Abstract
It is difficult to approximate a diffraction profile to Gaussian curves precisely by using a method of linear least squares. Therefore, a method to approximate it to multiple Gaussian curves by using a method of nonlinear least squares was developed. The present analytical method can be applied widely because it has the following advanteges.
1) A whole diffraction profile can be approximated with high accuracy.
2) The peek position, half value breadth of a diffraction profile, maximum intensity and background intensity can be obtained simultaneously.
3) The measurement system can store the profiles in the form of coefficients of diffraction profiles easily and reproduce them when needed.
4) Multiple diffraction curves can be separated easily.
5) The method makes it possible to separate an unnecessary diffraction profile from the necessary ones and then eliminate it.
6) When this method is utilized, an appropriate initial value of each parameter is necessary. The value decided by a method of linear least squares can be used as the initial value.
