How to plot Intensity vs wavelength of an image?

I want to take an image as input and detect the colors' wavelengths in that image. Then I need to determine the intensities of those wavelengths and plot intensity vs wavelength. Is it doable?

Answer 1

[Image Analyst]

In general, no, though attempts have been made with various assumptions about the illuminant and spectral responsivities of the camera sensor. You can have the same color with many, many different spectra, so which spectra do you pick?

See https://www.mathworks.com/matlabcentral/answers/240430-rgb-to-wavelength-is-it-possible#answer_191518

[Quintus]

Same color will definitely have different spectra. I want to get a plot like theremino spectrometer software which plots Intensity vs wavelength from a webcam video. Can the similar thing be done for an image in MATLAB?

[DGM]

The theremino projects don't just get wavelength from any webcam video. They use an aperture, grating, and modified camera to do the job. If you have built such a physical setup, then it should be a fairly simple matter to plot the intensity over a profile (e.g. see improfile()), perhaps with some averaging on the off-axis.

It's not the color of the image that matters; it's only the position. To some degree, you can do calibration by correlating peak locations to the wavelengths of known sources (gas discharge tubes). Calibrating intensity is another matter.

So, did you build the physical hardware to do this? If so, you can provide us with images (including those taken of calibration sources).

[Quintus]

I haven't made the physical hardware yet. I'm planning to make a DIY sprectrometer where light is incident on a slit and a DVD disk is used as a diffraction grating. The diffracted light is incident on a webcam and it detects it. From the webcam, the image/video is analysed on a computer (e.g. in the theremino spectrometer software). But I don't want to use the software. Instead, I want to take the image/video of the diffracted light from the webcam as input, analyse it on MATLAB and plot Intensity vs wavelength.

[Image Analyst]

I don't know what device that is but if it's like a diffraction pattern then you can get a rough idea of the wavelength by measuring the signal on your detector. One end of the detector will have the violet end of the range and the opposite side of the detector will have the red end of the spectrum. The gray level of your monochrome sensor will be the relative power of the wavelength at that location.

[DGM]

"Relative intensity" deserves a big asterisk here. We're talking about a color sensor with its IR mirror removed. That's why I'm assuming that some system modeling is required for intensity calibration, but frequency calibration seems fairly straightforward. That said, I imagine that intensity calibration isn't even needed for a lot of tasks. Looking at the screenshots, I'm not even sure they're doing any intensity calibration. I'd have to read more.

As to whether it could be done in MATLAB, I'm sure it could. I don't have a spectrometer, the images, or the information about the corresponding source spectra. You could make the project as a simple ad-hoc script, or you could build an entire GUI with calibration utilities or something. Depending on the goals, having Image Processing Toolbox may help make some parts of the task easier. Certainly, improfile() is part of IPT.

I grabbed an image off the website:

From that, I cropped this sample image chunk:

% get image
inpict = imread('specttrim.png');

% crop out relevant region
% this relies on the pattern being grid-aligned
inpict = imcrop(inpict,[72 68 305 20]);

% convert to grayscale somehow
%inpict = mean(im2double(inpict),3); % average?
%inpict = rgb2gray(im2double(inpict)); % BT601 luma?
inpict = imapplymatrix([0.2126 0.7152 0.0722],im2double(inpict)); % BT709 luma?
% ... or use some sort of system-specific intensity calibration information

% generate profile by averaging off-axis
% again, this relies on the pattern being grid-aligned
profile = mean(inpict,1);

% rough (linear) frequency calibration
lbref = [494 693]; % wavelengths of known peaks
idx = [77 209]; % the indices in profile corresponding to those peaks
lambda = interp1(idx,lbref,1:numel(profile),'linear','extrap');

% plot the profile
plot(lambda,profile)
xlim([min(lambda) max(lambda)])

You could underfill the curve with some pseudocolor image if you want. You could crop the image wider to get more range if you wanted. This is just a simple example.

[DGM]

I realized that underfilling the curve was a bit more of a hassle, so here's an example.

% get image
inpict = imread('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1277300/image.png');

% crop out relevant region
% this relies on the pattern being grid-aligned
inpict = imcrop(inpict,[72 68 305 20]);

% convert to grayscale somehow
%inpict = mean(im2double(inpict),3); % average?
%inpict = rgb2gray(im2double(inpict)); % BT601 luma?
inpict = imapplymatrix([0.2126 0.7152 0.0722],im2double(inpict)); % BT709 luma?
% ... or use some sort of system-specific intensity calibration information

% generate profile by averaging off-axis
% again, this relies on the pattern being grid-aligned
profile = mean(inpict,1);

% rough frequency calibration
lbref = [494 693]; % wavelengths of known peaks
idx = [77 209]; % the indices in profile corresponding to those peaks (manually picked)
lambda = interp1(idx,lbref,1:numel(profile),'linear','extrap');

% generate patch vertex coordinates
xx = [lambda fliplr(lambda)];
yy = [profile zeros(size(profile))];

% create color data for each vertex pair
CT = getcdata(lambda);
cc = [1:numel(lambda), numel(lambda):-1:1];

% plot the profile
patch(xx,yy,cc);
xlim([min(lambda) max(lambda)])
colormap(CT)

function CT = getcdata(vtxlambda)
    % location of gradient breakpoints (in wavelength)
    x0 = [312 381 403 419 440 492 512 580 646 652 779 927];
    CT0 = [0 0 0; 0 0 0; 0.353 0 0.563; 0.353 0 1; 0 0 1; 0 1 1;
	       0 1 0; 1 1 0; 1 0 0; 1 0 0; 0 0 0; 0 0 0];
    
    % look up colormap colors for each vertex lambda
    CT = interp1(x0,CT0,vtxlambda,'linear','extrap');
end

You could generate the pseudocolor map however you choose, but I derived this from the screenshot.