CN118348529A - Quantitative diffraction tomography method and system for weak scatterers - Google Patents
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- LFQSCWFLJHTTHZ-UHFFFAOYSA-N Ethanol Chemical compound CCO LFQSCWFLJHTTHZ-UHFFFAOYSA-N 0.000 description 3
- 238000013135 deep learning Methods 0.000 description 3
- 239000008157 edible vegetable oil Substances 0.000 description 3
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Abstract
The invention discloses a quantitative diffraction tomography aliasing correction method and a quantitative diffraction tomography aliasing correction system for a weak scatterer, wherein the method comprises the following steps: constructing an inversion calculation mathematical model based on the antenna array structure; performing Fourier transform on the inversion calculation mathematical model, and decoupling to obtain a relative dielectric constant and a conductivity which are decoupled under single frequency; performing two-dimensional Fourier inverse transformation on the relative dielectric constant space spectrum and the conductivity space spectrum after coherent accumulation to obtain a relative dielectric constant and a conductivity which are decoupled under multiple frequencies, obtaining complete scattering field information of an object to be tested according to the relative dielectric constant and the conductivity which are decoupled under single frequency and the relative dielectric constant and the conductivity which are decoupled under multiple frequencies, and outputting an image result of the relative dielectric constant and the conductivity of the object to be tested; the invention has the advantages that: and the quantitative inversion precision is improved.
Description
The application claims priority of China patent application filed in the year 2023, month 12 and 29 with the application number 2023118690975 and the application name of a quantitative diffraction tomography aliasing correction method and system of weak scatterers.
Technical Field
The invention relates to the field of electromagnetic scattering inversion, in particular to a quantitative diffraction tomography method and a quantitative diffraction tomography system for a weak scatterer.
Background
The electromagnetic backscattering problem, namely the electromagnetic inversion problem, is to calculate the relative dielectric constant of the target based on the information of the scattering field of the target and invert the characteristics of the target. Inversion technology has been widely used in many fields such as medical imaging and through-the-wall radar.
However, how to effectively solve the reliability and the calculation efficiency of inversion calculation is still a challenge so far. Common methods include various nonlinear iterative methods, deep learning methods, and linearization methods. Among them, the nonlinear iterative method based on the known determination and random achieves better results, but still has the problem of huge calculation amount. In addition, deep learning techniques based on neural networks are attracting more attention, for example, a fast imaging method for solving a highly nonlinear backscatter problem based on deep learning disclosed in chinese patent publication No. CN114255293a, which can improve accuracy and efficiency, but is not well applied due to poor generalization ability. Diffraction tomography (Diffraction Tomography, DT) is a linear method of solving the electromagnetic inversion problem and enables the calculation of the relationship between retrievable information content and measurement configuration, which is of great significance for inversion system involvement.
On the assumption of weak scattering, the contrast spatial spectrum at a particular frequency is a linear mapping of the scattered field data. Although better noise rejection performance can be achieved with more frequencies, aliasing of the spatial spectrum becomes severe with multi-frequency data, with reconstruction errors given a quantity of inversion, and lower accuracy of quantitative inversion.
Disclosure of Invention
The invention aims to provide a quantitative diffraction tomography method of a weak scatterer so as to improve quantitative inversion accuracy.
The invention solves the technical problems by the following technical means: a quantitative diffraction tomography method of a weak scatterer, comprising the steps of:
Step1, constructing an inversion calculation mathematical model based on an antenna array structure, wherein the inversion calculation mathematical model comprises scattered field data, and the scattered field data are dielectric constant and conductivity;
Step 2, performing Fourier transform on the inversion calculation mathematical model, multiplying the Fourier transform by a spatial spectrum under multiple frequencies to obtain a compensated contrast spatial spectrum, interpolating the contrast spatial spectrum, and performing inverse Fourier transform on the contrast spatial spectrum after interpolation to obtain a decoupled relative dielectric constant and conductivity under single frequency;
Step 3, performing two-dimensional Fourier transform on the antenna array signals to obtain a relative dielectric constant spatial spectrum and a conductivity spatial spectrum, performing coherent accumulation on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum, and performing two-dimensional Fourier inverse transform on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum after coherent accumulation to obtain a decoupled relative dielectric constant and conductivity under multiple frequencies;
and 4, obtaining the complete scattering field information of the object to be detected according to the relative dielectric constant and the electric conductivity of decoupling under single frequency and the relative dielectric constant and the electric conductivity of decoupling under multiple frequencies, and outputting an image result of the relative dielectric constant and the electric conductivity of the object to be detected.
Further, the step 1 of constructing an inversion calculation mathematical model includes:
Setting an antenna array structure, wherein the antenna array structure comprises a plurality of array units, each array unit comprises a transmitting antenna and a receiving antenna, the transmitting antenna irradiates a target object and propagates in free space, the receiving antenna detects a total field scattered by the target object and expands according to a scalar Grignard function, and therefore an inversion calculation mathematical model is formed:
Wherein E sct is the scattered field and E tot is the total field; Wave number corresponding to a certain frequency; omega is the angular frequency; epsilon 0 and mu 0 are the dielectric constant and conductivity, respectively, in free space; g is a scalar Grignard function; ρ R is the coordinates of the receiving antenna, ρ is the coordinates of the object to be measured; g (ρ R, ρ; ω) is the Green's function of the TM wave and
Wherein,As a first class of zero-order Hankel functions, χ is a contrast function defined as a complex form of dielectric constant and conductivity differences as follows:
Wherein epsilon r (ρ) is the relative dielectric constant of the object to be measured, sigma (ρ) is the electrical conductivity of the object to be measured, epsilon rb is the relative dielectric constant of the free space background, and j is the complex domain symbol form.
Further, the step2 includes:
Step 2.1, carrying out Fourier transform on the inversion calculation mathematical model, multiplying the Fourier transform by a spatial spectrum under multiple frequencies, and obtaining a compensated contrast spatial spectrum:
wherein, gamma res is the space spectrum coordinate of the receiving antenna, gamma r′es is the space spectrum coordinate of the transmitting antenna, Representing the spatial spectrum of the scattered field, I (ω) representing the excitation source spectrum, z' representing the z-direction spatial domain coordinates of the antenna array.
Step 2.2, carrying out one-dimensional interpolation operation of contrast space spectrum distance direction;
And 2.3, performing inverse Fourier transform (first inversion) on the contrast space spectrum after interpolation, and decoupling to obtain a relative dielectric constant epsilon r (rho) and a conductivity sigma (rho) which are decoupled at a single frequency.
Further, the step 3 includes:
Step 3.1, performing two-dimensional Fourier transform on the antenna array signals to obtain a relative dielectric constant spatial spectrum of N f frequencies And conductivity spatial spectrum
Step 3.2, spatial spectrum of relative dielectric constantAnd conductivity spatial spectrumPerforming coherent accumulation;
Step 3.3, performing two-dimensional Fourier transform (second inversion) on the relative dielectric constant and conductivity spatial spectrum after coherent accumulation to obtain the decoupled relative dielectric constant and conductivity under multiple frequencies:
wherein x is the x-direction space domain coordinate of the object to be measured, z is the z-direction space domain coordinate of the object to be measured, For estimating the relative permittivity, epsilon rb is the relative permittivity of the free space background,For the relative dielectric constant of decoupling at multiple frequencies, K x is the x-direction spectral domain coordinate of the object to be measured, K z is the z-direction spectral domain coordinate of the object to be measured,For decoupled conductivity at multiple frequencies, ω n is the nth angular frequency.
The invention also provides a quantitative diffraction tomography system of a weak scatterer, comprising:
the model construction module is used for constructing an inversion calculation mathematical model based on the antenna array structure, wherein the inversion calculation mathematical model comprises scattered field data, and the scattered field data are dielectric constant and conductivity;
The first inversion module is used for carrying out Fourier transform on the inversion calculation mathematical model, multiplying the Fourier transform by the spatial spectrum under multiple frequencies to obtain a compensated contrast spatial spectrum, interpolating the contrast spatial spectrum, and carrying out inverse Fourier transform on the contrast spatial spectrum after interpolation to obtain a decoupled relative dielectric constant and conductivity under single frequency;
The second inversion module is used for carrying out two-dimensional Fourier transform on the antenna array signals to obtain a relative dielectric constant spatial spectrum and a conductivity spatial spectrum, carrying out coherent accumulation on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum, and carrying out two-dimensional Fourier inverse transform on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum after coherent accumulation to obtain a relative dielectric constant and a conductivity which are decoupled under multiple frequencies;
And the result output module is used for obtaining the complete scattering field information of the object to be detected according to the decoupled relative dielectric constant and conductivity under single frequency and the decoupled relative dielectric constant and conductivity under multiple frequencies and outputting the image result of the relative dielectric constant and conductivity of the object to be detected.
Further, the model construction module constructs an inversion calculation mathematical model, including:
Setting an antenna array structure, wherein the antenna array structure comprises a plurality of array units, each array unit comprises a transmitting antenna and a receiving antenna, the transmitting antenna irradiates a target object and propagates in free space, the receiving antenna detects a total field scattered by the target object and expands according to a scalar Grignard function, and therefore an inversion calculation mathematical model is formed:
Wherein E sct is the scattered field and E tot is the total field; Wave number corresponding to a certain frequency; omega is the angular frequency; epsilon 0 and mu 0 are the dielectric constant and conductivity, respectively, in free space; g is a scalar Grignard function; ρ R is the coordinates of the receiving antenna, ρ is the coordinates of the object to be measured; g (ρ R, ρ; ω) is the Green's function of the TM wave and
Wherein,As a first class of zero-order Hankel functions, χ is a contrast function defined as a complex form of dielectric constant and conductivity differences as follows:
Wherein epsilon r (ρ) is the relative dielectric constant of the object to be measured, sigma (ρ) is the electrical conductivity of the object to be measured, epsilon rb is the relative dielectric constant of the free space background, and j is the complex domain symbol form.
Further, the first inversion module includes:
The first spatial spectrum calculation unit is used for carrying out Fourier change on the inversion calculation mathematical model, then multiplying the spatial spectrum under multiple frequencies, and then obtaining a compensated contrast spatial spectrum:
wherein, gamma res is the space spectrum coordinate of the receiving antenna, gamma r′es is the space spectrum coordinate of the transmitting antenna, Representing the spatial spectrum of the scattered field, I (ω) representing the excitation source spectrum, z' representing the z-direction spatial domain coordinates of the antenna array.
The interpolation unit is used for carrying out one-dimensional interpolation operation on the contrast space spectrum distance direction;
and the first decoupling unit is used for carrying out inverse Fourier transform (first inversion) on the contrast space spectrum after interpolation, and decoupling to obtain a relative dielectric constant epsilon r (rho) and a conductivity sigma (rho) which are decoupled at a single frequency.
Further, the second inversion module includes:
A second spatial spectrum calculation unit for performing two-dimensional Fourier transform on the antenna array signal to obtain N f frequencies of relative dielectric constant spatial spectrums And conductivity spatial spectrum
A coherent accumulation unit for spatial spectrum of relative dielectric constantAnd conductivity spatial spectrumPerforming coherent accumulation;
the second decoupling unit is used for performing two-dimensional Fourier transform (second inversion) on the relative dielectric constant and the conductivity spatial spectrum after coherent accumulation to obtain the relative dielectric constant and the conductivity which are decoupled under multiple frequencies:
wherein x is the x-direction space domain coordinate of the object to be measured, z is the z-direction space domain coordinate of the object to be measured, For estimating the relative permittivity, epsilon rb is the relative permittivity of the free space background,For the relative dielectric constant of decoupling at multiple frequencies, K x is the x-direction spectral domain coordinate of the object to be measured, K z is the z-direction spectral domain coordinate of the object to be measured,For decoupled conductivity at multiple frequencies, ω n is the nth angular frequency.
The invention has the advantages that:
(1) The first inversion is to perform Fourier transform on the contrast space spectrum after interpolation to obtain the relative dielectric constant and the electrical conductivity of decoupling under single frequency, and then the second inversion is to invert the space spectrum of the antenna array signal to obtain the relative dielectric constant and the electrical conductivity of decoupling under multiple frequencies, so that the problem of aliasing of the space spectrum under the condition of multi-frequency data is solved, reconstruction errors caused by quantitative inversion are reduced, inversion precision is provided, and secondly, the complete scattering field information of an object to be detected is obtained through the relative dielectric constant and the electrical conductivity of decoupling under the single frequency and the relative dielectric constant and the electrical conductivity of decoupling under the multi-frequency, so that the image result of the object to be detected is more clear, and the inversion precision is further improved.
(2) The present invention suppresses noise by enhancing a coherent signal after accumulation by using different frequency phase information of all spectrums including an aliasing region. There are many overlapping portions for the frequency bands where the phase information is very close to each other. When all data are used together, the effect of coherent superposition can be achieved, so that the signal-to-noise ratio is improved, noise is suppressed, and inversion of low-signal-to-noise ratio data is very important. The method is still valid for multi-base/multi-frequency measurement configurations such as GPR.
Drawings
FIG. 1 is a flow chart of a method for quantitative diffraction tomography of weak scatterers according to an embodiment of the present invention;
FIG. 2 is a diagram showing a distribution structure of an antenna array in a quantitative diffraction tomography method of a weak scatterer according to an embodiment of the present invention;
FIG. 3 is a real object display diagram of an object to be detected (alcohol, water and edible oil) in a quantitative diffraction tomography method of a weak scatterer according to an embodiment of the present invention;
Fig. 4 is a graph showing the result of inversion calculation of an object to be measured (alcohol, water and edible oil) in a quantitative diffraction tomography method of a weak scatterer according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
As shown in fig. 1, the present invention provides a quantitative diffraction tomography method of a weak scatterer, comprising the steps of:
S1, as shown in FIG. 2, FIG. 2 is a two-dimensional antenna array distribution structure diagram based on a linear array structure. Based on the array structure, an inversion calculation mathematical model is constructed. The relative permittivity epsilon and the conductivity sigma of the target object are set. The transmitting antenna irradiates the target object and propagates through the free space, and the receiving antenna detects the total field scattered by the target object, in this embodiment, in the free space, based on the antenna array, the millimeter wave radar signal is adopted to transmit electromagnetic waves to the object to be detected, and the echo signal reflected by the object to be detected is received; wherein, the object to be measured is set as water, alcohol and edible oil, and the physical diagram of the object to be measured is shown in fig. 3. Combining the measured information, developing according to a scalar green function, thereby forming an inversion calculation mathematical model:
Wherein E sct is the fringe field, which relates to ρ R,ρT; the function of ω, E tot is the total field, which is for ρ, ρ T; a function of ω; wave number corresponding to a certain frequency; omega is the angular frequency; epsilon 0 and mu 0 are the dielectric constant and conductivity, respectively, in free space; g is a scalar Grignard function; ρ R is the coordinates of the receiving antenna, ρ is the coordinates of the object to be measured, ρ T is the coordinates of the transmitting antenna; g (ρ R, ρ; ω) is the Green's function of the TM wave and
Wherein,As a first class of zero-order Hankel functions, χ is a contrast function defined as a complex form of dielectric constant and conductivity differences as follows:
Wherein epsilon r (ρ) is the relative dielectric constant of the object to be measured, sigma (ρ) is the electrical conductivity of the object to be measured, epsilon rb is the relative dielectric constant of the free space background, and j is the complex domain symbol form.
S2, performing Fourier transform on the inversion calculation mathematical model, multiplying the inversion calculation mathematical model by a spatial spectrum under multiple frequencies to obtain a compensated contrast spatial spectrum, interpolating the contrast spatial spectrum, performing inverse Fourier transform on the contrast spatial spectrum after interpolation to obtain a decoupled relative dielectric constant and conductivity under single frequency, wherein the specific process is as follows:
Step 2.1, carrying out Fourier transform on the inversion calculation mathematical model, multiplying the Fourier transform by a spatial spectrum under multiple frequencies, and obtaining a compensated contrast spatial spectrum:
wherein, gamma res is the space spectrum coordinate of the receiving antenna, gamma r′es is the space spectrum coordinate of the transmitting antenna, Representing the spatial spectrum of the scattered field, I (ω) representing the excitation source spectrum, z' representing the z-direction spatial domain coordinates of the antenna array.
Step 2.2, carrying out one-dimensional interpolation operation of contrast space spectrum distance direction;
And 2.3, performing inverse Fourier transform (first inversion) on the contrast space spectrum after interpolation, and decoupling to obtain a relative dielectric constant epsilon r (rho) and a conductivity sigma (rho) which are decoupled at a single frequency.
S3, performing two-dimensional Fourier transform on the antenna array signals to obtain a relative dielectric constant spatial spectrum and a conductivity spatial spectrum, performing coherent accumulation on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum, and performing two-dimensional Fourier inverse transform on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum after coherent accumulation to obtain a decoupled relative dielectric constant and conductivity under multiple frequencies; the specific process is as follows:
Step 3.1, performing two-dimensional Fourier transform on the antenna array signals to obtain a relative dielectric constant spatial spectrum of N f frequencies And conductivity spatial spectrumWherein, performing two-dimensional fourier transform on the antenna array signal refers to performing fourier transform on both the transmitting antenna array and the receiving antenna array.
Step 3.2, spatial spectrum of relative dielectric constantAnd conductivity spatial spectrumPerforming coherent accumulation;
Step 3.3, performing two-dimensional Fourier transform (second inversion) on the relative dielectric constant and conductivity spatial spectrum after coherent accumulation to obtain the decoupled relative dielectric constant and conductivity under multiple frequencies:
wherein x is the x-direction space domain coordinate of the object to be measured, z is the z-direction space domain coordinate of the object to be measured, For estimating the relative permittivity, epsilon rb is the relative permittivity of the free space background,For the relative dielectric constant of decoupling at multiple frequencies, K x is the x-direction spectral domain coordinate of the object to be measured, K z is the z-direction spectral domain coordinate of the object to be measured,For decoupled conductivity at multiple frequencies, ω n is the nth angular frequency.
S4, obtaining complete scattering field information of the object to be detected according to the relative dielectric constant and the electric conductivity of decoupling under single frequency and the relative dielectric constant and the electric conductivity of decoupling under multiple frequencies, and outputting an image result of the relative dielectric constant and the electric conductivity of the object to be detected. As shown in fig. 4. Among them, the test material is a strong scatterer, and the result is only qualitative.
Through the technical scheme, the invention enhances the coherent signal after accumulation by utilizing different frequency phase information of all frequency spectrums including the aliasing area, and suppresses noise. There are many overlapping portions for the frequency bands where the phase information is very close to each other. When all data are used together, the effect of coherent superposition can be achieved, so that the signal-to-noise ratio is improved, noise is suppressed, and inversion of low-signal-to-noise ratio data is very important. The method is still valid for multi-base/multi-frequency measurement configurations such as GPR.
Example 2
Based on embodiment 1, embodiment 2 of the present invention further provides a quantitative diffraction tomography system of a weak scatterer, including:
the model construction module is used for constructing an inversion calculation mathematical model based on the antenna array structure, wherein the inversion calculation mathematical model comprises scattered field data, and the scattered field data are dielectric constant and conductivity;
The first inversion module is used for carrying out Fourier transform on the inversion calculation mathematical model, multiplying the Fourier transform by the spatial spectrum under multiple frequencies to obtain a compensated contrast spatial spectrum, interpolating the contrast spatial spectrum, and carrying out inverse Fourier transform on the contrast spatial spectrum after interpolation to obtain a decoupled relative dielectric constant and conductivity under single frequency;
The second inversion module is used for carrying out two-dimensional Fourier transform on the antenna array signals to obtain a relative dielectric constant spatial spectrum and a conductivity spatial spectrum, carrying out coherent accumulation on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum, and carrying out two-dimensional Fourier inverse transform on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum after coherent accumulation to obtain a relative dielectric constant and a conductivity which are decoupled under multiple frequencies;
And the result output module is used for obtaining the complete scattering field information of the object to be detected according to the decoupled relative dielectric constant and conductivity under single frequency and the decoupled relative dielectric constant and conductivity under multiple frequencies and outputting the image result of the relative dielectric constant and conductivity of the object to be detected.
Specifically, the model construction module constructs an inversion calculation mathematical model, including:
Setting an antenna array structure, wherein the antenna array structure comprises a plurality of array units, each array unit comprises a transmitting antenna and a receiving antenna, the transmitting antenna irradiates a target object and propagates in free space, the receiving antenna detects a total field scattered by the target object and expands according to a scalar Grignard function, and therefore an inversion calculation mathematical model is formed:
Esct(ρR,ρT;ω)＝k2∫G(ρR,ρ;ω)χ(ρ;ω)Etot(ρ,ρT；ω)dρ
Wherein E sct is the fringe field, which relates to ρ R,ρT; the function of ω, E tot is the total field, which is for ρ, ρ T; a function of ω; wave number corresponding to a certain frequency; omega is the angular frequency; epsilon 0 and mu 0 are the dielectric constant and conductivity, respectively, in free space; g is a scalar Grignard function; ρ R is the coordinates of the receiving antenna, ρ is the coordinates of the object to be measured, ρ T is the coordinates of the transmitting antenna; g (ρ R, ρ; ω) is the Green's function of the TM wave and
Wherein,As a first class of zero-order Hankel functions, χ is a contrast function defined as a complex form of dielectric constant and conductivity differences as follows:
Wherein epsilon r (ρ) is the relative dielectric constant of the object to be measured, sigma (ρ) is the electrical conductivity of the object to be measured, epsilon rb is the relative dielectric constant of the free space background, and j is the complex domain symbol form.
More specifically, the first inversion module includes:
The first spatial spectrum calculation unit is used for carrying out Fourier change on the inversion calculation mathematical model, then multiplying the spatial spectrum under multiple frequencies, and then obtaining a compensated contrast spatial spectrum:
wherein, gamma res is the space spectrum coordinate of the receiving antenna, gamma r′es is the space spectrum coordinate of the transmitting antenna, Representing the spatial spectrum of the scattered field, I (ω) representing the excitation source spectrum, z' representing the z-direction spatial domain coordinates of the antenna array.
The interpolation unit is used for carrying out one-dimensional interpolation operation on the contrast space spectrum distance direction;
and the first decoupling unit is used for carrying out inverse Fourier transform (first inversion) on the contrast space spectrum after interpolation, and decoupling to obtain a relative dielectric constant epsilon r (rho) and a conductivity sigma (rho) which are decoupled at a single frequency.
More specifically, the second inversion module includes:
A second spatial spectrum calculation unit for performing two-dimensional Fourier transform on the antenna array signal to obtain N f frequencies of relative dielectric constant spatial spectrums And conductivity spatial spectrum
A coherent accumulation unit for spatial spectrum of relative dielectric constantAnd conductivity spatial spectrumPerforming coherent accumulation;
the second decoupling unit is used for performing two-dimensional Fourier transform (second inversion) on the relative dielectric constant and the conductivity spatial spectrum after coherent accumulation to obtain the relative dielectric constant and the conductivity which are decoupled under multiple frequencies:
wherein x is the x-direction space domain coordinate of the object to be measured, z is the z-direction space domain coordinate of the object to be measured, For estimating the relative permittivity, epsilon rb is the relative permittivity of the free space background,For the relative dielectric constant of decoupling at multiple frequencies, K x is the x-direction spectral domain coordinate of the object to be measured, K z is the z-direction spectral domain coordinate of the object to be measured,For decoupled conductivity at multiple frequencies, ω n is the nth angular frequency.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (8)
1. A method of quantitative diffraction tomography of a weak scatterer, comprising the steps of:
Step1, constructing an inversion calculation mathematical model based on an antenna array structure, wherein the inversion calculation mathematical model comprises scattered field data, and the scattered field data are dielectric constant and conductivity;
Step 2, performing Fourier transform on the inversion calculation mathematical model, multiplying the Fourier transform by a spatial spectrum under multiple frequencies to obtain a compensated contrast spatial spectrum, interpolating the contrast spatial spectrum, and performing inverse Fourier transform on the contrast spatial spectrum after interpolation to obtain a decoupled relative dielectric constant and conductivity under single frequency;
Step 3, performing two-dimensional Fourier transform on the antenna array signals to obtain a relative dielectric constant spatial spectrum and a conductivity spatial spectrum, performing coherent accumulation on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum, and performing two-dimensional Fourier inverse transform on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum after coherent accumulation to obtain a decoupled relative dielectric constant and conductivity under multiple frequencies;
and 4, obtaining the complete scattering field information of the object to be detected according to the relative dielectric constant and the electric conductivity of decoupling under single frequency and the relative dielectric constant and the electric conductivity of decoupling under multiple frequencies, and outputting an image result of the relative dielectric constant and the electric conductivity of the object to be detected.
2. The method of quantitative diffraction tomography of weak scatterers according to claim 1, wherein the constructing an inversion calculation mathematical model in step 1 comprises:
Setting an antenna array structure, wherein the antenna array structure comprises a plurality of array units, each array unit comprises a transmitting antenna and a receiving antenna, the transmitting antenna irradiates a target object and propagates in free space, the receiving antenna detects a total field scattered by the target object and expands according to a scalar Grignard function, and therefore an inversion calculation mathematical model is formed:
Esct＝k2∫G(ρR,ρ;ω)χ(ρ;ω)Etotdρ
Wherein E sct is the scattered field and E tot is the total field; wave number corresponding to a certain frequency; omega is the angular frequency; epsilon 0 and mu 0 are the dielectric constant and conductivity, respectively, in free space; g is a scalar Grignard function; ρ R is the coordinates of the receiving antenna, ρ is the coordinates of the object to be measured, ρ T is the coordinates of the transmitting antenna; g (ρ R, ρ; ω) is the Green's function of the TM wave and
Wherein,As a first class of zero-order Hankel functions, χ is a contrast function defined as a complex form of dielectric constant and conductivity differences as follows:
Wherein epsilon r (ρ) is the relative dielectric constant of the object to be measured, sigma (ρ) is the electrical conductivity of the object to be measured, epsilon rb is the relative dielectric constant in free space, and j is the complex domain symbol form.
3. The method for quantitative diffraction tomography aliasing correction of a weak scatterer of claim 2, wherein step 2 comprises:
Step 2.1, carrying out Fourier transform on the inversion calculation mathematical model, multiplying the Fourier transform by a spatial spectrum under multiple frequencies, and obtaining a compensated contrast spatial spectrum:
wherein, gamma res is the space spectrum coordinate of the receiving antenna, gamma r′es is the space spectrum coordinate of the transmitting antenna, Representing the spatial spectrum of the scattered field, I (ω) representing the excitation source spectrum, z' representing the z-direction spatial domain coordinates of the antenna array.
Step 2.2, carrying out one-dimensional interpolation operation of contrast space spectrum distance direction;
And 2.3, performing inverse Fourier transform on the contrast space spectrum after interpolation, and decoupling to obtain a relative dielectric constant epsilon r (rho) and a conductivity sigma (rho) which are decoupled under a single frequency.
4. A method of quantitative diffraction tomography of weak scatterers according to claim 3, wherein step 3 comprises:
Step 3.1, performing two-dimensional Fourier transform on the antenna array signals to obtain a relative dielectric constant spatial spectrum of N f frequencies And conductivity spatial spectrumn＝1、、、Nf；
Step 3.2, spatial spectrum of relative dielectric constantAnd conductivity spatial spectrumPerforming coherent accumulation;
step 3.3, performing two-dimensional Fourier transform on the relative dielectric constant and conductivity spatial spectrum after coherent accumulation to obtain the decoupled relative dielectric constant and conductivity under multiple frequencies:
wherein x is the x-direction space domain coordinate of the object to be measured, z is the z-direction space domain coordinate of the object to be measured, For estimating the relative permittivity, epsilon rb is the relative permittivity of the free space background,For the relative dielectric constant of decoupling at multiple frequencies, K x is the x-direction spectral domain coordinate of the object to be measured, K z is the z-direction spectral domain coordinate of the object to be measured,For decoupled conductivity at multiple frequencies, ω n is the nth angular frequency.
5. A quantitative diffraction tomography system for weak scatterers, comprising:
the model construction module is used for constructing an inversion calculation mathematical model based on the antenna array structure, wherein the inversion calculation mathematical model comprises scattered field data, and the scattered field data are dielectric constant and conductivity;
The first inversion module is used for carrying out Fourier transform on the inversion calculation mathematical model, multiplying the Fourier transform by the spatial spectrum under multiple frequencies to obtain a compensated contrast spatial spectrum, interpolating the contrast spatial spectrum, and carrying out inverse Fourier transform on the contrast spatial spectrum after interpolation to obtain a decoupled relative dielectric constant and conductivity under single frequency;
The second inversion module is used for carrying out two-dimensional Fourier transform on the antenna array signals to obtain a relative dielectric constant spatial spectrum and a conductivity spatial spectrum, carrying out coherent accumulation on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum, and carrying out two-dimensional Fourier inverse transform on the relative dielectric constant spatial spectrum and the conductivity spatial spectrum after coherent accumulation to obtain a relative dielectric constant and a conductivity which are decoupled under multiple frequencies;
And the result output module is used for obtaining the complete scattering field information of the object to be detected according to the decoupled relative dielectric constant and conductivity under single frequency and the decoupled relative dielectric constant and conductivity under multiple frequencies and outputting the image result of the relative dielectric constant and conductivity of the object to be detected.
6. A weak scatterer quantitative diffraction tomography system in accordance with claim 5, wherein the model construction module constructs an inverse computational mathematical model comprising:
Setting an antenna array structure, wherein the antenna array structure comprises a plurality of array units, each array unit comprises a transmitting antenna and a receiving antenna, the transmitting antenna irradiates a target object and propagates in free space, the receiving antenna detects a total field scattered by the target object and expands according to a scalar Grignard function, and therefore an inversion calculation mathematical model is formed:
Esct＝k2∫G(ρR,ρ;ω)χ(ρ;ω)Etotdρ
Wherein E sct is the scattered field and E tot is the total field; wave number corresponding to a certain frequency; omega is the angular frequency; epsilon 0 and mu 0 are the dielectric constant and conductivity, respectively, in free space; g is a scalar Grignard function; ρ R is the coordinates of the receiving antenna, ρ is the coordinates of the object to be measured, ρ T is the coordinates of the transmitting antenna; g (ρ R, ρ; ω) is the Green's function of the TM wave and
Wherein,As a first class of zero-order Hankel functions, χ is a contrast function defined as a complex form of dielectric constant and conductivity differences as follows:
Wherein epsilon r (ρ) is the relative dielectric constant of the object to be measured, sigma (ρ) is the electrical conductivity of the object to be measured, epsilon rb is the relative dielectric constant in free space, and j is the complex domain symbol form.
7. The quantitative diffraction tomography system of a weak scatterer of claim 6, wherein the first inversion module comprises:
The first spatial spectrum calculation unit is used for carrying out Fourier change on the inversion calculation mathematical model, then multiplying the spatial spectrum under multiple frequencies, and then obtaining a compensated contrast spatial spectrum:
wherein, gamma res is the space spectrum coordinate of the receiving antenna, gamma r′es is the space spectrum coordinate of the transmitting antenna, Representing the spatial spectrum of the scattered field, I (ω) representing the excitation source spectrum, z' representing the z-direction spatial domain coordinates of the antenna array.
The interpolation unit is used for carrying out one-dimensional interpolation operation on the contrast space spectrum distance direction;
And the first decoupling unit is used for carrying out inverse Fourier transform on the contrast space spectrum after interpolation and decoupling to obtain a relative dielectric constant epsilon r (rho) and a conductivity sigma (rho) which are decoupled under a single frequency.
8. The quantitative diffraction tomography system of a weak scatterer of claim 7, wherein the second inversion module comprises:
A second spatial spectrum calculation unit for performing two-dimensional Fourier transform on the antenna array signal to obtain N f frequencies of relative dielectric constant spatial spectrums And conductivity spatial spectrumn＝1、、、Nf；
A coherent accumulation unit for spatial spectrum of relative dielectric constantAnd conductivity spatial spectrumPerforming coherent accumulation;
the second decoupling unit is used for carrying out two-dimensional Fourier transform on the relative dielectric constant and the conductivity spatial spectrum after coherent accumulation to obtain the relative dielectric constant and the conductivity of decoupling under multiple frequencies:
wherein x is the x-direction space domain coordinate of the object to be measured, z is the z-direction space domain coordinate of the object to be measured, For estimating the relative permittivity, epsilon rb is the relative permittivity of the free space background,For the relative dielectric constant of decoupling at multiple frequencies, K x is the x-direction spectral domain coordinate of the object to be measured, K z is the z-direction spectral domain coordinate of the object to be measured,For decoupled conductivity at multiple frequencies, ω n is the nth angular frequency.
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