CN112711888A - Combined scattering joint calculation method for bidirectional reflection distribution function and scattering center - Google Patents

Combined scattering joint calculation method for bidirectional reflection distribution function and scattering center Download PDF

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CN112711888A
CN112711888A CN202110022284.4A CN202110022284A CN112711888A CN 112711888 A CN112711888 A CN 112711888A CN 202110022284 A CN202110022284 A CN 202110022284A CN 112711888 A CN112711888 A CN 112711888A
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盛新庆
牟媛
张尊
郭琨毅
杨明林
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a composite scattering joint calculation method of a bidirectional reflection distribution function and a scattering center, which realizes the fast and efficient calculation of scattering echoes of an ultra-electric large-size composite scene and SAR image simulation; the echo of a composite scene is divided into three parts, and an Attribute Scattering Center (ASC) is adopted to fit the scattering echo of an independent target; fitting a BRDF-based binning model (BRDF-FBM) to the scattered echoes of the coarse background; fitting multiple scattering components of the target and the background by using a four-path model; the invention uses a parameterized model, and expresses complex scattering echo integral operation by a simple mathematical algebraic expression, wherein the unknown quantity of the parametric expression is estimated by a Genetic Algorithm (GA). The method greatly improves the calculation efficiency, improves the operation speed by tens of thousands of times compared with a multilayer fast multipole algorithm (MLFMM), and simultaneously has the RCS error smaller than 4 db. The invention solves the problem of rapid calculation of the scattering and imaging of the large composite target of the super-electricity.

Description

Combined scattering joint calculation method for bidirectional reflection distribution function and scattering center
Technical Field
The invention relates to the technical field of electromagnetic scattering characteristic research, in particular to a composite scattering joint calculation method of a bidirectional reflection distribution function and a scattering center.
Background
Radar echo prediction is a forward problem in electromagnetic scattering research and has wide application in image interpretation, target guidance and target identification. With the development of new systems Synthetic Aperture Radar (SAR) technology, it is increasingly important to simulate more real echoes with higher efficiency. Therefore, the rapid modeling of the echo of the composite scene is greatly concerned. The current numerical algorithms for echo scattering of composite scenes include moment method (MoM), Finite Element Method (FEM), time domain finite difference method (FTDT), and the like. In order to further improve the computational efficiency, parallel algorithms such as multi-layer fast multipole (MLFMM) and region decomposition (DDM) have appeared. However, the full-wave numerical algorithm still has the defects of low calculation efficiency and large memory consumption, and is not suitable for electromagnetic calculation of a large-size ultra-power target.
Compared with a full-wave numerical algorithm, the high-frequency approximation method has higher calculation efficiency, so that the method is widely applied to calculation of a large composite scene of the super-electricity, such as a geometric optical method (GO), a physical optical method (PO), a ray tracing method (SBR) and the like. However, the high-frequency method generally adopts an approximation condition to simplify the scattering integral equation, so that the applicability of the algorithm is greatly limited, and the calculation accuracy is lower than that of a full-wave numerical algorithm. In order to effectively utilize the advantages of numerical algorithms and high frequency approximation, a large number of hybrid methods have emerged to calculate the scattering properties of the large composite scenes of the ultrasound. Such as a geometrical optics method, a physical diffraction method, a capillary surface element correction scattering model method (GO \ PO \ PTD-CWMSM), a finite element method (FEM-BIM) combined with a boundary integral equation, a bounce ray method (SBR-EEC) combined with equivalent current correction, a moment method (FEM-MoM) combined with a finite element and the like. In the aspect of efficiency, a GO \ PO \ PTD-CWMFSM mixing method is taken as an example, a composite scene SAR image of a 500 x 500m sea surface and a 166m long ship is simulated, and when the resolution is 1m, the time is 5800 s. Typically the echoes of a composite scene are divided into 3 parts: 1. independent target echo and scene echo; 2. multiple scattering components between the target and the scene; 3. the edge of the target diffracts the component. The nature of the hybrid algorithm is to use a targeted scattering model for different echo components for simulation and correction. For example, in a GO \ PO \ PTD-CWMFSM mixed algorithm, GO \ PO is adopted to calculate independent target scattering, CWMFSM is adopted to calculate background rough surface scattering, a multipath model is adopted to describe coupling scattering, and PTD is adopted to correct edge scattering. In the SBR-EEC theory, SBR is adopted to calculate independent target, background and coupling scattering components, and EEC theory is adopted to correct edge diffraction components;
compared with a full-wave numerical algorithm and a high-frequency approximation theory, the hybrid method improves the efficiency while ensuring the precision. However, the existing hybrid algorithm is mostly based on a grid model of a composite scene, and the number of grids of a scene-level super-electric large composite target can reach millions of orders. When the target surface microroughness is considered, the unit grid size is smaller than 1/5 wavelengths, further increasing the number of grids in the model. Meanwhile, a large amount of complex integral iteration still exists in the existing hybrid algorithm, and the simulation efficiency of the electromagnetic scattering of the large-size composite target is seriously reduced.
Therefore, the efficient and accurate calculation of the electromagnetic scattering in the large composite scene of the super-electricity is still a scientific difficult problem to be solved urgently. The invention provides a parameterized mixed calculation model according to the electromagnetic scattering characteristics of a composite scene, which simulates independent target scattering, rough background scattering and coupling scattering components of the composite scene by using an attribute scattering center model (ASC), a bin model (BRDF-FBM) based on a bidirectional reflection projection function and a four-path model (4-path) respectively. The method has the advantages that a scattering center model is used for replacing a complex independent target grid model, and a parameterized mathematical expression is used for simplifying a complex electromagnetic scattering integral equation; the BRDF has a simple relation with the scattering coefficient, and the model comprises information such as surface roughness, dielectric parameters, incident angles and the like, and can simulate a rough surface element, so that the BRDF is used for fitting the amplitude of the rough surface element, the constraint of incident wave frequency on the grid size is reduced, the grid number of the model and the computational complexity of a scattering field are reduced to the maximum extent, and the computational efficiency of the total scattering field of the composite scene is obviously improved.
Disclosure of Invention
The present invention aims to provide a method for joint calculation of a bidirectional reflectance distribution function and a composite scattering of a scattering center, so as to solve the problems proposed in the background art.
In order to achieve the purpose, the invention provides the following technical scheme: the combined calculation method of the bidirectional reflection distribution function and the composite scattering of the scattering center comprises the following steps;
the method comprises the following steps: modeling by using a composite target geometry;
step two: generating calibration scattering data;
based on the composite target model established in the first step, a full-wave algorithm is adopted to calculate independent targets, background topography and scattering fields of the composite targets under the condition that the azimuth angle phi is 0-360 degrees and the pitch angle theta is the incident angle (between 10-60 degrees) of the common spaceborne radar, and a target scattering echo standard database is formed
Figure RE-GDA0002986642310000031
Providing calibration for parameter estimation and model verification of subsequent steps, calculating scattering field of coarse bin with theta from-80 DEG to 80 DEG and phi within 0 DEG by using full wave algorithm (such as MLFMM) or high frequency algorithm (such as PO), and forming bin scattering standard data sigmaB(θ), providing a calibration for subsequent BRDF model parameter estimation;
step three: modeling an independent target scattering center;
modeling the independent target by utilizing the attribute scattering center model, and combining the target scattering calibration database in the second step
Figure RE-GDA0002986642310000032
Estimating scattering center amplitude and orientation dependent factors by adopting a genetic algorithm, and obtaining target scattering echoes under each wave band according to frequency dependence;
step four: estimating BRDF model parameters;
bin scattering standard data sigma based on step twoB(θ), estimating unknown parameters in the five-parameter BRDF model using a genetic algorithm;
step five: performing BRDF-FBM combined scattering modeling on background terrain;
calculating the scattering coefficient of each rough surface element of the background terrain based on the BRDF model obtained in the fourth step, correcting the position and the phase of each surface element to obtain the phase of each surface element, and superposing the components of each surface element to obtain a background scattering echo;
step six: calculating the coupling scattering of the composite target;
calculating the coupling scattering field of each single scattering center and the background terrain based on the target scattering center model established in the step three by combining the four-path effect, and finally superposing the coupling fields of all the scattering centers to calculate the coupling scattering of the target and the background;
step seven: checking the model;
summing the scattering components of the third step, the fourth step and the fifth step to obtain a scattering field of the composite target, mutually verifying the scattering field and the calibration data of the second step, establishing a parameterized model when the RCS error is less than 4dB, and returning to the third step to reevaluate the parameters when the RCS error is more than 4 dB;
step eight: and calculating the SAR or ISAR image by combining the composite scattering echo data in the step seven.
Preferably, in the step one, the specific operation steps of using the geometric modeling of the composite target are as follows:
s1, establishing a grid model of independent targets such as ships and vehicles by using CAD software;
s2, generating a rough background terrain grid model by using a Monte-Carlo method;
and S3, importing the grid models of the independent target and the background terrain into FEKO to generate a grid model of the composite target, so that the scattered field simulation result verification and the parameter model estimation are facilitated.
Preferably, in step five, the specific operation steps of the BRDF-FBM joint scattering modeling of the background topography are as follows:
s1, the scattering field form of the rough terrain is E ═ Sigma Aiexp(jφi) Wherein A isiFor each bin scattering amplitude, phiiScattering phase for each bin;
s2, equating the background terrain to a surface element scattering center model distributed according to grid coordinates, wherein each surface element has different gradients;
s3, calculating A by using bin inclination angle and BRDF modeliUsing grid positions and adding [0:2 π]Determining phi by the random asperity phase correction factori。
The invention provides a combined calculation method for the composite scattering of a bidirectional reflection distribution function and a scattering center, which has the beneficial effects that:
1. the invention introduces the concept of bidirectional reflection projection function (BRDF) into electromagnetic wave scattering modeling, calculates the scattering coefficient of a small background surface element by a full wave method, and establishes the rough background scattering coefficient and the scattering field with any shape and size;
2. the method combines an attribute scattering center model with a composite scene, and simultaneously considers a distributed scattering center (DSC-R) generated by surface reflection, a distributed scattering center (DSC-D) generated by edge diffraction and a Local Scattering Center (LSC) generated by sharp-top diffraction;
3. in the invention, the judgment of the coupling of the scattering center and the background is considered, and a more accurate scattering center four-path model is established;
in summary, the BRDF is used for fitting the amplitude of the rough surface element, the constraint of the incident wave frequency on the grid size is reduced, the grid number of the model and the calculation complexity of the scattered field are reduced to the maximum extent, the calculation efficiency of the total scattered field of the composite scene is obviously improved, and the BRDF can be applied to radar image interpretation, target guidance, target automatic identification technology and radar imaging technology.
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FIG. 1 is a flow chart of the present invention for establishing a composite scene echo based on the ASC-BRDF-FBM method;
FIG. 2 illustrates an example of an object model according to the present invention: a certain model of destroyer, (a) and (b) are respectively a left front view and a right back view;
FIG. 3 is a background model according to an embodiment of the present invention: three-stage sea surface of 200 x 200m
FIG. 4 is a time-frequency image comparison result of a scattering center model and a full-wave result of a destroyer target, wherein (a) and (b) are a scattering center model under VV polarization and an MLFMM result respectively;
FIG. 5 is a comparison of RCS of a destroyer target scattering center model with full-wave results;
FIG. 6 shows a destroyer target SAR imaging result;
FIG. 7 shows BRDF fitting results of three-level sea surface rough surface elements;
FIG. 8 is a comparison of RCS and high frequency PO measurements made with a three stage sea BRDF size of 10 by 10 meters;
FIG. 9 is a BRDF intensity result for each rough surface element of a three-level sea surface with dimensions of 100 x 100 meters;
FIG. 10 is the SAR imaging results for a three-level sea surface with dimensions of 100 x 100 meters;
fig. 11(a) and (b) are the imaging results of the-200 × 200m three-level sea surface composite scene SAR of the destroyer without the four-path model and with the four-path model, respectively;
FIG. 12 is a second object model of an embodiment of the present invention: a certain model of tank, wherein (a) and (b) are respectively a left front view and a right back view;
FIG. 13 is a background model of example two of the present invention: bare soil-cement pavement scenes;
FIGS. 14(a) and (b) are tank-road surface composite scene SAR imaging results without and with four-path models, respectively;
FIGS. 15(a) and (b) are cement panel and bare soil panel-BRDF, respectively.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-15, the present invention provides a technical solution: the combined calculation method of the bidirectional reflection distribution function and the composite scattering of the scattering center comprises the following steps;
the method comprises the following steps: establishing a geometric model of an independent target by using commercial CAD software CATIA and dividing the geometric model into grid files, establishing a coarse background terrain grid model by using a Monte-Carlo method, and leading the independent target grid model and the grid model of the background terrain into FEKO to generate a grid model of a composite target;
generating a calibration scattering database; adopting multilayer fast multipole algorithm to obtain independent object within 0-360 degree of azimuth angle phiTarget scattered field to form a target scattered database A1Providing calibration for the parameter estimation and model verification of the scattering center in the subsequent step; a multilayer fast multipole algorithm is adopted to obtain a background rough surface scattering field with a pitch angle theta of-80 degrees to 80 degrees and a size of 1m multiplied by 1m to form a scattering database A2Providing calibration for subsequent BRDF model parameter estimation;
step three: establishing a scattering echo of an independent target by using an attribute scattering center model; for a target echo under a high-frequency condition, the target echo can be equivalently expressed by a plurality of mutually independent scattering centers, the method adopts an attribute scattering center model, and the expression is as follows:
Figure RE-GDA0002986642310000071
wherein N represents the number of scattering centers of the target, AiRepresenting the amplitude of the scattering center; alpha is alphaiRepresenting a frequency dependent factor; l isiDenotes the length of the scattering center, when LiWhen the value is 0, the local scattering center is obtained; gamma rayiIs an orientation dependent factor. The method divides scattering components into a distributed scattering center (DSC-R) generated by reflection, a distributed scattering center (DSC-D) generated by edge diffraction, a Sliding Scattering Center (SSC) formed by curved surface reflection and a Local Scattering Center (LSC) formed by vertex diffraction for modeling, and uses a target scattering database A of the MLFMM1For reference, carrying out Genetic Algorithm (GA) parameter estimation on amplitude and orientation dependent factors of a scattering center, specifically carrying out mixed parameter estimation by using an RCS (phi) curve with the minimum root mean square error and the maximum time-frequency image similarity as an objective function, simultaneously ensuring the correctness of echo intensity and echo components, and obtaining the scattering echo under any waveband by using a frequency dependent principle of the scattering center;
step four: establishing an echo of a rough background terrain by utilizing a BRDF (surface element model) based; for the rough surface echo, firstly, a Monte-Carlo method is adopted to generate a rough surface, then a parametric surface element model is used for modeling, in the aspect of parametric modeling, a bidirectional reflection projection function (BRDF) is used as the parametric model, the BRDF contains information such as surface roughness, dielectric parameters, incident angles and the like, the relation between the scattering amplitude of the rough medium surface element and the incident and reflection angles can be represented efficiently, and the relation between the scattering amplitude and the scattering coefficient is as follows:
Figure RE-GDA0002986642310000072
wherein sigmabIs the scattering coefficient; thetaiIs an angle of incidence, θrFor angle of reflection, theta under single station conditionsi＝θr；；
Figure RE-GDA0002986642310000073
Namely BRDF, the expression of the five-parameter BRDF is as follows:
Figure RE-GDA0002986642310000074
wherein
Figure RE-GDA0002986642310000081
Figure RE-GDA0002986642310000082
Figure RE-GDA0002986642310000083
Figure RE-GDA0002986642310000084
Figure RE-GDA0002986642310000085
Figure RE-GDA0002986642310000086
The first term in the function represents the specular component, kbIn order to be a specular reflection coefficient,
Figure RE-GDA0002986642310000087
which is representative of the fresnel reflection function,
Figure RE-GDA0002986642310000088
is a masking function; the second term represents the diffuse reflection component, kdFor diffuse reflection coefficient, the parameter to be estimated is k in the functionb、krAlpha, b and kd；
The invention is formed by overlapping rough surfaces equivalent to rough surface elements with different inclination angles, and firstly, a pitch angle scattering database A of the rough surface elements with the size of 1 multiplied by 1 meter in the step two is used2For reference, performing GA (genetic algorithm) parameter estimation on five-parameter BRDF (bidirectional reflectance distribution function) by taking the minimum root mean square error of RCS (theta) curve as a target function, obtaining the scattering coefficients of rough surface elements with different inclination angles by a formula (2), and overlapping the scattering coefficients of all the rough surface elements to obtain the integral scattering coefficient of the rough surface, wherein for two-dimensional imaging, the invention adopts the concept of complex scattering coefficients, and adds one element of [0,2 pi ] on the basis of the phase position of the central coordinate of each surface element]Correcting random phase, and imaging;
step five: calculating multiple scattering before the target and the background by using a four-path model; the multiple scattering is equivalent to three components of target-rough surface, rough surface-target and rough surface-target-rough surface, and is combined with the single scattering of the target to form four paths, and the radar has a good effect when the radar incident angle theta is 30-50 degrees. The scattering center-background coupling field expression is as follows,
Figure RE-GDA0002986642310000091
wherein the content of the first and second substances,
Figure RE-GDA0002986642310000092
Figure RE-GDA0002986642310000093
L2＝2hsin2ψ (13)
L3＝2hsin2ψ (14)
L4＝4hsinψ (15)
ψ＝90-θi (16)
in the formula, gamma is a reflection coefficient, epsilonrThe rough surface dielectric parameter; l is2、L3And L4Paths 2, 3 and 4 are respectively a multi-path, h is the height of the scattering center, and psi is the angle of the ground; the invention simultaneously considers the shielding effect of the scattering center of the target, calculates the scattering field coupling each single scattering center of the target and the background, and divides the scattering components into: and the amplitude of the scattering center and the length of the scattering center in the sinc function are correspondingly changed without the four-path effect, with partial four-path effect and with the four-path effect. And finally, superposing the coupling fields of all the scattering centers, and calculating the scattering between the target and the background.
The first embodiment is as follows: a destroyer-sea surface model;
according to the invention, as shown in fig. 2, a destroyer target CAD model is established, wherein the length of the destroyer is 145 meters, the left and right maximum width is 21 meters, and the maximum width is 25 meters, as shown in fig. 1; a three-level sea surface with a sea surface size of 200 × 200m, a wind speed of 8.5 knots/second and a dielectric parameter of 71+ i50, as shown in fig. 3;
when target modeling is carried out, the maximum similarity of (a) and (b) in the graph 4 and the minimum root mean square error in the graph 5 are taken as target functions, parameters are circularly estimated until the precision requirement is met, under the frequency of 100M, the final modeling result is that the RCS root mean square error is 3.98db, the similarity of time-frequency images is 92%, and target scattering echoes required by the SAR imaging are obtained through scattering center frequency dependence correction; the result of estimating parameters of the sea surface bin BRDF model is shown in FIG. 7, the comparison of RCS built on a 10 x 10 meter sea surface is shown in FIG. 8, and as the BRDF is the parameterized model, the root mean square error of the curve is not taken as the standard in judgment, and the curve variation trend and the amplitude of the result are the same as the full-wave result. When the SAR radar parameters are shown in the following table, the resolution is 0.2 m, and the final SAR image result under VV polarization is shown in fig. 11(a) and fig. 11(b), where fig. 11(a) is the SAR image without considering the multiple scattering effect, fig. 11(b) is the SAR image with considering the multiple scattering effect, it can be seen that when the multiple scattering component is considered, a ghost image occurs on the irradiation side, and the imaging time of fig. 11(b) is about 57030 s;
Figure RE-GDA0002986642310000101
example two: tank-road surface model;
the invention establishes a tank target CAD model as shown in FIG. 12, the tank is 7.9 meters long in front and back, the vehicle body is 6.2 meters long, the gun barrel is 4 meters long, the width is 3.56 meters, the height is 1.9 meters, and the vehicle body is 1.4 meters high. When the pitch angle is 40 degrees, the crawler belt and the tire of the vehicle body cannot be seen due to the shielding of the baffle plate, and are not considered during modeling; the road surface is a cement road surface with the length of 100 meters and the width of 10 meters, the two sides of the cement road surface are respectively composed of bare soil with the width of 5 meters, and the geometrical parameters are shown in the following table.
Type (B) Dielectric parameter Root mean square height Correlation length
Cement
5 0.12cm 1.14cm
Bare soil 7.6+i0.2 1.1cm 6.8cm
The BRDF model modeling results of cement and bare soil surface elements are respectively shown in fig. 14(a) and 14(b), and it can be seen that when the incident angle is less than 50 degrees, the fitting effect is good; when imaging is performed with the same SAR parameters as in example one, the results are shown in fig. 15, (a) and (b) for the imaging effect without four-path addition and with four-path addition, respectively, and it can be seen that ghosting occurs on the irradiated side in consideration of the multiple scattering component.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (3)

1. The combined calculation method of the bidirectional reflection distribution function and the composite scattering of the scattering center is characterized in that: comprises the following steps;
the method comprises the following steps: performing geometric modeling on a composite target;
step two: generating calibration scattering data;
based on the composite target model established in the first step, a full-wave algorithm is adopted to calculate independent targets, background topography and scattering fields of the composite targets under the condition that the azimuth angle phi is 0-360 degrees and the pitch angle theta is the incident angle (between 10-60 degrees) of the common spaceborne radar, and a target scattering echo standard database is formed
Figure FDA0002889078020000011
Providing calibration for parameter estimation and model verification in subsequent steps, using full-wave algorithms (e.g. MLFMM) or high frequencyAn algorithm (such as PO) calculates the scattering field of rough surface elements with theta from-80 degrees to 80 degrees and phi within 0 degrees to form surface element scattering standard data sigmaB(θ), providing a calibration for subsequent BRDF model parameter estimation;
step three: modeling an independent target scattering center;
modeling the independent target by utilizing the attribute scattering center model, and combining the target scattering calibration database in the second step
Figure FDA0002889078020000012
Estimating the amplitude and the azimuth dependence factor of a scattering center by adopting a genetic algorithm, and calculating a target scattering echo under any frequency band by frequency dependence;
step four: estimating BRDF model parameters;
bin scattering standard data sigma based on step twoB(θ), estimating unknown parameters in the five-parameter BRDF model using a genetic algorithm;
step five: performing BRDF-FBM combined scattering modeling on background terrain;
calculating the scattering coefficient of each rough surface element of the background terrain based on the BRDF model obtained in the fourth step, correcting the position and the phase of each surface element to obtain the phase of each surface element, and superposing the components of each surface element to obtain a background scattering echo;
step six: calculating the coupling scattering of the composite target;
calculating the coupling scattering field of each single scattering center and the background terrain based on the target scattering center model established in the step three by combining the four-path effect, and finally superposing the coupling fields of all the scattering centers to calculate the coupling scattering of the target and the background;
step seven: checking the model;
summing the scattering components of the third step, the fourth step and the fifth step to obtain a scattering field of the composite target, mutually verifying the scattering field and the calibration data of the second step, establishing a parameterized model when the RCS error is less than 4dB, and returning to the third step to reevaluate the parameters when the RCS error is more than 4 dB;
step eight: and calculating the SAR or ISAR image by combining the composite scattering echo data in the step seven.
2. The method of claim 1, wherein the method comprises the steps of: in the first step, the concrete operation steps of geometric modeling by using the composite target are as follows:
s1, establishing a grid model of independent targets such as ships and vehicles by using CAD software;
s2, generating a rough background terrain grid model by using a Monte-Carlo method;
and S3, importing the grid models of the independent target and the background terrain into FEKO to generate a grid model of the composite target, so that the scattered field simulation result verification and the parameter model estimation are facilitated.
3. The method of claim 1, wherein the method comprises the steps of: in the fifth step, the specific operation steps of BRDF-FBM combined scattering modeling of the background terrain are as follows:
s1, the scattering field form of the rough terrain is E ═ Sigma Aiexp(jφi) Wherein A isiFor each bin scattering amplitude, phiiScattering phase for each bin;
s2, equating the background terrain to a surface element scattering center model distributed according to grid coordinates, wherein each surface element has different gradients;
s3, solving A by using bin inclination angle and BRDF modeliUsing grid positions and adding [0:2 π]Determining phi by the random asperity phase correction factori。
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