This paper proposes a numerical method for computing the amplitudes and phases required for a fixed setup of laser beams to create a specified interference pattern in two dimensions. The context of this work is atom lithography, where such a pattern of standing light waves is used to modulate the transverse intensity distribution of a collimated beam of atoms. Once deposited on a substrate, the atoms reproduce the interference pattern of the light. The paper first introduces the necessary mathematical bases and formulates the mathematical problem to be solved in detail, paying attention to some discretization issues in Fourier space. Then the method itself is presented. It involves the use of interpolation techniques in Fourier space to compute the amplitudes of some particular spectral components of the interference pattern to be created. Those amplitudes then enter the right-hand side of a system of nonlinear equations for the amplitudes and phases to be determined. The system is solved using a coordinate descent method. Finally, numerical results are presented, assessing the effectiveness of the algorithm, in particular in comparison to another existing technique known as the Nelder and Mead simplex method. It is found that the algorithm presented gives good results in comparison to other methods, though the quality of the reconstruction is principally determined by the choice of an appropriate setup of the laser beams for a given pattern.