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Narrowband array processing beamforming technique for electrical impedance tomography

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Fig. 1

Complete block diagram of the developed beamforming EIT system. The input current is injected into the electrodes adjacently through the multiplexer circuit. The individual voltages are measured by NI USB 6008 from the non-current carrying electrodes. The beamforming algorithm displays the location of the test objects in the form of two beams.
Complete block diagram of the developed beamforming EIT system. The input current is injected into the electrodes adjacently through the multiplexer circuit. The individual voltages are measured by NI USB 6008 from the non-current carrying electrodes. The beamforming algorithm displays the location of the test objects in the form of two beams.

Fig. 2

Complete experimental set up of the proposed study. The test objects are placed at electrode positions 4 and 8 respectively. The beamforming algorithm locates the test objects in the form of two beams after acquiring the data from the EIT system with eight electrodes.
Complete experimental set up of the proposed study. The test objects are placed at electrode positions 4 and 8 respectively. The beamforming algorithm locates the test objects in the form of two beams after acquiring the data from the EIT system with eight electrodes.

Fig. 3

A circular test tank of radius r1. The radii of the two concentric circles are r2 and r3. Voltages V1–V8 are the measured electrode voltages. The electrodes are separated by an angle of θ=45 degrees. Vb1–Vb8 are the voltages obtained from bi-curvilinear interpolation of V1–V8. The voltages V(i, j)’s are the nodal voltages, which are derived from Gauss-Seidel method.
A circular test tank of radius r1. The radii of the two concentric circles are r2 and r3. Voltages V1–V8 are the measured electrode voltages. The electrodes are separated by an angle of θ=45 degrees. Vb1–Vb8 are the voltages obtained from bi-curvilinear interpolation of V1–V8. The voltages V(i, j)’s are the nodal voltages, which are derived from Gauss-Seidel method.

Fig. 4

(a) = actual test object placed along the line of electrode 1, (b) = test object as located using beamforming algorithm. A thick circle represents the actual diameter of the test tank and (c) = test object as indicated by EIDORS. The circle represents the actual object while the stars indicate the contact impedance errors.
(a) = actual test object placed along the line of electrode 1, (b) = test object as located using beamforming algorithm. A thick circle represents the actual diameter of the test tank and (c) = test object as indicated by EIDORS. The circle represents the actual object while the stars indicate the contact impedance errors.

Fig. 5

Compiled one object test results for different locations.
Compiled one object test results for different locations.

Fig. 6

(a) = actual test objects placed along the line of electrode 3 and electrode 6 respectively, (b) = test objects as located using beamforming algorithm. A thick circle represents the actual diameter of the test tank and (c) = test objects as indicated by EIDORS. The circle represents the actual object while the stars indicate the contact impedance errors.
(a) = actual test objects placed along the line of electrode 3 and electrode 6 respectively, (b) = test objects as located using beamforming algorithm. A thick circle represents the actual diameter of the test tank and (c) = test objects as indicated by EIDORS. The circle represents the actual object while the stars indicate the contact impedance errors.

Figure 7

Compiled two object test results for different locations.
Compiled two object test results for different locations.

Fig. 8

(a) A single test object placed between electrode positions 5 and 6 (top). Two test objects placed between electrode positions 1–2 and 5–6 (bottom). (b) The beamforming algorithm gives a flat beam across electrode positions 5 and 6 (top) and a flat beam across electrode positions 1–2 and 5–6 (bottom). (c) EIDORS results for the given locations of the test objects.
(a) A single test object placed between electrode positions 5 and 6 (top). Two test objects placed between electrode positions 1–2 and 5–6 (bottom). (b) The beamforming algorithm gives a flat beam across electrode positions 5 and 6 (top) and a flat beam across electrode positions 1–2 and 5–6 (bottom). (c) EIDORS results for the given locations of the test objects.