An analysis of errors in the Fourier coefficients of the α₁ line profile

The errors in the Fourier coefficients of the α₁ component obtained by α₂ elimination are investigated analytically. The effects of counting statistics, of an incorrect intensity ratio of the α₁ and α₂ components and of an incorrect doublet separation are calculated. The mean-square error in the Fourier coefficient caused by counting statistics is a periodic function of the harmonic number, while errors in the intensity ratio and in the doublet separation primarily affect the first Fourier coefficients. The results are confirmed by computer simulations and by computations with experimental line profiles. The α₂ elimination methods assume a perfect shape identity of the α₁ and α₂ components, but this assumption is not completely justified. Deviations might be interpreted as local errors in the doublet separation and the intensity ratio.