CN103136398B - A kind of method obtaining electromagnetic response curvilinear characteristic parameter and device thereof - Google Patents

Abstract

The invention discloses method and the device thereof of a kind of electromagnetic response curvilinear characteristic parameter obtaining artificial electromagnetic material unit structure, described method includes: set up for describing the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter；According to the partitioning model of described foundation, determine the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured.By the way, the present invention can be when specifying construction unit size to be measured, it is instantly available the electromagnetic response curvilinear characteristic parameter that this construction unit under this size is corresponding, without spending the time to carry out electromagnetic material cellular construction feature measurement, conveniently realize artificial electromagnetic material automatization, standardized design cycle, provide guarantee for carrying out grand designs and commercial application.

Description

A kind of method obtaining electromagnetic response curvilinear characteristic parameter and device thereof

Technical field

The present invention relates to Meta Materials field, particularly relate to method and the device thereof of a kind of electromagnetic response curvilinear characteristic parameter obtaining artificial electromagnetic material unit structure.

Background technology

Standardization, the Automation Design scheme for artificial electromagnetic material are the current difficult problems needing solution badly the most in the world.And the electromagnetic property measurement for artificial electromagnetic material construction unit is an important step indispensable in artificial electromagnetic material design process.

Research and design to artificial electromagnetic material at present still rests on manual adjustment and the stage of design by rule of thumb, lacks standardized design cycle, it is impossible to carry out grand designs and commercial application.

Therefore, it is necessary to provide method and device, the problem efficiently solving above-mentioned existence of a kind of electromagnetic response curvilinear characteristic parameter obtaining artificial electromagnetic material unit structure.

Summary of the invention

The technical problem that present invention mainly solves is to provide method and the device thereof of a kind of electromagnetic response curvilinear characteristic parameter obtaining artificial electromagnetic material unit structure, the research that can make artificial electromagnetic material is in standardized design cycle, carries out grand designs and commercial application to facilitate.

For solving above-mentioned technical problem, the technical scheme that the present invention uses is: a kind of method providing electromagnetic response curvilinear characteristic parameter obtaining artificial electromagnetic material unit structure, including: set up for describing the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter；According to the partitioning model of described foundation, determine the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured.

Wherein, the step of the described electromagnetic response curvilinear characteristic parameter determined corresponding to electromagnetic material cellular construction geometric parameter to be measured includes: determine the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured by the method for interpolation.

Wherein, described foundation includes for describing the step of the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter: use Bayes's partitioning model to set up the partitioning model for describing the corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter.

Wherein, the step that described Bayes's partitioning model is set up includes:

(1) given described electromagnetic material cellular construction geometric parameter and the set T=(t of electromagnetic response curvilinear characteristic parameter sample space χ and M point₁, t₂... t_M), t_i∈ χ, i ∈ 1,2 ..., M}, dividing described space χ becomes M nonoverlapping region R₁, R₂..., R_MAs follows:

R_i=x ∈ χ: | | x-t_i||≤||x-t_j| | to all of i ≠ j}

Wherein ${\left|\right|x_1,x_2,...,x_p\left|\right|}^2={\mathrm{\Σ}}_1^p{\mathrm{\ω}}_i^2{x}_i^2,{\mathrm{\Σ}}_i{\mathrm{\ω}}_i^2=1;$

(2) described region R is counted_iIn each class observe event number be respectively n_i1, n_i2..., n_iK, the complete likelihood of the most described space χ is:

Wherein φ=(φ₁..., φ_M), φ_i=(φ_i1..., φ_ik) it is described region R_iIn the probability of each classification, n_i=∑_kn_ik, ∑_kφ_ik=1；

(3) determining priori, the probability distribution of described priori is Dirichlet distribution.Dirichlet distribution is conjugate prior, and d-dimension Dirichlet is distributed Di_d(x₁..., x_d) density function be:

$f(x_1,...,x_d)=\frac{\mathrm{\Γ}\left({\mathrm{\Σ}}_1^{d+1}{\mathrm{\α}}_i\right)}{{\mathrm{\Π}}_1^{d+1}\mathrm{\Γ}\left({\mathrm{\α}}_i\right)}\left\{\underset{1}{\overset{d}{\mathrm{\Π}}}{x}_i^{{\mathrm{\α}}_i-1}\right\}{(1-\underset{1}{\overset{d}{\mathrm{\Σ}}}{x}_i)}^{{\mathrm{\α}}_{d+1}-1}$

Wherein 0≤x₁..., x_d≤ 1,Γ (.) represents Gama function, uses uniform prior to determine, it is assumed that the φ of zones of different in each class in each region of described model partition_iIt is different, makes α_i=1, then the priori on φ is as follows:

$p\left(\mathrm{\φ}\right|M)=\underset{i=1}{\overset{M}{\mathrm{\Π}}}{\mathrm{Di}}_{k-1}({\mathrm{\φ}}_{i1},...,{\mathrm{\φ}}_{i,k-1}|1)$

P (T | M) and p (M) is appointed as uniform prior, the priori of M be 1 ..., n} is uniformly distributed, and the data that n is total are counted, and the priori P-dimension unit hypercube of ω is uniformly portrayed；

(4) use described priori that posteriority is analyzed, the described parameter in the conjugate prior requirement analytical integration region of use φ: φ, T, ω, M, and meet:

Model parameter θ=T, ω, M},

At region R_iThe predicted density at midpoint is:

$p(y=K|x\∈R_i,T,\mathrm{\ω},M)=\frac{n_{\mathrm{ik}}+1}{n_i+K},$ Wherein k=1 ..., K

For solving above-mentioned technical problem, another technical solution used in the present invention is: provide the device of a kind of electromagnetic response curvilinear characteristic parameter obtaining artificial electromagnetic material unit structure, including: model building module, for setting up for describing the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter；Parameter determination module, for the partitioning model according to described foundation, determines the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured.

Wherein, described parameter determination module specifically for determining the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured by the method for interpolation.

Wherein, described model building module is specifically for using Bayes's partitioning model to set up the partitioning model for describing the corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter.

The invention has the beneficial effects as follows: be different from the situation of prior art, the present invention sets up the partitioning model between electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter, according to described model, certain electromagnetic material cellular construction geometric parameter known, the electromagnetic response curvilinear characteristic parameter of correspondence can be obtained, there is this corresponding relation, without spending the time to carry out electromagnetic material cellular construction feature measurement, artificial electromagnetic material automatization, standardized design cycle can be conveniently realized, provide guarantee for carrying out grand designs and commercial application.

Accompanying drawing explanation

Fig. 1 is the flow chart that the present invention obtains method one embodiment of the electromagnetic response curvilinear characteristic parameter of artificial electromagnetic material unit structure；

Fig. 2 is that the data space of two predictor variables in Bayes's partitioning model of the present invention divides schematic diagram；

Fig. 3 is the schematic diagram that the present invention obtains device one embodiment of the electromagnetic response curvilinear characteristic parameter of artificial electromagnetic material unit structure.

Detailed description of the invention

The present invention is described in detail with embodiment below in conjunction with the accompanying drawings.

Fig. 1 is the flow chart that the present invention obtains method one embodiment of the electromagnetic response curvilinear characteristic parameter of artificial electromagnetic material unit structure, as it is shown in figure 1, described method comprises the steps:

Step 101: set up for describing the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter；

In a preferred embodiment, described foundation includes for describing the step of the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter: use Bayes's partitioning model to set up the partitioning model for describing the corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter.

Bayes's partitioning model is as a kind of probabilistic causal reasoning model, its range of application is the widest, for using method, Bayesian model is mainly used in probability inference and decision-making, specifically, it is simply that by observing the stochastic variable the most observable stochastic variable of deduction in the case of information is incomplete, and observable random variable can be not more than one, the general initial stage can not be set to random value by observation variable, then carries out probability inference.Its basic thought is: known conditions probability density parameter expression and prior probability；Bayesian formula is utilized to be converted into posterior probability；Decision Classfication is carried out according to posterior probability size.

Wherein, the step that described Bayes's partitioning model is set up includes:

(1) given described electromagnetic material cellular construction geometric parameter and the set T=(t of electromagnetic response curvilinear characteristic parameter sample space χ and M point₁, t₂... t_M), t_i∈ χ, i ∈ 1,2 ..., M}, dividing described space χ becomes M nonoverlapping region R₁, R₂..., R_MAs follows:

R_i=x ∈ χ: | | x-t_i||≤||x-t_j| | to all of i ≠ j}

Wherein ${\left|\right|x_1,x_2,...,x_p\left|\right|}^2={\mathrm{\Σ}}_1^p{\mathrm{\ω}}_i^2{x}_i^2,{\mathrm{\Σ}}_i{\mathrm{\ω}}_i^2=1;$

(2) described region R is counted_iIn each class observe event number be respectively n_i1, n_i2..., n_iK, the complete likelihood of the most described space χ is:

Wherein φ=(φ₁..., φ_M), φ_i=(φ_i1..., φ_ik) it is described region R_iIn the probability of each classification, n_i=∑_kn_ik, ∑_kφ_ik=1；Such as Fig. 2, it it is the data space division figure of two predictor variables；

(3) determining priori, the probability distribution of described priori is Dirichlet distribution, and Dirichlet distribution is conjugate prior, and d-dimension Dirichlet is distributed Di_d(x₁..., x_d) density function be:

$f(x_1,...,x_d)=\frac{\mathrm{\Γ}\left({\mathrm{\Σ}}_1^{d+1}{\mathrm{\α}}_i\right)}{{\mathrm{\Π}}_1^{d+1}\mathrm{\Γ}\left({\mathrm{\α}}_i\right)}\left\{\underset{1}{\overset{d}{\mathrm{\Π}}}{x}_i^{{\mathrm{\α}}_i-1}\right\}{(1-\underset{1}{\overset{d}{\mathrm{\Σ}}}{x}_i)}^{{\mathrm{\α}}_{d+1}-1}$

Wherein 0≤x₁..., x_d≤ 1,Γ (.) represents Gama function, uses uniform prior to determine, it is assumed that the φ of zones of different in each class in each region of described model partition_iIt is different, makes α_i=1, then the priori on φ is as follows:

$p\left(\mathrm{\φ}\right|M)=\underset{i=1}{\overset{M}{\mathrm{\Π}}}{\mathrm{Di}}_{k-1}({\mathrm{\φ}}_{i1},...,{\mathrm{\φ}}_{i,k-1}|1)$

P (T | M) and p (M) is appointed as uniform prior, the priori of M be 1 ..., n} is uniformly distributed, and the data that n is total are counted, and the priori P-dimension unit hypercube of ω is uniformly portrayed；

(4) use described priori that posteriority is analyzed, the described parameter in the conjugate prior requirement analytical integration region of use φ: φ, T, ω, M, and meet:

Model parameter θ=T, ω, M},

At region R_iThe predicted density at midpoint is:

$p(y=k|x\∈R_i,T,\mathrm{\ω},M)=\frac{n_{\mathrm{ik}}+1}{n_i+K},$ Wherein k=1 ..., K

Likelihood function is a kind of function about the parameter in statistical model, represents the likelihood in model parameter, if overall X obeys distribution P (x；θ) (being probability density when X is random variable of continuous type, be probability distribution when X is discontinuous variable), θ is parameter to be estimated, X1, X2 ... Xn comes from the sample of overall X, x1, x2 ... xn is sample X1, X2, ... an observed value of Xn, then Joint Distribution (being probability density when X is random variable of continuous type, be probability distribution when X is discontinuous variable) L (θ)=L (x1, the x2 of sample, ..., xn；θ)=∏ P (xi；θ) it is referred to as likelihood function.Priori is to describe a variable in the case of lacking certain fact；And posteriority is considering the conditional probability after a fact.Posteriority can pass through Bayesian formula, calculates with priori and likelihood function.

Step 102: according to the partitioning model of described foundation, determine the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured.

In a preferred embodiment, the step of the described electromagnetic response curvilinear characteristic parameter determined corresponding to electromagnetic material cellular construction geometric parameter to be measured includes: determine the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured by the method for interpolation.So-called interpolation method, it it is a kind of important method of function approximation, also known as " interpolation ", if utilizing the functional value that function f (x) is done in certain interval, make suitable specific function, these aspects take given value, by the value of this specific function as the approximation of function f (x) on other interval aspects.Interpolation herein, can use Lagrange's interpolation, Newton interpolation, Hermite interpolation or piecewise polynomial interpolation etc..

It is different from the situation of prior art, the present invention sets up the partitioning model between electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter, according to described model, certain electromagnetic material cellular construction geometric parameter known, the electromagnetic response curvilinear characteristic parameter of correspondence can be obtained, there is this corresponding relation, without spending the time to carry out electromagnetic material cellular construction feature measurement, artificial electromagnetic material automatization, standardized design cycle can be conveniently realized, provide guarantee for carrying out grand designs and commercial application.

Fig. 3 is the structural representation that the present invention obtains device one embodiment of the electromagnetic response curvilinear characteristic parameter of artificial electromagnetic material unit structure.As it is shown on figure 3, described device includes: model building module 301 and parameter determination module 302.

Model building module 301 is for setting up for describing the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter.

In a preferred embodiment, described model building module is specifically for using Bayes's partitioning model to set up the partitioning model for describing the corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter.Bayes's partitioning model is as a kind of probabilistic causal reasoning model, its range of application is the widest, for using method, Bayesian model is mainly used in probability inference and decision-making, specifically, it is simply that by observing the stochastic variable the most observable stochastic variable of deduction in the case of information is incomplete, and observable random variable can be not more than one, the general initial stage can not be set to random value by observation variable, then carries out probability inference.Its basic thought is: known conditions probability density parameter expression and prior probability；Bayesian formula is utilized to be converted into posterior probability；Decision Classfication is carried out according to posterior probability size.

Parameter determination module 302, for the partitioning model according to described foundation, determines the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured.

In a preferred embodiment, described parameter determination module specifically for determining the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured by the method for interpolation.So-called interpolation method, it it is a kind of important method of function approximation, also known as " interpolation ", if utilizing the functional value that function f (x) is done in certain interval, make suitable specific function, these aspects take given value, by the value of this specific function as the approximation of function f (x) on other interval aspects.Interpolation herein, can use Lagrange's interpolation, Newton interpolation, Hermite interpolation or piecewise polynomial interpolation etc..

It is different from the situation of prior art, the present invention sets up the partitioning model between electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter, according to described model, certain electromagnetic material cellular construction geometric parameter known, the electromagnetic response curvilinear characteristic parameter of correspondence can be obtained, there is this corresponding relation, without spending the time to carry out electromagnetic material cellular construction feature measurement, artificial electromagnetic material automatization, standardized design cycle can be conveniently realized, provide guarantee for carrying out grand designs and commercial application.

The foregoing is only embodiments of the invention; not thereby the scope of the claims of the present invention is limited; every equivalent structure utilizing description of the invention and accompanying drawing content to be made or equivalence flow process conversion; or directly or indirectly it is used in other relevant technical fields, the most in like manner it is included in the scope of patent protection of the present invention.

Claims (4)

1. the method for the electromagnetic response curvilinear characteristic parameter obtaining artificial electromagnetic material unit structure, it is characterized in that, including: set up for describing the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter；According to the partitioning model of described foundation, determine the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured；

Described foundation includes for describing the step of the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter: use Bayes's partitioning model to set up the partitioning model for describing the corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter；

The step that described Bayes's partitioning model is set up includes: (1) given described electromagnetic material cellular construction geometric parameter and the set T=(t of electromagnetic response curvilinear characteristic parameter sample space χ and M point₁, t₂... t_M), t_i∈ χ, i ∈ 1,2 ..., M}, dividing described space χ becomes M nonoverlapping region R₁, R₂..., R_MAs follows: R_i=x ∈ χ: | | x-t_i||≤||x-t_j| | to all of i ≠ j}

Wherein $\left|\right|x_1,x_2,...,x_p|{|}^2={\mathrm{\Σ}}_1^p{\mathrm{\ω}}_i^2{x}_i^2,{\mathrm{\Σ}}_i{\mathrm{\ω}}_i^2=1;$

(2) described region R is counted_iIn each class observe event number be respectively n_i1, n_i2..., n_iK, the complete likelihood of the most described space χ is:

WhereinIt is described region R_iIn the probability of each classification, n_i=∑_kn_ik,

(3) determining priori, the probability distribution of described priori is Dirichlet distribution, and Dirichlet distribution is conjugate prior, and d-dimension Dirichlet is distributed Di_d(x₁..., x_d) density function be:

$f(x_1,...,x_d)=\frac{\mathrm{\Γ}\left({\mathrm{\Σ}}_1^{d+1}{\mathrm{\α}}_i\right)}{{\Π}_1^{d+1}\mathrm{\Γ}\left({\mathrm{\α}}_i\right)}\left\{\underset{1}{\overset{d}{\Π}}{x}_i^{{\mathrm{\α}}_i-1}\right\}{(1-\underset{1}{\overset{d}{\mathrm{\Σ}}}{x}_i)}^{{\mathrm{\α}}_{d+1}-1}$

Wherein 0≤x₁..., x_d≤ 1,Γ (.) represents Gama function, uses uniform prior to determine, it is assumed that zones of different in each class in each region of described model partitionIt is different, makes α_i=1, thenOn priori as follows:

$p\left(\mathrm{\φ}\right|M)=\underset{i=1}{\overset{M}{\Π}}{\mathrm{Di}}_{k-1}({\mathrm{\φ}}_{i1},...,{\mathrm{\φ}}_{i,k-1}|1)$

P (T | M) and p (M) is appointed as uniform prior, the priori of M is { 1, ..., n} is uniformly distributed, n is total described electromagnetic material cellular construction geometric parameter and the data of electromagnetic response curvilinear characteristic parameter are counted, and the priori P-dimension unit hypercube of ω is uniformly portrayed；

(4) use described priori that posteriority is analyzed, useConjugate prior require the described parameter in analytical integration region:T, ω, M, and meet:

Model parameter θ={ T, ω, M}；At region R_iThe predicted density at midpoint is:

$p(y=k|x\∈R_i,T,\mathrm{\ω},M)=\frac{n_{ik}+1}{n_i+K},$

Wherein k=1 ..., K.

Method the most according to claim 1, it is characterized in that, the step of the described electromagnetic response curvilinear characteristic parameter determined corresponding to electromagnetic material cellular construction geometric parameter to be measured includes: determine the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured by the method for interpolation.

3. the device of the electromagnetic response curvilinear characteristic parameter obtaining artificial electromagnetic material unit structure, it is characterized in that, including: model building module, for setting up for describing the partitioning model of corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter；Parameter determination module, for the partitioning model according to described foundation, determines the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured；

Described model building module is set up for the partitioning model describing the corresponding relation between described electromagnetic material cellular construction geometric parameter and electromagnetic response curvilinear characteristic parameter for using Bayes's partitioning model；

The step that described Bayes's partitioning model is set up includes: (1) given described electromagnetic material cellular construction geometric parameter and the set T=(t of electromagnetic response curvilinear characteristic parameter sample space χ and M point₁, t₂... t_M), t_i∈ χ, i ∈ 1,2 ..., M}, dividing described space χ becomes M nonoverlapping region R₁, R₂..., R_MAs follows: R_i=x ∈ χ: | | x-t_i||≤||x-t_j| | to all of i ≠ j}

Wherein $\left|\right|x_1,x_2,...,x_p|{|}^2={\mathrm{\Σ}}_1^p{\mathrm{\ω}}_i^2{x}_i^2,{\mathrm{\Σ}}_i{\mathrm{\ω}}_i^2=1;$

(2) described region R is counted_iIn each class observe event number be respectively n_i1, n_i2..., n_iK, the complete likelihood of the most described space χ is:

WhereinIt is described region R_iIn the probability of each classification, n_i=∑_kn_ik,

(3) determining priori, the probability distribution of described priori is Dirichlet distribution, and Dirichlet distribution is conjugate prior, and d-dimension Dirichlet is distributed Di_d(x₁..., x_d) density function be:

$f(x_1,...,x_d)=\frac{\mathrm{\Γ}\left({\mathrm{\Σ}}_1^{d+1}{\mathrm{\α}}_i\right)}{{\Π}_1^{d+1}\mathrm{\Γ}\left({\mathrm{\α}}_i\right)}\left\{\underset{1}{\overset{d}{\Π}}{x}_i^{{\mathrm{\α}}_i-1}\right\}{(1-\underset{1}{\overset{d}{\mathrm{\Σ}}}{x}_i)}^{{\mathrm{\α}}_{d+1}-1}$

Wherein 0≤x₁..., x_d≤ 1,Γ (.) represents Gama function, uses uniform prior to determine, it is assumed that zones of different in each class in each region of described model partitionIt is different, makes α_i=1, thenOn priori as follows:

$p\left(\mathrm{\φ}\right|M)=\underset{i=1}{\overset{M}{\Π}}{\mathrm{Di}}_{k-1}({\mathrm{\φ}}_{i1},...,{\mathrm{\φ}}_{i,k-1}|1)$

P (T | M) and p (M) is appointed as uniform prior, the priori of M is { 1, ..., n} is uniformly distributed, n is total described electromagnetic material cellular construction geometric parameter and the data of electromagnetic response curvilinear characteristic parameter are counted, and the priori P-dimension unit hypercube of ω is uniformly portrayed；

(4) use described priori that posteriority is analyzed, useConjugate prior require the described parameter in analytical integration region:T, ω, M, and meet:

Model parameter θ={ T, ω, M}；At region R_iThe predicted density at midpoint is:

$p(y=k|x\∈R_i,T,\mathrm{\ω},M)=\frac{n_{ik}+1}{n_i+K},$

Wherein k=1 ..., K.

Device the most according to claim 3, it is characterised in that described parameter determination module specifically for determining the electromagnetic response curvilinear characteristic parameter corresponding to electromagnetic material cellular construction geometric parameter to be measured by the method for interpolation.