The ability to place surface samples with Poisson disk distribution can benefit a variety of graphics applications. Such a distribution satisfies the blue noise property, i.e. lack of low frequency noise and structural bias in the Fourier power spectrum. While many techniques are available for sampling the plane, challenges remain for sampling arbitrary surfaces. In this paper, we present new methods for Poisson disk sampling with spectrum analysis on arbitrary manifold surfaces. Our first contribution is a parallel dart throwing algorithm that generates high-quality surface samples at interactive rates. It is flexible and can be extended to adaptive sampling given a user-specified radius field. Our second contribution is a new method for analyzing the spectral quality of surface samples. Using the spectral mesh basis derived from the discrete mesh Laplacian operator, we extend standard concepts in power spectrum analysis such as radial means and anisotropy to arbitrary manifold surfaces. This provides a way to directly evaluate the spectral distribution quality of surface samples without requiring mesh parameterization. Finally, we implement our Poisson disk sampling algorithm on the GPU, and demonstrate practical applications involving interactive sampling and texturing on arbitrary surfaces.