title: Computing the FWHM of a star profile
body: <p>My goal is to compute the FWHM of a star profile.</p>
  
  <p>I've an image and a single star in it, as input. Each pixel, at position (x, y), has an intensity associated between 0 and 1.</p>
  
  <p>My idea was to compute the standard deviation of the entire dataset and then use the following formula:</p>
  
  <p><code>f(x, y)=[1/(√(2π)σ)]exp(-[(x - X)^2 + (y - Y)^2]/2σ^2])</code></p>
  
  <p>solving the equation:</p>
  
  <p><code>fmax/2=1/[2√(2π)σ]=[1/(√(2π)σ)]exp(-[(x - X)^2 + (y - Y)^2]/2σ^2]) =&gt;</code></p>
  
  <p><code>FWHM=2σ√(2ln2)</code></p>
  
  <p>With this approach I'm not getting the expected result looking at the data.</p>
  
  <p>Is there something I'm missing? Any other suggestion?</p>