CN105203033A - Method for measuring in-plane displacement of MEMS - Google Patents

Abstract

The invention discloses an image-based method for measuring the in-plane displacement of an MEMS. The method includes the following steps that S1, obtaining two images; S2, selecting a sample sub-region f(x,y) in the sample image, and selecting a target sub-region g(x,y) in the target image; S3, in order to improve processing accuracy, carrying out fractal interpolation on two sub-region images; S4, carrying out Fourier transformation on the sample sub-region image; S5, filtering the image transformed in the step 4, and obtaining a vortex image; S6, calculating an eccentricity ratio parameter and a phase parameter of a vortex point; S7, finding optimal matching, and obtaining a displacement value. By means of the method, the problems that in traditional digital speckles, a laser source is required when digital speckle images are obtained with an optical method, and meanwhile distribution of tiny objects is difficult are solved, the defect that when related operation is carried out, the calculated amounted is large, the time consumed by an algorithm is long, the measuring resolution can not meet the sub-pixel-level measuring requirement of the in-plane displacement of the MEMS, and measuring accuracy and measuring efficiency can be improved.

Description

MEMS in-plane displacement measurement method

Technical field

The present invention relates to a kind of MEMS dynamic measurement method research field, particularly relate to a kind of MEMS in-plane displacement measurement method.

Background technology

MEMS (micro electro mechanical system) (MEMS:Micro-electro-Mechanical-Systems) is the research frontier of the multi-crossed disciplines developed on the basis of microelectronic technique, relates to various engineering technology and the science such as micro mechanics, microelectronics, control automatically, physics, chemistry, biology and materialogy.The technical development of MEMS opens a brand-new technical field and industry, volume is little, quality is light, low in energy consumption, reliability strong, be easy to the advantages such as intellectuality, digitizing, so have very important application prospect in the wide field such as precision optical machinery, information communication, Aero-Space, biologic medical and military affairs to adopt the microsensor, microactrator, micro parts, Micromechanical Optics device, vacuum microelectronic device, power electronic devices etc. of MEMS technology making to have.Explore by the multiple means such as highly integrated and microminiaturized the new principle and New function that realize MEMS, this is a complete brand-new field, the knowledge growth point of the following necessarily key areas such as national economy and military research and innovative point.MEMS technology plays indelible effect by the development gradually in national economy, the progress of scientific research technology and the guarantee of Defence business.

MEMS runs through from the links being designed into encapsulation the demand measured, efficient measuring method not only provides qualitative or quantitative evaluation for crudy, repeatability and level of processing, simultaneously also for encapsulation process provides effective measurement means, problem can be encapsulated by Timeliness coverage, improve the yields of product.In addition, measurement result is also evaluate the basis of device architecture or system performance quality.And in the dynamic characteristic test research of MEMS, MEMS in-plane displacement measurement is an important content, and corresponding measurement demand also becomes more and more urgent.Therefore the research of MEMS dynamic test Theories and methods has very important significance to micro-electromechanical system (MEMS) design, manufacture and reliability.

At home and abroad, MEMS technique of dynamic measurement has obtained the great attention of many research institutions, the MEMS dynamic test set of the developments such as the ChristianRembe during UCBerkeley university of U.S. BSAC studies, be integrated with the micro-vision of stroboscopic and interference technique, adopt least square method and phase shift algorithm etc., three-dimensional real time kinematics and the dynamic structural deformations of MEMS can be tested, realize measuring in high-precision.The MEMS dynamic test system based on computation vision of research group's development of america's MIT micro-system laboratory professor Freeman leader.University Of Tianjin achieves large development in the research of MEMS dynamic characteristic test.The Central China University of Science and Technology thanks to brave monarch and waits employing integrated Strobed imaging, Computer go and micro-interference technology, have developed the three-dimensional quiet dynamic test system of MEMS, system can carry out the measurements such as rigid motion in MEMS face, surface topography, vertical distortion, and reaches nano-precision.But more than research is for obtaining high-acruracy survey result, need do a large amount of related operation, calculated amount is comparatively large, cannot measure in real time.And adopting traditional interpolation algorithm to cause image smoothing to speckle image, when making finally to solve displacement, in related operation there is error in measurement result.

Summary of the invention

The present invention is intended at least solve the technical matters existed in prior art, innovatively proposes a kind of MEMS in-plane displacement measurement method based on image procossing.

In order to realize above-mentioned purpose of the present invention, the invention provides a kind of MEMS in-plane displacement measurement method, comprising the following steps:

S1, obtains two width MEMS images: piece image be the MEMS microstructure image in zero phase moment as sample image, another piece image is be not that the MEMS microstructure moving image in zero phase moment is as target image;

S2, chooses sample subarea f (x, y) in sample image, chooses target subarea g (x, y) in the target image; S3, carries out fractal interpolation process to two width subarea images;

S4, carries out Fourier transform by the subarea image after Fractal process;

S5, carries out filtering by the image after conversion in step S4, obtains sample subarea vortex image and target subarea vortex image;

S6, calculating vortex point eccentricity parameter and phase parameter, is vortex image again assignment;

S7, finds optimum matching, obtains shift value.

The present invention does not need the digital speckle correlation measurement light path adopting laser instrument as light source, but directly adopts the image gathered by micro imaging system in general lighting situation to process, and obtains the sub-pixel displacement of MEMS in face.

In the preferred embodiment of the present invention, there is following relation in sample subarea f (x, y) and target subarea g (x, y):

g(x,y)＝f(x+u,y+v)，

Wherein, (u, v) is relative translation size between sample subarea f (x, y) and target subarea g (x, y).

In the preferred embodiment of the present invention, the computing method of fractal interpolation process are:

Fractal interpolation process based on random mid point is carried out to two width subarea images, Method of Random Mid-point Displacement (x _mi, y _mi) represent interpolated point:

x _mi＝(x _i+x _i+1)/2+s·w·rand()，

y _mi＝(y _i+y _i+1)/2+s·w·rand()，

Wherein, (x _i, y _i) represent the pixel coordinate of i-th pixel, (x _i+1, y _i+1) be (x _i, y _i) horizontal ordinate of point on pixel coordinate and ordinate increase the adjoint point coordinate after 1 respectively; S and w is followed successively by the parameter controlling to move left and right direction and displacement respectively, and rand () is stochastic variable; Represent stochastic variable swrand () with normal random function stdev*N (0,1), wherein stedv represents poor based on sample standard of appraisal, and N (0,1) is standardized normal distribution;

If the pixel of image is (i, j):

Work as i, when j is odd number, the gray-scale value of interpolation point is known, and gray-scale value I represents;

Work as i, when j is even number, the gray-scale value of interpolation point is:

I＝[I(i-1,j-1)+I(i+1,j+1)+I(i-1,j+1)+I(i+1,j-1)]/4+ΔI；

Work as i, when j is a strange idol, the gray-scale value of interpolation point is:

I＝[I(i-1,j)+I(i,j+1)+I(i,j+1)+I(i+1,j)]/4+ΔI；

Wherein parameter G is Gaussian random variable, and obey N (0,1) distribution, H is fractal parameter, represents the change of the standard deviation between new district, can generate various FBM curved surface; σ is the mean square deviation of pixel grey scale.

Employing fractal interpolation avoids the deficiency such as edge fog, reduction picture quality that traditional interpolation method brings, and improves detection resolution.

In the preferred embodiment of the present invention, the computing method that filtering adopts are:

$H_{LG}=(f_x,f_y)=(f_x+{\mathrm{jf}}_y)\exp \[-(f_x^2+f_y^2)/{\mathrm{\ω}}^2\]=\mathrm{\ρ}\exp (-\mathrm{\ρ}/{\mathrm{\ω}}^2)\exp \left(j\mathrm{\β}\right),$

Wherein, with β=arctan (f _y/ f _x) be tied to polar coordinate system Parameters variation formula for rectangular coordinate; ω=f _xx+f _yy, ω are phase place; f _xfor x-axis component under rectangular coordinate system, f _yfor y-axis component under rectangular coordinate system; The exponential function at exp to be e the be end; J is imaginary part.

In the preferred embodiment of the present invention, the method for vortex image assignment is again:

If I (x, y) is original speckle image light distribution, the vortex image after filtering be defined as:

$\tilde{I}(x,y)=\mathrm{\ζ}+j\mathrm{\η}=F^{-1}\{F\[I(x,y)\]\·H_{LG}\},$

Wherein, ζ is signal real part, and η is signal imaginary part; F represents Fourier transform, F ^-1represent inverse Fourier transform, represent dot product;

Vortex image real part Zero value line and the intersection point vortex point of imaginary part Zero value line, vortex point positional representation is:

$\mathrm{Re}\[\tilde{I}(x,y)\]=a_{i}x+b_{i}y+c_i,$

$\mathrm{Im}\[\tilde{I}(x,y)\]=a_{j}x+b_{j}y+c_j,$

Wherein, for vortex image real part Zero value line, for the imaginary part Zero value line of vortex image; Coefficient a _i, b _i, c _i, a _j, b _j, c _jobtained by pixel least square fitting near vortex point;

Replace the gray-scale value of vortex point with the eccentric ratio e of each vortex point, and calculate the phase value of this vortex point, eccentric ratio e and the phase value θ calculation expression of vortex point are:

$e=\sqrt{1-\frac{({a_i}^2+{a_j}^2+{b_i}^2+{b_j}^2)-\sqrt{{({a_i}^2+{a_j}^2-{b_i}^2-{b_j}^2)}^2+4{(a_i{b}_i+a_j{b}_j)}^2}}{({a_i}^2+{a_j}^2+{b_i}^2+{b_j}^2)+\sqrt{{({a_i}^2+{a_j}^2-{b_i}^2-{b_j}^2)}^2+4{(a_i{b}_i+a_j{b}_j)}^2}}},$

$\mathrm{\&theta;}=\left\{\begin{array}{c}|arctan\&lsqb;(a_i{b}_j-a_j{b}_i)/a_i{a}_j+b_i{b}_j\&rsqb;|,\left|\mathrm{\&theta;}\right|<\mathrm{\&pi;}/2\\ 2\mathrm{\&pi;}-|arctan\&lsqb;(a_i{b}_j-a_j{b}_i)/(a_i{a}_j+b_i{b}_j)\&rsqb;|,\left|\mathrm{\&theta;}\right|>\mathrm{\&pi;}/2\end{array}\right.,$

Judge that vortex point is positive vortex or negative vortex according to θ value, each vortex point just has unique nuclear structure parameter like this; Aligning the gray-scale value of vortex, remain eccentric ratio e, to the gray-scale value of negative vortex point, is the negative value of eccentric ratio e, and the gray scale completing the image after to degeneration is determined.

Because vortex image is only containing vortex point and zero point, during correlation computations, calculated amount die-offs, and improves counting yield.

In the preferred embodiment of the present invention, the method finding optimum matching is: calculated by formula of correlation coefficient, search sample subarea after displacement with the optimum matching in sample subarea, namely when related coefficient obtains maximum value, target subarea and sample subarea autocorrelation the most by force, are optimum matching subarea; Sample subarea barycenter, to the displacement of target subarea barycenter, is sub-pixel displacement value in MEMS face.

In the preferred embodiment of the present invention, the computing method of related coefficient are:

$C=\frac{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}f(x,y)\&times;g(x,y)}{\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}f{(x,y)}^2}\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}g{(x,y)}^2}}$

Or

$C=\frac{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}\&lsqb;f(x,y)-\stackrel{\&OverBar;}{f}\&rsqb;\&times;\&lsqb;g(x,y)-\stackrel{\&OverBar;}{g}\&rsqb;}{\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}{\&lsqb;f(x,y)-\stackrel{\&OverBar;}{f}\&rsqb;}^2}\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}{\&lsqb;g(x,y)-\stackrel{\&OverBar;}{g}\&rsqb;}^2}},$

Wherein, m represents the coordinate of subarea scope, with be followed successively by the average of picture signal f (x, y) and g (x, y) respectively.

Vortex related algorithm reduces the problem that in sample subarea and target subarea related operation matching process, calculated amount is large, improves the noise immunity of algorithm.

In the preferred embodiment of the present invention, the size in sample subarea is 41 × 41 pixels.

In sum, owing to have employed technique scheme, the invention has the beneficial effects as follows: the invention solves related operation calculated amount in the problem and conventional digital speckle that texture features is lost after speckle high frequency imaging interpolation large, algorithm is consuming time longer, Measurement Resolution can not meet the measurement of MEMS in-plane displacement sub-pixel and requires defect, measuring accuracy and efficiency can be improved, and improve the noise immunity of algorithm.

Accompanying drawing explanation

Fig. 1 is schematic flow sheet of the present invention.

Embodiment

Be described below in detail embodiments of the invention, the example of described embodiment is shown in the drawings, and wherein same or similar label represents same or similar element or has element that is identical or similar functions from start to finish.Being exemplary below by the embodiment be described with reference to the drawings, only for explaining the present invention, and can not limitation of the present invention being interpreted as.

The present invention is directed to related operation calculated amount in conventional digital speckle large, algorithm is consuming time longer, Measurement Resolution can not meet the situation proposition that MEMS in-plane displacement sub-pixel measures the defects such as requirement, on the basis that further investigation digital speckle is relevant, first before displacement, sample subarea is chosen in image, calculate the fractal dimension in this subarea, the fractal dimension calculated is utilized to carry out fractal interpolation to speckle image, after solving speckle image interpolation with this, texture features smoothly loses problem, singular point special in speckle image after interpolation is analyzed, to utilize in optical eddy special nature by speckle image after Fourier Transform Filtering, the speckle non-singular matrix of former figure is just converted to the vortex sparse matrix image only containing vortex point and null value, effectively reduce the calculated amount of related operation, improve efficiency of algorithm and the stability of algorithm under noise.

The invention provides a kind of MEMS in-plane displacement measurement method, comprise the following steps:

S1, without the need to laser lighting, by micro imaging system, obtain two width MEMS images: piece image be the MEMS microstructure image in zero phase moment as sample image, another piece image is be not that the MEMS microstructure moving image in zero phase moment is as target image;

S2, chooses sample subarea f (x, y) in sample image, chooses target subarea g (x, y) in the target image; In the present embodiment, there is following relation in sample subarea f (x, y) and target subarea g (x, y):

g(x,y)＝f(x+u,y+v)，

Wherein, (u, v) is relative translation size between sample subarea f (x, y) and target subarea g (x, y).

S3, carries out fractal interpolation process to two width subarea images; In the present embodiment, the computing method of fractal interpolation process are:

Fractal interpolation process based on random mid point is carried out to two width subarea images, Method of Random Mid-point Displacement (x _mi, y _mi) represent interpolated point:

x _mi＝(x _i+x _i+1)/2+s·w·rand()，

y _mi＝(y _i+y _i+1)/2+s·w·rand()，

Wherein, (x _i, y _i) represent the pixel coordinate of i-th pixel, (x _i+1, y _i+1) be (x _i, y _i) horizontal ordinate of point on pixel coordinate and ordinate increase the adjoint point coordinate after 1 respectively; S and w is followed successively by the parameter controlling to move left and right direction and displacement respectively, and rand () is stochastic variable; Represent stochastic variable swrand () with normal random function stdev*N (0,1), wherein stedv represents poor based on sample standard of appraisal, and N (0,1) is standardized normal distribution;

If the pixel of image is (i, j):

Work as i, when j is odd number, the gray-scale value of interpolation point is known, and gray-scale value I represents;

Work as i, when j is even number, the gray-scale value of interpolation point is:

I＝[I(i-1,j-1)+I(i+1,j+1)+I(i-1,j+1)+I(i+1,j-1)]/4+ΔI；

Work as i, when j is a strange idol, the gray-scale value of interpolation point is:

I＝[I(i-1,j)+I(i,j+1)+I(i,j+1)+I(i+1,j)]/4+ΔI；

Wherein parameter G is Gaussian random variable, and obey N (0,1) distribution, H is fractal parameter, represents the change of the standard deviation between new district, can generate various FBM curved surface; σ is the mean square deviation of pixel grey scale.

S4, carries out Fourier transform by the subarea image after Fractal process;

S5, carries out filtering by the image after conversion in step S4, obtains sample subarea vortex image and target subarea vortex image; In the present embodiment, the computing method that filtering adopts are:

$H_{LG}=(f_x,f_y)=(f_x+{\mathrm{jf}}_y)\exp \&lsqb;-(f_x^2+f_y^2)/{\mathrm{\&omega;}}^2\&rsqb;=\mathrm{\&rho;}\exp (-\mathrm{\&rho;}/{\mathrm{\&omega;}}^2)\exp \left(j\mathrm{\&beta;}\right),$

Wherein, with β=arctan (f _y/ f _x) be tied to polar coordinate system Parameters variation formula for rectangular coordinate; ω=f _xx+f _yy, ω are phase place; f _xfor x-axis component under rectangular coordinate system, f _yfor y-axis component under rectangular coordinate system; The exponential function at exp to be e the be end; J is imaginary part.

S6, calculating vortex point eccentricity parameter and phase parameter, is vortex image again assignment; In the present embodiment, the method for vortex image assignment is again:

If I (x, y) is original speckle image light distribution, the vortex image after filtering be defined as:

$\tilde{I}(x,y)=\mathrm{\&zeta;}+j\mathrm{\&eta;}=F^{-1}\{F\&lsqb;I(x,y)\&rsqb;\&CenterDot;H_{LG}\},$

Wherein, ζ is signal real part, and η is signal imaginary part; F represents Fourier transform, F ^-1represent inverse Fourier transform, represent dot product;

Vortex image real part Zero value line and the intersection point vortex point of imaginary part Zero value line, vortex point positional representation is:

$\mathrm{Re}\&lsqb;\tilde{I}(x,y)\&rsqb;=a_{i}x+b_{i}y+c_i,$

$\mathrm{Im}\&lsqb;\tilde{I}(x,y)\&rsqb;=a_{j}x+b_{j}y+c_j,$

Wherein, for vortex image real part Zero value line, for the imaginary part Zero value line of vortex image; Coefficient a _i, b _i, c _i, a _j, b _j, c _jobtained by pixel least square fitting near vortex point;

Replace the gray-scale value of vortex point with the eccentric ratio e of each vortex point, and calculate the phase value of this vortex point, eccentric ratio e and the phase value θ calculation expression of vortex point are:

$e=\sqrt{1-\frac{({a_i}^2+{a_j}^2+{b_i}^2+{b_j}^2)-\sqrt{{({a_i}^2+{a_j}^2-{b_i}^2-{b_j}^2)}^2+4{(a_i{b}_i+a_j{b}_j)}^2}}{({a_i}^2+{a_j}^2+{b_i}^2+{b_j}^2)+\sqrt{{({a_i}^2+{a_j}^2-{b_i}^2-{b_j}^2)}^2+4{(a_i{b}_i+a_j{b}_j)}^2}}},$

$\mathrm{\&theta;}=\left\{\begin{array}{c}|arctan\&lsqb;(a_i{b}_j-a_j{b}_i)/a_i{a}_j+b_i{b}_j\&rsqb;|,\left|\mathrm{\&theta;}\right|<\mathrm{\&pi;}/2\\ 2\mathrm{\&pi;}-|arctan\&lsqb;(a_i{b}_j-a_j{b}_i)/(a_i{a}_j+b_i{b}_j)\&rsqb;|,\left|\mathrm{\&theta;}\right|>\mathrm{\&pi;}/2\end{array}\right.,$

Judge that vortex point is positive vortex or negative vortex according to θ value, each vortex point just has unique nuclear structure parameter like this; Aligning the gray-scale value of vortex, remain eccentric ratio e, to the gray-scale value of negative vortex point, is the negative value of eccentric ratio e, and the gray scale completing the image after to degeneration is determined.

Because vortex image is only containing vortex point and zero point, substantially reduces calculated amount during correlation computations, improve counting yield.

S7, finds optimum matching, obtains shift value.In the present embodiment, finding the method for optimum matching is: calculated by formula of correlation coefficient, search sample subarea after displacement with the optimum matching in sample subarea, namely when related coefficient obtains maximum value, target subarea and sample subarea autocorrelation the most by force, are optimum matching subarea; Sample subarea barycenter, to the displacement of target subarea barycenter, is sub-pixel displacement value in MEMS face.In the preferred embodiment of the present invention, the computing method of related coefficient are:

$C=\frac{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}f(x,y)\&times;g(x,y)}{\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}f{(x,y)}^2}\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}g{(x,y)}^2}}$

Or

$C=\frac{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}\&lsqb;f(x,y)-\stackrel{\&OverBar;}{f}\&rsqb;\&times;\&lsqb;g(x,y)-\stackrel{\&OverBar;}{g}\&rsqb;}{\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}{\&lsqb;f(x,y)-\stackrel{\&OverBar;}{f}\&rsqb;}^2}\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}{\&lsqb;g(x,y)-\stackrel{\&OverBar;}{g}\&rsqb;}^2}},$

Wherein, m represents the coordinate of subarea scope, with be followed successively by the average of picture signal f (x, y) and g (x, y) respectively.

In the preferred embodiment of the present invention, the size in sample subarea and target subarea is 41 × 41 pixels.

In the description of this instructions, specific features, structure, material or feature that the description of reference term " embodiment ", " some embodiments ", " example ", " concrete example " or " some examples " etc. means to describe in conjunction with this embodiment or example are contained at least one embodiment of the present invention or example.In this manual, identical embodiment or example are not necessarily referred to the schematic representation of above-mentioned term.And the specific features of description, structure, material or feature can combine in an appropriate manner in any one or more embodiment or example.

Although illustrate and describe embodiments of the invention, those having ordinary skill in the art will appreciate that: can carry out multiple change, amendment, replacement and modification to these embodiments when not departing from principle of the present invention and aim, scope of the present invention is by claim and equivalents thereof.

Claims (8)

1. a MEMS in-plane displacement measurement method, is characterized in that, comprises the following steps:

S1, obtains two width MEMS images: piece image be the MEMS microstructure image in zero phase moment as sample image, another piece image is be not that the MEMS microstructure moving image in zero phase moment is as target image;

S2, chooses sample subarea f (x, y) in sample image, chooses target subarea g (x, y) in the target image;

S3, carries out fractal interpolation process to two width subarea images;

S4, carries out Fourier transform by the subarea image after Fractal process;

S5, carries out filtering by the image after conversion in step S4, obtains sample subarea vortex image and target subarea vortex image;

S6, calculating vortex point eccentricity parameter and phase parameter, is vortex image again assignment;

S7, finds optimum matching, obtains shift value.

2. MEMS in-plane displacement measurement method according to claim 1, is characterized in that, sample subarea f (x, y) and target subarea g (x, y) exist following relation:

g(x,y)＝f(x+u,y+v)，

Wherein, (u, v) is relative translation size between sample subarea f (x, y) and target subarea g (x, y).

3. MEMS in-plane displacement measurement method according to claim 1, is characterized in that, the computing method of fractal interpolation process are:

Fractal interpolation process based on random mid point is carried out to two width subarea images, Method of Random Mid-point Displacement (x _mi, y _mi) represent interpolated point:

x _mi＝(x _i+x _i+1)/2+s·w·rand()，

y _mi＝(y _i+y _i+1)/2+s·w·rand()，

Wherein, (x _i, y _i) represent the pixel coordinate of i-th pixel, (x _i+1, y _i+1) be (x _i, y _i) horizontal ordinate of point on pixel coordinate and ordinate increase the adjoint point coordinate after 1 respectively; S and w is followed successively by the parameter controlling to move left and right direction and displacement respectively, and rand () is stochastic variable; Represent stochastic variable swrand () with normal random function stdev*N (0,1), wherein stedv represents poor based on sample standard of appraisal, and N (0,1) is standardized normal distribution;

If the pixel of image is (i, j):

Work as i, when j is odd number, the gray-scale value of interpolation point is known, and gray-scale value I represents;

Work as i, when j is even number, the gray-scale value of interpolation point is:

I＝[I(i-1,j-1)+I(i+1,j+1)+I(i-1,j+1)+I(i+1,j-1)]/4+ΔI；

Work as i, when j is a strange idol, the gray-scale value of interpolation point is:

I＝[I(i-1,j)+I(i,j+1)+I(i,j+1)+I(i+1,j)]/4+ΔI；

Wherein parameter G is Gaussian random variable, and obey N (0,1) distribution, H is fractal parameter, represents the change of the standard deviation between new district, can generate various FBM curved surface; σ is the mean square deviation of pixel grey scale.

4. MEMS in-plane displacement measurement method according to claim 1, is characterized in that, the computing method that filtering adopts are:

$H_{LG}=(f_x,f_y)=(f_x+{\mathrm{jf}}_y)\exp \&lsqb;-(f_x^2+f_y^2)/{\mathrm{\&omega;}}^2\&rsqb;=\mathrm{\&rho;}\exp (-\mathrm{\&rho;}/{\mathrm{\&omega;}}^2)\exp \left(j\mathrm{\&beta;}\right),$

Wherein, with β=arctan (f _y/ f _x) be tied to polar coordinate system Parameters variation formula for rectangular coordinate; ω=f _xx+f _yy, ω are phase place; f _xfor x-axis component under rectangular coordinate system, f _yfor y-axis component under rectangular coordinate system; The exponential function at exp to be e the be end; J is imaginary part.

5. MEMS in-plane displacement measurement method according to claim 1, is characterized in that, the method for vortex image assignment is again:

If I (x, y) is original speckle image light distribution, the vortex image after filtering be defined as:

$\tilde{I}(x,y)=\mathrm{\&zeta;}+j\mathrm{\&eta;}=F^{-1}\{F\&lsqb;I(x,y)\&rsqb;\&CenterDot;H_{LG}\},$

Wherein, ζ is signal real part, and η is signal imaginary part; F represents Fourier transform, F ^-1represent inverse Fourier transform, represent dot product;

Vortex image real part Zero value line and the intersection point vortex point of imaginary part Zero value line, vortex point positional representation is:

$\mathrm{Re}\&lsqb;\tilde{I}(x,y)\&rsqb;=a_{i}x+b_{i}y+c_i,$

$\mathrm{Im}\&lsqb;\tilde{I}(x,y)\&rsqb;=a_{j}x+b_{j}y+c_j,$

Wherein, for vortex image real part Zero value line, for the imaginary part Zero value line of vortex image; Coefficient a _i, b _i, c _i, a _j, b _j, c _jobtained by pixel least square fitting near vortex point;

Replace the gray-scale value of vortex point with the eccentric ratio e of each vortex point, and calculate the phase value of this vortex point, eccentric ratio e and the phase value θ calculation expression of vortex point are:

$e=\sqrt{1-\frac{({a_i}^2+{a_j}^2+{b_i}^2+{b_j}^2)-\sqrt{{({a_i}^2+{a_j}^2-{b_i}^2-{b_j}^2)}^2+4{(a_i{b}_i+a_j{b}_j)}^2}}{({a_i}^2+{a_j}^2+{b_i}^2+{b_j}^2)+\sqrt{{({a_i}^2+{a_j}^2-{b_i}^2-{b_j}^2)}^2+4{(a_i{b}_i+a_j{b}_j)}^2}}},$

$\mathrm{\&theta;}=\left\{\begin{array}{c}|arctan\&lsqb;(a_i{b}_j-a_j{b}_i)/a_i{a}_j+b_i{b}_j\&rsqb;|,\left|\mathrm{\&theta;}\right|<\mathrm{\&pi;}/2\\ 2\mathrm{\&pi;}-|arctan\&lsqb;(a_i{b}_j-a_j{b}_i)/(a_i{a}_j+b_i{b}_j)\&rsqb;|,\left|\mathrm{\&theta;}\right|>\mathrm{\&pi;}/2\end{array}\right.,$

Judge that vortex point is positive vortex or negative vortex according to θ value, each vortex point just has unique nuclear structure parameter like this;

Aligning the gray-scale value of vortex, remain eccentric ratio e, to the gray-scale value of negative vortex point, is the negative value of eccentric ratio e, and the gray scale completing the image after to degeneration is determined.

6. MEMS in-plane displacement measurement method according to claim 1, it is characterized in that, the method finding optimum matching is: calculated by formula of correlation coefficient, search sample subarea after displacement with the optimum matching in sample subarea, namely when related coefficient obtains maximum value, target subarea and sample subarea autocorrelation the most by force, are optimum matching subarea; Sample subarea barycenter, to the displacement of target subarea barycenter, is sub-pixel displacement value in MEMS face.

7. MEMS in-plane displacement measurement method according to claim 6, is characterized in that, the computing method of related coefficient are:

$C=\frac{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}f(x,y)\&times;g(x,y)}{\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}f{(x,y)}^2}\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}g{(x,y)}^2}}$

Or

$C=\frac{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}\&lsqb;f(x,y)-\stackrel{\&OverBar;}{f}\&rsqb;\&times;\&lsqb;g(x,y)-\stackrel{\&OverBar;}{g}\&rsqb;}{\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}{\&lsqb;f(x,y)-\stackrel{\&OverBar;}{f}\&rsqb;}^2}\sqrt{\underset{x=-m}{\overset{m}{\&Sigma;}}\underset{y=-m}{\overset{m}{\&Sigma;}}{\&lsqb;g(x,y)-\stackrel{\&OverBar;}{g}\&rsqb;}^2}},$

Wherein, m represents the coordinate of subarea scope, with be followed successively by the average of picture signal f (x, y) and g (x, y) respectively.

8. MEMS in-plane displacement measurement method according to claim 1, is characterized in that, the size in sample subarea is 41 × 41 pixels.