help with curve fitting sinc^2(x)

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Patrick Bevington
Patrick Bevington 2016-3-19
评论： Star Strider 2016-3-19
Hi, I have written some code to plot the intensity of light seen by a diffraction grating and I want to fit the curve to some data points I have but I can't get it work. Can anyone see where might be going wrong? What ever values I pick for starting point I can't get the data to plot. The code named 'Intensity.m' is for plotting the curve I want i.e. the distribution I want, and the code named 'CurveFit.m' is to try and fit the curve to my data points.
'Intensity.m'
clear all, clc
a = 0.9*20.4e-6; % Width - amplitude, increase a -> amp smaller
d = 2.1*20.4e-6; % Seperation - peak on x, increase d -> peaks closer
l = 780e-9; % Wavelength
s = 1; % Distance
thetamax = pi/50; % Angle
theta = -thetamax : 1e-5 :thetamax;
x=s*tan(theta); % Order seperation
alpha=pi*d*sin(theta)/l;
y1=cos(alpha).^2; % Interference
beta = pi*a*sin(theta)/l;
y2 = (sin(beta)./beta).^2; % Diffraction envolpe
y = y1 .* y2; % Interference Pattern
figure(1)
plot(x,y)
title('Grating pattern');
xlabel('Distance');
ylabel('Intensity');
% axis([-0.02,0.02,0,inf])
Here I used the symbolic function in matlab to generate an equation for y, give to be
y = (l^2*cos((pi*d*sin(theta))/l)^2*sin((pi*a*sin(theta))/l)^2)/(a^2*pi^2*sin(theta)^2)
This is my attempt at the curve fitting. I need it so my data points y1,y2,y3... fit on top of the central peak and the two either side.
'CurveFit.m'
clear all, clc
y1 = [0.2685, 1, 0.2981]; % Data to fit
y2 = [0.3339, 1, 0.3290];
y3 = [0.3039, 1, 0.3012];
y4 = [0.4269, 1, 0.4354];
y5 = [0.3232, 1, 0.3608];
y6 = [0.3582, 1, 0.4291];
y7 = [0.3767, 1, 0.4491];
y8 = [0.3186, 1, 0.4245];
x = linspace(-pi,pi,3)';
aa = 20.4e-6; % Width a
bb = 20.4e-6; % Seperation d
startPoints = [aa bb];
% y = (l^2*cos((pi*d*sin(theta))/l)^2*sin((pi*a*sin(theta))/l)^2)/(a^2*pi^2*sin(theta)^2)
FitEquation = fittype('(780e-9^2 * cos( (pi * b * sin(x) )/780e-9 )^2 * sin( (pi * a * sin(x)) /780e-9 )^2 )/(a^2 * pi^2 * sin(x)^2)');
f1 = fit(x,y1,FitEquation,'Start',startPoints);
figure(99)
plot(f1,x,y1)
  1 个评论
Star Strider
Star Strider 2016-3-19
Your objective function may be wrong. I did the fit with this:
% MAPPING: B(1) = a, B(2) = b
diffrax = @(B,x) (780e-9^2 * cos( (pi * B(2) .* sin(x) )/780e-9 ).^2 .* sin( (pi * B(1) .* sin(x)) /780e-9 ).^2 )./(B(1).^2 * pi^2 * sin(x).^2);
y1 = [0.2685, 1, 0.2981]; % Data to fit
y2 = [0.3339, 1, 0.3290];
y3 = [0.3039, 1, 0.3012];
y4 = [0.4269, 1, 0.4354];
y5 = [0.3232, 1, 0.3608];
y6 = [0.3582, 1, 0.4291];
y7 = [0.3767, 1, 0.4491];
y8 = [0.3186, 1, 0.4245];
D = [y1; y2; y3; y4; y5; y6; y7; y8];
D = sortrows(D, 1);
SSECF = @(B) sum((D(:,3) - diffrax(B,D(:,1))).^2);
B0 = [2E-5; 2E-5]*0.001;
[EstB, SSE] = fminsearch(SSECF, B0);
figure(1)
plot(D(:,1), D(:,3), 'bp')
hold on
plot(D(:,1), diffrax(EstB,D(:,1)), '-r')
hold off
grid
and did not get an acceptable result.
I’m not submitting this as an Answer because it isn’t one.

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