Gaussian profile estimation in two dimensions.

@article{Hagen2008GaussianPE,
  title={Gaussian profile estimation in two dimensions.},
  author={Nathan A Hagen and Eustace L. Dereniak},
  journal={Applied optics},
  year={2008},
  volume={47 36},
  pages={6842-51}
}
We extend recent results for estimating the parameters of a one-dimensional Gaussian profile to two-dimensional profiles, deriving the exact covariance matrix of the estimated parameters. While the exact form is easy to compute, we provide a set of close approximations that allow the covariance to take on a simple analytic form. This not only provides new insight into the behavior of the estimation parameters, but also lays a foundation for clarifying previously published work. We also show how… CONTINUE READING