# Two dielectric cylinders (obstacle to Fresnel in 2D: twodielTM_8f.exp)

For reference see incontrastsRef.html.

## Contents

- Positions of the obstacles
- Other parameters of the obstacles
- References

## Positions of the obstacles

- Theoretical, see [1], position should be left and right from origin, but Fresnel data are rotated 270 degrees mathematical positive.
- Actually the cylinders are above and below the origin.

## Other parameters of the obstacles

See fresnel_op1_dielTM.html (because it is a dielectric too).

## References

- [1] Kamal Belkebir and Marc Saillard. Special section on testing inversion algorithms against experimental data. Inverse Problems, 17(6):1565-1571, 2001. URL: https://doi.org/10.1088/0266-5611/17/6/301.
- [2] Florian Bürgel, Kamil S. Kazimierski, and Armin Lechleiter. A sparsity regularization and total variation based computational framework for the inverse medium problem in scattering. Journal of Computational Physics, 339:1-30, 2017. URL: https://doi.org/10.1016/j.jcp.2017.03.011.

    function q = fresnel_op1_twodielTM(X1,X2,varargin)
    % two dielectric cylinders

    qBall = 2 + 1i*0; % dielectricum, so imaginary part is 0
    rBall = 15E-3; % 15 mm

    % correct the position:

    positionmethod = 1; % 1 or 2: both are manually corrections of the obstacles position
    % method 1 is used in [2].

    switch positionmethod

      case 1 % method 1--------------------------------------------------
    % 1) a little shift by shifting the grid

    xshift = -8E-3;
    yshift = +1E-3;

    X1 = X1-xshift;
    X2 = X2-yshift;

    % 2) rotation by rotation of grid in this file:

    gamma = 8; %rotation angle in degrees (mathematical positive)

    %rotation matrix:
    R = @(alpha) [cos(alpha), -sin(alpha); sin(alpha), cos(alpha)]; % alpha is angle in rad...

    Xrot = R(gamma*2*pi/360)*[X1;X2];
    X1 = Xrot(1,:);
    X2 = Xrot(2,:);

    %-----------------------------------------------------

    dist = 45E-3; % distance from origin

    r1 = hypot(X1,X2-dist); % 45 mm below origin
    r2 = hypot(X1,X2+dist); % 45 mm above origin

    % this is changed because of shift and rotation of X1 and X2

      case 2 % method 2------------------------------------------

    % set positions manually

    p = @(n) -0.06+n/90*0.12;

    pos1 = [p(44); p(78)];
    pos2 = [p(36); p(15)];

    r1 = hypot(X1-pos1(1),X2-pos1(2)); % pos1
    r2 = hypot(X1-pos2(1),X2-pos2(2)); % pos2

    end

    q1 = ( r1 < rBall );
    q2 = ( r2 < rBall );
    q = qBall*(q1 | q2);
    q = double(q);

    % Be careful: this does not work... you end up with 0 and 1 entries:
    % q1 = qBall*( r1 < rBall ); % OK
    % q2 = qBall*( r2 < rBall ); % OK
    % q = q1 | q2;               % this resuts in 0 or 1 entries...

    end