Maxwell-Boltzmann Fit with different constant (air-absorption) for each data Point

Hello together,

I measuerd with a spectrometer a x-Ray-spectrum. I found Bremsstrahlung and characteristic radiation. I like to do a fit using the Maxwell-Boltzman distribution. The measurment is done under atmosphere of air, so I need to take into account the energy dependend apsorption of air, which is differnet for each data point. The peaks (red in pot) of characteristic radiation I smoothed with a linear function. (blue curve in the plot)

Maxwell-Boltzmann equation is the following: (where x=E is an array E=2:0.077:20 , dE=0.077)

(orange curve in plot)

and air Absorption with Lambert-Beers-law is

~

d ist the distance from the spectrometer to the x-Ray point source d=0.15m and µ(E) is the mass specific absorption coefficient of air which dependes on E: my=µ=[µ1,µ2,....µN] with N=length(E). Finally every data point of the upper Maxwell-Boltzmann distribution has to be multiplied with

=>.* to get the correct fit. (black curve in plot, found by manual paying with the parameters)

I couldn't give the fit function for every data point an other value of my=µ whitch I want to input as an array

ft = fittype('A*exp(-d*my).*sqrt(4*x/(pi*(B)^3)).*exp(-x/B)','options',fo);

From the fit parameter B I want to extract electron temerature T_e.

How can I get a fit and input an array of which will be took into account for each data point in the fitroutine?

Answer 1

[Alan Stevens]

You could try using fminsearch to estimate B. Something along the lines of:

data = % enter your data to be fitted
my = % enter your mu values
E = % enter your energy values

B0 = % supply an initial guess for B
B = fminsearch(@(B), fn(B,E,my,data), B0);

function F = fn(B,E,my,data)
         d = 0.15;
         fit = exp(-d*my).*sqrt(4*E/(pi*(B)^3)).*exp(-E/B);
         F  = norm(data - fit);
end