Turbulence Spectra from Doppler-broadened Spectral Lines: Tests of the   Velocity Channel Analysis and Velocity Coordinate Spectrum Techniques
  Turbulent motions induce Doppler shifts of observable emission and absorption lines motivating studies of turbulence using precision spectroscopy. We provide the numerical testing of the two most promising techniques, Velocity Channel Analysis (VCA) and Velocity Coordinate Spectrum (VCS). We obtain an expression for the shot noise that the discretization of the numerical data entails and successfully test it. We show that the numerical resolution required for recovering the underlying turbulent spectrum from observations depend on the spectral index of velocity fluctuations, which makes low resolution testing misleading. We demonstrate numerically that, dealing with absorption lines, sampling of turbulence along just a dozen directions provides a high quality spectrum with the VCS technique. 
A. Chrupnov and A. Lazarian