help with curve fitting sinc^2(x)

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)

[Star Strider]

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.