Electromagnetic field momentum-based electrical tomography method and signal detection device thereof

Abstract

The application discloses an electrical tomography imaging method based on electromagnetic field momentum and a signal detection device thereof, and introduces ET-EMM by taking a current source or a charge source excitation detection mode as an example. The steps of the ET-EMM method are as follows: under the excitation of the current source or the charge source, the boundary value problem of a measurement area is solved to obtain the spatial distribution F of electromagnetic fields of an imaging area; the ET-EMM sensitivity matrix is constructed according to the spatial distribution F of the electromagnetic fields; the electric field intensity or the magnetic induction intensity of a receiving unit of an electromagnetic sensor is obtained through a signal detection part; and finally, image reconstruction is carried out by using the ET-EMM sensitivity matrix. The signal detection device of the ET-EMM mainly comprises a signal generation part, an electromagnetic sensor, a signal detection part, a signal amplification part and a signal acquisition and imaging algorithm part. The ET-EMM method disclosed by the application obtains higher-order tensor information than the measurement parameters of the electrical tomography, and further improves the resolution of the electromagnetic characteristic parameter distribution image.

Description

Technical Field

[0001] This invention relates to the field of electrical impedance tomography, specifically to an electrical impedance tomography (ET-EMM) method based on electromagnetic momentum and its signal detection device. Background Technology

[0002] Electrical tomography (ET) is an imaging technique based on the principle of electrical sensitivity. It reflects changes in the distribution of electromagnetic parameters within a measured area by measuring changes in data from electromagnetic sensors. It includes electrical resistance tomography (ERT), electrical capacitance tomography (ECT), and electromagnetic tomography (EMT). ERT focuses on conductivity imaging, ECT on dielectric constant imaging, and EMT on both conductivity and permeability imaging, but their mathematical models can be uniformly expressed. ET technology is widely used in medicine, petroleum, chemical, power, and metallurgy due to its wide applicability, fast response speed, simple sensor structure, low cost, and high safety.

[0003] The reciprocity of existing electrical tomography (ET) can be described using Green's reciprocity theorem or Lorentz's reciprocity theorem. An electromagnetic excitation source and an electromagnetic sensor constitute a set of reciprocal processes. Process 1 involves electromagnetic excitation source A applying current source J1, and electromagnetic sensor B detecting the electric field intensity E2; process 2 involves electromagnetic excitation source B applying current source J2, and electromagnetic sensor A detecting the electric field intensity E1. The following relationship exists between the current source and the electric field intensity it generates in this set of reciprocities:

[0004]

[0005] In equation (1), V is the volume of the study area, r is the coordinate in the study area, ω is the frequency, j is the imaginary unit, σ is the conductivity, ε is the dielectric constant, μ is the magnetic permeability, H is the magnetic field strength, and the letter subscripts indicate the number of the two measurement processes in a set of reciprocal.

[0006] Existing electrical tomography (ET) methods are based on the reciprocity of electromagnetic field energy. The spatial resolution of the imaging is related to the amount of independent measurement data, which in turn is related to the number of electromagnetic sensors. Therefore, increasing the number of electromagnetic sensors can improve the imaging resolution to some extent. However, due to limitations in hardware systems and imaging areas, the number of electromagnetic sensors cannot be arbitrarily increased. Overall, existing ET methods have low spatial resolution and poor image quality. Electromagnetic fields possess both energy and momentum, meaning that a reciprocity relationship between two electromagnetic systems can be established from both energy and momentum perspectives. In 2020, Liu et al. derived the momentum reciprocity theorem for electromagnetic fields in homogeneous media, and in 2022, they derived it for non-homogeneous media. This relationship, like the energy-based reciprocity theorem, can be used for ET. Existing ET methods simply increase the number of electromagnetic sensors to improve resolution without changing the tensor order of the measurement data (scalars are zero-order tensors, and vectors are first-order tensors). ET has low imaging resolution and poor ability to identify medium boundaries. Electrical tomography based on electromagnetic momentum (ET-EMM) improves the sensitivity of the imaging system to electromagnetic characteristic parameters in different directions, has a strong ability to identify medium boundaries, and has higher image resolution. Summary of the Invention

[0007] To address the low resolution issue of existing electrical tomography (ET) systems, this invention provides an electrical tomography method based on electromagnetic field momentum and its signal detection device, enabling signal acquisition for the ET-EMM method. The signal detection unit of this device can detect ET-EMM signals and is suitable for signal measurement using the ET-EMM method.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] An electrical tomography method based on electromagnetic field momentum, using a current source or charge source excitation mode, includes the following steps:

[0010] Step 1: Under the excitation of a current source or charge source, solve the analytical or numerical solution of the boundary value problem of the measurement area to obtain the spatial distribution of the electromagnetic field F of the imaging area, that is, the spatial distribution of the electric field intensity E or the spatial distribution of the magnetic field intensity H.

[0011] Step 2: Based on the spatial distribution of the electromagnetic field F, i.e., the spatial distribution of electric field intensity E or the spatial distribution of magnetic field intensity H, construct the ET-EMM sensitivity matrix; ET-EMM represents electrical tomography based on electromagnetic field momentum.

[0012] Step 3: Obtain the electric field strength or magnetic induction intensity of the electromagnetic sensor receiving unit through the signal detection unit;

[0013] Step 4: Reconstruct the image using the ET-EMM sensitivity matrix.

[0014] Furthermore, the calculation method in step one includes:

[0015] The distribution of electromagnetic characteristic parameters γ(r) within a given region is defined, and an excitation current source or charge source is provided; the electromagnetic field boundary value problem is solved to obtain the spatial distribution of the electromagnetic field F, i.e., the spatial distribution of electric field intensity E(r) or the spatial distribution of magnetic field intensity H(r); the electromagnetic characteristic parameters include conductivity, dielectric constant and permeability.

[0016] Furthermore, step two includes:

[0017] Based on the electromagnetic field spatial distribution F obtained in step one, i.e., the electric field intensity spatial distribution E(r) or the magnetic field intensity spatial distribution H(r), construct the ET-EMM sensitivity matrix S; the matrix elements of S constructed from E(r) or H(r) are:

[0018] S ij (r)=F i (r)·F j (r) (4a)

[0019] or

[0020]

[0021] In equations (4a) and (4b), the sensitive field matrix element S ij (r) and S ij (r) represents a scalar and a vector, respectively, and i and j represent the numbers of the electromagnetic sensors, where i ≠ j; F i (r) represents the spatial distribution of the electromagnetic field in the measurement area when electrode i is excited, F j (r) represents the spatial distribution of the electromagnetic field in the measurement area when electrode j is excited.

[0022] Furthermore, step three includes:

[0023] The electric field strength of the electric field sensor receiving unit arranged in the imaging area is obtained through the signal detection unit, or the magnetic induction intensity of the magnetic field sensor receiving unit arranged in the imaging area is obtained through the signal detection unit.

[0024] Furthermore, step four includes:

[0025] Based on the ET-EMM sensitivity matrix S obtained in step two and the electric field strength or magnetic induction intensity obtained in step three, an image reconstruction algorithm is used for reconstruction. For ERT-EMM, the conductivity or its gradient image is obtained; for ECT-EMM, the dielectric constant or its gradient image is obtained; for EMT-EMM, the permeability or its gradient image is obtained in the magnetic medium, and the conductivity or its gradient image is obtained in the conductive medium.

[0026] Furthermore, the electro-tomographic imaging method based on electromagnetic field momentum includes two excitation detection modes: one is in the current source or charge source excitation mode, where the measured data is electric field strength or magnetic induction intensity; the other is in the electric field source or magnetic field source excitation mode, where the measured data is current or charge.

[0027] The present invention also provides a signal detection device applying the above-described electro-tomographic imaging method based on electromagnetic field momentum, comprising: a signal generating unit, an electromagnetic sensor, a signal detection unit, a signal amplification unit, and a signal acquisition and imaging algorithm unit; the output end of the signal generating unit is connected to the transmitting unit of the electromagnetic sensor, the receiving unit of the electromagnetic sensor is connected to the input end of the signal detection unit, the output end of the signal detection unit is connected to the input end of the signal amplification unit, and the output end of the signal amplification unit is connected to the signal acquisition and imaging algorithm unit.

[0028] Furthermore, the electromagnetic sensor includes a measuring chamber and a sensor unit, the sensor unit including a transmitting unit and a receiving unit; the outer wall of the measuring chamber is electromagnetically shielded to shield external electromagnetic interference on the measuring signal; the sample to be tested is placed within the electromagnetic sensor area.

[0029] Furthermore, the signal generating unit includes a signal generator connected to the transmitting unit of the electromagnetic sensor;

[0030] The signal detection unit is used to measure the electric field strength or magnetic induction intensity of the electromagnetic sensor receiving unit;

[0031] The input terminal of the signal amplification unit is connected to the output terminal of the signal detection unit to amplify the electric field strength or magnetic induction intensity signal;

[0032] The signal acquisition and imaging algorithm unit includes a computer with signal acquisition capabilities and a built-in image reconstruction algorithm, used to process the sensor's acquired data and apply the built-in reconstruction algorithm to perform image reconstruction.

[0033] Beneficial effects:

[0034] This invention proposes an electrical tomography based on electromagnetic momentum (ET-EMM) method, based on the electromagnetic momentum reciprocity theorem. From a measurement principle perspective, ET-EMM differs fundamentally from existing electrical tomography (ET), as they are based on different measurement reciprocities: ET is based on the electromagnetic field energy reciprocity relationship, while ET-EMM is based on the electromagnetic field momentum reciprocity relationship.

[0035] ET-EMM acquires higher-order tensor information than the ET measurement parameters (e.g., the measurement parameters change from potential to electric field strength; from induced electromotive force to magnetic flux density; from a component of magnetic flux density to the gradient of magnetic flux density, etc.), thereby improving the sensitivity of the imaging system to electromagnetic characteristic parameters in different directions and obtaining higher resolution images of electromagnetic characteristic parameter distribution. Attached Figure Description

[0036] Figure 1 A schematic diagram of excitation measurement for a set of reciprocal processes in ERT-EMM;

[0037] Figure 2 A schematic diagram of excitation measurement for a set of reciprocal processes in ECT-EMM;

[0038] Figure 3 A schematic diagram of the excitation measurement of a set of reciprocal processes in EMT-EMM;

[0039] Figure 4 Schematic diagram of an ET-EMM device under current source or charge source excitation mode. Detailed Implementation

[0040] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0041] This invention proposes an electrical tomography method based on electromagnetic field momentum and its signal detection device. The imaging methods include electrical resistance tomography based on electromagnetic momentum (ERT-EMM), electrical capacitance tomography based on electromagnetic momentum (ECT-EMM), and electromagnetic tomography based on electromagnetic momentum (EMT-EMM).

[0042] According to the electromagnetic momentum reciprocity theorem, if both excitation sources are within the measurement region, and the medium outside the measurement region is homogeneous, the gradient of the electromagnetic property parameters is zero, i.e., there is no change in conductivity gradient, dielectric constant gradient, or magnetic permeability gradient. Then, the reciprocity process of ET-EMM satisfies the following relationship:

[0043]

[0044] or

[0045]

[0046] In equations (2a) and (2b), V is the volume of the study region, r is the coordinate in the study region, ω is the frequency, and j is the imaginary unit. Here, σ is the Nabla operator, ε is the dielectric constant, μ is the permeability, J is the current density, E is the electric field strength, B is the magnetic induction, and H is the magnetic field strength. The letter subscripts indicate the number of the two measurement processes in a set of reciprocal processes. The letter subscript 1 indicates the first measurement process in a set of reciprocal processes, and the letter subscript 2 indicates the second measurement process in a set of reciprocal processes.

[0047] From equations (2a) and (2b), by applying a small perturbation to the working fluid and linearizing, we can obtain:

[0048] Sg=λ (3)

[0049] In equation (3), This is the normalized sensitivity matrix. This is the normalized amount to be reconstructed. This is the normalized measurement data matrix, where M is the number of independent measurements and N is the number of pixels in the measured region. For ERT-EMM, g is the conductivity or its gradient; for ECT-EMM, g is the dielectric constant or its gradient; for EMT-EMM, g is the permeability or its gradient in magnetic media and the conductivity or its gradient in conductive media.

[0050] ET-EMM has two excitation and detection modes. The first is under excitation by a current source or charge source, where the measured data is electric field strength or magnetic flux density. The second is under excitation by an electric field source or magnetic field source, where the measured data is current or charge. This invention uses the first excitation and detection mode as an example to introduce the ET-EMM method. It should be noted that from an imaging method perspective, there is no essential difference between the two excitation and detection modes; only the excitation and detection parameters are interchanged. Therefore, the ET-EMM method using the second excitation and detection mode is also within the scope of this invention.

[0051] The electromagnetic momentum-based electrical tomography (ET-EMM) method of the present invention, based on a current source or charge source excitation mode, includes the following steps:

[0052] Step 1: Under the excitation of a current source or charge source, solve the analytical or numerical solution of the boundary value problem of the measurement area to obtain the spatial distribution of the electromagnetic field F of the imaging area, that is, the spatial distribution of the electric field intensity E or the spatial distribution of the magnetic field intensity H.

[0053] Step 2: Based on the spatial distribution of the electromagnetic field F, i.e. the spatial distribution of the electric field intensity E or the spatial distribution of the magnetic field intensity H, construct the ET-EMM sensitivity matrix.

[0054] Step 3: Obtain the electric field strength or magnetic induction intensity of the electromagnetic sensor receiving unit through the signal detection unit;

[0055] Step 4: Reconstruct the image using the ET-EMM sensitivity matrix.

[0056] Furthermore, the calculation method in step one includes:

[0057] Given a region containing electromagnetic property parameters (conductivity, dielectric constant, and permeability) γ(r), and a given excitation current source or charge source, solve the electromagnetic field boundary value problem to obtain the spatial distribution F of the electromagnetic field, i.e., the spatial distribution E(r) of the electric field intensity or the spatial distribution H(r) of the magnetic field intensity.

[0058] Furthermore, step two includes:

[0059] Based on the electromagnetic field spatial distribution F obtained in step one, i.e., the electric field intensity spatial distribution E(r) or the magnetic field intensity spatial distribution H(r), the ET-EMM sensitivity matrix S is constructed. The sensitive field matrix elements of S constructed from E(r) or H(r) are:

[0060] S ij (r)=F i (r)·F j (r) (4a)

[0061] or

[0062]

[0063] In equations (4a) and (4b), the sensitive field matrix element S ij (r) and S ij (r) represents a scalar and a vector, respectively, and i and j represent the numbers of the electromagnetic sensors, where i ≠ j. F i (r) represents the spatial distribution of the electromagnetic field in the measurement area when electrode i is excited, F j (r) represents the spatial distribution of the electromagnetic field in the measurement area when electrode j is excited.

[0064] Furthermore, step three includes:

[0065] The electric field strength of the electric field sensor receiving unit arranged in the imaging area is obtained through the signal detection unit, or the magnetic induction intensity of the magnetic field sensor receiving unit arranged in the imaging area is obtained through the signal detection unit.

[0066] Furthermore, step four includes:

[0067] Equation (3) is the reconstruction formula. Based on the ET-EMM sensitivity matrix in step two and the electric field strength or magnetic induction intensity obtained in step three, an image reconstruction algorithm is used for reconstruction. For ERT-EMM, the conductivity or its gradient image is obtained; for ECT-EMM, the dielectric constant or its gradient image is obtained; for EMT-EMM, the permeability or its gradient image is obtained for magnetic media, and the conductivity or its gradient image is obtained for conductive media.

[0068] The signal detection device of the present invention using the ET-EMM method includes: a signal generation unit, an electromagnetic sensor, a signal detection unit, a signal amplification unit, and a signal acquisition and imaging algorithm unit.

[0069] The output of the signal generator is connected to the transmitting unit of the electromagnetic sensor, the receiving unit of the electromagnetic sensor is connected to the input of the signal detection unit, the output of the signal detection unit is connected to the input of the signal amplification unit, and the output of the signal amplification unit is connected to the signal acquisition and imaging algorithm unit.

[0070] The electromagnetic sensor includes a measuring chamber and a sensor unit, such as electrodes and coils. The sensor unit includes a transmitting unit and a receiving unit. Electromagnetic shielding is applied to the outer wall of the measuring chamber to prevent external electromagnetic interference with the measurement signal. The sample to be measured is placed within the electromagnetic sensor area.

[0071] The core component of the signal generating unit is a signal generator, which is connected to the transmitting unit of the electromagnetic sensor.

[0072] The signal detection unit is used to measure the electric field strength or magnetic induction intensity of the electromagnetic sensor receiving unit. The input terminal of the signal amplification unit is connected to an electric field or magnetic field sensor to amplify the electric field strength or magnetic induction intensity signal.

[0073] The main body of the signal acquisition and imaging algorithm unit is a computer with signal acquisition capabilities and built-in image reconstruction algorithms. This computer can process the data acquired by the sensor and apply built-in reconstruction algorithms, such as the Landweber algorithm, the Tikhonov algorithm, and filtered back projection, to reconstruct the image.

[0074] Example 1

[0075] For ERT-EMM, the electromagnetic sensor is an electric field sensor, and the sensor unit is an electrode, including a transmitting electrode and a receiving electrode.

[0076] In the ERT-EMM method, equations (2a) and (2b) simplify to:

[0077]

[0078] or

[0079]

[0080] In equations (5a) and (5b), V represents the volume of the study area, and r represents the coordinates within the study area. Here, σ is the Nabla operator, J is the current density, and E is the electric field strength. The letter subscripts indicate the numbers of the two measurement processes in a set of reciprocal processes. The letter subscript 1 indicates the first measurement process in a set of reciprocal processes, and the letter subscript 2 indicates the second measurement process in a set of reciprocal processes.

[0081] The steps of the ERT-EMM method of the present invention are as follows:

[0082] Step 1: Under the excitation of the current source, solve the analytical or numerical solution of the boundary value problem in the measurement area to obtain the spatial distribution E of the electric field intensity in the imaging area.

[0083] Step 2: Construct the ERT-EMM sensitivity matrix based on the spatial distribution E of the electric field intensity;

[0084] Step 3: Obtain the electric field strength of the receiving electrode of the electric field sensor through the signal detection unit;

[0085] Step 4: Reconstruct the image using the ERT-EMM sensitivity matrix.

[0086] Furthermore, in step one, the calculation method includes:

[0087] Consider a measurement region V, with a boundary Γ. The corresponding boundary value problem is:

[0088]

[0089] In equation (6), u(r) is the potential distribution, n is the normal of Γ, and A and B are the sensor positions, i.e., the electrode positions.

[0090] Given the conductivity distribution σ(r) within a defined region, the divergence of the excitation current density at electrodes A and B is calculated. δ is the Dirac function, r A For the position of electrode A, r B Let B be the location of electrode B, and I be the excitation current. The spatial distribution of the electric field intensity E(r) is solved through numerical calculation.

[0091] Furthermore, step two includes:

[0092] Based on the spatial distribution of electric field intensity E(r) obtained in step one, the sensitivity matrix S of ERT-EMM is constructed. The matrix elements of the two construction methods are S. ij (r)=E i (r)·E j (r) or

[0093] Furthermore, step three includes:

[0094] The electric field strength of the electric field sensor arranged in the imaging area is obtained through the signal detection unit.

[0095] Furthermore, step four includes:

[0096] definition According to equation (5), the elements of the measurement data matrix λ are:

[0097]

[0098] In the formula, i and j are the numbers of a pair of excitation electrodes, and m and n are the numbers of another pair of detection electrodes, with i and j having different values ​​from m and n. K ij and K mn Let K represent the current density applied between electrodes i and j, and the current density applied between electrodes m and n, respectively. Since both the excitation and measurement electrodes are a pair of electrodes, then K... ij =I ij [δ(rr i )-δ(rr j )], K mn =I mn[δ(rr m )-δ(rr n )], here I ij and I mn If the excitation current is a unit current, then equation (7) can be simplified to:

[0099] λ ij,mn =E ij (r m )-E ij (r n )+E mn (r i )-E mn (r j (8)

[0100] In equation (8), E ij (r m )-E ij (r n E represents the difference in electric field strength measured on electrodes m and n when a unit current is injected through electrodes i and j. mn (r i )-E mn (r j The difference in electric field strength measured on electrodes i and j when a unit current is injected through electrodes m and n is represented. Figure 1 This is a schematic diagram of the excitation measurement of a set of reciprocal processes in ERT-EMM. The excitation source is a current source, and the detected quantity is the electric field strength on the electrode.

[0101] By measuring the data matrix λ and the sensitivity matrix S, and using a reconstruction algorithm, such as the Tikhonov regularization method, to solve equation (3), the quantity to be reconstructed g can be obtained.

[0102] Based on the sensitive field constructed according to equation (5a), the quantity to be reconstructed, g, is the conductivity distribution σ(p) on P pixels of the measurement region, where p = 1, 2, ..., P. Based on the sensitive field constructed according to equation (5b), the quantity to be reconstructed, g, is the conductivity gradient on P pixels of the measurement region. This reflects the boundary information of conductivity. That is, the ERT-EMM method proposed in this invention can simultaneously reconstruct the conductivity distribution image and its gradient distribution image.

[0103] like Figure 4As shown, the signal detection device of ERT-EMM mainly includes: a signal generation unit 1, a sensor 2, a signal detection unit 3, a signal amplification unit 4, and a signal acquisition and imaging algorithm unit 5. The output terminal of the signal generation unit 1 is connected to the transmitting electrode of the sensor 2, the receiving electrode of the sensor 2 is connected to the input terminal of the signal detection unit 3, the output terminal of the signal detection unit 3 is connected to the input terminal of the signal amplification unit 4, and the output terminal of the signal amplification unit 4 is connected to the signal acquisition and imaging algorithm unit 5.

[0104] The sensor 2 includes electrodes and a cylindrical measuring chamber. The electrodes are connected to the signal generating unit 1, and the excitation mode of the signal generating unit 1 is controlled to achieve the two-electrode excitation mode. The outer wall of the cylindrical measuring chamber is grounded to shield against external electromagnetic interference, and the sample to be tested is placed inside the cylindrical measuring chamber. The signal detection unit 3 measures the difference in electric field strength between the two receiving electrodes. The signal amplification unit 4 amplifies the signal acquired by the signal detection unit 3. The main body of the signal acquisition and imaging algorithm unit 5 is a computer, which can process the data acquired by the signal detection unit and perform image reconstruction using the built-in Tikhonov algorithm.

[0105] Example 2

[0106] For ECT-EMM, the electromagnetic sensor is an electric field sensor, and the sensor unit is an electrode, including a transmitting electrode and a receiving electrode.

[0107] In the ECT-EMM method, equations (2a) and (2b) simplify to:

[0108]

[0109] or

[0110]

[0111] In equations (9a) and (9b), V represents the volume of the study area, and r represents the coordinates within the study area. Here, ρ is the Nabla operator, E is the electric field strength, and the letter subscripts indicate the numbers of two measurement processes in a set of reciprocal processes. The letter subscript 1 indicates the first measurement process in a set of reciprocal processes, and the letter subscript 2 indicates the second measurement process in a set of reciprocal processes.

[0112] The steps of the ECT-EMM method of the present invention are as follows:

[0113] Step 1: Under the excitation of the charge source, solve the analytical or numerical solution of the boundary value problem in the measurement area to obtain the spatial distribution E of the electric field intensity in the imaging area;

[0114] Step 2: Construct the ECT-EMM sensitivity matrix based on the spatial distribution E of the electric field intensity;

[0115] Step 3: Obtain the electric field strength of the receiving electrode of the electric field sensor through the signal detection unit;

[0116] Step 4: Reconstruct the image using the ECT-EMM sensitivity matrix.

[0117] Furthermore, the calculation method in step one includes:

[0118] Consider a measurement region V, with a boundary Γ, and the corresponding electromagnetic field boundary value problem.

[0119]

[0120] In equation (10), u(r) represents the potential distribution.

[0121] Given a dielectric constant distribution ε(r) within a defined region, and at sensor position A, i.e., electrode A, a given excitation charge density ρ = qδ(rr). A ), where δ is the Dirac function, r A Let A be the position of electrode A, and q be the excitation charge. The spatial distribution of the electric field intensity E(r) is solved through numerical calculation.

[0122] Furthermore, step two includes:

[0123] The ECT-EMM sensitivity matrix S is constructed based on the spatial distribution of electric field intensity E(r) obtained in step one. The matrix elements of the sensitivity matrix constructed from E(r) are S. ij (r)=E i (r)·E j (r) or

[0124] Furthermore, step three includes:

[0125] The electric field strength of the electric field sensor arranged in the imaging area is obtained by signal detection.

[0126] Furthermore, step four includes:

[0127] According to equation (9), the elements of the measurement data matrix λ are:

[0128] λ ij =∫ V [ρ i E j (r)+ρ j E i (r)]dV (11)

[0129] In the formula, i and j represent the electrode numbers, and i ≠ j. ρ i and ρ jLet ρ represent the charge density applied to electrodes i and j, respectively. The charge density of the excitation and measurement electrodes can be expressed as ρ. i =q i δ(rr i ), ρ j =q j δ(rr j ), here q i and q j Let r be the unit excitation charge, δ be the Dirac function, and r be the excitation charge. i and r j Let i and j represent the spatial position coordinates, and the coordinates of electrodes i and j, respectively. Then equation (11) can be simplified to:

[0130] λ ij =E j +E i (12)

[0131] In equation (12), E i and E j These represent the electric field strengths measured on sensor electrodes i and j, respectively. Figure 2 This is a schematic diagram of the excitation measurement of a set of reciprocal processes in ECT-EMM, where the excitation source is electric charge and the detected quantity is electric field strength.

[0132] By measuring the data matrix λ and the sensitivity matrix S, and using a reconstruction algorithm, such as the iterative method to solve equation (3), the quantity to be reconstructed g can be obtained.

[0133] Based on the sensitive field constructed according to equation (9a), the quantity to be reconstructed, g, is the dielectric constant distribution ε(p) on P pixels of the measurement region, where p = 1, 2, ..., P. Based on the sensitive field constructed according to equation (9b), the quantity to be reconstructed, g, is the dielectric constant gradient on N pixels of the measurement region. It reflects the boundary information of the dielectric constant. That is, the ECT-EMM method proposed in this invention can simultaneously reconstruct the dielectric constant distribution image and its gradient distribution image.

[0134] Signal detection devices that apply the ECT-EMM method, such as Figure 4 As shown, the detection device is the same as the signal detection device of the ERT-EMM method.

[0135] The sensor 2 includes electrodes and a cylindrical measuring chamber. The electrodes are connected to the signal generating section 1, and single-electrode excitation is achieved by controlling the excitation mode of the signal generating section 1. The outer wall of the cylindrical measuring chamber is grounded to shield against external electromagnetic interference, and the sample to be tested is placed inside the cylindrical measuring chamber. The signal detection section 3 measures the electric field strength of the single electrode. The signal amplification section 4 amplifies the signal acquired by the signal detection section 3. The main body of the signal acquisition and imaging algorithm section 5 is a computer, which can process the data acquired by the signal detection section and perform image reconstruction using the built-in Landweber reconstruction algorithm.

[0136] Example 3

[0137] For EMT-EMM, the electromagnetic sensor is a magnetic field sensor, and the sensor unit is a coil, including a transmitting coil and a receiving coil.

[0138] For magnetically non-conductive media, in the EMT-EMM method, equation (2) simplifies to

[0139]

[0140] or

[0141]

[0142] In equations (13a) and (13b), V represents the volume of the study region, and r represents the coordinates within the study region. Here, μ is the Nabla operator, J is the current density, H is the magnetic field strength, and B is the magnetic flux density. The letter subscripts indicate the numbers of the two measurement processes in a set of reciprocal processes. The letter subscript 1 indicates the first measurement process in a set of reciprocal processes, and the letter subscript 2 indicates the second measurement process in a set of reciprocal processes.

[0143] For magnetically non-conductive media, the steps of the EMT-EMM method of the present invention are as follows:

[0144] Step 1: Under the excitation of the current source, solve the analytical or numerical solution of the boundary value problem in the measurement area to obtain the spatial distribution H of the magnetic field intensity in the imaging area;

[0145] Step 2: Construct the EMT-EMM sensitivity matrix based on the spatial distribution H of the magnetic field intensity;

[0146] Step 3: Obtain the magnetic induction intensity of the magnetic field sensor receiving coil through the signal detection unit;

[0147] Step 4: Reconstruct the image using the EMT-EMM sensitivity matrix.

[0148] Furthermore, the calculation method in step one includes:

[0149] Assume the boundary of the region at infinity is Γ ∞ The corresponding electromagnetic boundary value problem is:

[0150]

[0151] In equation (14), A is the vector magnetic potential.

[0152] Given the permeability distribution μ(r) within a defined region, and a given excitation current source J = Iδ(r) a )e a I is the current amplitude, δ is the Dirac function, r is the region coordinates, a is the coil position, and r a Let e ​​be the coordinate of the coil. a Let be the unit vector along the coil. After solving the electromagnetic field boundary value problem, the spatial distribution H(r) of the magnetic field intensity in the measurement region V is obtained.

[0153] Furthermore, step two includes:

[0154] Based on the spatial distribution of magnetic field intensity H(r) obtained in step one, the EMT-EMM sensitivity matrix S can be constructed in two ways, with its matrix elements being S. ij (r)=H i (r)·H j (r) or

[0155] Furthermore, step three includes:

[0156] The magnetic induction intensity of the magnetic field sensor receiving coil placed in the imaging area is measured by the signal detection unit.

[0157] Furthermore, step four includes:

[0158] According to equation (2), the elements of the measurement data matrix λ are:

[0159]

[0160] In the formula, i and j represent the coil numbers, and i ≠ j. i and J j These represent the current density applied to the coil, i.e., J. i =I i δ(rr i )e i J j =I j δ(rr j )e j Here I i and I j Let e ​​be the electric current, δ represent the Dirac function, and e be the electric current. i e is the unit vector along coil i.j Let r and r' be unit vectors along coil j. i and r j These represent the spatial position coordinates, the coordinates of coil i, and the coordinates of coil j, respectively. i and m j Let i and j represent the magnetic moments of coils i and j, respectively. Ψ i and Ψ j Let represent the areas of the surfaces enclosed by coils i and j, respectively, and Ψ represent the normal direction of the surface containing the coils. Let e ​​be the direction of the three coordinate axes of the rectangular coordinate system. x e y With e z Direction. For example... Figure 3 As shown, assuming the coil is placed in the xoy plane, i.e., the coil detects the magnetic induction intensity e z The direction component then has Here m i and m j Let be the unit magnetic moment. Then equation (15) can be simplified to:

[0161]

[0162] In equation (16), B iz and B jz e represents the magnetic induction intensity on coils i and j, respectively. z Directional component, where t is time. It is a partial derivative operator. e is the magnetic flux density on coil i z Directional components in e x e y With e z The derivative of the direction. e is the magnetic flux density on coil j z The directional components are in three directions in a Cartesian coordinate system, namely e. x e y With e z The derivative of the direction. Figure 3 This is a schematic diagram of an excitation measurement of a reciprocal process. The excitation source is electric current, and the detected quantity is magnetic flux density. The magnetic flux density e is obtained through four parallel coils. z Directional components in e x e y With e z The derivative in direction. Specifically, for the first reciprocal process, current I is applied to each of the four parallel excitation coils i. i The magnetic induction intensity e of the four parallel detection coils j is measured respectively. z Directional component B jz B jzx B jzy With Bjzz Let d be the distance d between the x, y, and z axes of the four parallel detection coils and point O, then the magnetic induction intensity e z Directional components in e x e y With e z The derivatives in the directions are approximately (B) jzx -B jz ) / d、(B jzy -B jz ) / d and (B jzz -B jz For the second reciprocal process, current I is applied to each of the four parallel excitation coils j. j The magnetic induction intensity e of the four parallel detection coils i is measured respectively. z Directional component B iz B izx B izy With B izz Let d be the distance d between the x, y, and z axes of the four parallel detection coils and point O, then the magnetic induction intensity e z Directional components in e x e y With e z The derivatives in the directions are approximately (B) izx -B iz ) / d、(B izy -B iz ) / d and (B izz -B iz ) / d.

[0163] By measuring the data matrix λ and the sensitivity matrix S, and using a reconstruction algorithm, such as the iterative method to solve equation (3), the quantity to be reconstructed g can be obtained.

[0164] Based on the sensitive field constructed according to equation (13a), the quantity to be reconstructed, g, is the magnetic permeability distribution μ(p) on P pixels of the measurement region, where p = 1, 2, ..., P. Based on the sensitive field constructed according to equation (13b), the quantity to be reconstructed, g, is the magnetic permeability gradient on N pixels of the measurement region. It reflects the boundary information of magnetic permeability. That is, the EMT-EMM method proposed in this invention under magnetically non-conductive media can simultaneously reconstruct the magnetic permeability distribution image and its gradient distribution image.

[0165] The signal detection device that applies the EMT-EMM method is as follows:

[0166] like Figure 4As shown, for magnetically non-conductive media, the signal detection device of EMT-EMM mainly includes: a signal generating unit 1, a magnetic field sensor 2, a signal detection unit 3, a signal amplification unit 4, and a signal acquisition and imaging algorithm unit 5. The signal detection unit 3 detects the magnetic induction intensity of the receiving coil of the magnetic field sensor. The output terminal of the signal generating unit 1 is connected to the transmitting coil of the magnetic field sensor 2, the receiving coil of the magnetic field sensor 2 is connected to the input terminal of the signal detection unit 3, the output terminal of the signal detection unit 3 is connected to the input terminal of the signal amplification unit 4, and the output terminal of the signal amplification unit 4 is connected to the signal acquisition and imaging algorithm unit 5.

[0167] The magnetic field sensor 2 includes a sensor coil and a cylindrical measuring chamber. The sensor coil consists of a transmitting coil and a receiving coil. The sensor coil comprises four parallel coils, positioned at positions O, e, and e respectively. x axis, e y axis and e z The sensor's transmitting coil is connected to the signal generating unit 1, and current is applied to the sensor's transmitting coil by controlling the signal generating unit 1. The outer wall of the cylindrical measuring chamber is grounded to shield against external electromagnetic interference, and the sample to be tested is placed inside the cylindrical measuring chamber. The signal detection unit 3 measures the magnetic induction intensity of the magnetic field sensor's receiving coil. The signal amplification unit 4 amplifies the signal acquired by the magnetic field sensor. The main body of the signal acquisition and imaging algorithm unit 5 is a computer, which can process the data acquired by the signal detection unit and perform image reconstruction using the built-in Tikhonov algorithm.

[0168] Example 4

[0169] For EMT-EMM, the electromagnetic sensor is a magnetic field sensor, and the sensor unit is a coil, including a transmitting coil and a receiving coil.

[0170] For non-magnetic conductive media, neglecting displacement current, in the EMT-EMM method, equation (2) simplifies to:

[0171]

[0172] or

[0173]

[0174] In equations (17a) and (17b), V is the volume of the study region, r is the coordinate in the study region, and ω is the frequency. Here, σ is the Nabla operator, E is the electric field strength, B is the magnetic induction intensity, and J is the current density. The letter subscripts indicate the numbers of the two measurement processes in a set of reciprocal processes. The letter subscript 1 indicates the first measurement process in a set of reciprocal processes, and the letter subscript 2 indicates the second measurement process in a set of reciprocal processes.

[0175] For non-magnetic conductive media, neglecting displacement current, the steps of the EMT-EMM method of the present invention are as follows:

[0176] Step 1: Under the excitation of the current source, solve the analytical or numerical solution of the boundary value problem in the measurement area to obtain the spatial distribution E of the electric field intensity in the imaging area.

[0177] Step 2: Construct the EMT-EMM sensitivity matrix based on the spatial distribution E of the electric field intensity;

[0178] Step 3: Obtain the magnetic induction intensity of the magnetic field sensor receiving coil through the signal detection unit;

[0179] Step 4: Reconstruct the image using the EMT-EMM sensitivity matrix.

[0180] Furthermore, the calculation method in step one includes:

[0181] Assume the boundary of the region at infinity is Γ ∞ The corresponding electromagnetic field boundary value problem is divided into the eddy current region, the air region, and the excitation source region. Since the medium is non-magnetic, the permeability in the region is approximately equal to the permeability μ0 of air.

[0182] The field equations for the vortex region are:

[0183]

[0184] The field equations for the air region are:

[0185]

[0186] The field equations for the excitation source region are:

[0187]

[0188] In equations (18a), (18b), and (18c), u(r) represents the potential distribution, and t represents time. It is a partial derivative operator.

[0189] In addition, initial conditions for A and u are specified, and A and u are zero at infinity.

[0190] Given the conductivity distribution σ(r) within a defined region, and a given excitation current source J = Iδ(rr) a )e a I is the current amplitude, δ is the Dirac function, r is the region coordinates, a is the coil position, and r a Let e ​​be the coordinate of the coil. a Let be the unit vector along the coil. After solving the electromagnetic field boundary value problem, the spatial distribution of the electric field intensity E(r) in the measurement region V is obtained.

[0191] Furthermore, step two includes:

[0192] Based on the spatial distribution of electric field intensity E(r) obtained in step one, the EMT-EMM sensitivity matrix S is constructed. The matrix elements of the sensitivity matrix constructed using E(r) are S. ij (r)=E i (r)·E j (r) or

[0193] Furthermore, step three includes:

[0194] The magnetic induction intensity of the magnetic field sensor receiving coil arranged in the imaging area is measured by the signal detection unit.

[0195] Furthermore, step four includes:

[0196] According to equation (17), the elements of the measurement data matrix λ are:

[0197]

[0198] In the formula, i and j represent the coil numbers, and i ≠ j. i and J j The charge density applied to the coil, i.e., J i =I i δ(rr i )e i J j =I j δ(rr j )e j Here I i and I j Let r be the electric current, δ represent the Dirac function, and r, r i and r j These represent the spatial position coordinates, the coordinates of coil i, and the coordinates of coil j, respectively. i and m j Let i and j represent the magnetic moments of coils i and j, respectively. Ψ i and Ψ j Let represent the areas of the surfaces enclosed by coils i and j, respectively, and Ψ represent the normal direction of the surface containing the coils. Let e ​​be the direction of the three coordinate axes of the rectangular coordinate system. x e y With e z Direction. For example... Figure 3 As shown, assuming the coil is placed in the xoy plane, i.e., the coil detects the magnetic induction intensity e z The direction component then has Here m i and m j Let be the unit magnetic moment. Then equation (19) can be simplified to:

[0199]

[0200] In equation (20), B iz and B jz e represents the magnetic induction intensity on coils i and j, respectively. z Directional component, where t is time. It is a partial derivative operator. e is the magnetic flux density on coil i z Directional components in e x e y With e z The derivative of the direction. e is the magnetic flux density on coil j z Directional components in e x e y With e z The derivative of the direction. Figure 3 This is a schematic diagram of an excitation measurement of a reciprocal process. The excitation source is electric current, and the detected quantity is magnetic flux density. The magnetic flux density e is obtained through four parallel coils. z Directional components in e x e y With e z The derivative in direction. Specifically, for the first reciprocal process, current I is applied to each of the four parallel excitation coils i. i The magnetic induction intensity e of the four parallel detection coils j is measured respectively. z Directional component B jz B jzx B jzy With B jzz Let d be the distance d between the x, y, and z axes of the four parallel detection coils and point O, then the magnetic induction intensity e z Directional components in e x e y With e z The derivatives in the directions are approximately (B) jzx -B jz ) / d、(B jzy -B jz ) / d and (B jzz -B jz For the second reciprocal process, current I is applied to each of the four parallel excitation coils j. j The magnetic induction intensity e of the four parallel detection coils i is measured respectively. z Directional component B iz B izx B izy With B izz Let d be the distance d between the x, y, and z axes of the four parallel detection coils and point O, then the magnetic induction intensity ez Directional components in e x e y With e z The derivatives in the directions are approximately (B) izx -B iz ) / d、(B izy -B iz ) / d and (B izz -B iz ) / d.

[0201] By measuring the data matrix λ and the sensitivity matrix S, and using a reconstruction algorithm, such as the iterative method to solve equation (3), the quantity to be reconstructed g can be obtained.

[0202] Based on the sensitive field constructed according to equation (17a), the quantity to be reconstructed, g, is the conductivity distribution σ(p) on P pixels of the measurement region, where p = 1, 2, ..., P. Based on the sensitive field constructed according to equation (17b), the quantity to be reconstructed, g, is the conductivity gradient on P pixels of the measurement region. This reflects the boundary information of conductivity. In other words, the EMT-EMM method proposed in this invention for non-magnetic conductive media can simultaneously reconstruct the conductivity distribution image and its gradient distribution image.

[0203] The signal detection device using the EMT-EMM method is the same as that in Example 3.

Claims

1. An electrical tomography method based on electromagnetic field momentum, characterized in that, Based on current source or charge source excitation mode, the following steps are included: Step 1: Under the excitation of a current source or charge source, solve the analytical or numerical solution for the boundary value problem of the measurement area to obtain the spatial distribution of the electromagnetic field in the imaging area. That is, the spatial distribution of electric field intensity or spatial distribution of magnetic field strength ; Step 2, based on the spatial distribution of the electromagnetic field That is, the spatial distribution of electric field intensity or spatial distribution of magnetic field strength Construct the ET-EMM sensitivity matrix; ET-EMM represents electro-tomography based on electromagnetic field momentum, including: Based on the electromagnetic field spatial distribution obtained in step one That is, the spatial distribution of electric field intensity or spatial distribution of magnetic field strength Constructing the ET-EMM sensitivity matrix ;Depend on or Constructed The matrix elements are: （4a） or （4b） In equations (4a) and (4b), the elements of the sensitive field matrix are... and They are scalar and vector, respectively. and These represent the serial numbers of the electromagnetic sensors, and ; Indicates electrode The spatial distribution of the electromagnetic field in the measurement area when excited. Indicates electrode Spatial distribution of electromagnetic field in the measurement area when excited; Step 3: Obtain the electric field strength or magnetic induction intensity of the electromagnetic sensor receiving unit through the signal detection unit; Step four, image reconstruction using the ET-EMM sensitivity matrix, including: Based on the ET-EMM sensitivity matrix in step two The electric field strength or magnetic induction intensity obtained in step three are used to reconstruct the image using an image reconstruction algorithm; for ERT-EMM, the conductivity or its gradient image is obtained; for ECT-EMM, the dielectric constant or its gradient image is obtained; for EMT-EMM, the permeability or its gradient image is obtained in the magnetic medium, and the conductivity or its gradient image is obtained in the conductive medium.

2. The electrical tomography method based on electromagnetic field momentum according to claim 1, characterized in that, The calculation method in step one includes: Distribution of electromagnetic characteristic parameters within a defined area Given an excitation current source or charge source, solve the electromagnetic field boundary value problem to obtain the spatial distribution of the electromagnetic field. That is, the spatial distribution of electric field intensity or spatial distribution of magnetic field strength The electromagnetic property parameters include conductivity, dielectric constant, and magnetic permeability.

3. The electrical tomography method based on electromagnetic field momentum according to claim 1, characterized in that, Step three includes: The electric field strength of the electric field sensor receiving unit arranged in the imaging area is obtained through the signal detection unit, or the magnetic induction intensity of the magnetic field sensor receiving unit arranged in the imaging area is obtained through the signal detection unit.

4. The electrical tomography method based on electromagnetic field momentum according to claim 1, characterized in that, The described electro-tomographic imaging method based on electromagnetic field momentum includes two excitation detection modes: one is in the current source or charge source excitation mode, where the measured data is electric field strength or magnetic induction intensity; the other is in the electric field source or magnetic field source excitation mode, where the measured data is current or charge.

5. A signal detection device using an electro-tomographic imaging method based on electromagnetic field momentum as described in any one of claims 1-4, characterized in that, include: The system comprises a signal generator, an electromagnetic sensor, a signal detection unit, a signal amplification unit, and a signal acquisition and imaging algorithm unit. The output of the signal generator is connected to the transmitting unit of the electromagnetic sensor, the receiving unit of the electromagnetic sensor is connected to the input of the signal detection unit, the output of the signal detection unit is connected to the input of the signal amplification unit, and the output of the signal amplification unit is connected to the signal acquisition and imaging algorithm unit.

6. The signal detection device according to claim 5, characterized in that, The electromagnetic sensor includes a measuring chamber and a sensor unit, which includes a transmitting unit and a receiving unit. The outer wall of the measuring chamber is electromagnetically shielded to block external electromagnetic interference with the measuring signal. The sample to be tested is placed within the electromagnetic sensor area.

7. The signal detection device according to claim 5, characterized in that, The signal generating unit includes a signal generator connected to the transmitting unit of the electromagnetic sensor; The signal detection unit is used to measure the electric field strength or magnetic induction intensity of the electromagnetic sensor receiving unit; The input terminal of the signal amplification unit is connected to the output terminal of the signal detection unit to amplify the electric field strength or magnetic induction intensity signal; The signal acquisition and imaging algorithm unit includes a computer with signal acquisition capabilities and a built-in image reconstruction algorithm, used to process the sensor's acquired data and apply the built-in reconstruction algorithm to perform image reconstruction.

Images