Predefined contrasts in folder "incontrasts"

Reference to the predefined contrasts in folder "incontrasts" and their usage in the computational framework.

Contents

Syntax

Example of syntax for a ball in 2D and 3D. You can find a list of all predefined contrasts below.

q = referenceBall2D(X1,X2,seti)     % 2D
q = referenceBall3D(X1,X2,X3,seti)  % 3D

Description

q = referenceBall2D(X1,X2,seti) evaluates the contrast in the full grid described by X1 and X2 and stores it as a vector 1 x n. Note that X1 and X2 are produced with meshgrid, but stored as vectors 1 x n.

q = referenceBall3D(X1,X2,X3,seti) evaluates the contrast in the full grid described by X1, X2 and X3 and stores it as a vector 1 x n. Note that X1, X2, and X3 are produced with meshgrid, but stored as vectors 1 x n.

Input Arguments

Output Arguments

Examples in 2D

Triangle in 2D

For this example make sure to be in the folder code/incontrasts/2D.

% Prepare a grid
h = 0.016;
r = 0.2;
x1 = (-r:h:r-h);
[X1,X2] = meshgrid(x1,x1);
X1 = transpose(X1(:));
X2 = transpose(X2(:));
% Evaluate predefined contrast corner2D on the grid an plot result
seti.rCD = 2*r;
q = triangle2D(X1,X2,seti);
l = length(x1);
qMatrix = reshape(q,[l l]);
imagesc(real(qMatrix)); axis xy; colorbar;

Ball in 2D

For this example make sure to be in the folder code.

% add all pathes of rebis (needed in case of checkfield)
init;
% Prepare a grid
h = 0.016;
r = 0.2;
x1 = (-r:h:r-h);
[X1,X2] = meshgrid(x1,x1);
X1 = transpose(X1(:));
X2 = transpose(X2(:));
% set strcut seti
seti.qBall = 0.8;
seti.rBall = 0.1;
% Evaluate predefined contrast referenceBall2D on the grid an plot result
q = referenceBall2D(X1,X2,seti);
l = length(x1);
qMatrix = reshape(q,[l l]);
imagesc(real(qMatrix)); axis xy; colorbar;

List of all predefined Contrasts

Folders in incontrasts:

Predefined contrasts in 2D

Folder: incontrasts/2D

StringDescription
empty2DEmpty contrast with q = 0 everywhere (to test)
corner2DCorner
top and left line with q = 1
cornerBallSparse2DNon-constant corner, ball (filled circle) and broken corner
Corner with non-constant contrast q
Ball with q = 1
Broken corner with q = 1 (corner consisting of squares and a thin line - very sparse)
cornerBallSparseMod2DNon-constant corner, ball (filled circle) and broken corner
Same as cornerBallSparse2D, but rotated 180 degrees.
cross2DCross with q = 1
rectangle2DRectangle with q = 0.5
referenceBall2DBall (filled circle)
with contrast value q = seti.qBall (default: 0.8) and radius seti.rBall (default: 0.015)
referenceBallSmooth2DSmooth ball (filled circle)
with contrast value seti.qBall and radius seti.rBall
shepp2DModified Shepp-Logan phantom from MATLAB
triangle2DTrianlge with q = 0.8
twoCorners2DTwo corners with q = 1
twoCornersOneBall2DTwo corners and one ball
Two corners with q = 0.8
Ball with q = 1

Predefined contrasts in 2D corresponding to real-world data from Institute Fresnel

Folder: incontrasts/2DFresnel

The obstacles corresponds to the described ones in [1].

Note that dielectricum means that the imaginary part of the contrast vanishes.

StringDescription
fresnel_op1_dielTM One dielectric cylinder
Contrast value q = 2 + 0 i.
Ball with radius 15 mm
Distance of center of the ball from origin is approximately 30 mm.
(Note: Position was manually corrected.)
fresnel_op1_twodielTM Two dielectric cylinders
Contrast value q = 2 + 0 i.
Balls with radius 15 mm
Distance of center of the balls from origin is approximately 45 mm.
(Note: Position was manually corrected.)
fresnel_op1_rectTM_cent Rectangle (experimentally!)
This obstacle is experimentally and may contain errors, because the contrast value is assumed because reconstruction.
The obstacle is out of metal, i.e. the refractive index is highly dependent on wavelength.
Metal is perfectly conducting, i.e. the imaginary part is infinity.
In a first approach we assume the contrast value q = 0.5 + 1E6 i.
(Note: This contrast is experimentally.)

Predefined contrasts in 3D

StringDescription
empty3DEmpty contrast with q = 0 everywhere (to test)
corner3D Corner (tripod)
first horizontal arc with q = 1.0,
second horizontal arc with q = 0.8,
vertical horizontal arc with q = 0.6.
cross3D Cross
first horizontal bar: q = 0.8,
second horizontal bar with q = 0.6,
vertical bar with q = 1.0.
referenceBall3D Ball
with contrast value q = seti.qBall (default: 0.8) and radius seti.rBall (default: 0.015).
twoTripods3D Two tripods
all arcs with q = 1.0.
cubeLike3D Edges of a cube
with contrast value q = 1.

Usage in computational framework

Usage of predefined contrasts in computational framework

Syntax

seti.contrast = str;

Description

seti.contrast = str uses the contrast defined in function str.

Example

Define in inseti/example.m: (see example.html)

seti.contrast = 'cornerBallSparse2D';

References