This paper presents an efficient spiral scanning/sampling method and its associated reconstruction algorithm for echo planar Magnetic Resonance Imaging (MRI) systems. The spiral scan data are represented in terms of evenly spaced samples from a nonlinear two-dimensional transformation of the Cartesian spatial frequency domain. This transformation enables us to use unified Fourier reconstruction sampling principles  to obtain an accurate reconstruction based on a set of constraints imposed on the spiral parameters. The results are then utilized to develop efficient sampling strategies for spiral scans. Sampling efficiency for spiral data, analogous to the sampling efficiencies of hexagonally and rectangularly sampled data, is defined. A sampling scheme on a spiral is introduced that possesses a uniform sampling efficiency comparable to the sampling efficiency of rectangularly sampled data.