The laser field can be effectively reconstructed using phase retrieval methods by measuring intensity distributions on two planes perpendicular to the beam propagation direction. To address the phase retrieval challenge in laser beams, an initial phase estimation strategy based on ray mapping is proposed, which provides a rapid and accurate initial phase distribution. A more precise phase distribution is achieved by superimposing radial basis function components onto this initial phase and determining their weights through the gradient descent method. The spatial intensity distribution of the laser is then calculated using the angular spectrum method, with the beam width fitted using the second-moment method and the least squares method. This approach facilitates the calculation of the beam quality factor (M²). Simulations of single-mode and multimode laser beams and experimental results from a helium-neon laser demonstrate that the proposed method enables high-precision laser phase reconstruction, leading to the effective calculation of M².