傅里叶光学 （一）

Functions used in optics

Contents

• cyl function (circular aperture)
• somb (sombrero) function
• ring delta function
• composite function example
• anamorphic functions
• 2D triangle function (separable)
• 2D triangle function (radially symmetric)
• polygon function

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);

somb (sombrero) function

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);

ring delta function

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);

composite function example

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]);

anamorphic functions

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

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

2D triangle function (separable)

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

imshow(z);

2D triangle function (radially symmetric)

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);

polygon function

% 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);

文中所用的程序可在 http://www.johnloomis.org/eop513/notes/  下载

原文地址：http://www.johnloomis.org/eop513/notes/functions/foptics.html