Because you used
gaussian_fn= @(q,x) (q(1)^2.*exp(-2.*((x-q(2)).^2)/q(3).^2));
as your fitting function -- in which q(1) is squared --
>> q=[0.9522,559.2633,425]; % from your screenshot
>> q(1)^2
ans =
0.9067
>>
For comparison,
>> gaussian_fn(q,q(2)) % at peak center is max value
ans =
0.9067
>> gaussian_fn(q,555) % where you evaluated on plot
ans =
0.9065
>>
Use
gaussian_fn= @(q,x) (q(1).*exp(-2.*((x-q(2)).^2)/q(3).^2));
if you want the peak amplitude to be same as coefficient.
