The assumption of white noise is appropriate for most of the observed radio spectral line maps. The crucial point is that the phases of the image and noise Fourier transform are completely uncorrelated. The corresponding -variance is shown by the dark triangles in the bottom panel. This applies even if we assume pure white noise. The power spectrum then follows Eq.
Similar fluctuations are present in the -variance.
5.2 Influence of the finite telescope beam For a quantitative treatment we consider a telescope beam of Gaussian profile and HPBW . In the lower panel, the -variance of the original and the convolved image are compared. Clearly, the influence of the finite beam size is noticeable for lags up to , and a linear fit to the -variance has to be limited to larger lags. This might be a problem for observed maps because of their limited dynamical range in linear resolution, often little more than one decade. A quantitative description is therefore highly desirable in order to extend the fit to smaller lags, and to evaluate the -variance for smaller maps.