CN102103078A - High-accuracy surface plasmon resonance (SPR) detection method - Google Patents

Abstract

The invention discloses a high-accuracy surface plasmon resonance (SPR) detection method. In the method, signal acquisition is performed on the same SPR detection system for multiple times under the same experimental condition to acquire a plurality of SPR curves with micro random translation, relative micro translation among the plurality of SPR curves is estimated, and an expected absolute position vector is further estimated on the basis, so that position uncertainty in the acquisition process of the SPR curves is avoided; meanwhile, by fusing different information among the plurality of SPR curves with the micro translation, a more accurate SPR curve with higher sampling density is acquired through estimation at the expected absolute position, so that the accuracy of the acquired SPR sensing information and the detection limit of an SPR system are improved.

Description

A kind of high-precision surface plasma resonance detection method

Technical field

The present invention relates to sensor and field of sensing technologies.The present invention is specifically related to realize the detection method and the relevant information disposal route of surface plasma resonance sensing.

Background technology

Surface plasma resonance (Surface Plasmon Resonance, SPR) be a kind of physical optics phenomenon that occurs on metallic film and the dielectric interphase, since 20 th Century are found, because of advantages such as it is unmarked, real-time, not damaged detection are widely used in sensing, bio-sensing field particularly.

The SPR sensor-based system comprises optical system, sensing arrangement, detector and data handling system etc.In the optical system, light source output P polarized light is coupled into sensor by certain optical element.Be extensive use of at present and the SPR coupled structure of the easiest realization is based on the Kretschman structure of prism-coupled mode, its typical structure comprises three layers: glass prism-metal level-solution layer to be measured.

When the incident light of P polarization when necessarily being mapped to prism/metal interphase greater than the angle of the angle of total reflection, the evanescent wave that forms in metallic film vibrates with metal surface free electron generation surface plasma.When surface plasma-wave wave vector and incident light when the wave vector component of metal tangential direction equates, the incident light energy is coupled to surface plasma-wave, reaches surface plasma resonance, thereby causes energy of reflection light significantly to reduce, and the phase place marked change.Be embodied in the spr signal that observes, intensity of reflected light spectrum goes up because light intensity sharply reduces to produce a sharp-pointed resonance absorbing peak, and the phase place of reflecting light also produces saltus step thereupon, and this moment, corresponding incident angle of light or wavelength was called resonance angle or resonant wavelength.Because spr signal is very responsive to the variation of the SOLUTION PROPERTIES to be measured on metallic film surface, the SPR sensing technology is exactly by the detection to intensity of reflected light or phase spectrum, obtain the information such as kinetic parameter of refractive index, concentration and the biochemical reaction of sensing surface solution to be measured, thereby reach the purpose of biochemistry detection.

According to the difference of SPR transducing signal check and analysis method in the system, the SPR sensor-based system can be divided into following four kinds:

(1) angle scanning intensity detection: monochromatic light incident, change incident angle, the normalized intensity of detection of reflected light is with the situation of change of incident angle, and record intensity of reflected light incident angle hour, just resonance angle;

(2) length scanning intensity detection: polychromatic light incident, be fixed into firing angle, catoptrical spectrum is analyzed, obtain reflectivity with the wavelength change curve, and the record resonant wavelength;

(3) intensity modulated: the angle and the wavelength of incident light are all fixed, by the mutation analysis change of refractive of detection of reflected light intensity; Must set up the relation between resonance point place reflective light intensity and the refractive index.

(4) phase modulation (PM): the angle and the wavelength of incident light are all fixed, observation incident light and catoptrical phase differential; Must set up the relation between resonance phase place and the refractive index.

In these four kinds of methods, (3) to plant the error that disturbed movable property gives birth to bigger, not too practical, generally is used for the fast change procedure of test sample refractive index; The sensitivity of last a kind of method is the highest, but system needs a series of high-frequency circuit; Therefore preceding two kinds application is the most general.

In traditional angle scanning intensity detection SPR system, light source is fixed, and sensor-based system and detector are placed on the turntable, realizes the angle scanning of sensing surface incident light by rotating table.Point of the every scanning of traditional method will change the angle of an incident light, so obtain the chronic of a SPR angle scanning curve consumption.The proposition of focused light angle scanning SPR sensor-based system has overcome the shortcoming of using traditional SPR sensor-based system angle scanning length consuming time.In focused light angle scanning SPR sensor-based system, the light of light emitted arrives the metal surface by a lens focus, photodetector array (as CCD, CMOS or photodiode array) is accepted the reflected light from each angle of focus point, thereby disposablely obtained a SPR angle scanning sensing curve, significantly reduced sweep time.Therefore focused light angle scanning SPR system has obtained widespread use.

In the spr signal gatherer process,, promptly on position axis, there be " little translation " because the moving introducing of perturbations such as system mechanics vibration can cause between the SPR curve of repeatedly gathering to have small site error inevitably.Repeatedly the little translation between the SPR curve of Cai Jiing shows as the integral body of curve on position axis and moves, and each intensity noise of introducing of gathering has random character.Therefore, in order to overcome the position uncertainty in the SPR curve gatherer process, the present invention proposes to have the SPR curve of little translation and estimate little relatively translation between them by gathering many, thereby further estimates to obtain an expectation absolute position vector.This expectation absolute position vector is that the nothing that the spr signal that once do not have a site error is gathered resultant position vector is estimated partially, and its estimation has utilized the probability distribution information of little relatively translation between many curves.

On the other hand, the order of accuarcy of SPR heat transfer agent also is subjected to the restriction of SPR curve sampling density.Sampling density is big more, and the interval between the check point is more little, and SPR sensing curve approaches continuously more, thereby the heat transfer agent that is obtained is also accurate more.And have different information between the SPR sensing curve that repeatedly collects with little translation, should be fully used.If accurately between estimation curve less than the little translation at interval of sampled point, by merging these many different information between the SPR curve with little translation, then can increase SPR curve sampling density, thereby improve the accuracy of SPR heat transfer agent and the detection limit of SPR system.

Summary of the invention

Therefore, task of the present invention is: for the position uncertain problem that is brought by the moving grade of perturbation in the spr signal gatherer process, have the SPR curve of little translation and to estimate little relatively translation between them by under same experimental conditions, repeatedly gathering, thereby further to estimate an expectation absolute position vector; Simultaneously, by merging many different information between the SPR curve with little translation, in the pairing position range of this expectation absolute position vector, estimate to obtain a SPR curve more accurate, that sampling interval is littler, thereby improve the accuracy of the SPR heat transfer agent that obtains and the detection limit of SPR system.

This method comprises following step:

1. many spr signal collections

In the SPR detection system, under same experimental conditions, carry out N spr signal collection, obtain the SPR curve Y that the N bar has small translation at random ₁, Y ₂... Y _N

2. little translation is estimated

Choose any SPR curve Yr as the reference curve, estimate each SPR curve Y _i(i=1,2 ..., N) and the little translation Motion between the reference curve _{R, i}(i=1,2 ..., N).Wherein, Motion _{R, i}Be 0, and estimate little translation Motion _{R, j}Accuracy requirement less than a unit sampling interval.Can be lower than 1/q sampling interval if estimate little translation precision, SPR curve sampling density can improve q doubly so.The concrete grammar that little translation is estimated between curve can adopt related function method, intensity method of interpolation, the differential method, phase correlation method etc.

3. expectation absolute position vector is estimated

If each SPR curve all has L data point, reference curve Y _rOn j point Y _{R, j}Pairing position is P _{R, j}(j=1,2 ..., L).Utilize each SPR curve Y _iWith respect to reference curve Y _rLittle translation Motion _{R, i}(i=1,2 ..., N), estimate expectation absolute position vector with respect to reference curve Y _rThe integral translation deviation delta Motion of pairing absolute position vector.Δ Motion is equivalent to each SPR curve Y _i(i=1,2 ..., N) with respect to reference curve Y _rAn expectation skew, so expectation absolute position vector is P _{R, j}+ Δ Motion (j=1,2 ..., L), each SPR curve Y _iCorresponding absolute position vector is Motion with respect to little translation of expectation absolute position vector _{R, i}-Δ Motion (i=1,2 ..., N).Wherein, the method for estimation of Δ Motion can be different according to the probability distribution of repeatedly gathering the little translation between the SPR curve, comprise square estimation, least-squares estimation and maximum likelihood estimation etc.

4. information fusion

On the basis of accurately estimating expectation absolute position vector and relative its little translation of each SPR curve, in the pairing position range of the expectation absolute position of above-mentioned estimation vector, utilize information fusion algorithm to merge many SPR curve Y ₁, Y ₂... Y _NBetween different information, and add some prior-constrained to the SPR curvilinear characteristic, the slickness that comprises the SPR curve, and the various features of the SPR curve that calculates with Fresnel equation scheduling theory formula etc., thus obtain expecting the SPR curve of a high sampling density on the vector of absolute position

Wherein, information fusion algorithm can use maximum a posteriori probability (MAP, Maximum A Posterior) the constrained optimization problem is converted into unconstrained optimization problem, also can directly uses convex set projection (POCS, Projections On Convex Sets) method to solve the constrained optimization problem.When the no constrained minimization problem that uses the MAP algorithm that former constrained optimization problem is transformed into, can use no constrained minimization algorithms such as method of conjugate gradient and quasi-Newton method.

5.SPR information extraction

From the more high sampling density curve of estimating through information fusion algorithm to obtain

In, adopt general information extraction, disposal route to the SPR curve, can extract SPR heat transfer agents such as obtaining resonant position, system's detection limit.

The present invention has the following advantages:

1. the present invention has on the SPR curve basis of small translation at random many of collections, probability distribution according to little translation between curve, estimate to obtain an expectation absolute position vector, and on this expectation absolute position vector, calculate a new curve that merges these many SPR calibration curve informations, thereby can eliminate because the position uncertainty that little translation of introducings such as the little shake of system brings.

2. the way of the present invention by signal Processing merges many different information between the low sampling density SPR curve with little translation, by algorithm it is merged synthetic one and have the more high precision SPR curve of high sampling density, this means and to improve sampling precision by repeated measurement under same experimental conditions, thereby can improve the precision that the SPR heat transfer agent is extracted, and the system of improvement detection limit, for the lower SPR system of scanning accuracy own (primary curve that experiment obtains is low sampling density SPR curve), this method can be by increasing certain hour cost (generally very little), significantly improve the precision and the detection limit of system, have high precision, advantage cheaply.

Description of drawings

Below, describe embodiments of the invention in conjunction with the accompanying drawings in detail, wherein:

Fig. 1 is a high precision SPR sensing detection method process flow diagram proposed by the invention;

Fig. 2 is corresponding to a kind of focused light angle scanning SPR sensor-based system synoptic diagram in the embodiment;

Fig. 3 is in the focused light angle scanning SPR system, repeatedly the little translation synoptic diagram between the SPR curve of Cai Jiing;

Fig. 4 is the theoretical high sampling density spr signal that obtains according to the wave optics Theoretical Calculation;

Fig. 5 is many low sampling density SPR curve collection models with little translation;

Fig. 6 is many low sampling density SPR curves with little translation that emulation obtains;

Fig. 7 is the little translation method of estimation process flow diagram that uses among the present invention;

Fig. 8 is to use the evaluated error of 100 low sampling density curves of little translation method of estimation processing among the present invention;

Fig. 9 is to use the MAP information fusion algorithm to handle many results with low sampling density SPR curve of little translation among Fig. 5;

Figure 10 is the partial enlarged drawing of Fig. 9;

Embodiment

The invention provides a kind of high precision SPR sensing detection method.Have the low sampling density SPR curve of little translation and to estimate little relatively translation between them by under same experimental conditions, repeatedly gathering, thereby further estimate an expectation absolute position vector, then by merging many different information between the low sampling density SPR curve with little translation, in the corresponding position range of this expectation absolute position vector, estimate to obtain more accurate more high sampling density sensing curve, thereby improve the accuracy of the SPR heat transfer agent that obtains and the detection limit of SPR system.

Fig. 1 has provided the process flow diagram of this detection method, and it mainly comprises repeatedly spr signal collection 101, and little translation estimates 102, and expectation absolute position vector estimates 103, information fusion 104, and 105 5 steps of SPR information extraction.

SPR system in this example adopts focused light angle scanning SPR sensor-based system, and its structure as shown in Figure 2.The diverging light that light source 201 sends focuses on the interface of prism 204 and metallic film 205 through lens 202 and polaroid 203 formation monochromatic light.Photodetector array 207 is accepted from the reflected light of each angle of focus point and is translated into electric signal, thus a SPR angle scanning of disposable acquisition sensing curve.Electric signal enters computing machine 209 by digital-to-analog conversion 208 and carries out signal Processing, to obtain the heat transfer agent about detected solution 206.

Because there is whole little translation in the existence that the perturbations such as relative shake that are difficult to avoid between photoelectronic detecting array 207 and the sensor-based system are moving between the SPR angle scanning curve of repeatedly gathering under same experimental conditions, its concrete implication can be illustrated by Fig. 3.Shown in solid line among the figure, establish reflected light and disperse on the 1st to L pixel of detector, if each pixel is regarded as the combination of q sub-pixel, reflected light is equivalent to disperse on the 1st to qL sub-pixel so; If a small shake takes place between photodetector array 207 and the sensor-based system in the acquired signal process, reflected light is dispersed on the 2nd to qL+1 sub-pixel, as shown in phantom in FIG..Because little shake has randomness,, have different information between them under same experimental conditions so the SPR angle scanning curve of repeatedly gathering has sub-sampling little translation at interval.The present invention is exactly by estimating many little translations between the low sampling density SPR curve with little translation, further estimate to obtain an expectation absolute position vector, and on this absolute position vector, pass through to merge more accurate high sampling density curve of different information calculations of these many curves.

Through step 101, obtain many low sampling density SPR curves with little translation.

In order to verify that better the present invention proposes the performance of algorithm, the gatherer process of many low sampling density SPR curves with little translation has been carried out modeling and simulating.

With the light intensity of continuous function x (p) expression moment t on detector array column position p.If detector array is on average divided L the pixel that width is w, make Y (k), (k=1,2 ..., L) k optical signal value that pixel collects of expression has

$Y\left(k\right)={\∫}_{\mathrm{wk}}^{w(k+1)}x\left(p\right)\mathrm{dp}---\left(1\right)$

If the sampling density of detector array is increased q doubly, each pixel is divided into q sub-pixel, then the optical signal value X (l) (l=1,2 that collect of each sub-pixel ..., qL) be

$X\left(l\right)=q{\∫}_{\frac{w}{q}l}^{\frac{w}{q}(l+1)}x\left(p\right)\mathrm{dp}---\left(2\right)$

In order to keep same relative signal intensity, (2) have been multiplied by spreading factor q behind integration.

Under the situation that does not have little translation and noise, by (1) (2) formula can find out low sampling density curve Y (k) (k=1,2 ..., L) with high sampling density curve X (l) (l=1,2 ..., qL) between just like the integral relation that rolls off the production line

$Y\left(k\right)=\frac{1}{q}\underset{l=\mathrm{qk}}{\overset{q(k+1)-1}{\mathrm{\Σ}}}X\left(l\right)---\left(3\right)$

Being write as matrix form is

Y _L×1＝D _L×qLX _qL×1 (4)

Wherein the line integral matrix is

Fig. 4 has provided the theoretical high sampling density spr signal that calculates.According to the wave optics theory, theoretical high sampling density SPR curve X can calculate by fresnel formula.The theoretical high sampling density SPR curve that obtains by modeling and simulating for after the estimation high sampling density SPR curve that obtains by algorithm of the present invention provide an accurate comparison other, therefore better evaluation algorithms effect.

Fig. 5 has provided many low sampling density SPR curve collection models with little translation, high sampling density curve X is the vector of qL * 1, pass through little translation Mi, line integral D respectively, and add separate additive white Gaussian noise ni, just obtained the low sampling density SPR curve Yi (i=1 of reality that the N bar has little translation, 2 ..., N):

Y _i＝DM _iX+n _i，i＝1，2，....N (6)

Wherein, Mi is little translation matrix of qL * qL, makes mobile at random mi the sub-pixel of X respectively.(6) Mi in the formula can merge into Di with the line integral matrix D, shows as to make the mobile at random mi row of D:

Y _i＝D _iX+n _i，i＝1，2，....N (7)

Being write (7) formula as a matrix equation is

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ Y_N\end{array}\right]=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="DM"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">DM</figure-callout>}}_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\mathrm{DM}}_N\end{array}\right]X+\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_N\end{array}\right]=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ D_N\end{array}\right]X+\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_N\end{array}\right]\&DoubleLeftRightArrow;Y=\mathrm{DX}+n---\left(8\right)$

Fig. 6 is that many of obtaining according to above-mentioned gatherer process model emulation have the actual sampling density SPR curve that hangs down of little translation.Wherein, low sampling density curved line is counted N=5, and the angle scanning scope is 34～37 °.In the emulation of this example, suppose that collecting catoptrical photodetector array 207 is Larry-USB 1024-D7231 detector arrays of AMES Photonics company.According to laser radius and detector array specification (Pixel Dimensions, dark current noise, read noise and half full well productivity), can calculate low sampling density curve sampled point probably about 400, signal to noise ratio (S/N ratio) surpasses 10 ⁵Therefore, the noise that adds 50dB in the emulation to low sampling density curve.

Accurately the little translation in interval of the sub-sampling between estimation curve is the precondition of different information between blend curve, and it is relevant with sampling density target raising multiple q that estimated accuracy requires, and estimates that little translation precision should be lower than 1/q sampling interval at least.What use in this example is the way of intensity interpolation, and Fig. 7 has provided the little translation method of estimation of the step of using in this example 102 process flow diagram.

701. given initial value: interpolation point multiple q, smothing filtering coefficient p, current translation precision pixAcc=1, target translation precision aimPixAcc; Selected Y ₁Be the low sampling density curve Y of reference _r, low sampling density curve Y after the translation _i, Y _iWith respect to reference curve Y _rCurrent translation be Motion _{R, i}=0, (i=1,2 ..., N);

702. to curve Y after the translation _iWith reference curve Y _rCarry out p rank smothing filtering, promptly adjacent p point is averaged, and obtains FY _iAnd FY _r

703. for k=-q ,-(q-1) ..., (q-1), q, translation reference curve Y _r, obtain transFY _{R, i}(k)=trans (FY _r, Motion _{R, i}+ k*pixAcc), curve transFY after the calculating translation _{R, i}(k) and FY _iBetween related function Corr _i(k)=and ∑ | transFY _{R, i}(k)-FY _i|;

704. ask the related function minimum value, pairing k value kmin _i=argmin (Corr _i(k)) be translation renewal amount under the current precision pixAcc;

705. the renewal translational movement, Motion _{R, i}=Motion _{R, i}+ kmin _i* pixAcc;

706. if current translation precision pixAcc greater than target translation precision aimPixAcc, continued to enter 707 steps,, finish algorithm if do not satisfy;

707. to FY _rAnd FY _iCarry out spline interpolation, FY _r=spline (FY _r, q), FY _i=spline (FY _i, q), and upgrade current translation precision pixAcc=pixAcc/q, returned for 702 steps.

Fig. 8 has provided and has used above-mentioned little translation method of estimation, and 100 400 low sampling density SPR curves that add the 50dB white Gaussian noise are carried out the evaluated error that little shake is estimated, mean absolute error is 0.0282 sampling interval.Therefore as can be seen, the estimated accuracy of above-mentioned little shift method can satisfy the requirement of merging tens low sampling density calibration curve informations.

Owing to have little at random translation between the SPR angle scanning curve of under same experimental conditions, repeatedly gathering, in order to obtain accurate SPR information, need be according to the pairing angle position of data point on this SPR curve of repeatedly gathering, estimate an expectation absolute position vector, and on this vector basis, expectation absolute position, calculate a high sampling density SPR curve X who merges these many SPR calibration curve informations.In this example, expectation absolute position vector is with respect to reference curve Y _rCriterion of least squares is adopted in the estimation of the integral translation deviation delta Motion of pairing position vector, shown in (9) formula,

$\mathrm{\&Delta;}\widehat{\mathrm{Motion}}=\arg \mathrm{Min}\left(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(\mathrm{\&Delta;Motion}-{\mathrm{Motion}}_{r,i})}^2\right)---\left(9\right)$

Wherein, selecting wherein, a curve is reference curve Y _r, Motion _{R, i}Represent each bar low-density sampling curve Y _i(i=1,2 ..., N) with respect to reference curve Y _rLittle translation.Can prove, calculate by (9) formula

Be that expectation absolute position vector is with respect to reference curve Y _rThe integral translation deviation of institute's correspondence position vector asymptotic consistent do not have partially to be estimated.If each low sampling density curve all has L data point, reference curve Y _rOn j point Y _{R, j}Pairing angle position is P _{R, j}(j=1,2 ..., L), so expectation absolute position vector is estimated as (j=1,2 ..., L), each low sampling density curve Y _i(=1,2 ..., N) Dui Ying position vector with respect to little translation of expectation absolute position vector is

(i=1,2 ..., N).

From (8) formula as can be seen, the low sampling density SPR curve Y that has little translation from the N bar _i(i=1,2 ..., the N) problem of a high sampling density SPR curve X of estimation, actual is the problem of finding the solution of an ill-condition matrix equation.By matrix theory as can be known, if there is not the existence of noise item, by high sampling density curve X=Pinv (D) Y that the pseudoinverse Pinv (D) that asks D tries to achieve, actual is the least square solution of this equation, just makes || Y-DX|| ²Minimum separates.But because the adding of random noise has aggravated the pathosis of problem.Thereby, ill-conditioning problem obtains unique solution for being retrained, on little shake basis of accurately estimating between low sampling density SPR curve, can utilize maximum a posteriori probability (MAP, Maximum A Posterior) or convex set projection (POCS, Projection On Convex Sets) method introduce some prior-constrained conditions.Adopt the MAP information fusion method in this example.

According to bayesian theory, known N bar hangs down sampling density curve Y _i(i=1,2 ..., N) posterior probability of a high sampling density SPR curve X of estimation can be expressed as

$P(X/{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;,Y_N)=\frac{P({\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;Y_N/X)P\left(X\right)}{P({\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;Y_N)}---\left(9\right)$

Here P (Y ₁, Y ₂... Y _N/ when being known high sampling density SPR curve X X) low sampling density SPR curve be Yi (i=1,2 ..., conditional probability N); P (X) and P (Y ₁, Y ₂... Y _N) represent the prior probability of high sampling density curve and low sampling density curve respectively.Selection high sampling density curve X by suitable makes posterior probability P (X/Y ₁, Y ₂... Y _N) reach maximum, at this moment Dui Ying X is exactly the optimum estimate of high sampling density curve.Have this moment

$\hat{X}=\arg \mathrm{Max}\left\{P(X/{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;Y_N)\right\}=\arg \mathrm{Max}\left\{\frac{P({\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;Y_N/X)P\left(X\right)}{P({\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;Y_N)}\right\}---\left(10\right)$

P (Y ₁, Y ₂... Y _N) be known, so this formula is equivalent to

$\hat{X}=\arg \mathrm{Max}\{\ln \left(P({\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;Y_N/X)\right)+\ln \left(P\left(X\right)\right)\}---\left(11\right)$

Can suppose low sampling density curve Y _i(i=1,2 ..., it is N) separate,

$P({\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000372206100021.png,HSA00000372206100022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;Y_N/X)=\underset{i=1}{\overset{N}{\mathrm{\&Pi;}}}P(Y_i/X)---\left(12\right)$

Conditional probability P (Y _i/ X) expression noise item and is supposed its Y _iL sampled point satisfy independent Gaussian distribution, have

$P(Y_i/X)=\frac{1}{{\left(2\mathrm{\&pi;}\right)}^{\frac{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">L</figure-callout>}}{2}}{\mathrm{\&sigma;}}_i^L}\exp \left(\frac{1}{-2{\mathrm{\&sigma;}}_i^2}{\left|\right|Y_i-D_{i}X\left|\right|}^2\right)---\left(13\right)$

The prior probability P (X) of high sampling density curve X has adopted Markov random field,

$P\left(X\right)=\frac{1}{Z}\exp \left(\frac{1}{-2\mathrm{\&beta;}}\underset{x\&Element;X}{\mathrm{\&Sigma;}}{\mathrm{\&rho;}}_T\left(d_x\left(X\right)\right)\right)---\left(14\right)$

Wherein, d _x(X) expression curve X is at the second order difference at x point place, ρ _T() selected for use can fine maintenance sharp signal details the Huber function

${\mathrm{\&rho;}}_T\left(x\right)=\left\{\begin{array}{cc}{x}^2,& \left|x\right|\&le;T\\ 2T\left|x\right|-{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HSA00000372206100021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2,& \left|x\right|>T\end{array}\right.---\left(15\right)$

By (12)～(16) formula, (11) but the final abbreviation of formula is a no constrained minimization problem

$\hat{X}=\arg \mathrm{Min}\{\underset{x\&Element;X}{\mathrm{\&Sigma;}}{\mathrm{\&rho;}}_T\left(d_x\left(X\right)\right)+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{\mathrm{\&beta;}}{{\mathrm{\&sigma;}}_i^2}{\left|\right|Y_i-D_{i}X\left|\right|}^2\}---\left(16\right)$

If

And order

(16) become

$\hat{X}=\arg \mathrm{Min}\{\underset{x\&Element;X}{\mathrm{\&Sigma;}}{\mathrm{\&rho;}}_T\left(d_x\left(X\right)\right)+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&lambda;}{\left|\right|Y_i-D_{i}X\left|\right|}^2\}---\left(17\right)$

Given suitable parameter T and λ can select for use quasi-Newton method, method of conjugate gradient etc. to solve the no constrained minimization problem that (17) formula is described, thereby obtain the best high sampling density curve under the MAP estimation

This example adopts quasi-Newton method.

Fig. 9 is on the basis of 5 400 low sampling density SPR curves of adding 50dB white Gaussian noise shown in Figure 6, uses the estimated result that the MAP information fusion algorithm obtains among the present invention.Wherein establish T=0.002, the high sampling density curve that obtains is estimated in λ=0.01

Shown in " x " among the figure.

Figure 10 is the partial enlarged drawing of Fig. 9, and the theoretical high sampling density curve of representing with solid line is a standard, and estimation obtains as can be seen Not only sampled point has been increased to 2000 from 400, and compared with the low sampling density curve Yr of the reference of ". " expression more near theoretical curve.

The MAP information fusion algorithm has been attached to the image priori in the middle of the mathematical model easily, utilizes prior-constrainedly, successfully solved the former problem of morbid state.

With theoretical SPR curve X in the emulation is standard, and this paper has adopted least absolute error MAE, and as estimating the estimation curve standard of accruacy, it has reflected the average degree of closeness of curve each point and typical curve.

$\mathrm{MAE}=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}|\hat{X}\left(i\right)-X\left(i\right)|---\left(17\right)$

As the estimated result among Fig. 9, the low sampling density curve Y of reference before MAP estimates _rWith the MAE of theoretical curve be 1.087e-3, the estimation high sampling density curve after MAP estimates

With the MAE of theoretical curve be 5.685e-4.As can be seen, the MAP algorithm has improved the accuracy of curve greatly when having increased the curve sampling density.

Claims (10)

1. high-precision surface plasma resonance detection method may further comprise the steps:

(1) repeatedly the SPR curve is gathered: under same experimental conditions, same SPR detection system is carried out signals collecting N time, in each the collection, obtain a SPR curve by identical sampling interval, thereby obtain the SPR curve Y that the N bar has small translation at random ₁, Y ₂... Y _N

(2) little translation is estimated: choose in the above-mentioned N bar SPR curve one as reference curve Y _r, estimate each SPR curve Y _i(i=1,2 ..., N) and the little translation Motion between reference curve _{R, i}

(3) expectation absolute position vector is estimated: establish reference curve Y _rPairing absolute position vector is P _r, utilize above-mentioned each SPR curve Y _iWith respect to reference curve Y _rLittle translation Motion _{R, i}, estimate expectation absolute position vector with respect to reference curve Y _rThe integral translation deviation delta Motion of absolute position vector, the expectation absolute position that obtains estimating vector P _r+ Δ Motion;

(4) information fusion: on the basis of accurately estimating expectation absolute position vector and relative its little translation of each SPR curve, in the pairing position range of the expectation absolute position of above-mentioned estimation vector, utilize information fusion algorithm to merge many SPR curve Y ₁, Y ₂... Y _NBetween different information, add the prior-constrained of SPR curve, thereby obtain expecting a SPR curve on the vector of absolute position with littler sampling interval

(5) SPR information extraction: from the SPR curve of above-mentioned low sampling interval The middle extraction obtains the SPR heat transfer agent.

2. according to claim 1 described detection method, it is characterized in that, have small integral translation at random between the SPR curve of repeatedly gathering in the described step (1), show as the integral body of curve on position axis and move, and each intensity noise of introducing of gathering has random character.

3. according to claim 1 described detection method, it is characterized in that the estimated accuracy of the little translation method of estimation in the described step (2) must be less than a unit sampling interval.

4. according to claim 1 described detection method, it is characterized in that the little translation method of estimation in the described step (2) comprises related function method, intensity method of interpolation, the differential method and phase correlation method.

5. detection method according to claim 1 is characterized in that, in the described step (3), the Δ Motion that estimates is that expectation absolute position vector is with respect to reference curve Y _rThe nothing of the integral translation deviation of absolute position vector is estimated partially.

6. according to claim 1 and 5 described detection methods, it is characterized in that, in the described step (3) to expectation absolute position vector with respect to reference curve Y _rThe nothing of the integral translation of absolute position vector estimates that partially its method of estimation comprises square estimation, least-squares estimation and maximum likelihood estimation according to the probability distribution difference of repeatedly gathering the little translation between the SPR curve.

7. detection method according to claim 1 is characterized in that, the information fusion algorithm in the described step (4), and when minimizing the intensity noise error, adding is prior-constrained to the SPR curve, to overcome the pathosis of problem.

8. according to the detection method described in claim 1 and 7, it is characterized in that, information fusion algorithm in the described step (4) comprises the maximum a posteriori probability method that the constrained optimization problem is converted into unconstrained optimization problem, and the convex set projecting method that directly solves the constrained optimization problem.

9. the information fusion algorithm described in according to Claim 8, it is characterized in that, for the maximum a posteriori probability method of the no constrained minimization problem that former constrained optimization problem is transformed into, use the no constrained minimization algorithm that comprises method of conjugate gradient and quasi-Newton method to solve.

10. according to the detection method described in claim 1 and 7, it is characterized in that, when carrying out the information fusion of described step (4), the prior-constrained slickness and the style characteristic that comprises theoretical SPR curve to the SPR curve of adding.

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