm{eff}}\underset{R^3}{\&Integral;}p(n,\stackrel{\&RightArrow;}{r})\mathrm{dV}$

And P ₁(n=0) :=0.Useful capacity by

$V_{\mathrm{eff}}:=\underset{R^3}{\&Integral;}(1-p(n=0,\stackrel{\&RightArrow;}{r}))\mathrm{dV}$

Provide.

Be at time point t ₀Be in the position

Individual molecule at time interval t ∈ [t ₀, t ₀+ Δ t) distribution of the photo-event number of counting during.Distribute

Calculating in general be the task of a theoretical property.Consider the diffusion motion of molecule, distribute

Can formally be write as

$p(n,\stackrel{\&RightArrow;}{r})=\underset{N\&RightArrow;\&infin;}{\lim }\underset{R^3}{\&Integral;}\mathrm{<figure-callout\; id="0"\; label="d\; V"\; filenames="A2007800510310034H1.png,A2007800510310035H2.png"\; state="\{\{state\}\}">d</figure-callout>}{V}_{}{}_0\underset{j=1}{\overset{N}{\mathrm{\&Pi;}}}{\mathrm{dV}}_{1}G\left(\right|{\stackrel{\&RightArrow;}{r}}_j-{\stackrel{\&RightArrow;}{r}}_{j-1}|,\mathrm{\&Delta;t}/N)$

$\mathrm{Poi}(n,1/(N+1)\underset{i=0}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&mu;}\left({\stackrel{\&RightArrow;}{r}}_i\right))$

Form, G represents the Greens function that spreads in the formula.

$G(x,\mathrm{\&tau;}):=1/{\left[4\mathrm{\&pi;D\&tau;}\right]}^{3/2}{e}^{-x^2\left(4\mathrm{D\&tau;}\right)}$

Slowly spreading under the limiting case of D → 0, by

$\underset{D\&RightArrow;0}{\lim }p(n,\stackrel{\&RightArrow;}{r})=\mathrm{Poi}(n,\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right))$

Obtained classical Mandel formula.This example shows the single particle distribution function P that introduces above ₁(n) notion can extend to complicated measurement situation at an easy rate.But should be pointed out that in theory and consider under the untouchable situation P ₁(n) and V _EffCan determine by experiment.

From single particle probability distribution P ₁(n) set out the following P that obtained ₁(n) and the contact between the distribution function p (n) that measures.

Under real physical conditions, average number＜m 〉=cV _EffParticle simultaneously signal is worked.Use Markovian process theory, (n c) obtains by the effect addition with all m particle the probability distribution p of given concentration c

$p(n,c)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{Poi}(m,\&lang;m\&rang;)P_m\left(n\right)$

P in the formula _m(n) be meant single particle probability distribution P ₁(n) m convolution

$P_m\left(n\right)=\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{P}_{m-1}(n-i)P_1\left(i\right),m=\mathrm{2,3}...,$

And P ₀(n)=δ _N0Replacedly, p (n, c) can calculate by recursion formula:

$p(n,c)=\frac{{\mathrm{cV}}_{\mathrm{eff}}}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}i{P}_1\left(i\right)p(n-i,c)$

Wherein, and p (n=0, c)=exp (cV _Eff).

Ignore ground unrest, the concentration of particle is that 0 probability is determined by obtaining counting rate fully:

c＝-ln(p(n＝0，c))/V _eff。

If the consideration ground unrest, the concentration c of particle is 0 probability and noise contributions＜n by obtaining counting rate 〉 _NoiseDetermine:

c＝[-ln(p(n＝0，c))-<n> _noise]/V _eff。

Average number＜the m of particle〉be that 0 probability is determined by obtaining counting rate:

<m>＝-ln(p(n＝0，c))。

Consider noise contributions, the average number＜m of particle〉by

＜m 〉=-ln (p (n=0, c))-＜n) _NoiseObtain.

Single particle probability distribution function P ₁(n) can pass through recursion formula:

$P_1\left(n\right)=\frac{1}{p(0,c)}[\frac{p(n,c)}{\&lang;m\&rang;}-\frac{1}{n}\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{\mathrm{iP}}_1\left(i\right)p(n-i,c)]$

Calculate.

Distribution function p (n, c) may must with Poisson distribution Poi (n,＜n 〉 _Noise) convolution to be to consider extra background signal (for example random noise of hardware):

$p_{\mathrm{tot}}(n,c,{\&lang;n\&rang;}_{\mathrm{noise}})=(p\left(c\right)\&CircleTimes;\mathrm{Poi}\left({\&lang;n\&rang;}_{\mathrm{noise}}\right))\left(n\right).$

Consider according to above-mentioned theory, to given experiment assembling, working concentration c, luminance function

Useful capacity V _EffWith single particle distribution P ₁(n) will contain the sample characteristicsization of fluorescent particles (as molecule).Because the noise contributions＜n in great majority experiment assembling 〉 _NoiseCan not ignore, also must consider noise contributions＜n 〉 _NoiseFollow the standard that in FIDA and PCH algorithm, illustrates, can determine these parameters by for example Marquard-Levenberg algorithm or the non-linear multi-parameter fitting process that is suitable for any other numerical standard approximating method of this task.Therefore, luminance function

Must be similar to by analytic function with a plurality of adjustable parameters.

Analytical form can be chosen as Gaussian function (in top example), the contracing or the function of any other suitable shape of several Gaussian functions.

All adjustable parameters

And concentration c and noise contributions＜n 〉 _NoiseMust determine by the distribution p (n) of theoretical model and actual measured amount is carried out nonlinear fitting.As indicated above, useful capacity V _EffWith single particle distribution P ₁(n) directly come from right

Integration.

The interchangeable process of nonlinear fitting process is the square method, and it adopts precalculated to adjustable parameter

Concentration c and noise contributions＜n 〉 _NoiseThe tabulation of the desired square of any class value.Because this tabulation can calculate in advance and store the parameter in the OK range, so this is the fastest possible process that is used for online application.The square of distribution p (n) by

$v_i=\underset{n=0}{\mathrm{\&Sigma;}}p\left(n\right)n^i$

Definition.

With a _i, i=1,2 ..., the k that k indicates a to determine parameter.At parameter a _iThe suitable scope of value in, can calculate the square v of expectation _i, i=1,2 ..., l.Parameter value a to all possible group _i, i=1,2 ..., the k precomputation first rank l square v has produced a mapping

(a ₁，a ₂，…，a _k)→(v ₁，v ₂，…，v _l)。

The grid of discrete parameter value has reduced the calculating dynamics, and the square of the not expectation of the parameter value on this grid must for example be extrapolated with batten and inferred.Select the number of square l low as far as possible, but enough high to guarantee that above-mentioned mapping is a bijective function.This mapping can be turned around

(v ₁，v ₂，…，v _l)→(a ₁，a ₂，…，a _k)

This is any one group of square μ i that measures, i=1, and 2 ..., l has provided the parameter that needs.

The square of the probability distribution function of single particle passes through recursion formula:

$v_k\left(P_1\right)=\frac{1}{\&lang;m\&rang;}[v_k\left(p\right)-{\&lang;n\&rang;}_{\mathrm{noise}}-\underset{l=1}{\overset{k-1}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}k-1\\ l-1\end{array}\right)v_{k-l}\left(p\right)\{{\&lang;n\&rang;}_{\mathrm{noise}}+\&lang;m\&rang;v_l\left(P_1\right)\left\}\right]$

Calculate.Can use the noise contributions＜n of the direct experiments of measuring assembling of media fluid of the sample that does not have fluorescent particles 〉 _NoiseThe media fluid of sample can same or analogous by having (light) character liquid replace.Determine in advance＜n 〉 _Noise, this parameter can be maintained fixed in nonlinear fitting process and square method.Like this, the decreased number of the parameter that in these processes, needs one.

The particle sample of single species is paid close attention in above-mentioned consideration.

The present invention also clearly is applicable to the sample of the particle (potpourris of particle species) that contains N different plant species.

Under the situation of particle species potpourri, it is to finish in multistep process that the concentration of each species is established a capital really.At first, be necessary for each the species s that exists in the potpourri and given experiment alignment measurement useful capacity V _Eff ^(s)With single particle distribution P ₁ ^(s)(n).This finishes by one in the said process.

According to the character V that determines _Eff ^(s)And P ₁ ^(s)(n), the total distributed p (n of expectation; c ₁, c ₂..., c _N) can be by the effect p of single species ^(s)(n; c _s), s=1,2 ..., the convolution of N is represented:

$p(n;{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A2007800510310034H1.png,A2007800510310034H2.png"\; state="\{\{state\}\}">c</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A2007800510310035H2.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,...,c_N)=$

$p^{\left(1\right)}(n;c_1)\&CircleTimes;p^{\left(2\right)}(n;c_2)\&CircleTimes;\&CenterDot;\&CenterDot;\&CenterDot;\&CircleTimes;p^{\left(N\right)}(n;c_N)\&CircleTimes;\mathrm{Poi}(n,{\&lang;n\&rang;}_{\mathrm{noise}}).$

The parameter of determining is a concentration c _s, s=1,2 ..., N and noise contributions＜n 〉 _Noise

The parameter that requires can be determined the nonlinear fitting of measurement data and theoretical model by using.Identical with nonlinear fitting process described above, can the application standard numerical technique.In some cases, generating may be accelerated p (n; c ₁, c ₂..., c _N) calculating.

With nonlinear fitting replacedly, as mentioned above, available square method is determined parameter.This process is utilized p (n; c ₁, c ₂..., c _N) square can be expressed as p ^(s)(n; c _s) long-pending such fact and be simplified technically, s=1 wherein, 2 ..., N.

Carry out V without any the knowledge of model or molecule luminance function aspect _EffAnd P ₁(n) measurement is possible.These character may be passed through the analysis to measure distribution p, and (n c) directly determines.Because measuring distribution is noisy data,, the error propagation effect extracts P so can being used in ₁(n) numerical method instability.

For this reason, P ₁(n) integral body represents it is favourable.A powerful method is that so-called discrete Galerkin approaches, and its form is

$P_1\left(n\right)=\underset{k=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{a}_k\mathrm{\&Psi;}(n,p,\mathrm{\&lambda;})l_k(n,p,\mathrm{\&lambda;})$

A wherein _kBe the broad sense square, (n, p λ) are the weighting function with adjustable parameter p and λ, l to Ψ _k(n, p λ) are corresponding polynomial expression.Parameter p and λ are by P ₁(n) first moment is determined.The Galerkin prediction of this error control is the thorough method of research in the numerical mathematics, usually be applicable to that high polymer chemistry is [referring to P.Deuflhard and J.Ackermann:Adaptive Discrete GalerkinMethods for Macromolecular Processes, in H.P.Dikshit and CharlesA.Michelli, editors:Advances in Computational Mathematics, WorldScientific Publishing Co., Inc., (1993); J.Ackermann and M.Wulkow:MACRON-A Program Package for Macromolecular ReactionKinectics, Konrad-Zuse-Zentrum, Preprint SC-90-14, (1990), M.Wulkow and J.Ackermann:Numerical Simulation ofMacromolecular Kinetics-Recent Developments, IU-PAC WorkingParty, Macro group, (1990); M.Wulkow and J.Ackermann:TheTreatmeant of Macromolecular Processes withChain-Length-Dependent Reaction Coefficients-An Example fromSoot Formation, Konrad-Zuse-Zentrum Berlin, Preprint-91-18, (1991); U.Budde and M.Wulkow:Computation of molecular weightdistributions for free radical polymerization systems, Chem.Ing.Sci.46, pages 497-508, (1991), M.Wulkow:Numerical Treatment ofCountable Systems of Ordinary Differential Equations, Thesis andTechnical Report-90-8, Konrad-Zuse-Zentrum Berlin, (1990); M.Wulkow:Adaptive Treatment of Polyreactions in Weighted SequenceSpaces, IMPACT Comput.Sci.Engrg.4, pages 152-193, (1992)].This parameter of approaching (being similar to) can utilize fit procedure (referring to non-linear multi-parameter fitting process described above) or (n c) obtains from p with the similar square method of square method described above.

A useful properties is the mean molecule brightness that generates n photon in this respect, is defined as

${\&lang;\mathrm{\&mu;}\&rang;}_n:=\frac{{\&Integral;}_{R^3}\mathrm{Poi}(n,\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right))\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right)\mathrm{dV}}{{\&Integral;}_{R^3}\mathrm{Poi}(n,\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right))\mathrm{dV}}$

＜μ 〉 _nWith the form of useful photon productive rate with spatial brightness

Characterization, by

${\&lang;\mathrm{\&mu;}\&rang;}_n=\frac{(n+1)P_1(n+1)}{P_1\left(n\right)}$

With probability distribution P ₁(n) association.Generally, to low counting rate n, molecule brightness is linear to increase＜μ 〉 _n≈ n, the molecule at the center of exciting light focus become constant when being in high-high brightness.This character makes the individual molecule signal obviously be different from and provides constant distribution＜μ 〉 _nThe random noise signal of=constant.

On the basis of three embodiment below, above and other objects of the present invention, aspect and advantage will be better understood, and wherein analyze the potpourri of polystyrene microsphere face suspension series, dyestuff rhodamine (dye Rhodamine) 6G dilution series and polystyrene microsphere face and rhodamine 6G dyestuff in an embodiment.Use the fluorescence spectrum unit of prior art to collect experimental data, described fluorescence spectrum equipment is included in light source, built-in highly sensitive photomultiplier and the digital correlator of emission 532nm exciting light under the intensity of 50 microwatts.Employed fluorescence spectrum unit has the reaction time of 30 nanoseconds.The counting clock pulse that is used between twice photon registration is in succession realized data acquisition.According to these data of collecting, can calculate several light intensity tracks for different interval width Δ t.

Sample 1: the microballoon face suspends serial

As first embodiment, a fluorescence polystyrene microsphere face suspension series is analyzed.

Fig. 1 shows to containing volumetric molar concentration C _MThe sample record of the polystyrene microsphere face (dripping) of ≈ 1.9E-10Mol/L reaches 3.2 seconds typical intensity of illumination trace.

Fig. 2 shows autocorrelator trace (average to 100 3.2 seconds traces shown in Figure 1).

Fig. 3 show interval width Δ t=0.1 millisecond corresponding photon counting distribution p (n, c).

Fig. 4 shows the number (dotted line) of the molecule of being obtained by fluorescence correlation spectroscopy (FCS) of each sample and the number (solid line) of the molecule obtained by the method according to this invention.As a reference, also show theoretical decline gradient (square that does not connect).

Fig. 1 shows to containing known molar concentration C_M≈ 1.9E-10 mole/L's is 0.014 little The typical intensity of illumination trace of the sample record of dripping of rice. Interval time adjusted is 1 millisecond. Intensity peak represents the transformation by the molecule that focuses on the FCS capacity.

Fig. 2 shows corresponding autocorrelator trace (average to 100 3.2 seconds rings). Match is led Caused τ diffusion time=1.74 millisecond and in focusing on the FCS capacity, had n=0.1529 and dripped. Right Be τ=1.91 ± 0.33 millisecond the diffusion time that several FCS measurements are averaging. This diffusion time Determined droplet by focusing on the FCS required time of capacity. According to the information of manufacturer, employing Fluorescence spectrum equipment has V_FCSThe ascend to heaven FCS capacity of (fL) of ≈ 1.

Fig. 3 show interval width Δ t=0.1 millisecond corresponding photon counting distribution p (n, C). Probability p (n=0, c)=0.79976 means among Fig. 1 that all photon countings of about 80% are Zero. Use the measurement of pure water to provide background noise level＜n 〉_noise＝0.0230642。

According to the present invention, available capacity V_effIn the average number＜m of molecule provide c V by following formula_eff＝<m>＝-ln(p(n＝0，c))-<n> _noise=0,20038. And therefore, according to available capacity V of the present invention_effThe result is at (C_M＝1.9E-10Mol/L， N _A＝6.022E23)

V _eff＝<m>/(C _M N _A) ≈ 1.75fL On the amplitude of magnitude, therefore, be a bit larger tham the capacity that focuses on FCS. Can notice, by subtracting Few (increase) interval width Δ t or excitating light strength, this is worth V_effMay descend (increase) data Do not show. Usually, V_effDepend on instrument parameter and molecular parameter.

What Fig. 4 showed each sample analyzes the number (void of the molecule of gained by standard FC S Line). Each sample is carried out twice measurement; Measure each time respectively with point (measuring I) and star Shown in (measuring II). The measurement of this series is with predetermined C_M=2.44E-8Mol/L's is initially molten Liquid is from step 1.

This initial soln dilutes in 12 steps with " mixed point-score ". The sample of 50 μ L is with 50 The dilution of μ L water; Half measurement of being taken away of 100 μ L of gained, second half is as the next one of sample The sample of " the mixed branch " step. It is desirable to, the concentration that the microballoon face drips is under each dilution step Twice is fallen. Reach the least concentration of microballoon face in step 13, caused C_M=3E-12Mol/L. In the logarithmic scale of Fig. 4, should be such as the side that does not connect by the number that drips of standard FC S gained Piece is linear decline like that.

May come from during series " the mixed branch " step from little the departing from of this theoretical behavior Uncertainty in the reason low capacity. Yet, clearly, with standard FC S carry out to the same The result of this twice measurement differs between 10% and 50%. This difference indicates definite Not sizable statistical error of dripping of number and the concentration that similarly obtained by FCS not true Qualitative. But, the performance that fiercer is at the FCS of low concentration. To being lower than C_M=3.8E-10M Concentration, the FCS method can't be determined correct concentration, and gives the high value make mistake. FCS is Sample in dilution step 13 has provided the too high value that amplitude is higher than two orders of magnitude. On This performance of the FCS that states is well-known, presented the FCS method particularly to low concentration Serious restriction.

To see that below with respect to the FCS method of prior art, method of the present invention is produced Given birth to the number of determining more accurately fluorescent particles. As implied above, according to the present invention, the fluorescence grain The concentration of son is namely at V_effNumber＜the m of middle particle〉can be determined by p (n=0, c). Can notice, P (n=0, c) can measure with high statistical accuracy under the low concentration state. The respective number of molecule Be shown in Fig. 4 (solid line).

Method of the present invention has been applied to the identical image data record with the use of FCS method In. Therefore, do not carry out these results that extra measurement obtains method of the present invention. With The value that FCS draws is compared,＜m〉statistics variations much lower (to approximately C_MThe concentration of=5E-10Mol/L 1% and to minimum concentration C_M=3E-12M 10% it Between). The more important thing is that the concentration of measurement is followed correct theoretical linear decline gradient, low To C_MAlso have no detectable limit during the concentration of=3E-12M.

Sample 2: dyestuff rhodamine 6G dilution series

To the dilution series of dyestuff rhodamine 6G (condition identical with sample 1), obtained class Like the result. Here, the detectable limit of FCS is true by the sensitivity of device (apparus) Fixed, be at C_MThe magnitude of=3E-9Mol/L. The present invention proof make concentration certainty of measurement even Lower by 2% than the detectable limit of FCS, data are not shown. To rhodamine 6G, to the fluorescence spectrum list The setter parameter of unit, the value of available capacity reduces to V_eff≈0.2fL。

In order to improve the statistical significance of the photon counting signal that fluorescent particles produces, select quite big Interval width may be useful. Compare the present invention with standard method of analysis and follow-up method thereof Can be with splendid simplicity and the low-down concentration of accuracy detection.

Sample 3: the mixture that drips (bead) and rhodamine 6G

Drip and the measurement of the sample of the mixture of dyestuff rhodamine 6G (Rh6G) is given for containing Gone out the average number＜m of the particle in the available capacity 〉=2.2 (experiment condition is as above). This value with FCS value＜m 〉_FCS=2.35 is similar. But two parameter F CS can't determine separately each thing The concentration of planting. According to the present invention, drip with the concentration of Rh6G and can determine by the whole bag of tricks. One Individual way is to utilize the square method.

For dripping and Rh6G, from superincumbent sample 1, calculate respectively the first moment that individual molecule distributes: v in the measurement of explanation₁(P ₁ ^(beads))=1.55 and v₁(P ₁ ^(Rh6G))=1.06. Therefore, be applied in the distribution v of measurement₁(p _tot) first moment and individual molecule distribution v₁(P ₁) square between relation

v ₁(p _tot)＝<n> _noise+<m>v ₁(P ₁) can notice value v₁(P ₁ ^(beads)) and v₁(P ₁ ^(Rh6G)) with each Species Characteristics, with Its actual concentrations is irrelevant. The first moment of the individual molecule signal that mixture is obtained provides v₁ (P ₁ ^(beads+Rh6G))=1.30, neither with the square match of dripping also not with the square match of dyestuff. For Calculate v₁(P ₁ ^(beads+Rh6G)), use relational expression:

v ₁(p _tot ^(beads+Rh6G))＝<n> _noise+

(<m> ^(beads)+<m> ^(Rh6G))*v ₁(P ₁ ^(beads+Rh6G))

Drip the agency part to the signal in the mixture

x：＝<m> ^(beads)/(<m> ^(beads)+<m> ^(Rh6G))

Can be by relational expression

v ₁(P ₁ ^(beads+Rh6G))＝x*v ₁(P ₁ ^(beads))+(1-x)*v ₁(P ₁ ^(Rh6G)) Obtain easily. We draw:

<m> _beads＝x*<m>＝0.95

<m> _Rh6G=(1-x) *＜m 〉=1.25 The concentration (take mol/L as unit) that produces is

c _M(beads)＝<m> _beads/(V _eff(beads)*N _A)≈1E-9Mol/L

c _M(Rh6G)＝<m> _Rh6G/(V _eff(Rh6G)*N _A) ≈ 1E-8Mol/L The concentration of measuring for the dilution series of this sample is that two species generate under the correct concentration again Fall, data are not shown.

The alternative method of determining ratio x be relatively drip respectively, the individual molecule distribution P of Rh6G and mixture₁(n=1) first nonzero component.

Use relational expression

p _tot(1)＝<m>exp(-<m>-<n> _noise)P ₁(1)+<n> _noise exp(-<n> _noise) with the p from measuring_tot(n=1) obtain individual molecule distribution P₁(1). Utilize

x＝[P ₁(1) ^(beads+Rh6G)-P ₁(1) ^(Rh6G)]/[P ₁(1) ^(beads)-P ₁(1) ^(Rh6G)] Determine ratio x, the value of obtaining x ≈ 0.36 ± 0.15. Above-mentioned two kinds of methods can both with mixture with Pure solution makes a distinction and determines the magnitude of the concentration amplitude of each species in the mixture.

Said method and sample are applicable to characteristic properties fixing of the sample of determining to contain particle Interval time Δ t. These character depend on the optical physics attribute of molecular species, and it can be from being Extract in the intensity of illumination trace of interocclusal record in the time of between the given area. Therefore, the selection of interval width is right Result by the said method gained is influential.

The present invention extends to as the function of Δ t and determines suitable or optimum interval width and determine to contain the characteristic properties E of sample of the mixture of a species particle or several different plant species₁，…，E _LOther method.

Can utilize method that the dependence of interval width Δ t is come moving by for example its diffusion time Step response carries out characterization to molecular species.

A kind of standard method of measuring diffusion time is fluorescence correlation spectroscopy (FCS), and it has utilized The time behavior of optical track line, but ignored the different optical physics attribute of species. Therefore, when When the molecular species of different brightness is present in the sample, the application difficult of FCS method [ginseng See E.Van Craenenbroeck, G.Matthys, J.Beirlant, and Y. Engelborghs: " A statistical analysis of fluorescence correlation data ": Journal of Fluorescence, 9, pages 325-331,1999]. In with Publication about Document, illustrate The effect of parameters of interval time to the PCH method, [Thomas D.Perroud, Bo Huang, Ricard N.Zare, " Effect of bin time on the photon counting Histogram for one-photon excitation ", ChemPhysChem:6, pages 905-912, (2005)] and to the effect of parameters of FIDA [referring to Kaopo Palo,

Mets， Stefan

Peet Kask, and Karsten Gall: " Fluorescence intensity Multiple distribution analysis:Concurrent determination of diffusion Times and molecular brightness ", Biophysical J.79, pages 2858-2866, (2000)]. These methods are called as respectively between time dependence photon counting multi-region (PCMH) and the many distributional analysis of fluorescence intensity (FIMDA). PCMH and FIMDA are Be used to measure simultaneously diffusion time and the molecule brightness of molecular species. Demonstrated by mixing Thing is determined the FIMDA of the interactional binding constant of concentration and definite protein-ligand Use.

The application of FIMDA and the application of PCMH have several shortcomings.

1. determining molecule brightness for each interval width needs on a complexity, the time-consuming and numerical value Unsettled nonlinear fitting process.

2. these two kinds of methods all depend on complicated formula and illustrate that model parameter is to interval width Dependence.

3. in addition, these formula are based on ad hoc hypothesis (the ad hoc that does not preserve Assumption).

Other method according to the present invention relates to be determined to contain to a series of different time width Δ t The characteristic properties of the sample of the particle of with good grounds above-mentioned first method explanation of the present invention. To solid Decide characteristic properties that interval width determines and be interpreted as function as interval width Δ t here.

Therefore, other method of the present invention comprises the steps:

1) will be in observing time $T=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;t}}_i$ Continuous predetermined time interval Δ t_i＝[t _i-1，t _i) (i=1 ..., N) the number n of the photo-event of interior registration_i(counting rate) registered and counted, wherein Δ t_i=: Δ t=constant,

2) determine the photo-event number n in predetermined time interval Δ t distribution function p (n) and

3) other step of above-mentioned first method of executive basis the present invention;

Also comprise further step:

4) use different time interval Δ t^k(k=1 ..., K) repeating step 1) and to 3) K time, and determine identical characteristic properties E by every a series of these steps₁，…，E _L，

5) determine characteristic properties E₁，…，E _LTo Δ t^kDependence and

6) from according to step 5) the dependence of measurement determine suitable or optimum Δ t or particle Other characteristic.

Can utilize as the knowledge of the characteristic properties of the function of interval time Δ t and carry out following operation:

1. be above-mentioned suitable or optimum value of interval selection of time according to first method of the present invention,

2. characterization molecular species,

3. obtain another feature character by the dependence match with given analytic function and measurement,

4. molecular species and calculate its concentration in the identification mixture.

The time interval (interval width) Δ t^k(k=1 ..., K) can be 10^-6Choosing between second and several seconds Select.

An example of characteristic properties is effective brightness of individual molecule, for little interval wide Degree, effectively brightness is high, for big interval width, effectively brightness descends (referring to sample 4). The decline of brightness comes from visible molecule away from the diffusion of laser spot. Therefore, maximum brightness With the slope characteristics of brightness molecular species.

The discrete segment width can be chosen as on logarithmic scale equidistant, for example Δ t^k＝0.8 ^kSecond, k=0 ..., 72.

Maximum brightness μ_maxDependence to interval width has generated the attenuation function of testing, and it is The feature of the brightness of the molecule of specific species and size. Calculate this letter by the dependence of measuring Number is (within several seconds) execution at a high speed. In principle, can be to the grain of single species The son all character determine this dependence to interval width Δ t, its as above to according to this The first method of invention is illustrated.

Can be by standard fit procedure that given analytic function and characteristic properties is wide to the interval The measurement of degree Δ t relies on match.

Characteristic properties can be the specific species of the molecule in the sample that will measure.

In the mixture of the molecule that further characteristic properties can be the several species in the sample Part concentration.

The dependence of measuring can be compared with the dependence of having measured or theory function, to determine sample In the specific species of molecule or the part concentration of molecule.

According to the stack of the dependence of having measured or theory function by nonlinear fitting with characteristic The measurement of confrontation interval width Δ t relies on to be introduced, to determine the specific species of the particle in the sample Or the part concentration of the particle of specific species.

In the application-specific an of the method according to this invention, measured distribution function p (n^k， Δt ^k) (k=1 ..., K), and by suitable fit procedure, from p (μ^k，Δt ^k) determine the high-high brightness function mu_max(Δt ^k) as characteristic properties.

Said method also can further comprise, by suitable fitting function, from μ_max(Δ t) determines the μ of time period Δ t → 0_max(Δ t), diffusion motion, diffusion time τ_DAnd/or device Structural parameters SP.

As further step, from μ_max(Δ t) determines τ die-away time_μAnd/or in the sample The ratio of the particle of specific species.

In another sample of the method according to this invention, can measure the sample of the particle that several species are arranged, wherein determine μ_max(Δt ^k), pass through formula

${\mathrm{\&mu;}}_{\max }\left(\mathrm{\&Delta;t}\right)=\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\max ,s}^2\left(\mathrm{\&Delta;t}\right)\&CenterDot;X_s/\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\max ,s}\left(\mathrm{\&Delta;t}\right)\&CenterDot;X_s$

By μ previous measurement or that otherwise determine_max，s(Δ t) determines the molar ratio X of species s in the sample_s Replacedly, by with parameter 0≤X_s≤ 1) (s=1 ..., S) and boundary condition $\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}\mathrm{Xs}=1$ Carry out the molar ratio X of species in the incompatible definite sample of Nonlinear Quasi_s。

In the other sample 4 and 5 below, illustration feature to interval width Δ t value Rely on.

Example 4:

An illustrative example of characteristic properties is by formula

${\mathrm{\&mu;}}_{\max }=\frac{v_2\left(p\right)-{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="A2007800510310034H1.png,A2007800510310034H2.png"\; state="\{\{state\}\}">v</figure-callout>}}_1^2\left(p\right)-v_1\left(p\right)}{v_1\left(p\right)-{\&lang;n\&rang;}_{\mathrm{noise}}}$

The brightness value μ that calculates_max, v wherein₁(p) and v₂(p) be the first moment of the probability distribution of measurement And second moment. In the situation of high brightness, namely to v₁(p)＞＞<n> _noise, noise contributions＜n 〉_noiseCan ignore. Brightness value μ by following formula calculating_maxIt is Gaussian Profile $\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right):{\mathrm{\&mu;}}_{\max }\exp (-2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A2007800510310035H2.png"\; state="\{\{state\}\}">r</figure-callout>}}^2/a^2)$ Luminance functionMaximum, but also be the feature brightness value of other distribution pattern. ConSense detection system (FIuIT Biosystems, St Augustine (Sankt Augustin), Germany, http://www.fluit-biosystems.de) in measured to contain and rubbed The dyestuff ATTO's 532 of you concentration C=56E-10M (ATTO TEC, uncommon root, Germany) Sample. Recorded the optical track of 3 minutes fluorescence intensity, and with virtual laboratory software (FIuIT Biosystems) analyze. To from 1 second to several microseconds (10^-6Second) scope in various interval the time Between, made up probability distribution p (n, c). Particularly, we select discrete segment time Δ t_n＝ Δt ₀0.8 ⁿSecond, n=0,1,2,3 ..., 72, Δ t₀=1s. For each interval time and corresponding probability Distribution p (n, c) is once calculated brightness value μ with second moment by p (n, c)_max, see top public affairs Formula. The μ of gained_maxValue depends on the interval time of application, has drawn μ corresponding to Δ t at Fig. 5_max Therefore, characteristic properties μ_maxBe understood to be the function of Δ t, below with μ_max(Δ t) Expression.

High-high brightness μ_maxCan be interpreted as the brightness of individual molecule at the center of laser spot. By the diffusion, the individual molecule that is positioned at the center moves apart the center, and its brightness (take the per second counting as Unit CPS) descends. Therefore, to long interval time Δ t, effective high-high brightness of measurement μ_max(Δ t) descends. To the short interval time, effectively high-high brightness becomes big.

(effectively) brightness value of species depends on interval width Δ t. The curve of drawing in Fig. 5 can And have parameter μ_max(Δt＝0)、τ _μAnalytic function with SP

${\mathrm{\&mu;}}_{\max }\left(\mathrm{\&Delta;t}\right)={\mathrm{\&mu;}}_{\max }(\mathrm{\&Delta;t}=0)\sqrt{\frac{1}{1+\mathrm{\&Delta;t}/{\mathrm{\&tau;}}_{\mathrm{\&mu;}}}}\sqrt{\sqrt{\frac{1}{1+\mathrm{\&Delta;t}/(\mathrm{SP}*\mathrm{SP}*{\mathrm{\&tau;}}_{\mathrm{\&mu;}})}}}$

Match. Parameter μ_max(Δt＝0)、τ _μRefer to respectively when short interval time of the limit with SP The structural parameters of high-high brightness, die-away time and optics assembling. Match provides: brightness value μ_max(Δ t=0)=15.1kcps, die-away time τ_μ=0.731ms and structural parameters 2.

Brightness value μ_max(Δ t=0) and die-away time τ_μIt is the molecule thing in given optics assembling The characteristic properties of planting. Brightness value μ_max(Δ t=0) depends on optical physics character and the maximum of molecule The local laser luminous intensity. Die-away time τ_μWith the diffusion constant of molecule, i.e. its hydrodynamic radius Be directly proportional with the confocal detection capacity.

For the impact of optics assembling is described, to containing molar concentration 3.010^-11The dyestuff of M The sample of ATTO has been measured twice. At first, be that the pin hole of 100 μ m reduces with diameter Ambient noise uses the ConSense detection system to record the light of the fluorescent intensity degree of 3 minutes samples Mark. In second assembling, replace and measure 30 seconds identical with the pin hole of 75 μ m diameters Sample. Two of the analysis of fluorescence luminous intensity optical tracks as mentioned above; Figure 6 illustrates acquisition The luminance function of two assemblings. The diameter of pinhole diameter reduces to 75 μ m from 100 μ m also to be caused Die-away time τ_μDrop to 0.343 millisecond from 0.567 millisecond. Littler pinhole diameter produces inspection The littler size of survey capacity, and therefore reduced die-away time.

Sample 5:

In order to distinguish the different molecular species in the sample, can utilize characteristic properties to the interval time Dependence. In the first step, must measure characteristic to all possible molecular species in the probe Matter and to the dependence of interval time. In Fig. 7 and table 1, described a typical situation.

Measured luminance function μ for fluorescent dye_max(Δ t); As shown in sample 4, Through determined parameter μ with nonlinear fitting_max(Δ t=0) and τ_μ Used this dye marker A kind of antibody. Because antibody will be far longer than dyestuff, so this decay that labelled antibody is measured (fade out) time τ_μ=255 μ s are longer than τ die-away time that measures into pure dye far away_μ=33 μ s. The antibody of mark is different from dyestuff with die-away time and its higher brightness value. Have most May be that each antibody molecule is by two dye molecule marks; This is by the high luminance values μ of antibody_max(Δ t=0) indicates.

On the other hand, antibody capable is attached on (bind) protein. Resist for characterization is complicated Body+protein, surpassing sample provides protein. Can notice that protein molecule does not have Mark, and when not being added on the fluorescence antibody, deceive. Than long τ die-away time_μ=663 μ s are corresponding to the diameter of the increase of complex. The combination of protein has reduced antibody molecule Brightness value, this shows that protein has replaced in two dye molecules.

Protein can be incorporated on the polymer. Surpassing the generation of solution ground interpolation polymer only comprises The sample of complicated antibody+protein+polymer (with black molecule). By long τ die-away time_μ=1611 μ s indicate, and this compound is sizable. The brightness value that reduces can be interpreted as There is the molecule of suitable large group to be in the electronics triplet. Triplet lifetime and colony can pass through document In the explanation to triplet to the impact of brightness carry out modeling [Jerker Widengren,Mets, and Rudolf Rigler:Fluorescence Correlation Spectroscopy of Triplet States in Solution:A Theoretical and Experimental Study, Journal of Physical Chemistry, 99, pages 13368-13379 (1995)] and adopt non-Linear fit method obtains.

Can select an interval time Δ t suitable or optimum to distinguish an interval time Different compounds. Therefore, must select so interval time, namely in this interval time The time each species brightness value be mutual fine separation. Among Fig. 7 with Δ T₁Show an example, at Δ T₁Repertoire all has different brightness values. Referring to Fig. 7, bad choosing Selecting is Δ T₂, because complicated antibody+protein+polymer has identical with dyestuff in this interval time Brightness.

In the mixture of antibody, protein and polymer, may at the compound that table 1 is listed Occur. Can utilize the characteristic properties of individual molecule that mixture is determined in the dependence of interval time In these compounds in each molar concentration. This is for measuring with the standard dilution series Binding constant is particular importance. The brightness song of sample that contains the mixture of S kind different plant species Line (has predetermined luminance function μ separately_max，s(Δ t), s=1,2 ..., S) by

${\mathrm{\&mu;}}_{\max }\left(\mathrm{\&Delta;t}\right)=\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\max ,s}^2\left(\mathrm{\&Delta;t}\right)\&CenterDot;X_s/(\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\max ,s}\left(\mathrm{\&Delta;t}\right)\&CenterDot;X_s)$

Provide. Parameter X_sS=1,2 ..., S can enough nonlinear fittings determines, and described the relative molfraction of ingredient s,

$X_s=c_s\&CenterDot;/\underset{i=1}{\overset{S}{\mathrm{\&Sigma;}}}{c}_i$

c _sThe concentration of component s. In this example, referring to table 1, the number of component is 4. Must use Four luminance functions shown in Figure 7 come to obtain corresponding molfraction by the Nonlinear Quasi hop algorithm X_s s＝1，2，3，4。

Claims (48)

1. the method for the characteristic properties of the sample of a particle of determining to contain at least one species, the emission in the observation capacity of described particle, scattering and/or refraction photon is characterized in that this method comprises the steps:

1) will be in observing time $T=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{t}_i$ Continuous time interval Δ t _i=[t _I-1, t _i) (i=1,2,3 ...) and in the number n of photo-event of registration _i(counting rate) registered and counted,

2) determine the photo-event number n in the interval of delta t at the fixed time distribution function p (n) and

3) use distribution function p (n), concentration c, each photo-event in expectation just to be derived from the gedanken experiment of single particle the single particle distribution function P of the photo-event number n that expects in the interval of delta t at the fixed time ₁(n) and useful capacity V _ErrThe m of :=＜〉/ theory relation between the c determines P ₁(n), V _Eff, concentration c and/or further feature character, wherein＜m be the average of particle that each counting rate is worked, it can carry out match by the p (n) with these character and measurement and determine.

2. the method for claim 1 is characterized in that, based on the single particle distribution function P of Markovian process theory ₁(n) provide by following formula

$P_1\left(n\right)=1/V_{\mathrm{eff}}\underset{R^3}{\&Integral;}\mathrm{Poi}(n,\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right))\mathrm{dV},$

Wherein, P ₁(n=0)=0, wherein

The luminance function of expression particle, it is by in the position The mean value of photo-event of single particle and Poisson distribution Poi (n, μ)=exp (μ) μ ⁿ/ n! Definition.

3. method as claimed in claim 1 or 2 is characterized in that luminance function By to a plurality of positions

Measure μ and between these positions interpolation μ determine.

4. method as claimed in claim 1 or 2 is characterized in that luminance function

By determining based on the theoretical model of molecular fluorescence spectral theory and the given model of space laser intensity.

5. as arbitrary described method in the claim 1 to 4, it is characterized in that P ₁(n) by luminance function

Determine.

6. as arbitrary described method in the claim 1 to 4, it is characterized in that V _EffBy luminance function

Determine.

7. method as claimed in claim 1 or 2 is characterized in that luminance function

By P ₁(n) or V _EffDetermine.

8. method as claimed in claim 7 is characterized in that P ₁(n) or V _EffDirectly measured.

9. as arbitrary described method in the claim 1 to 8, it is characterized in that the particle of same species fluoresces or uses fluorescence labeling, and is excited by laser beam.

10. method as claimed in claim 9 is characterized in that luminance function

Maximal value determine by the first moment of distribution function

${\mathrm{\&mu;}}_{\max }=\frac{v_2\left(p\right)-v_1^2\left(p\right){-v}_1\left(p\right)}{v_1\left(p\right)}$

11. method as claimed in claim 9 is characterized in that, luminance function

Maximal value determine by the first moment and the noise contributions of distribution function

${\mathrm{\&mu;}}_{\max }=\frac{v_2\left(p\right)-v_1^2\left(p\right){-v}_1\left(p\right)}{v_1\left(p\right)-{<n>}_{\mathrm{noise}}}$

12. method as claimed in claim 9 is characterized in that, luminance function

By having parameter a _jWith different luminance functions (j=1,2 ..., different luminance function K)

$\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right)=\underset{j}{\mathrm{\&Sigma;}}{a}_j{\mathrm{\&mu;}}_j\left(\stackrel{\&RightArrow;}{r}\right)$

Stack come modeling.

13. method as claimed in claim 12 is characterized in that, each luminance function

(j=1,2 ..., K) by M characteristic parameter μ of given number _Jk(k=1,2 ..., M) determine.

14. method as claimed in claim 9 is characterized in that, luminance function

By the space Gaussian distribution

$\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right):={\mathrm{\&mu;}}_{\max }\exp (-2r^2/a^2),$

Come modeling, wherein μ _MaxBe in the heart the brightness of particle in the laser spot, a represents the waist parameter of laser beam.

15. method as claimed in claim 9 is characterized in that, luminance function

By having parameter μ _J1And μ _J2(j=1,2 ..., Gaussian distribution K)

$\mathrm{\&mu;}\left(\stackrel{\&RightArrow;}{r}\right)=\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&mu;}}_{j1}\exp (-2r^2/{\mathrm{\&mu;}}_{j2}^2)$

Stack come modeling.

16. method as claimed in claim 13 is characterized in that, characteristic parameter μ _Jk(j=1,2 ..., K; K=1,2 ..., M) determine by the standard method of deconvoluting.

17. method as claimed in claim 13 is characterized in that, characteristic parameter μ _Jk(j=1,2 ..., K; K=1,2 ..., M) determine by iteration Richardson-Lucy deconvolution algorithm.

18. the method for claim 1 is characterized in that, single particle distribution function P ₁(n) by

$P_1\left(n\right)=1/V_{\mathrm{eff}}\underset{R^3}{\&Integral;}P(n,\stackrel{\&RightArrow;}{r})\mathrm{dV}$

Provide, wherein

Be at time point t ₀Be positioned at the position

Single particle at time interval t ∈=[t ₀, t ₀+ Δ t) distribution of the number of the photo-event of counting during.

19., it is characterized in that based on the Markovian process theory, (n is c) with single particle distribution function P at probability distribution function p in use as arbitrary described method in the claim 1 to 18 ₁(n) theory relation between

$p(n,c)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{Poi}(m,<m>)P_m\left(n\right),$

P wherein _m(n) expression single particle distribution function P ₁(n) m convolution

$P_m\left(n\right)=\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{P}_{m-1}(n-i)P_1\left(i\right),$ m＝2，3，...，

，

With

P ₀(n)＝δ _n，0。

20., it is characterized in that (n c) passes through recursion formula to probability distribution function p as arbitrary described method in the claim 1 to 19

$p(n,c)=\frac{c{V}_{\mathrm{eff}}}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}i{P}_1\left(i\right)p(n-i,c)$

Calculate, wherein,

p(n＝0，c)＝exp(-cV _eff)。

21., it is characterized in that the concentration c of particle is that 0 probability is determined by obtaining counting rate as arbitrary described method in the claim 1 to 20:

c＝-ln(p(n＝0，c))/V _eff。

22., it is characterized in that the concentration c of particle is 0 probability and noise contributions＜n by obtaining counting rate as arbitrary described method in the claim 1 to 20 〉 _NoiseDetermine:

c＝[-ln(p(n＝0，c))-<n> _noise]/V _eff。

23., it is characterized in that the average number＜m of particle as arbitrary described method in the claim 1 to 22〉be that 0 probability is determined by obtaining counting rate:

<m>＝-ln(p(n＝0，c))。

24., it is characterized in that the average number＜m of particle as arbitrary described method in the claim 1 to 22〉be 0 probability and noise contributions＜n by obtaining counting rate _NoiseDetermine:

<m>＝-ln(p(n＝0，c))-<n> _noise。

25., it is characterized in that single particle probability distribution function P as arbitrary described method in the claim 1 to 24 ₁(n) pass through recursion formula:

$P_1\left(n\right)=\frac{1}{p(0,c)}[\frac{p(n,c)}{<m>}-\frac{1}{n}\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}i{P}_1\left(i\right)p(n-i,c)]$

Calculate.

26. as arbitrary described method in the claim 1 to 25, it is characterized in that, distribution function p (n, c) by with the Poisson distribution convolution

$p_{\mathrm{tot}}(n,c,{<n>}_{\mathrm{noise}})=(p\left(c\right)\&CircleTimes;\mathrm{Poi}\left({<n>}_{\mathrm{noise}}\right))\left(n\right)$

Determine to consider extra background signal (for example random noise of hardware).

27. as arbitrary described method in the claim 1 to 26, it is characterized in that, determine by standard nonlinear multi-parameter fitting process according to the characteristic properties of the step (3) of claim 1.

28. as arbitrary described method in the claim 1 to 26, it is characterized in that, determine by standard square method according to the characteristic properties of the step (3) of claim 1.

29. method as claimed in claim 28 is characterized in that, the square of single particle probability distribution function passes through recursion formula:

$v_k\left(P_{\text{1}}\right)=\frac{1}{<m>}[v_k\left(p\right)-{<n>}_{\mathrm{noise}}-\underset{l=1}{\overset{k-1}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}k-1\\ l-1\end{array}\right)v_{k-1}\left(p\right)\{{<n>}_{\mathrm{noise}}+<m>v_l\left(P_1\right)\left\}\right]$

Calculate.

30. as arbitrary described method in the claim 24,26 and 29, it is characterized in that noise contributions＜n 〉 _NoiseBy use without any the media fluid of the sample of described species particle or use and sample have same or similar character liquid so that＜n _NoiseIn the step (3) of claim 1, fix and directly measure.

31. the method for the characteristic properties of the sample of the potpourri of a particle of determining to contain N different plant species, the emission in the observation capacity of described particle, scattering and/or refraction photon is characterized in that the population distribution function p (n of potpourri; c ₁, c ₂..., c _N) by single species effect p ^(s)(n; c _s), s=1,2 ..., the convolution of N is determined:

$p(n;c_1,c_2,\&CenterDot;\&CenterDot;\&CenterDot;,c_N)=$

$p^{\left(1\right)}(n;c_1)\&CircleTimes;p^{\left(2\right)}(n;c_2)\&CircleTimes;\&CenterDot;\&CenterDot;\&CenterDot;\&CircleTimes;p^{\left(N\right)}(n;c_N)$

$\&CircleTimes;\mathrm{Poi}(n,{<n>}_{\mathrm{noise}}),$

Single thus species effect p ^(s)(n; c _s) be according to one of in the claim 1 to 30 by predetermined useful capacity V _Eff, each species s of in potpourri, existing single particle distribution function P ₁ ^(s)(n) and given experiment assembling determine.

32. method as claimed in claim 31 is characterized in that, parameter c _s, (s=1,2 ..., N) and noise contributions＜n _NoiseDetermine by the nonlinear fitting that uses preset parameter and theoretical model.

33., it is characterized in that p (n as claim 31 or 32 described methods; c ₁, c ₂..., c _N) calculating accelerate by generating.

34., it is characterized in that the parameter of requirement is definite by the square method, thus p (n as claim 31 or 32 described methods; c ₁, c ₂..., c _N) square by p ^(s)(n; c _s) the product of square represent, s=1,2 ..., N.

35. the characteristic properties E of the sample of a particle of determining to contain at least one species ₁..., E _LMethod, the emission in predetermined observation capacity of described particle, scattering and/or refraction photon is characterized in that this method comprises the steps:

1) will be in observing time $T=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{t}_i$ Continuous predetermined time interval Δ t _i=[t _I-1, t _i) (i=1,2,3 ...) and in the number n of photo-event of registration _i(counting rate) registered and counted, wherein Δ t _i=: Δ t=constant,

2) determine the photo-event number n in the interval of delta t at the fixed time distribution function p (n) and

3) according to carrying out other step one of in the claim 1 to 34;

Also comprise further step:

4) use different time interval Δ t ^k(k=1 ..., K) repeating step 1) to 3) K time, determine identical characteristic properties E by these steps of each series ₁..., E _L,

5) determine characteristic properties E ₁..., E _LTo Δ t ^kDependence,

6) from determine other characteristic of optimum Δ t or particle according to the dependence of the measurement of step 5).

36. method as claimed in claim 35 is characterized in that, time interval Δ t ^k(k=1 ..., K) 10 ^-6Between second and 1 second.

37., it is characterized in that time interval Δ t as claim 35 or 36 described methods ^k(k=1 ..., K) be chosen as on logarithmically calibrated scale equidistant.

38. method as claimed in claim 37 is characterized in that, Δ t ^k=0.8 ^kSecond, k=0 wherein ..., 72.

39. as the described method of claim 35 to 38, it is characterized in that, by standard fit procedure match carried out in the dependence of given analytic function and measurement according to step 5).

40., it is characterized in that, according to step 4) and 5 as arbitrary described method in the claim 35 to 39) characteristic properties E ₁..., E _LIn one be the specific species of the particle in the sample.

41., it is characterized in that, according to step 4) and 5 as arbitrary described method in the claim 35 to 40) characteristic properties E ₁..., E _LIn at least some be the part concentration of the particle of several species in the potpourri in the sample.

42., it is characterized in that, will rely on according to the measurement of step 5) and compare, with the part concentration of the particle of the specific species of the particle in the recognition sample or specific species with dependence of having measured or theory function as arbitrary described method in the claim 35 to 41.

43. method as claimed in claim 39 is characterized in that, will measure to rely on by nonlinear fitting according to the stack of the dependence of having measured or theory function and introduce, with the part concentration of the particle of the specific species of determining the particle in the sample or specific species.

44. method as claimed in claim 42 is characterized in that, measures distribution function p (n ^k, Δ t ^k) (k=1 ..., K), and by suitable fit procedure, from p (μ ^k, Δ t ^k) determine high-high brightness μ _Max(Δ t) is as characteristic properties.

45. method as claimed in claim 44 is characterized in that, as further step, by suitable fitting function, from μ _Max(Δ t) determines the μ of limit Δ t → 0 o'clock _Max(Δ t), diffusion motion, diffusion time τ _DAnd/or the structural parameters SP of device.

46. as claim 44 or 45 described methods, it is characterized in that, wherein, as further step, from μ _Max(Δ t) determines τ die-away time _μAnd/or the ratio of the specific species of particle in the sample.

47. method as claimed in claim 44 is characterized in that, in the sample of the particle that several species are arranged, determines μ _Max(Δ t), and pass through formula

${\mathrm{\&mu;}}_{\max }\left(\mathrm{\&Delta;t}\right)=\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\max ,s}^2\left(\mathrm{\&Delta;t}\right)\&CenterDot;X_s/\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\max ,s}\left(\mathrm{\&Delta;t}\right)\&CenterDot;X_s$

By μ previous measurement or that otherwise determine _{Max, s}(Δ t) determines the molar ratio X of species s in the sample _s

48. method as claimed in claim 44 is characterized in that, in the sample of the particle that several species s is arranged, determines μ _Max(Δ t), and pass through parameter 0≤X _s≤ 1 (s=1 ..., S) and boundary condition $\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}{X}_s=1$ Carry out nonlinear fitting and determine the molar ratio X of species in the sample _s

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