Why does this nlinfit of a cos^2 not work? (Malus law for polaroïd filters)

I have a list of measured intensities (to test Malus law) and i'd like to fit this to a*cos(angle)^2. This should give me the value of a. The value it gives me is way off from what it should be, and the variance is huge. What am i doing wrong?

I=[0.0 0.9 2.4 4.4 7.4 10.5 13.3 15.4 16.5 16.7 16.0 14.8 11.9 9.3 6.8 4.2 2.1 0.5 0.0 0.5 1.9 4.2 6.4 9.4 12.6 14.6 15.9 16.6 16.4 14.8 12.5 10.0 6.5 4.2 1.7 0.5];

Theta= diag(ones(length(I)));

   for i=1:length(I);

    Theta(i) =(i-1)*10/180*pi+3.1415/2; % the 10 stands for 10 degrees

end

Cos2 = cos(Theta).^2;

funct = @(a,x)(a(1)*cos(x).^2);

B0=17;
[B R J covB]=nlinfit(Cos2,I,funct,B0);

x=1.5:0.1:(2*pi+1.5);

hold on

plot(Theta,I,'bo');

plot(x,funct(B,x));

Answer 1

[Star Strider]

Your independent variable is ‘Theta’, not ‘Cos2’. (You also don’t need a loop to generate ‘Theta’.)

This (corrected) version of your original code works, and gives a good visual fit:

I=[0.0 0.9 2.4 4.4 7.4 10.5 13.3 15.4 16.5 16.7 16.0 14.8 11.9 9.3 6.8 4.2 2.1 0.5 0.0 0.5 1.9 4.2 6.4 9.4 12.6 14.6 15.9 16.6 16.4 14.8 12.5 10.0 6.5 4.2 1.7 0.5];

Theta = [0:length(I)-1]*10/180*pi+pi/2;  
funct = @(a,x)(a(1)*cos(x).^2);  
B0=17  
[B R J covB]=nlinfit(Theta,I,funct,B0);

x=1.5:0.1:(2*pi+1.5);

figure(1)
plot(Theta,I,'bo');
hold on
plot(x,funct(B,x));
hold off

[Florian Partous]

Thank you, i should have seen than.

[Star Strider]

My pleasure!