Errors in elliptical Gaussian fits

Elliptical Gaussian fits are used in astronomy for accurate measurements of fundamental source parameters such as central position, peak flux density, and angular size. The full value of a noise-limited image can be realized only if the effects of noise on the fitted parameters are estimated accurately. This paper presents the equations of error propagation for two-dimensional elliptical Gaussian fits in the presence of Gaussian noise plus a new method that simplifies the use of a priori size constraints to reduce amplitude errors.