How to control color and the intensity in a pcolor figure?

I'm try in to simulate a Coronae (diffraction of droplet). There are color depends by wavelength, and intensity depends by diffraction. How can I control both color by wavelength (lambda) and intensity (I) ?

I can only control lambda to have different color of diffraction pattern now.

lambda=400;  % wavelength [nm] 
a=10e3;  % obstruct disc radius [nm](um)
x=linspace(-0.2,0.2,1000);
y=x;
[X,Y]=meshgrid(x,y);
r=sqrt(X.^2+Y.^2);
% diffraction pattern
u=2.*pi.*a./lambda;
J=besselj(1,u.*sin(r));
I=sqrt((u.*((1+cos(r))./2).*(J./sin(r))).^2);  % Intensity
% colormap
w=lambda;
if (w >= 380) && (w < 440)
    R = -(w - 440.) / (440. - 380.);
    G = 0.0;
    B = 1.0;
    elseif (w >= 440) && (w < 490)
        R = 0.0;
        G = (w - 440.) / (490. - 440.);
        B = 1.0;
    elseif (w >= 490) && (w < 510)
        R = 0.0;
        G = 1.0;
        B = -(w - 510.) / (510. - 490.);
    elseif (w >= 510) && (w < 580)
        R = (w - 510.) / (580. - 510.);
        G = 1.0;
        B = 0.0;
    elseif (w >= 580) && (w < 645)
        R = 1.0;
        G = -(w - 645.) / (645. - 580.);
        B = 0.0;
    elseif (w >= 645) && (w <= 780)
        R = 1.0;
        G = 0.0;
        B = 0.0;
    else
        R = 0.0;
        G = 0.0;
        B = 0.0;
end
c=[R,G,B]; 
h=linspace(0,1,256);  % illumination (intensity) from [0,1]
for i=1:length(h)
    S{i}=h(i).*c;
end
map=cell2mat(S');
% figure
pcolor(X,Y,I); shading flat; axis image; title([num2str(lambda)]);
colormap(map);

This is what I'm trying to simulate. (picture from google search)

And this is what I get so far (can change color by wavelength)

[Walter Roberson]

This is sort of a follow-on from https://www.mathworks.com/matlabcentral/answers/672553-can-i-pcolor-base-on-wavelength-any-colormap-can-do-so

[Image Analyst]

You'd have to make an array out of lambda, then do the operations for each value of lambda.

By the way, it's it's a liquid droplet, you'd get refraction, not diffraction. You're programming up the Sombrero function which is the diffraction pattern for a round hole, like a plane wave hitting a pinhole in an opaque barrier.

[Bjorn Gustavsson]

@Image Analyst, if there are small droplets in the atmosphere light will be diffracted, leading to coronae around light-sources (sun, moon etc): Corona

[chia ching lin]

@Image Analyst, Can you give me an example of how to done it?

Answer 1

[Bjorn Gustavsson]

You could try something like this:

lambda = 400:700; % Wavelengths in nm.
I_of_lambda = % Solar-spectral intensity as a function of wavelength
rgb_of_lambda = % your RGB-colour-map, one tripplet for each wavelength, like yours above
C_of_lambda = ones(size(lambda)); % Relative sensitivity at each wavelength, compare with ccd quantum efficiency. This is jus a placeholder
a=10e3;  % obstruct disc radius [nm](um)
x=linspace(-0.2,0.2,1000);
y=x;
[X,Y]=meshgrid(x,y);
r=sqrt(X.^2+Y.^2);
Img_rgb = zeros([size(X),3]);
% diffraction pattern
for i_lambda = 1:numel(lambda)
  % Here we calculate the diffraction-pattern wavelength-by-wavelength, and add their
  % contributions to the R, G and B-channels together, one by one.
  u=2.*pi.*a./lambda(i_lambda);
  J=besselj(1,u.*sin(r));
  I=sqrt((u.*((1+cos(r))./2).*(J./sin(r))).^2);  % Intensity
  Img_rgb(:,:,1) = Img_rgb(:,:,1) + I*rgb_of_lambda(i_lambda,1)*C_of_lambda(i_lambda);
  Img_rgb(:,:,2) = Img_rgb(:,:,2) + I*rgb_of_lambda(i_lambda,2)*C_of_lambda(i_lambda);
  Img_rgb(:,:,3) = Img_rgb(:,:,3) + I*rgb_of_lambda(i_lambda,3)*C_of_lambda(i_lambda);
end
Img_rgb = Img_rgb/max(Img_rgb(:)); % scale to 0-1
imagesc(X(1,:),Y(:,1),Img_rgb); shading flat; axis image; title('4000 - 7000 Å');

This should give you something to work with. You might have to scale the blue channel up. The colour-balancing in these type of tasks are notoriously confusing due to the characteristics of the colour-vision of our eyes.

HTH