# Metallic rectangle (obstacle to Fresnel in 2D: rectTM_cent.exp)

This file contains an assumption, i.e. is experimentally.

For reference see incontrastsRef.html.

## Contents

- Geometry and position of the obstacle
- Other parameters of the obstacles
- References

## Geometry and position of the obstacle

- Geometry of rectangle: 24.5 mm, 12.7 mm.
- One metallic rectangle centered.
- Mathematical positive rotation of 270 degrees, see fresnel_op1_dielTM.html.

## Other parameters of the obstacles

- The metallic objects in [1] are perfectly conducting, i.e. , so

- See, e.g. [2, p. 110] for where is the conductivity.

- Refractive index n, .

- Contrast (in other literature you can find ).

- Finally, because the obstacle is metal, i.e. perfectly conducting, the imaginary part of the contrast is : .

- We assume(!): q = 0.5 + i 1E6.

- The real part of contrast is assumed from reconstruction... (nothing found in [1])

- Metal: refractive index is highly dependent on wavelength...., i.e. our predefined contrast should depend on the choosen frequency so will be a question of choosen frequency

- But: `FmeasData` seems not to be highly dependent from choosen qValue...

## 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] Andreas Kirsch. An integral equation approach and the interior transmission problem for Maxwell's equations. Inverse Problems and Imaging,1(1):107-127, 2007. URL: https://doi.org/10.3934/ipi.2007.1.159.

    function q = fresnel_op1_rectTM_cent(X1,X2,varargin)

    qValue = 0.5 + 1i*1E6; % perfectly conducting, so imaginary part is infinity...
    % real part from reconstruction... not sure if correct...

    w = 12.7E-3; % width = 12.7 mm
    h = 24.5E-3; % height = 24.5 mm

    right = 0; % move it right
    up    = -3E-3; % move it up (or down with a negative number)
    % shift the target 3 mm down... and it does visual better fit to Fresnel data

    q = (-w/2+right <= X1) & (X1 <= w/2+right) & (-h/2+up <= X2) & (X2 <= h/2+up);
    q = qValue*q;
    q = double(q);

    end