matlab - matlab中光波叠加的可视化

Question

我编写了一些快速代码，用于可视化空间中具有不同幅度的两个波的叠加，点源几何。这适用于 khanacademy CS 平台。 http://www.khanacademy.org/cs/superposition/1245709541但我无法在 matlab 中重现确切的现象。我得到的只是一张嘈杂的图像。这与随机数生成的差异有关吗？我不知道 random(0,1)(在 JS 中)和 rand(在 matlab 中)有多么不同。

这是matlab代码

像平面上点x,y的波叠加函数

function S = Super(refamp,objamp,x,y,a,lambda)
    r1 = sqrt(a*a+x*x+y*y); %a is in z-axis
    S = refamp+(objamp*cos(2*pi*r1/(lambda/(10^6))));

测试脚本

close all;
clear all;
clc;

a=10;       %distance from source to image plane

width = 1024;
height =1024;

im = zeros(width); % the image
x=1;
y=1;
A0 = 3; % amplitude of reference wave
A1 = 1; % amplitude of object wave  A0>>A1: A0/A1>=3
lambda = 632; % wavelength in nanometers
% generate the superposition in space width*height at a along z-axis
for y=1:height
    for x=1:width
        s = Super(A0,A1,x-(width/2),y-(height/2),a, lambda);
        r=rand;
        if(r<(s/(A0+A1)))
            im(x,y) = 1;
    end
end

%display the image
figure
imshow(im,[])
title('test image')

Answer 1

主要问题是您的天平已关闭，因此您看不到干涉图案。如果你尝试一下所有东西的大小/距离，它就会正确，你可以看到模式。

第二个问题是您的代码确实会从矢量化中受益。我在下面展示了这一点 - 这样做可以显着加快执行速度。

function Interference
a=1000 * 10^-9;       #% distance from source to image plane
width = 10000 * 10^-9;
height= 10000 * 10^-9;
size = 700;
A0 = 3; %# amplitude of reference wave
A1 = 1; %# amplitude of object wave  A0>>A1: A0/A1>=3
lambda = 632 * 10^-9; #% wavelength in nanometers

x=linspace(0,width,size); #% vector from 0 to width
y=linspace(0,height,size); #% vector from 0 to height
[X,Y]=meshgrid(x,y); #% matrices of x and y values at each position

s=Super(A0, A1, X-(width/2), Y-(height/2), a, lambda); #% size-by-size (700x700) 
r=rand(size); #% 700x700 matrix of random values on [0 1]

im = zeros(size);
im(r<(s/(A0+A1))) = 1; %# do this all at once instead of pixel-by-pixel

#% display the image
figure
imshow(im,[])
title('test image')
end #% end of function Interference


#% Super is now vectorized, so you can give it a matrix of values for x and y
function S = Super(refamp,objamp,x,y,a,lambda)
    r1 = sqrt(a.*a+x.*x+y.*y); #% dot notation: multiply element-wise
    S = refamp+(objamp*cos(2*pi*r1/(lambda)));
end #% end of function Super