Functions used in optics

cyl function (circular aperture)

close all;
[x,y] = meshgrid(linspace(-4,4,251));
r = sqrt(x.*x+y.*y);
z = cyl(x/3,y/3);
mysurf(x,y,z);

imshow(z);

$\mbox{somb}(r) = \frac{2J_1(\pi r)}{\pi r}$

close all;
[x,y] = meshgrid(linspace(-4,4,251));
r = sqrt(x.*x+y.*y);
z = somb(r);
mysurf(x,y,z);

r = linspace(-4,4,251);
z = somb(r);
plot(r,z);

close all;
[x,y] = meshgrid(linspace(-4,4,251));
r = sqrt(x.*x+y.*y);
z = gaus((r-2)/0.2);
mysurf(x,y,z);

imshow(z);

$\mbox{comb}(x) = \pi \delta(\sin(\pi x)$

We use gaus to simulate delta function

x = linspace(-2,2,401);
y = gaus(sin(pi*x)/0.2);
plot(x,y,'k','LineWidth',2);
axis([-2 2 0 1.5]);

[x,y] = meshgrid(linspace(-4,4,251));
z = rect(x/3).*rect(y/2);
imshow(z);

z = cyl(x/3,y/2);
imshow(z);

close all;
[x,y] = meshgrid(linspace(-4,4,251));
z = tri(x/2).*tri(y/2);
mysurf(x,y,z);

imshow(z);

close all;
[x,y] = meshgrid(linspace(-4,4,251));
r = sqrt(x.*x+y.*y);
z = tri(r/2);
mysurf(x,y,z);

imshow(z);

% triangle
[x y] = meshgrid(linspace(-4,4,251));
z = polygon(x,y);
imshow(z);

% hexagon
theta = (pi/3)*(0:5);
p = [cos(theta') sin(theta')];
z = polygon(x,y,3*p);
imshow(z);