In this paper we revisit the problem of blue noise sampling with a strong focus on the spectral behavior of the sampling patterns. We use the mathematical relationship between the radial power spectrum and the radial distribution function to synthesize two types of blue noise patterns: ideal blue noise patterns that have a power spectrum in form of a step function and produce almost no coherent aliasing, and effective blue noise patterns that have a high effective Nyquist frequency and produce a controlled amount of aliasing. We give a definition for this effective Nyquist frequency in stochastic sampling and propose an error metric that characterizes the amount and spectral distribution of aliasing. We show that our blue noise sets avoid most of the artifacts caused by oscillations in the power spectra of existing blue noise patterns. Finally, we present a new algorithm for constructing point sets with a given power spectrum.