Method of measurement by electrical impedance tomography

Abstract

The present invention relates to an electrical impedance tomography method for the measurement of a body (6) comprising a cylindrical portion containing a fluid, the method comprising the following steps: i. e ii.n electrodes (2) e Simultaneously exciting each of the electrodes (2), each of which is energized with a carefully selected type of potential V n exc iii. The electrical characteristic V of the body (6) is measured using the electrode (2). n meas and iv. processing the data from measuring step iii to obtain a signed data matrix representing the image.

Description

[Technical field]

[0001] The present invention relates to the field of electrical impedance tomography.

[0002] The invention more particularly relates to an electrical impedance tomography measurement method using simultaneous trigonometric signals to excite the electrodes used.

[0003] The invention also relates to a computer program product arranged to implement this measurement method.

[0004] The primary application addressed by the present invention is monitoring fluid flows that are subject to sudden changes, such as those occurring in fluids flowing under high pressure and temperature.

[0005] One particularly interesting application is monitoring pipes in nuclear facilities, although other applications may be envisaged within the context of the present invention. [Background technology]

[0006] Electrical impedance tomography (EIT) is a non-invasive and non-destructive technique that allows images of the interior of an object to be generated in real time and continuously by measuring the electrical properties (current and potential) of the object's surface. This robust technique is particularly suitable for performing non-invasive measurements in high pressure and / or high temperature environments.

[0007] EIT, more precisely, consists in injecting a current or potential by means of a set of non-invasive electrodes placed on the surface of the monitored object, and then measuring the potential or current on the object's surface.

[0008] The electrodes need only contact the exterior surface of the object, however, if the surface of the object is metallic, the electrodes must penetrate the wall and contact the fluid.

[0009] A map of the impedance inside the object is reconstructed by solving the associated inverse problem.

[0010] It is known to implement time division multiplexing, in which an excitation signal is applied to a single pair of electrodes at a time, and various pairs of electrodes are sequentially selected by a multiplexer or electrical switch to enable an EIT image to be acquired.

[0011] The EIT image contains the measurement data of all excited electrode pairs.

[0012] These data can be used to solve inverse problems that determine the distribution of electric potentials and reconstruct the distribution of material properties (conductivity, permittivity, etc.) within the object.

[0013] However, time division multiplexing does not allow for fast acquisition of EIT data.

[0014] Frequency multiplexing allows a superposition of simultaneously injected signals to be generated, which allows for higher data acquisition rates.

[0015] Paper [1] discloses a method for measuring the mass flow rates of various components of a mixture using an impedance tomography technique with frequency multiplexing.

[0016] Publications [2], [3], and [4] each describe multi-frequency methods for simultaneously exciting multiple electrodes in the context of EIT measurement methods.

[0017] According to this method, each electrode is paired with each of the other electrodes, thus forming a set of paired electrodes, and excitation is simultaneously generated between each pair of electrodes by applying a potential to these electrodes, and then a measurement of the electrical properties is made.

[0018] The EIT methods described in publications [2], [3], and [4] have been successfully implemented in a functional prototype with 16 electrodes, corresponding to a set of 120 electrode pairs.

[0019] However, this method has some limitations.

[0020] Performing 120 simultaneous measurements with 120 pairs of electrodes results in a significant degree of redundancy in the collected data. As a result, the measurement operation creates significantly more data than the minimum required. The measurements therefore become more complicated to utilize, especially at the hardware level. In particular, the generation of 120 excitation signals requires expensive programmable logic arrays with particularly large memories.

[0021] These redundancies also imply the use of a large number of excitation frequencies, i.e. 120 different frequencies, which requires a wide bandwidth of the order of 500 kHz for an optimized image acquisition rate of 3906 images per second.

[0022] Furthermore, exciting electrodes in pairs leads to data being acquired that is not optimized for solving the inverse problem and reconstructing the image.

[0023] Finally, the image acquisition rate with this method is limited to 3906 images per second.

[0024] However, certain applications require much higher acquisition rates, for example when monitoring nuclear installations: the measurement of high-velocity two-phase flows, for example to monitor the appearance of breaks in the pipes of a nuclear reactor, requires a series of measurements made at an acquisition rate of more than 10,000 images per second.

[0025] There is therefore a need to provide an EIT measurement method that overcomes the drawbacks of the prior art, in particular to improve the speed of image acquisition and to optimize the amount of data generated and its processing. [Prior art documents] [Non-patent literature]

[0026] [Non-Patent Document 1] [1]Teague, G.(2002). Mass flow measurement of multi-phase mixtures by means of tomographic techniques.University of Cape Town, Faculty of Engineering, Department of Electrical Engineering [Non-Patent Document 2] [2] Dupre, A., Mylvaganam, S. (2017). Simultaneous and Continuous Excitation Strategy for High Speed ​​EIT: the ONE-SHOT method. In Proceedings of the 9th World Congress on Industrial Process Tomography, pp. 667-674. [Non-Patent Document 3] [3] Darnajou, M., Dupre, A., Dang, C., Ricciardi, G., Bourennane, S., Bellis, C. (2019). On the implementation of simultaneous multi-frequency excitations and measurements for electrical impedance tomography. Sensors, 19(17) [Non-Patent Document 4] [4] Darnajou, M., Dupre, A., Dang, C., Ricciardi, G., Bourennane, S., Bellis, C., Mylvaganam, S. (2020). High Speed ​​EIT with Multifrequency Excitation using FPGA and Response Analysis using FDM. IEEE Sensors [Non-Patent Document 5] [5]https: / / www.math.colostate.edu / ~siamcsu / files / NOSER.pdf Summary of the Invention [Problem to be solved by the invention]

[0027] It is an object of the present invention to at least partially fulfill this need. [Means for solving the problem]

[0028] To this end, the subject of the invention, according to one of its aspects, is a method for electrical impedance tomography measurement of a body comprising a cylindrical portion containing a fluid, comprising the following steps: i. Around the cylindrical part of the main body e placing electrodes; ii.n e simultaneously exciting each of the electrodes, each electrode comprising:

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[0029] The measurement method therefore consists essentially in implementing frequency multiplexing, in which an excitation signal is applied simultaneously to all electrodes.

[0030] To allow for signal differentiation, each electrode is excited by a signal in triangular form.

[0031] Simultaneous excitation of all electrodes avoids the redundancy seen in data obtained by sequentially exciting paired electrodes.

[0032] The method according to the invention therefore enables the amount of data generated and their processing speed to be optimized, and therefore the number of images acquired per second is significantly improved.

[0033] Advantageously, the trigonometric form of the excitation signal is particularly well suited to distinguish between various materials having similar electrical conductivities.

[0034] According to one advantageous feature, the potential V n exc The set of conditions,

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[0035] Preferably, the image is generated using a one-step iterative least-squares reconstruction algorithm applied to the signed data matrix.

[0036] According to one particular embodiment, the electrodes are equidistant from each other. This is because n =2πn / n e In other words, the electrodes are angularly distributed in a regular manner around the body.

[0037] The invention also relates to the use of the method just described for carrying out tomographic measurements of two-phase flows, the body of which is a pipe in a nuclear facility.

[0038] According to another of its aspects, the present invention also relates to a computer program product comprising a medium and instructions stored on said medium and readable by a processor such that, when executed, the instructions enable an acquisition system to be controlled to perform the measurement method according to the present invention.

[0039] Finally, the present invention relates to an acquisition system comprising at least one programmable logic array, a module for generating an analog signal, and a module for measuring the analog signal; a computer configured to control the acquisition system; Multiple electrodes connected to an acquisition system The present invention also relates to a device for implementing the method according to the invention, comprising: [Brief description of the drawings]

[0040] [Figure 1] FIG. 1 shows an apparatus for implementing a measurement system according to the invention. [Diagram 2] FIG. 2 illustrates a spatial cosine pattern. [Diagram 3] FIG. 1 shows part of the electronic circuit that allows the electrodes to be excited. [Figure 4] FIG. 1 illustrates a method for generating an excitation signal. [Diagram 5] FIG. 1 illustrates a method for measuring a signal generated by an electrode. [Figure 6]FIG. 2 illustrates, in graphical form, an excitation signal and some of its characteristics. [Figure 7] FIG. 1 shows the code matrix for a device with 16 electrodes. [Figure 8] FIG. 1 shows the code matrix for a device with 32 electrodes. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0041] FIG. 1 shows a device 1 for implementing the EIT measurement method according to the invention.

[0042] The method aims to perform a measurement of a body 6 containing a fluid by means of EIT.

[0043] The device 1 comprises 16 electrodes (references 2) arranged non-invasively on the circumference of the body 6. The electrodes 2 are preferably distributed angularly around the circumference of the body 6 in a regular manner.

[0044] The electrodes 2 are connected to a printed circuit board 3 which is itself connected to a data acquisition system 4. A screen 5 allows the data and images generated from that data to be viewed. The data acquisition system 4 includes a Linux® operating system (HOST) which controls a programmable logic array (FPGA) which is also contained within the data acquisition system 4.

[0045] The acquisition system 4 enables analog excitation signals to be generated and analog measurement signals delivered by the electrodes 2 to be measured.

[0046] The system 4 comprises, for example, a cRIO-9039 controller from the manufacturer National Instruments, which includes a programmable logic network NI-9262 module from the manufacturer National Instruments for generating an analog excitation signal and an NI-9223 module from the manufacturer National Instruments for measuring the analog signal delivered by the electrode 2.

[0047] Here, an embodiment of a measurement method according to the present invention using a device as shown in FIG. 1 will be described.

[0048] In the first step of the measurement method, n e The electrodes 2 are arranged around the cylindrical portion of the body 6 .

[0049] Exciting the electrodes In a second step of the measurement method, the electrodes are simultaneously excited by a potential having an appropriately selected form.

[0050] The electrodes 2 form a set of linearly independent electrodes, which are used to induce electrical excitation on the surface of the body and to measure its electrical properties.

[0051] n e For electrodes, (n e -1) linearly independent excitation patterns. To describe these linearly independent patterns, the equation

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[0052] The method according to the invention consists in exciting all of the electrodes simultaneously using a triangular form of excitation.

[0053] This set of simultaneous excitations is decomposed into Fourier-based spatial and temporal oscillations.

[0054] Different frequencies are used to establish a distinction between the different frequency multiplexed trigonometric signals.

[0055] For each trigonometric excitation pattern, each electrode E n is one static voltage V n sta is associated with.

[0056] n e Static voltage V n sta The set of sine and cosine functions with various spatial frequencies m are formed.

[0057] Figure 2 shows the spatial cosine patterns for m varying from 1 to 5. The sine patterns are not shown.

[0058] n e The electrodes are positioned on a periphery ∂Ω of the body, which is shown by the dashed lines in Figure 2. The solid lines represent the excitation potentials applied to the electrodes.

[0059] Each electrode E n The electrostatic potential V associated with n,m sta is 1 and n e For n between and,

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[0060] n e For a given set of electrodes, all independent excitation patterns are (n e -1) completely described using distinct spatial frequencies.

[0061] θ n =2πn / n e For certain cases, the electrodes are regularly distributed over the body.

[0062] Each spatial frequency m corresponds to a temporal frequency f m and are applied simultaneously to each of the electrodes.

[0063] Therefore, each simultaneous excitation potential V n exc is (n e -1) trigonometric functions, each function having a particular frequency f m The excitation signal for electrode n is given by

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[0064] The method according to the invention is carried out by determining the potential V n exc(t) for each electrode E n and simultaneously applying

[0065] For any time t, n e Care is taken to ensure that the sum of the excitation voltages of the electrodes is zero. This satisfies the condition

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[0066] Measure the electrical characteristics of the main body In a third step of the measurement method, the electrical properties of the body 6 are measured using the electrodes 2 .

[0067] The computer controls the programmable logic network of the acquisition system 4 to generate 16 excitation signals with the characteristics described. These 16 digital signals are converted to analog signals by the NI-9262 module and transmitted by coaxial cables to the electrodes 2.

[0068] The printed circuit board 3 comprises one excitation circuit for each electrode 2, each of which comprises a resistor R, as shown in FIG. 3. As can be seen in this figure, the potential V n exc is applied to one side of resistor R, and the other side is connected to electrode E. n is connected to.

[0069] Electrode E n The Neumann boundary condition at n This current flows through the resistor, as a voltage V n meas =RI n It is obtained by measuring V n exc For, this signal is a sum of trigonometric functions.

[0070] Process the data In a fourth step of the measurement method, the data measured in the third step is processed to obtain a signed data matrix representing the image.

[0071] Data point M n Generate In the first substep of the fourth step of the measurement method, for each electrode n, a data point M n is calculated.

[0072] The measured signal V n meas The Fourier transform of the P-point current measurement sequence I n (p), where p is the discrete time, considering O≦p≦P, i.e.,

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[0073] The Fourier transform is performed at frequencies f, corresponding to the frequencies at which the P Fourier coefficients are calculated. 1 It can be calculated in

[0074] Voltage V n exc Frequency f m f 1 This allows to distinguish between the measured signals. Each coefficient k is therefore chosen to be a harmonic of one particular frequency f m is associated with.

[0075] Therefore, the data is 1 and the resolution in Fourier space is Δf=f m+1 -f m =f1 The highest frequency is the Nyquist frequency of the system, f Nyq It should be noted that the time t is selected to be lower than 1 / 2Δp, where Δp is the sampling time.

[0076] Data point M n (k) is the coefficient of each Fourier coefficient k for each electrode n,

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[0077] Each data point defines a given trigonometric pattern of current at a given electrode. n The set (k) forms the measurement data.

[0078] The excitation frequency is determined by the sampling frequency f of the data acquisition system. DAQ is the voltage V n exec The maximum frequency f m and limit the Nyquist frequency f Nyq =f DAQ / 2 is the upper limit.

[0079] f DAQ For a data acquisition system such as =1 MS / s, the Nyquist frequency is equal to 500 kHz.

[0080] To avoid small residual voltage errors resulting from energy stored in the electrode-electrolyte contact impedance, a continuous signal must be delivered. To generate a continuous signal at a range of frequencies, the signal is delivered at the lowest frequency f 1 are chosen to be harmonics of

[0081] When the application of the potential to the electrode is stopped, some of the electrical energy is stored at the interface between the electrode and the medium for a few tens of microseconds. The effect of this contact impedance leads to errors in the measurement and means that it is necessary to introduce a dead time between two successive excitations to allow this energy to dissipate. The generation of a continuous signal has the advantage that the applied voltage never stops, thus avoiding the errors related to the contact impedance and the need to introduce a dead time.

[0082] Using 16 electrodes, a set of excitation signals at 15 different frequencies is generated. Given a sampling rate of the acquisition system, e.g., 1 MS / s, the frequencies are f i =i*f 0 where f 0 is the fundamental frequency, where i is between 1 and 15.

[0083] Furthermore, since only positive results are considered, the discrete Fourier transform can be performed at P=32 points. This is 1*10 6 This results in an image data acquisition rate of 32 / 32 = 31250 images. This selection is based on the lowest frequency f 1 must be equal to the computation frequency of the discrete Fourier transform.

[0084] highest frequency f 15 =15*f 0 is 468.875 kHz, which is below the Nyquist limit of 500 kHz for the system under consideration.

[0085] The excitation amplitude is determined as follows.

[0086] The voltage generation and acquisition module operates in the interval of ±10 V. The voltage V n excConsidering this, the amplitude A of the sine waves must be significantly smaller than the sum of the sine waves that would be produced due to constructive interference. However, the amplitude A of the signal must be as large as possible to minimize the signal-to-noise ratio.

[0087] Another limit to be taken into account is the maximum permissible variation between two successively generated potentials. Real-time control in the acquisition system makes it possible to select a satisfactory value of A=0.15 V, which gives a resonant peak of ±2.25 V. The rapid transition between positive and negative values ​​of the signal prevents the appearance of electrolysis effects. For example, when DC voltages higher than 1.2 V are applied, effects related to electrolysis appear in water. At AC voltages higher than 1.2 V, this effect does not appear if these voltages change quickly enough.

[0088] Get the data matrix D In the second substep, data point M n The data matrix D is obtained from

[0089] For the 16-electrode system in question using the NI-9223 module, a fixed-point data format of 20 numeric bits, including 5 bits for precision digits, can be used. The electrode index n, between 1 and 16, and the Fourier coefficient k, between 1 and 15, can be described by a binary number coded on 4 bits.

[0090] For a 32-electrode system, the coefficient M for each data point n (k) has the following format:

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[0091] For a given Fourier coefficient k, i.e., a given frequency f m About e n measured at electrodes e The data points are represented as the following data vector:

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[0092] n e - one vector can be concatenated into the data matrix D,

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[0093] In this case, the size of the data is S=n e (n e -1).

[0094] Only the coefficients of the Fourier transform form part of the data.

[0095] For an image, the size of the data is S*32 bits = 4 kB. In comparison, the methods described in publications [2], [3], and [4] result in 127 kB of data per image, without any additional information about the boundary conditions.

[0096] The method according to the invention therefore allows a higher image acquisition rate and reduces the size of the data by a factor n with respect to the methods described in publications [2], [3] and [4]. e It is also possible to shrink it by / 2.

[0097] Get the signed data matrix In a third sub-step, a signed data matrix representing the image is obtained.

[0098] The Fourier transform yields the coefficients and the phase. The sign of each data point is deduced from the phase.

[0099] Therefore, the format,

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[0100] The phase of the signal is

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[0101] frequency f m At electrode E l The current I measured at l meas The phase of (t) is

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[0102] Assuming synchronous sampling of the analog signal AI input and the sampled signal AO output, the phase shift between the excitation potential and the measured current is

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[0103] The phase shift depends on the design of the EIT sensor and the nature of the flow within the body. If the phase shift is large, wraparound effects may make it impossible to reconstruct the sign of the data. Specifically, the phase is symmetric with respect to a transformation of 2πN, where N is an integer. If the phase is larger than 2π, it will wrap around on itself.

[0104] In the following two cases:

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[0105] In the first case, the sign of the data point is calculated using the formula above, where the element of the signed data matrix corresponding to the kth Fourier coefficient and the nth electrode is:

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[0106] In the second case, the wraparound effect is D n k This prevents the estimation of the sign of . Then, a sign matrix Σ is introduced to assign arbitrary signs to the data.

[0107] The code matrix Σ is the V n meas Sign function using

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[0108] The sign matrix Σ is more specifically defined such that its rows represent the signs of cosine functions alternating with the signs of sine functions with an integer number of periods in each row: the first two rows have a single period, and the number of periods increases by one for each pair of subsequent rows.

[0109] In other words, the rows of the code matrix Σ have the i-th element of the j-th row as cosine([2π / ([j+1] / 2)]*(i-1) / n e ), for even j, it is sine([2π / (j / 2)]*(i-1) / n e ) is defined to be the sign of

[0110] For example, the first element of the first row of the sign matrix is ​​the sign of cosine(0), i.e., +. eIf the number of n is equal to 16, then the fifth element in the first row is the sign of cosine(2π*[4 / 16]), i.e., 0.

[0111] Thus, the first row of the code matrix contains the code for one period of the cosine function, i.e., cosine(2π*(i-1) / n e ). The second row represents the sign of one period of the sine function, i.e., sine(2π*(i-1) / n e The third row represents the sign of two periods of the cosine function, i.e., cosine([2π / 2]*(i-1) / n e The fourth row represents the sign of two periods of the sine function, i.e., sine([2π / 2]*(i-1) / n e The fifth row represents the sign of the three periods of the cosine function, i.e., cosine([2π / 3]*(i-1) / n e ), and similarly (n e -1)th line.

[0112] For example, for a 16 electrode device, the code matrix takes the form shown in Figure 7. For a device with 32 electrodes, the code matrix takes the form shown in Figure 8.

[0113] The use of such a sign matrix makes it possible to optimize the processing of the data to form the image: it allows the sign of each data point to be estimated and the image to be reconstructed.

[0114] For large phase shifts, i.e., π / 2 or more, n e n of electrodes e The arbitrary signed amplitude of one excitation pattern, in other words the element of the signed data matrix corresponding to the k-th Fourier coefficient and the n-th electrode, is given by

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[0115] Algorithm implementation The HOST portion of the acquisition system 4 continuously transmits frequency and amplitude parameters to the FPGA of the acquisition system 4 .

[0116] FIG. 4 shows an algorithm for generating excitation signals for the 16 electrodes 2 .

[0117] In the system under consideration, the FPGA receives 16x16 data points in a loop clocked at 1 MS / s to create 16 analog signals.

[0118] In the first step, the system is initialized.

[0119] Initially the FPGA is empty. The HOST loads the FPGA, then the NI-9262 module is reset.

[0120] In a second step, an interrupt request is sent and received.

[0121] A hardware interrupt is used to notify the HOST when the FPGA is ready to start data acquisition. The FPGA waits for HOST validation to start acquisition.

[0122] In the third step, the sampling is checked.

[0123] The Generate Sample Pulse function is called to initiate the generation of data points. The frequency with which the function is called determines the sampling rate used to generate data points. In parallel, the Write I / O Status function is called with the same frequency to check the status of each generated sample.

[0124] In a fourth step, a digital excitation signal function is generated.

[0125] The HOST commands the FPGA to begin generating the excitation signal function.

[0126] In the fifth step, analog excitation signals are generated: 16 excitation signals are sent to the electrodes.

[0127] In a sixth step, the HOST verifies the generation of the signals and reports any errors at the HOST or FPGA level.

[0128] Steps 1 and 2 are performed once when the algorithm is launched. Steps 3 to 6 are repeated for each output point at the sampling frequency.

[0129] The sampling frequency may be comprised between 10 kHz and 500 MHz, preferably between 500 kHz and 50 MHz.

[0130] FIG. 5 shows an algorithm for processing the data received from the electrodes 2.

[0131] Measurement of the voltage across the terminals of resistor R allows the Neumann boundary conditions used in the embodiment of the image reconstruction algorithm to be estimated. An acquisition rate of 1 MS / s on 16 channels corresponds to a data rate of 320 MB / s.

[0132] The use of Fast Fourier Transforms while considering only the Fourier coefficients relevant to the generated signal allows the size of the data to be reduced without affecting its quality. It also acts as an effective bandpass filter. However, the real-time calculation of 16 Fast Fourier Transforms requires high computational power. FPGAs, which allow the transformation of signals in several channels into their Fourier components in real time and in parallel, are suitable tools to perform this task.

[0133] In the first step A, the system is initialized.

[0134] The FPGA resets the NI-9223 analog signal acquisition module.

[0135] In a second step B, the memory is configured.

[0136] The HOST configures and initiates direct access to the FPGA's memory. The FPGA configures and initiates 16 first-in-first-out queues to ensure communication between the 16 measurement channels and their Fast Fourier Transform calculations.

[0137] In a third step C, an interrupt request is sent and received.

[0138] Hardware interrupts make it possible to ensure that queues and direct memory accesses are ready.

[0139] In a fourth step D, the sampling is checked.

[0140] The sample pulse generator function is called to control the sampling frequency, and the I / O status read function is called with the same frequency to check the status of each sample and report any errors to the HOST.

[0141] In a fifth step E, an analog measurement signal is acquired.

[0142] The I / O Read function is configured to read a single sample from each channel of each NI-9223 module. This function is called at 1MHz and is timed by the Generate Sample Pulse function.

[0143] In a sixth step F, the fast Fourier transform of each channel is calculated in a 1 MHz loop. The calculation time is determined by the number of points P considered in the Fourier transform. Once P measured data points are transferred for the Fourier transform calculation, the function returns P Fourier coefficients one by one in each iteration of the Fourier transform loop. The amplitudes of the Fourier coefficients are then calculated at a frequency of 1 MHz.

[0144] In a seventh step G, the data is addressed.

[0145] The amplitude data points in U32 format, together with the corresponding Fourier coefficients (in U16 format) and the corresponding channels (in U16 format), form data elements in U64 format. At each iteration of the Fourier transform loop, 16 elements for the 16 channels are written to the direct access memory for transmission to the HOST.

[0146] In an eighth step H, a data matrix is ​​constructed.

[0147] The HOST waits for the direct access memory to collect at least 240 elements that represent the complete data image. The address of the nth electrode, and the Fourier coefficients associated with the amplitude, are used to form the data matrix D.

[0148] In a ninth step I, the data matrix is ​​stored.

[0149] The data is then used or stored to perform real-time image reconstruction, which is based on a one-step iterative least-squares reconstruction algorithm, such as that described in the publication [5].

[0150] Real-time image reconstruction can produce approximately 100 images per second.

[0151] In a tenth step J, signal acquisition is verified and an error check is performed.

[0152] The synchronization of the analog signal generation module and the measurement module is checked and any errors are reported.

[0153] Steps A through C are executed once when the algorithm is launched. Steps D through G are repeated for each output point at the sampling frequency. e *(n e Once a complete data matrix containing −1) data points has been acquired, the algorithm proceeds to step H. Steps H through J are repeated at the image acquisition frequency.

[0154] The sampling frequency may be comprised between 10 kHz and 500 MHz, preferably between 500 kHz and 50 MHz.

[0155] Figure 6 shows in the left graph the excitation signals of 6 of the 16 electrodes 2. Each signal is composed of a sum of 15 sine functions.

[0156] The solid line in the right graph of Figure 6 represents, in the equivalent Fourier space, the voltage V measured across resistor R shown in Figure 2. meas where R = 200 Ω. The dashed-dotted line represents the Fourier transform of the voltage of the generated signal.

[0157] The invention is not limited to the examples just described, and the features of the examples shown can in particular be combined together in variants not shown.

[0158] However, further variations and improvements can be envisaged without departing from the scope of the invention, in particular the method according to the invention can be implemented by acquisition systems other than the one described. [Explanation of symbols]

[0159] 1 Device 2 electrodes 3. Printed Circuit Board 4 Data Acquisition System, Acquisition System 5 Screen 6 Main unit

Claims

1. A method for electrical impedance tomography measurement of a body (6) with a cylindrical portion containing a fluid, comprising the following steps: i. n holes around the cylindrical portion of the body ｅ placing electrodes (2); ii. The n ｅ simultaneously exciting each of the electrodes, each electrode comprising: [0010] A potential V having the form ｎ ｅｘｃ where A is the signal amplitude and θ ｎ is the angular position of electrode n, and f ｍ = m * f ０ is the oscillation frequency, and f ０ But, f ｍ is the fundamental frequency chosen to be less than the Nyquist frequency of the system for all m, δ is the Kronecker delta, [0025] is the set of odd integers, [0030] is a set of even non-zero integers, and iii. Measure the electrical properties of the body using the electrodes V ｎ ｍｅａｓ and measuring iv. Processing the data generated in the measuring step iii, comprising the following sub-steps: a) Each electrode E ｎ About [0045] A data point M defined by ｎ where R is the voltage across the resistor terminals, ｎ ｍｅａｓ is the resistance of the resistor used to measure V ｎ ｍｅａｓ = R.I. ｎ and P is the current I ｎ is the number of points in the discrete sequence of measurements of ｅ -1), and β ｐ = (2πp / P), b) formula, [0050] For all n and all k, the data points M ｎ constructing a data matrix D from (k); c) The phase shift Φ between the excitation potential at electrode l and the current measured at electrode n ｎ，ｌ If (k) is less than π / 2, the element is [006] and the phase shift Φ between the excitation potential at electrode l and the current measured at electrode n is defined by ｎ，ｌ If (k) is equal to or greater than π / 2, the element satisfies the following formula: [0070] where Σ is a signed data matrix defined by the formula: ｅ ), and for even j, it is sine([2π(j / 2)]*(i-1) / n ｅ ), the sign matrix defined to be the sign of Steps A method comprising:

2. Potential V ｎ ｅｘｃ A set of conditions, [0080] The method of claim 1 , wherein

3. The method of claim 2 , wherein the image is generated using a one-step iterative least-squares reconstruction algorithm applied to the signed data matrix.

4. 4. The method according to claim 1, wherein the electrodes are angularly distributed in a regular manner around the body.

5. Use of the method according to any one of claims 1 to 4 for carrying out tomographic measurements of two-phase flows, wherein the body is a pipe of a nuclear facility.

6. A computer program product comprising a medium and instructions stored on said medium and readable by a processor such that, when executed, said instructions enable an acquisition system (4) to be controlled to perform the measurement method according to any one of claims 1 to 4.

7. an acquisition system (4) comprising at least one programmable logic array, a module for generating an analog signal, and a module for measuring the analog signal; a computer configured to control the acquisition system; A plurality of electrodes (2) connected to the acquisition system; A device for carrying out the method according to any one of claims 1 to 4, comprising:

Images