Reconstruction of a grounded object in an electrostatic halfspace with an indicator function

Figures & data

Figure 1. (a) Schematic illustration of the measurement. (b) A test function is used to establish if points lie inside or outside the unknown domain.

Figure 2. Illustration of the test object used for the numerical simulations. The left image illustrates the object located 30 mm above the sensor/display. The other two images give cross sections in the x₂ = 0 plane and the planes, respectively.

Figure 3. Reconstruction results of the test object above a test display using the factorisation method. (a) 256 sampling points in a 16×16 array, (b) 32 measurement points in a linear edge array, (c) 32 measurement points using truncated SVD regularisation (half the singular values).

Figure 4. (a) Singular values of Λ_D for the two simulated experiments. Terms of the P(z) sum for typical internal and external points. (b) for the 'noise free' 2D electrode array and (c) for 32 edge electrodes with  1% noise.

Figure 5. (a) Cross section of P(z) for z₁ = 0, z₃ = 30 for the three experiments in figure 3, (b) Asymmetry in the reconstruction and standard deviation under different noise draws function of SVD truncation N.

Figure 6. Reconstruction results of the test object above a test display using the linear sampling method. (a) 256 sampling points in a 16×16 array, (b) 32 measurement points in a linear edge array, (c) 32 measurement points using truncated SVD regularisation (half the singular values).