Plasma Spectrum Fitting

Matlab classes for fitting low resolution optical emission spectrum of atmospheric pressure plasma jets

Example usage

% Load the example SpectralLines object
%  - This object has emission groups for the following species
%      H, He , O, O2+, NO, OH, N2_1PS, N2_2PS, N2_1NS, OH2
%    as well as two groups with lines that were not identified
%      Unknown_N2_related, Unknown_O2_related.
%  - Note the emission lines in these groups are simply the lines that were
%    observed in the emission spectrum of our plasma source.
load('specLines.mat')
show(specLines) % Display the different EmissionGroups and their emission lines

% Load two different example spectrum.
%  - The first spectrum is from a He plasma jet surrounded with N2 and in
%    contact with a liquid surface.
%  - The second spectrum is from a He plasma jet surrounded with O2 and in
%    contact with a liquid surface.
load('exampleSpectra.mat')

% Fit the spectra with N2, and do not include the O2 related emission groups
% while fitting
groups_to_use = ~contains(specLines.names, "O2");
[p, group_idx] = specLines.fit(x1,y1, groups_to_use);

% Plot the spectrum and the fit
%  - This will result in the figure on the left above.
figure
line(x1,y1,'Color',0.5*[1 1 1],'LineWidth',2)
specLines.plotfit(x1, p, group_idx)

% Fit the spectra with O2, and do not include several of the N2 related
% emission groups while fitting
% - Note: The O2 spectra observed have a continuous background emission.
%   This background must be taken into account to correctly fit the spectrum.
%   The fit function already has an empirical profile for this continuous
%   background. Note that the background is specifically for the spectrum
%   observed in our experiments using O2 surrounding the He jet, and is not
%   necessarily general.
groups_to_use = ~contains(specLines.names, ["N2_1PS", "Unknown_N2", "N2+"]);
fit_O2_background = true;
[p, group_idx, fitter] = specLines.fit(x2,y2, groups_to_use, fit_O2_background);

% Plot the spectrum and the fit
%  - This will result in the figure on the right above.
figure
line(x2,y2,'Color',0.5*[1 1 1],'LineWidth',2)
background = fitter.bg; % extract the fit background.
specLines.plotfit(x2, p, group_idx, background)

% For more detailed plotting, see example.m located in the example folder

Description

The code works by performing a constrained minimization of the difference between a model spectrum and an experimental spectrum. The model spectrum is created using a set of Guassians at wavelengths specified by the user.

The spectral lines of the model are divided into different groups. Each group can represent the emission lines of a single species (i.e. He emission lines, or atomic O emission lines, or NO emission lines, ...), or more generally, a group can be any set of lines could be dependent on one another. For example, the amplitude of each emission line of the Nitrogen 1st positive system (N₂^1PS) should generally be within some percent of the lines around it; thus, these emission lines can be grouped together.

Each of these different groups are contained in an instance of the class EmissionGroup, and all of the different groups are contained in an instance of the class SpectralLines.

SpectralLines

The class SpectralLines contains all the different EmissionGroups used to fit an experimental spectrum. SpectralLines contains the method of fitting an experimental spectrum:

  % fit()
  %
  % Input -
  % x : wavelength values of the experimental spectrum
  % y : intensities of the experimental spectrum
  %
  % Output -
  % gauss_params : n x 3 array, each row gives (A, mu, sig^2) for a gaussian
  % group_idx : n x 1 array, where the i'th value gives the EmissionGroup index
  %   that the gauss_params(i,:) belongs too.
  [gauss_params, group_idx] = fit(SpectralLines_obj, x, y)
  [gauss_params, group_idx] = fit(SpectralLines_obj, x, y, groups_to_use)

as well as several other useful methods

  obj = addGroup(obj, group_name, group_lines_wavelengths) % Add a new EmissionGroup
  obj = addLine(obj, group_name, line_wavelength) % Add a line to an EmissionGroup
  show(obj) % display the name and lines of each EmissionGroup

  % Plot the emission lines to a figure. Clicking on one of the plotted lines
  % will display the group to which the line belongs as well as its wavelength
  plot(obj)
  plot(obj, ax, groups_to_plot)

  % Plot the gaussians returned by the fit() function
  plotfit(obj,wavelengths, gauss_params, group_idx)

More details can be found by studying the example SpectralLines class included (specLines.mat) and the EmissionGroups contained in it.

EmissionGroup

The class EmissionGroup contains a list of the emission lines belonging to the group, and it contains a function handle, nonLinFitConstraint(), for the non-linear constraints to apply to the lines of the group. The output of this function to be the same as is expected for the non-linear constraint functions used by Matlab's fmincon(), which this program uses.

nonLinFitConstraint() should take in two arguments (p, idx), where p is a list of all of the gaussian parameters for all of the EmissionGroups in a SpectralLines object, idx is a logical array indicating which gaussians belong to this specific EmissionGroup. These two parameters are automatically computed for you in the fit() function of SpectralLines. If your constraint function needs additional parameters, then simply use an anonymous function: examples of this, and constrain functions, can be seen in the OH, N2_1PS, and N2_2PS, EmissionGroups provided in the example SpectralLines class, specLines.mat, as well as the constraint functions OH_Constraint.m, N2_1PS_Constraint.m, and N2_2PS_Constraint.m.

This class additionally contains the initial Gaussian sigmas, s0, as well as two parameters dc and ds that control how much each line is allowed to move when fitting, dc, and how much the Gaussian sigma is allowed to change when fitting ds.

More details can be found by studying the EmissionGroup.m file and the example files provided.