The transport-of-intensity equation provides a new non-interferometric and non-iterative access to quantitative information about the phase of a light wave by measuring intensity distributions. This equation can be used to implement a simple and accurate spatial phase measurement for optical testing of spherical surfaces. The method requires only a CMOS camera, which records transverse field intensity distributions in several planes. Processing of experimental measurements with specialized software allows one to reconstruct the value of the radius of curvature of the spherical surface under test with high accuracy. The method is compared with measurements made by an interferometer, showing the difference between the values of the surface radius of curvature to be 0.01 % or less and indicating good agreement of the results.